LMFDB - Embedded newform 504.2.r.e.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(169,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.r (of order $3$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.2091141441.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 $ x^8 - x^7 + x^6 + 3x^5 - 15x^4 + 9x^3 + 9x^2 - 27*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.4
Root			$0.199732 + 1.72050i$ of defining polynomial
Character	$\chi$	$=$	504.169
Dual form			504.2.r.e.337.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58986 - 0.687275i) q^{3} +(-0.300268 - 0.520080i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.05531 - 2.18534i) q^{9} +O(q^{10})$	\(q+(1.58986 - 0.687275i) q^{3} +(-0.300268 - 0.520080i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.05531 - 2.18534i) q^{9} +(0.800268 - 1.38611i) q^{11} +(-0.165178 - 0.286096i) q^{13} +(-0.834822 - 0.620487i) q^{15} -1.44990 q^{17} +2.57918 q^{19} +(0.199732 - 1.72050i) q^{21} +(-0.924682 - 1.60160i) q^{23} +(2.31968 - 4.01780i) q^{25} +(1.76571 - 4.88695i) q^{27} +(-1.75950 + 3.04755i) q^{29} +(4.81034 + 8.33176i) q^{31} +(0.319678 - 2.75372i) q^{33} -0.600537 q^{35} +0.600537 q^{37} +(-0.459236 - 0.341330i) q^{39} +(-3.31034 - 5.73368i) q^{41} +(-1.81481 + 3.14334i) q^{43} +(-1.75370 - 0.412734i) q^{45} +(-1.95477 + 3.38576i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.30514 + 0.996481i) q^{51} -9.27166 q^{53} -0.961181 q^{55} +(4.10054 - 1.77261i) q^{57} +(6.93476 + 12.0113i) q^{59} +(2.59433 - 4.49351i) q^{61} +(-0.864909 - 2.87262i) q^{63} +(-0.0991952 + 0.171811i) q^{65} +(5.90467 + 10.2272i) q^{67} +(-2.57085 - 1.91080i) q^{69} -4.17972 q^{71} +4.13969 q^{73} +(0.926627 - 7.98199i) q^{75} +(-0.800268 - 1.38611i) q^{77} +(-4.06538 + 7.04144i) q^{79} +(-0.551441 - 8.98309i) q^{81} +(2.78959 - 4.83171i) q^{83} +(0.435359 + 0.754064i) q^{85} +(-0.702858 + 6.05444i) q^{87} -3.83069 q^{89} -0.330355 q^{91} +(13.3740 + 9.94029i) q^{93} +(-0.774447 - 1.34138i) q^{95} +(0.974782 - 1.68837i) q^{97} +(-1.38432 - 4.59773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} - 3 q^{5} + 4 q^{7} - q^{9}+O(q^{10}) $ 8 * q - q^3 - 3 * q^5 + 4 * q^7 - q^9	$ 8 q - q^{3} - 3 q^{5} + 4 q^{7} - q^{9} + 7 q^{11} + 3 q^{13} - 11 q^{15} + 6 q^{17} - 8 q^{19} + q^{21} + 2 q^{23} - 5 q^{25} + 11 q^{27} - 9 q^{29} + 3 q^{31} - 21 q^{33} - 6 q^{35} + 6 q^{37} + 2 q^{39} + 9 q^{41} + 8 q^{43} + 7 q^{45} + 3 q^{47} - 4 q^{49} - 18 q^{51} + 12 q^{53} - 56 q^{55} + 34 q^{57} + 10 q^{59} + 20 q^{61} - 2 q^{63} + q^{65} + 11 q^{67} - 17 q^{69} - 6 q^{71} - 48 q^{73} + 52 q^{75} - 7 q^{77} + 21 q^{79} - 25 q^{81} + 8 q^{83} + 9 q^{85} - 15 q^{87} + 12 q^{89} + 6 q^{91} + 29 q^{93} + 36 q^{95} + 16 q^{97} + 18 q^{99}+O(q^{100}) $ 8 * q - q^3 - 3 * q^5 + 4 * q^7 - q^9 + 7 * q^11 + 3 * q^13 - 11 * q^15 + 6 * q^17 - 8 * q^19 + q^21 + 2 * q^23 - 5 * q^25 + 11 * q^27 - 9 * q^29 + 3 * q^31 - 21 * q^33 - 6 * q^35 + 6 * q^37 + 2 * q^39 + 9 * q^41 + 8 * q^43 + 7 * q^45 + 3 * q^47 - 4 * q^49 - 18 * q^51 + 12 * q^53 - 56 * q^55 + 34 * q^57 + 10 * q^59 + 20 * q^61 - 2 * q^63 + q^65 + 11 * q^67 - 17 * q^69 - 6 * q^71 - 48 * q^73 + 52 * q^75 - 7 * q^77 + 21 * q^79 - 25 * q^81 + 8 * q^83 + 9 * q^85 - 15 * q^87 + 12 * q^89 + 6 * q^91 + 29 * q^93 + 36 * q^95 + 16 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.58986	−	0.687275i	0.917906	−	0.396799i
$3$	1.58986	−	0.687275i	0.917906	−	0.396799i
$4$		0			0
$5$	−0.300268	−	0.520080i	−0.134284	−	0.232587i	0.791040	−	0.611765i	$-0.209540\pi$
$5$	−0.300268	−	0.520080i	−0.134284	−	0.232587i	−0.925324	+	0.379178i	$0.876207\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$	2.05531	−	2.18534i	0.685102	−	0.728447i
$10$		0			0
$11$	0.800268	−	1.38611i	0.241290	−	0.417926i	−0.719792	−	0.694190i	$-0.755763\pi$
$11$	0.800268	−	1.38611i	0.241290	−	0.417926i	0.961082	+	0.276263i	$0.0890962\pi$
$12$		0			0
$13$	−0.165178	−	0.286096i	−0.0458120	−	0.0793487i	0.842210	−	0.539149i	$-0.181254\pi$
$13$	−0.165178	−	0.286096i	−0.0458120	−	0.0793487i	−0.888022	+	0.459801i	$0.847921\pi$
$14$		0			0
$15$	−0.834822	−	0.620487i	−0.215550	−	0.160209i
$16$		0			0
$17$	−1.44990			−0.351652			−0.175826	−	0.984421i	$-0.556260\pi$
$17$	−1.44990			−0.351652			−0.175826	+	0.984421i	$0.556260\pi$
$18$		0			0
$19$	2.57918			0.591705			0.295852	−	0.955234i	$-0.404396\pi$
$19$	2.57918			0.591705			0.295852	+	0.955234i	$0.404396\pi$
$20$		0			0
$21$	0.199732	−	1.72050i	0.0435850	−	0.375443i
$22$		0			0
$23$	−0.924682	−	1.60160i	−0.192809	−	0.333956i	0.753371	−	0.657596i	$-0.228427\pi$
$23$	−0.924682	−	1.60160i	−0.192809	−	0.333956i	−0.946180	+	0.323640i	$0.895093\pi$
$24$		0			0
$25$	2.31968	−	4.01780i	0.463936	−	0.803560i
$26$		0			0
$27$	1.76571	−	4.88695i	0.339812	−	0.940493i
$28$		0			0
$29$	−1.75950	+	3.04755i	−0.326732	+	0.565916i	−0.981861	−	0.189601i	$-0.939281\pi$
$29$	−1.75950	+	3.04755i	−0.326732	+	0.565916i	0.655130	+	0.755517i	$0.272614\pi$
$30$		0			0
$31$	4.81034	+	8.33176i	0.863963	+	1.49643i	0.868073	+	0.496436i	$0.165358\pi$
$31$	4.81034	+	8.33176i	0.863963	+	1.49643i	−0.00411031	+	0.999992i	$0.501308\pi$
$32$		0			0
$33$	0.319678	−	2.75372i	0.0556488	−	0.479361i
$34$		0			0
$35$	−0.600537			−0.101509
$36$		0			0
$37$	0.600537			0.0987276			0.0493638	−	0.998781i	$-0.484281\pi$
$37$	0.600537			0.0987276			0.0493638	+	0.998781i	$0.484281\pi$
$38$		0			0
$39$	−0.459236	−	0.341330i	−0.0735366	−	0.0546565i
$40$		0			0
$41$	−3.31034	−	5.73368i	−0.516989	−	0.895450i	−0.999805	−	0.0197291i	$-0.993720\pi$
$41$	−3.31034	−	5.73368i	−0.516989	−	0.895450i	0.482817	−	0.875721i	$-0.339614\pi$
$42$		0			0
$43$	−1.81481	+	3.14334i	−0.276756	+	0.479355i	−0.970577	−	0.240793i	$-0.922593\pi$
$43$	−1.81481	+	3.14334i	−0.276756	+	0.479355i	0.693821	+	0.720148i	$0.255926\pi$
$44$		0			0
$45$	−1.75370	−	0.412734i	−0.261425	−	0.0615267i
$46$		0			0
$47$	−1.95477	+	3.38576i	−0.285132	+	0.493864i	−0.972641	−	0.232312i	$-0.925371\pi$
$47$	−1.95477	+	3.38576i	−0.285132	+	0.493864i	0.687509	+	0.726176i	$0.258704\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−2.30514	+	0.996481i	−0.322784	+	0.139535i
$52$		0			0
$53$	−9.27166			−1.27356			−0.636780	−	0.771046i	$-0.719734\pi$
$53$	−9.27166			−1.27356			−0.636780	+	0.771046i	$0.719734\pi$
$54$		0			0
$55$	−0.961181			−0.129606
$56$		0			0
$57$	4.10054	−	1.77261i	0.543129	−	0.234788i
$58$		0			0
$59$	6.93476	+	12.0113i	0.902828	+	1.56374i	0.823806	+	0.566872i	$0.191846\pi$
$59$	6.93476	+	12.0113i	0.902828	+	1.56374i	0.0790221	+	0.996873i	$0.474820\pi$
$60$		0			0
$61$	2.59433	−	4.49351i	0.332169	−	0.575334i	−0.650768	−	0.759277i	$-0.725553\pi$
$61$	2.59433	−	4.49351i	0.332169	−	0.575334i	0.982937	+	0.183943i	$0.0588861\pi$
$62$		0			0
$63$	−0.864909	−	2.87262i	−0.108968	−	0.361916i
$64$		0			0
$65$	−0.0991952	+	0.171811i	−0.0123036	+	0.0213105i
$66$		0			0
$67$	5.90467	+	10.2272i	0.721370	+	1.24945i	0.960451	+	0.278450i	$0.0898206\pi$
$67$	5.90467	+	10.2272i	0.721370	+	1.24945i	−0.239081	+	0.971000i	$0.576846\pi$
$68$		0			0
$69$	−2.57085	−	1.91080i	−0.309494	−	0.230033i
$70$		0			0
$71$	−4.17972			−0.496041			−0.248021	−	0.968755i	$-0.579780\pi$
$71$	−4.17972			−0.496041			−0.248021	+	0.968755i	$0.579780\pi$
$72$		0			0
$73$	4.13969			0.484514			0.242257	−	0.970212i	$-0.422112\pi$
$73$	4.13969			0.484514			0.242257	+	0.970212i	$0.422112\pi$
$74$		0			0
$75$	0.926627	−	7.98199i	0.106998	−	0.921681i
$76$		0			0
$77$	−0.800268	−	1.38611i	−0.0911990	−	0.157961i
$78$		0			0
$79$	−4.06538	+	7.04144i	−0.457391	+	0.792224i	−0.998822	−	0.0485208i	$-0.984549\pi$
$79$	−4.06538	+	7.04144i	−0.457391	+	0.792224i	0.541431	+	0.840745i	$0.317883\pi$
$80$		0			0
$81$	−0.551441	−	8.98309i	−0.0612713	−	0.998121i
$82$		0			0
$83$	2.78959	−	4.83171i	0.306197	−	0.530349i	−0.671330	−	0.741159i	$-0.734277\pi$
$83$	2.78959	−	4.83171i	0.306197	−	0.530349i	0.977527	+	0.210809i	$0.0676099\pi$
$84$		0			0
$85$	0.435359	+	0.754064i	0.0472213	+	0.0817897i
$86$		0			0
$87$	−0.702858	+	6.05444i	−0.0753542	+	0.649104i
$88$		0			0
$89$	−3.83069			−0.406053			−0.203026	−	0.979173i	$-0.565078\pi$
$89$	−3.83069			−0.406053			−0.203026	+	0.979173i	$0.565078\pi$
$90$		0			0
$91$	−0.330355			−0.0346306
$92$		0			0
$93$	13.3740	+	9.94029i	1.38682	+	1.03076i
$94$		0			0
$95$	−0.774447	−	1.34138i	−0.0794565	−	0.137623i
$96$		0			0
$97$	0.974782	−	1.68837i	0.0989741	−	0.171428i	−0.812286	−	0.583259i	$-0.801777\pi$
$97$	0.974782	−	1.68837i	0.0989741	−	0.171428i	0.911260	+	0.411831i	$0.135111\pi$
$98$		0			0
$99$	−1.38432	−	4.59773i	−0.139129	−	0.462089i
$100$		0			0
$101$	−8.79520	+	15.2337i	−0.875155	+	1.51581i	−0.0185572	+	0.999828i	$0.505907\pi$
$101$	−8.79520	+	15.2337i	−0.875155	+	1.51581i	−0.856598	+	0.515985i	$0.827426\pi$
$102$		0			0
$103$	5.30547	+	9.18935i	0.522764	+	0.905454i	0.999649	+	0.0264880i	$0.00843237\pi$
$103$	5.30547	+	9.18935i	0.522764	+	0.905454i	−0.476885	+	0.878966i	$0.658234\pi$
$104$		0			0
$105$	−0.954769	+	0.412734i	−0.0931759	+	0.0402787i
$106$		0			0
$107$	−3.43949			−0.332508			−0.166254	−	0.986083i	$-0.553167\pi$
$107$	−3.43949			−0.332508			−0.166254	+	0.986083i	$0.553167\pi$
$108$		0			0
$109$	−5.55010			−0.531603			−0.265802	−	0.964028i	$-0.585637\pi$
$109$	−5.55010			−0.531603			−0.265802	+	0.964028i	$0.585637\pi$
$110$		0			0
$111$	0.954769	−	0.412734i	0.0906226	−	0.0391750i
$112$		0			0
$113$	−4.38079	−	7.58775i	−0.412110	−	0.713796i	0.583010	−	0.812465i	$-0.301875\pi$
$113$	−4.38079	−	7.58775i	−0.412110	−	0.713796i	−0.995120	+	0.0986691i	$0.968541\pi$
$114$		0			0
$115$	−0.555305	+	0.961817i	−0.0517825	+	0.0896899i
$116$		0			0
$117$	−0.964708	−	0.227045i	−0.0891873	−	0.0209903i
$118$		0			0
$119$	−0.724950	+	1.25565i	−0.0664561	+	0.115105i
$120$		0			0
$121$	4.21914	+	7.30777i	0.383558	+	0.664342i
$122$		0			0
$123$	−9.20360	−	6.84063i	−0.829860	−	0.616799i
$124$		0			0
$125$	−5.78879			−0.517765
$126$		0			0
$127$	−11.1521			−0.989590			−0.494795	−	0.869010i	$-0.664757\pi$
$127$	−11.1521			−0.989590			−0.494795	+	0.869010i	$0.664757\pi$
$128$		0			0
$129$	−0.724950	+	6.24474i	−0.0638283	+	0.549819i
$130$		0			0
$131$	2.59993	+	4.50322i	0.227157	+	0.393448i	0.956964	−	0.290205i	$-0.0937235\pi$
$131$	2.59993	+	4.50322i	0.227157	+	0.393448i	−0.729807	+	0.683653i	$0.760390\pi$
$132$		0			0
$133$	1.28959	−	2.23364i	0.111822	−	0.193681i
$134$		0			0
$135$	−3.07179	+	0.549083i	−0.264378	+	0.0472575i
$136$		0			0
$137$	−4.39399	+	7.61062i	−0.375404	+	0.650219i	−0.990387	−	0.138321i	$-0.955829\pi$
$137$	−4.39399	+	7.61062i	−0.375404	+	0.650219i	0.614983	+	0.788540i	$0.289163\pi$
$138$		0			0
$139$	4.50934	+	7.81040i	0.382477	+	0.662469i	0.991416	−	0.130748i	$-0.0417378\pi$
$139$	4.50934	+	7.81040i	0.382477	+	0.662469i	−0.608939	+	0.793217i	$0.708404\pi$
$140$		0			0
$141$	−0.780859	+	6.72634i	−0.0657602	+	0.566460i
$142$		0			0
$143$	−0.528746			−0.0442159
$144$		0			0
$145$	2.11329			0.175499
$146$		0			0
$147$	−1.39013	−	1.03322i	−0.114656	−	0.0852186i
$148$		0			0
$149$	0.525620	+	0.910400i	0.0430604	+	0.0745829i	0.886752	−	0.462245i	$-0.152956\pi$
$149$	0.525620	+	0.910400i	0.0430604	+	0.0745829i	−0.843692	+	0.536828i	$0.819623\pi$
$150$		0			0
$151$	6.48932	−	11.2398i	0.528094	−	0.914685i	−0.471370	−	0.881936i	$-0.656240\pi$
$151$	6.48932	−	11.2398i	0.528094	−	0.914685i	0.999464	−	0.0327494i	$-0.0104263\pi$
$152$		0			0
$153$	−2.97999	+	3.16853i	−0.240918	+	0.256160i
$154$		0			0
$155$	2.88879	−	5.00352i	0.232033	−	0.401893i
$156$		0			0
$157$	9.86699	+	17.0901i	0.787471	+	1.36394i	0.927511	+	0.373795i	$0.121944\pi$
$157$	9.86699	+	17.0901i	0.787471	+	1.36394i	−0.140040	+	0.990146i	$0.544723\pi$
$158$		0			0
$159$	−14.7406	+	6.37218i	−1.16901	+	0.505347i
$160$		0			0
$161$	−1.84936			−0.145750
$162$		0			0
$163$	−22.9214			−1.79534			−0.897672	−	0.440664i	$-0.854743\pi$
$163$	−22.9214			−1.79534			−0.897672	+	0.440664i	$0.854743\pi$
$164$		0			0
$165$	−1.52814	+	0.660596i	−0.118966	+	0.0514273i
$166$		0			0
$167$	−1.61508	−	2.79740i	−0.124978	−	0.216469i	0.796746	−	0.604314i	$-0.206553\pi$
$167$	−1.61508	−	2.79740i	−0.124978	−	0.216469i	−0.921725	+	0.387845i	$0.873220\pi$
$168$		0			0
$169$	6.44543	−	11.1638i	0.495803	−	0.858755i
$170$		0			0
$171$	5.30101	−	5.63640i	0.405378	−	0.431026i
$172$		0			0
$173$	−7.08052	+	12.2638i	−0.538322	+	0.932401i	0.460672	+	0.887570i	$0.347608\pi$
$173$	−7.08052	+	12.2638i	−0.538322	+	0.932401i	−0.998995	+	0.0448312i	$0.985725\pi$
$174$		0			0
$175$	−2.31968	−	4.01780i	−0.175351	−	0.303717i
$176$		0			0
$177$	19.2804	+	14.3303i	1.44920	+	1.07713i
$178$		0			0
$179$	7.06790			0.528280			0.264140	−	0.964484i	$-0.414912\pi$
$179$	7.06790			0.528280			0.264140	+	0.964484i	$0.414912\pi$
$180$		0			0
$181$	−19.6207			−1.45839			−0.729197	−	0.684304i	$-0.760106\pi$
$181$	−19.6207			−1.45839			−0.729197	+	0.684304i	$0.760106\pi$
$182$		0			0
$183$	1.03634	−	8.92706i	0.0766084	−	0.659907i
$184$		0			0
$185$	−0.180322	−	0.312327i	−0.0132575	−	0.0229627i
$186$		0			0
$187$	−1.16031	+	2.00971i	−0.0848502	+	0.146965i
$188$		0			0
$189$	−3.34936	−	3.97263i	−0.243630	−	0.288966i
$190$		0			0
$191$	10.1096	−	17.5104i	0.731505	−	1.26700i	−0.224734	−	0.974420i	$-0.572151\pi$
$191$	10.1096	−	17.5104i	0.731505	−	1.26700i	0.956240	−	0.292584i	$-0.0945152\pi$
$192$		0			0
$193$	−8.89473	−	15.4061i	−0.640257	−	1.10896i	−0.985375	−	0.170398i	$-0.945495\pi$
$193$	−8.89473	−	15.4061i	−0.640257	−	1.10896i	0.345119	−	0.938559i	$-0.387839\pi$
$194$		0			0
$195$	−0.0396248	+	0.341330i	−0.00283759	+	0.0244431i
$196$		0			0
$197$	8.04150			0.572933			0.286467	−	0.958090i	$-0.407519\pi$
$197$	8.04150			0.572933			0.286467	+	0.958090i	$0.407519\pi$
$198$		0			0
$199$	14.0332			0.994790			0.497395	−	0.867524i	$-0.334290\pi$
$199$	14.0332			0.994790			0.497395	+	0.867524i	$0.334290\pi$
$200$		0			0
$201$	16.4165	+	12.2017i	1.15793	+	0.860638i
$202$		0			0
$203$	1.75950	+	3.04755i	0.123493	+	0.213896i
$204$		0			0
$205$	−1.98798	+	3.44328i	−0.138847	+	0.240489i
$206$		0			0
$207$	−5.40054	−	1.27102i	−0.375363	−	0.0883421i
$208$		0			0
$209$	2.06404	−	3.57502i	0.142772	−	0.247289i
$210$		0			0
$211$	−7.32622	−	12.6894i	−0.504358	−	0.873574i	−0.999987	−	0.00503962i	$-0.998396\pi$
$211$	−7.32622	−	12.6894i	−0.504358	−	0.873574i	0.495629	−	0.868534i	$-0.334938\pi$
$212$		0			0
$213$	−6.64516	+	2.87262i	−0.455319	+	0.196829i
$214$		0			0
$215$	2.17972			0.148656
$216$		0			0
$217$	9.62068			0.653095
$218$		0			0
$219$	6.58153	−	2.84511i	0.444738	−	0.192255i
$220$		0			0
$221$	0.239491	+	0.414811i	0.0161099	+	0.0279032i
$222$		0			0
$223$	7.02696	−	12.1711i	0.470560	−	0.815034i	−0.528873	−	0.848701i	$-0.677385\pi$
$223$	7.02696	−	12.1711i	0.470560	−	0.815034i	0.999433	+	0.0336670i	$0.0107185\pi$
$224$		0			0
$225$	−4.01262	−	13.3271i	−0.267508	−	0.888473i
$226$		0			0
$227$	−2.40601	+	4.16733i	−0.159692	+	0.276596i	−0.934758	−	0.355286i	$-0.884384\pi$
$227$	−2.40601	+	4.16733i	−0.159692	+	0.276596i	0.775065	+	0.631881i	$0.217717\pi$
$228$		0			0
$229$	−1.68419	−	2.91710i	−0.111294	−	0.192767i	0.804998	−	0.593277i	$-0.202166\pi$
$229$	−1.68419	−	2.91710i	−0.111294	−	0.192767i	−0.916292	+	0.400510i	$0.868833\pi$
$230$		0			0
$231$	−2.22495	−	1.65371i	−0.146391	−	0.108806i
$232$		0			0
$233$	20.9137			1.37010			0.685051	−	0.728495i	$-0.259780\pi$
$233$	20.9137			1.37010			0.685051	+	0.728495i	$0.259780\pi$
$234$		0			0
$235$	2.34782			0.153155
$236$		0			0
$237$	−1.62397	+	13.9889i	−0.105488	+	0.908679i
$238$		0			0
$239$	−9.60614	−	16.6383i	−0.621370	−	1.07624i	−0.989231	−	0.146363i	$-0.953243\pi$
$239$	−9.60614	−	16.6383i	−0.621370	−	1.07624i	0.367861	−	0.929881i	$-0.380090\pi$
$240$		0			0
$241$	8.88912	−	15.3964i	0.572599	−	0.991770i	−0.423699	−	0.905803i	$-0.639269\pi$
$241$	8.88912	−	15.3964i	0.572599	−	0.991770i	0.996298	−	0.0859672i	$-0.0273980\pi$
$242$		0			0
$243$	−7.05057	−	13.9029i	−0.452294	−	0.891869i
$244$		0			0
$245$	−0.300268	+	0.520080i	−0.0191834	+	0.0332267i
$246$		0			0
$247$	−0.426023	−	0.737894i	−0.0271072	−	0.0469510i
$248$		0			0
$249$	1.11434	−	9.59896i	0.0706184	−	0.608309i
$250$		0			0
$251$	20.5531			1.29730			0.648649	−	0.761088i	$-0.275335\pi$
$251$	20.5531			1.29730			0.648649	+	0.761088i	$0.275335\pi$
$252$		0			0
$253$	−2.95997			−0.186092
$254$		0			0
$255$	1.21041	+	0.899644i	0.0757988	+	0.0563379i
$256$		0			0
$257$	12.6943	+	21.9871i	0.791846	+	1.37152i	0.924823	+	0.380399i	$0.124213\pi$
$257$	12.6943	+	21.9871i	0.791846	+	1.37152i	−0.132976	+	0.991119i	$0.542453\pi$
$258$		0			0
$259$	0.300268	−	0.520080i	0.0186578	−	0.0323162i
$260$		0			0
$261$	3.04362	+	10.1088i	0.188396	+	0.625717i
$262$		0			0
$263$	15.3557	−	26.5969i	0.946874	−	1.64003i	0.194918	−	0.980820i	$-0.437556\pi$
$263$	15.3557	−	26.5969i	0.946874	−	1.64003i	0.751956	−	0.659213i	$-0.229111\pi$
$264$		0			0
$265$	2.78398	+	4.82200i	0.171019	+	0.296213i
$266$		0			0
$267$	−6.09026	+	2.63274i	−0.372718	+	0.161121i
$268$		0			0
$269$	13.7402			0.837757			0.418878	−	0.908042i	$-0.362423\pi$
$269$	13.7402			0.837757			0.418878	+	0.908042i	$0.362423\pi$
$270$		0			0
$271$	7.64977			0.464690			0.232345	−	0.972633i	$-0.425360\pi$
$271$	7.64977			0.464690			0.232345	+	0.972633i	$0.425360\pi$
$272$		0			0
$273$	−0.525218	+	0.227045i	−0.0317877	+	0.0137414i
$274$		0			0
$275$	−3.71273	−	6.43064i	−0.223886	−	0.387782i
$276$		0			0
$277$	4.19174	−	7.26030i	0.251857	−	0.436229i	−0.712180	−	0.701997i	$-0.752292\pi$
$277$	4.19174	−	7.26030i	0.251857	−	0.436229i	0.964037	+	0.265768i	$0.0856254\pi$
$278$		0			0
$279$	28.0945	+	6.61206i	1.68197	+	0.395854i
$280$		0			0
$281$	12.7786	−	22.1333i	0.762310	−	1.32036i	−0.179347	−	0.983786i	$-0.557398\pi$
$281$	12.7786	−	22.1333i	0.762310	−	1.32036i	0.941657	−	0.336574i	$-0.109268\pi$
$282$		0			0
$283$	−5.46132	−	9.45928i	−0.324641	−	0.562296i	0.656798	−	0.754066i	$-0.271910\pi$
$283$	−5.46132	−	9.45928i	−0.324641	−	0.562296i	−0.981440	+	0.191771i	$0.938577\pi$
$284$		0			0
$285$	−2.15316	−	1.60035i	−0.127542	−	0.0947965i
$286$		0			0
$287$	−6.62068			−0.390807
$288$		0			0
$289$	−14.8978			−0.876341
$290$		0			0
$291$	0.389390	−	3.35422i	0.0228264	−	0.196628i
$292$		0			0
$293$	−13.9994	−	24.2477i	−0.817853	−	1.41656i	−0.907261	−	0.420569i	$-0.861831\pi$
$293$	−13.9994	−	24.2477i	−0.817853	−	1.41656i	0.0894073	−	0.995995i	$-0.471503\pi$
$294$		0			0
$295$	4.16457	−	7.21325i	0.242471	−	0.419972i
$296$		0			0
$297$	−5.36078	−	6.35833i	−0.311064	−	0.368948i
$298$		0			0
$299$	−0.305473	+	0.529095i	−0.0176660	+	0.0305984i
$300$		0			0
$301$	1.81481	+	3.14334i	0.104604	+	0.181179i
$302$		0			0
$303$	−3.51336	+	30.2642i	−0.201837	+	1.73863i
$304$		0			0
$305$	−3.11598			−0.178420
$306$		0			0
$307$	−33.0259			−1.88489			−0.942443	−	0.334367i	$-0.891477\pi$
$307$	−33.0259			−1.88489			−0.942443	+	0.334367i	$0.891477\pi$
$308$		0			0
$309$	14.7506	+	10.9635i	0.839131	+	0.623689i
$310$		0			0
$311$	13.0143	+	22.5415i	0.737975	+	1.27821i	0.953406	+	0.301692i	$0.0975513\pi$
$311$	13.0143	+	22.5415i	0.737975	+	1.27821i	−0.215430	+	0.976519i	$0.569115\pi$
$312$		0			0
$313$	5.46618	−	9.46771i	0.308967	−	0.535146i	−0.669170	−	0.743110i	$-0.733350\pi$
$313$	5.46618	−	9.46771i	0.308967	−	0.535146i	0.978137	+	0.207963i	$0.0666834\pi$
$314$		0			0
$315$	−1.23429	+	1.31238i	−0.0695441	+	0.0739441i
$316$		0			0
$317$	5.98593	−	10.3679i	0.336203	−	0.582321i	−0.647512	−	0.762055i	$-0.724190\pi$
$317$	5.98593	−	10.3679i	0.336203	−	0.582321i	0.983715	+	0.179734i	$0.0575237\pi$
$318$		0			0
$319$	2.81615	+	4.87772i	0.157674	+	0.273100i
$320$		0			0
$321$	−5.46830	+	2.36388i	−0.305211	+	0.131939i
$322$		0			0
$323$	−3.73956			−0.208074
$324$		0			0
$325$	−1.53264			−0.0850153
$326$		0			0
$327$	−8.82388	+	3.81445i	−0.487962	+	0.210939i
$328$		0			0
$329$	1.95477	+	3.38576i	0.107770	+	0.186663i
$330$		0			0
$331$	−11.6176	+	20.1223i	−0.638561	+	1.10602i	0.347188	+	0.937796i	$0.387137\pi$
$331$	−11.6176	+	20.1223i	−0.638561	+	1.10602i	−0.985749	+	0.168224i	$0.946197\pi$
$332$		0			0
$333$	1.23429	−	1.31238i	0.0676384	−	0.0719179i
$334$		0			0
$335$	3.54597	−	6.14180i	0.193737	−	0.335562i
$336$		0			0
$337$	−3.89594	−	6.74796i	−0.212225	−	0.367585i	0.740185	−	0.672403i	$-0.234738\pi$
$337$	−3.89594	−	6.74796i	−0.212225	−	0.367585i	−0.952411	+	0.304818i	$0.901404\pi$
$338$		0			0
$339$	−12.1797	−	9.05265i	−0.661512	−	0.491672i
$340$		0			0
$341$	15.3983			0.833862
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−0.221824	+	1.91080i	−0.0119426	+	0.102874i
$346$		0			0
$347$	9.26198	+	16.0422i	0.497209	+	0.861192i	0.999995	−	0.00321932i	$-0.00102474\pi$
$347$	9.26198	+	16.0422i	0.497209	+	0.861192i	−0.502785	+	0.864411i	$0.667691\pi$
$348$		0			0
$349$	0.958498	−	1.66017i	0.0513072	−	0.0888667i	−0.839231	−	0.543775i	$-0.816995\pi$
$349$	0.958498	−	1.66017i	0.0513072	−	0.0888667i	0.890538	+	0.454908i	$0.150328\pi$
$350$		0			0
$351$	−1.68979	+	0.302050i	−0.0901944	+	0.0161223i
$352$		0			0
$353$	0.869778	−	1.50650i	0.0462936	−	0.0801829i	−0.841950	−	0.539555i	$-0.818592\pi$
$353$	0.869778	−	1.50650i	0.0462936	−	0.0801829i	0.888244	+	0.459372i	$0.151926\pi$
$354$		0			0
$355$	1.25504	+	2.17379i	0.0666104	+	0.115373i
$356$		0			0
$357$	−0.289591	+	2.49455i	−0.0153268	+	0.132025i
$358$		0			0
$359$	−3.07616			−0.162354			−0.0811768	−	0.996700i	$-0.525868\pi$
$359$	−3.07616			−0.162354			−0.0811768	+	0.996700i	$0.525868\pi$
$360$		0			0
$361$	−12.3478			−0.649885
$362$		0			0
$363$	11.7303	+	8.71861i	0.615681	+	0.457608i
$364$		0			0
$365$	−1.24302	−	2.15297i	−0.0650625	−	0.112692i
$366$		0			0
$367$	6.17871	−	10.7018i	0.322526	−	0.558632i	−0.658482	−	0.752596i	$-0.728801\pi$
$367$	6.17871	−	10.7018i	0.322526	−	0.558632i	0.981009	+	0.193964i	$0.0621346\pi$
$368$		0			0
$369$	−19.3338	−	4.55023i	−1.00648	−	0.236876i
$370$		0			0
$371$	−4.63583	+	8.02949i	−0.240680	+	0.416870i
$372$		0			0
$373$	−12.3999	−	21.4773i	−0.642044	−	1.11205i	−0.984976	−	0.172693i	$-0.944753\pi$
$373$	−12.3999	−	21.4773i	−0.642044	−	1.11205i	0.342931	−	0.939360i	$-0.388580\pi$
$374$		0			0
$375$	−9.20335	+	3.97849i	−0.475259	+	0.205448i
$376$		0			0
$377$	1.16252			0.0598730
$378$		0			0
$379$	−11.9650			−0.614602			−0.307301	−	0.951612i	$-0.599426\pi$
$379$	−11.9650			−0.614602			−0.307301	+	0.951612i	$0.599426\pi$
$380$		0			0
$381$	−17.7303	+	7.66457i	−0.908350	+	0.392668i
$382$		0			0
$383$	−5.85810	−	10.1465i	−0.299335	−	0.518463i	0.676649	−	0.736306i	$-0.263431\pi$
$383$	−5.85810	−	10.1465i	−0.299335	−	0.518463i	−0.975984	+	0.217843i	$0.930098\pi$
$384$		0			0
$385$	−0.480590	+	0.832407i	−0.0244932	+	0.0424234i
$386$		0			0
$387$	3.13929	+	10.4265i	0.159579	+	0.530009i
$388$		0			0
$389$	−19.1360	+	33.1445i	−0.970232	+	1.68049i	−0.275384	+	0.961334i	$0.588805\pi$
$389$	−19.1360	+	33.1445i	−0.970232	+	1.68049i	−0.694848	+	0.719156i	$0.744528\pi$
$390$		0			0
$391$	1.34070	+	2.32215i	0.0678019	+	0.117436i
$392$		0			0
$393$	7.22848	+	5.37261i	0.364628	+	0.271012i
$394$		0			0
$395$	4.88282			0.245681
$396$		0			0
$397$	12.8396			0.644402			0.322201	−	0.946671i	$-0.395577\pi$
$397$	12.8396			0.644402			0.322201	+	0.946671i	$0.395577\pi$
$398$		0			0
$399$	0.515144	−	4.43747i	0.0257895	−	0.222152i
$400$		0			0
$401$	−11.1570	−	19.3245i	−0.557155	−	0.965021i	−0.997732	−	0.0673063i	$-0.978560\pi$
$401$	−11.1570	−	19.3245i	−0.557155	−	0.965021i	0.440577	−	0.897715i	$-0.354774\pi$
$402$		0			0
$403$	1.58912	−	2.75244i	0.0791598	−	0.137109i
$404$		0			0
$405$	−4.50634	+	2.98413i	−0.223922	+	0.148283i
$406$		0			0
$407$	0.480590	−	0.832407i	0.0238220	−	0.0412609i
$408$		0			0
$409$	3.76605	+	6.52299i	0.186219	+	0.322541i	0.943987	−	0.329984i	$-0.107043\pi$
$409$	3.76605	+	6.52299i	0.186219	+	0.322541i	−0.757767	+	0.652525i	$0.773710\pi$
$410$		0			0
$411$	−1.75524	+	15.1197i	−0.0865796	+	0.745799i
$412$		0			0
$413$	13.8695			0.682474
$414$		0			0
$415$	−3.35050			−0.164470
$416$		0			0
$417$	12.5371	+	9.31828i	0.613945	+	0.456318i
$418$		0			0
$419$	14.1245	+	24.4644i	0.690029	+	1.19517i	0.971828	+	0.235692i	$0.0757357\pi$
$419$	14.1245	+	24.4644i	0.690029	+	1.19517i	−0.281798	+	0.959474i	$0.590931\pi$
$420$		0			0
$421$	−9.53395	+	16.5133i	−0.464656	+	0.804808i	−0.999186	−	0.0403414i	$-0.987155\pi$
$421$	−9.53395	+	16.5133i	−0.464656	+	0.804808i	0.534530	+	0.845150i	$0.320489\pi$
$422$		0			0
$423$	3.38140	+	11.2306i	0.164409	+	0.546051i
$424$		0			0
$425$	−3.36330	+	5.82541i	−0.163144	+	0.282574i
$426$		0			0
$427$	−2.59433	−	4.49351i	−0.125548	−	0.217456i
$428$		0			0
$429$	−0.840631	+	0.363394i	−0.0405860	+	0.0175448i
$430$		0			0
$431$	−22.9786			−1.10684			−0.553421	−	0.832902i	$-0.686678\pi$
$431$	−22.9786			−1.10684			−0.553421	+	0.832902i	$0.686678\pi$
$432$		0			0
$433$	−29.0806			−1.39752			−0.698762	−	0.715354i	$-0.746265\pi$
$433$	−29.0806			−1.39752			−0.698762	+	0.715354i	$0.746265\pi$
$434$		0			0
$435$	3.35984	−	1.45241i	0.161092	−	0.0696379i
$436$		0			0
$437$	−2.38492	−	4.13081i	−0.114086	−	0.197603i
$438$		0			0
$439$	7.36777	−	12.7613i	0.351644	−	0.609066i	−0.634893	−	0.772600i	$-0.718956\pi$
$439$	7.36777	−	12.7613i	0.351644	−	0.609066i	0.986538	+	0.163534i	$0.0522893\pi$
$440$		0			0
$441$	−2.92021	−	0.687275i	−0.139058	−	0.0327274i
$442$		0			0
$443$	17.2548	−	29.8861i	0.819799	−	1.41993i	−0.0860314	−	0.996292i	$-0.527419\pi$
$443$	17.2548	−	29.8861i	0.819799	−	1.41993i	0.905830	−	0.423641i	$-0.139248\pi$
$444$		0			0
$445$	1.15024	+	1.99227i	0.0545264	+	0.0944425i
$446$		0			0
$447$	1.46136	+	1.08616i	0.0691198	+	0.0513737i
$448$		0			0
$449$	11.5508			0.545115			0.272557	−	0.962140i	$-0.412131\pi$
$449$	11.5508			0.545115			0.272557	+	0.962140i	$0.412131\pi$
$450$		0			0
$451$	−10.5966			−0.498977
$452$		0			0
$453$	2.59225	−	22.3297i	0.121794	−	1.04914i
$454$		0			0
$455$	0.0991952	+	0.171811i	0.00465034	+	0.00805463i
$456$		0			0
$457$	−18.6995	+	32.3884i	−0.874724	+	1.51507i	−0.0176677	+	0.999844i	$0.505624\pi$
$457$	−18.6995	+	32.3884i	−0.874724	+	1.51507i	−0.857056	+	0.515223i	$0.827709\pi$
$458$		0			0
$459$	−2.56011	+	7.08558i	−0.119496	+	0.330727i
$460$		0			0
$461$	9.13929	−	15.8297i	0.425659	−	0.737263i	−0.570823	−	0.821073i	$-0.693376\pi$
$461$	9.13929	−	15.8297i	0.425659	−	0.737263i	0.996482	+	0.0838101i	$0.0267089\pi$
$462$		0			0
$463$	−4.24610	−	7.35447i	−0.197333	−	0.341791i	0.750330	−	0.661064i	$-0.229895\pi$
$463$	−4.24610	−	7.35447i	−0.197333	−	0.341791i	−0.947663	+	0.319273i	$0.896561\pi$
$464$		0			0
$465$	1.15396	−	9.94029i	0.0535138	−	0.460970i
$466$		0			0
$467$	−14.6746			−0.679060			−0.339530	−	0.940595i	$-0.610268\pi$
$467$	−14.6746			−0.679060			−0.339530	+	0.940595i	$0.610268\pi$
$468$		0			0
$469$	11.8093			0.545305
$470$		0			0
$471$	27.4327	+	20.3896i	1.26403	+	0.939501i
$472$		0			0
$473$	2.90467	+	5.03103i	0.133557	+	0.231327i
$474$		0			0
$475$	5.98287	−	10.3626i	0.274513	−	0.475470i
$476$		0			0
$477$	−19.0561	+	20.2617i	−0.872518	+	0.927722i
$478$		0			0
$479$	−18.7151	+	32.4156i	−0.855117	+	1.48111i	0.0214198	+	0.999771i	$0.493181\pi$
$479$	−18.7151	+	32.4156i	−0.855117	+	1.48111i	−0.876537	+	0.481335i	$0.840152\pi$
$480$		0			0
$481$	−0.0991952	−	0.171811i	−0.00452291	−	0.00783391i
$482$		0			0
$483$	−2.94023	+	1.27102i	−0.133785	+	0.0578335i
$484$		0			0
$485$	−1.17078			−0.0531626
$486$		0			0
$487$	33.3216			1.50994			0.754972	−	0.655757i	$-0.227650\pi$
$487$	33.3216			1.50994			0.754972	+	0.655757i	$0.227650\pi$
$488$		0			0
$489$	−36.4418	+	15.7533i	−1.64796	+	0.712390i
$490$		0			0
$491$	19.9456	+	34.5467i	0.900131	+	1.55907i	0.827323	+	0.561726i	$0.189863\pi$
$491$	19.9456	+	34.5467i	0.900131	+	1.55907i	0.0728078	+	0.997346i	$0.476804\pi$
$492$		0			0
$493$	2.55110	−	4.41864i	0.114896	−	0.199006i
$494$		0			0
$495$	−1.97552	+	2.10051i	−0.0887930	+	0.0944108i
$496$		0			0
$497$	−2.08986	+	3.61974i	−0.0937430	+	0.162368i
$498$		0			0
$499$	−11.0370	−	19.1167i	−0.494086	−	0.855781i	0.505891	−	0.862597i	$-0.331164\pi$
$499$	−11.0370	−	19.1167i	−0.494086	−	0.855781i	−0.999977	+	0.00681602i	$0.997830\pi$
$500$		0			0
$501$	−4.49033	−	3.33746i	−0.200613	−	0.149107i
$502$		0			0
$503$	−9.30820			−0.415032			−0.207516	−	0.978232i	$-0.566538\pi$
$503$	−9.30820			−0.415032			−0.207516	+	0.978232i	$0.566538\pi$
$504$		0			0
$505$	10.5637			0.470077
$506$		0			0
$507$	2.57471	−	22.1787i	0.114347	−	0.984990i
$508$		0			0
$509$	2.88466	+	4.99637i	0.127860	+	0.221460i	0.922847	−	0.385166i	$-0.125856\pi$
$509$	2.88466	+	4.99637i	0.127860	+	0.221460i	−0.794987	+	0.606626i	$0.792522\pi$
$510$		0			0
$511$	2.06985	−	3.58508i	0.0915646	−	0.158595i
$512$		0			0
$513$	4.55410	−	12.6043i	0.201068	−	0.556495i
$514$		0			0
$515$	3.18613	−	5.51854i	0.140398	−	0.243176i
$516$		0			0
$517$	3.12868	+	5.41903i	0.137599	+	0.238329i
$518$		0			0
$519$	−2.82841	+	24.3640i	−0.124153	+	1.06946i
$520$		0			0
$521$	−13.2989			−0.582634			−0.291317	−	0.956627i	$-0.594093\pi$
$521$	−13.2989			−0.582634			−0.291317	+	0.956627i	$0.594093\pi$
$522$		0			0
$523$	4.27523			0.186943			0.0934713	−	0.995622i	$-0.470204\pi$
$523$	4.27523			0.186943			0.0934713	+	0.995622i	$0.470204\pi$
$524$		0			0
$525$	−6.44930	−	4.79348i	−0.281470	−	0.209205i
$526$		0			0
$527$	−6.97451	−	12.0802i	−0.303815	−	0.526222i
$528$		0			0
$529$	9.78993	−	16.9567i	0.425649	−	0.737246i
$530$		0			0
$531$	40.5019	+	9.53217i	1.75763	+	0.413661i
$532$		0			0
$533$	−1.09359	+	1.89415i	−0.0473686	+	0.0820448i
$534$		0			0
$535$	1.03277	+	1.78881i	0.0446505	+	0.0773370i
$536$		0			0
$537$	11.2370	−	4.85759i	0.484911	−	0.209621i
$538$		0			0
$539$	−1.60054			−0.0689400
$540$		0			0
$541$	−12.2130			−0.525076			−0.262538	−	0.964922i	$-0.584560\pi$
$541$	−12.2130			−0.525076			−0.262538	+	0.964922i	$0.584560\pi$
$542$		0			0
$543$	−31.1941	+	13.4848i	−1.33867	+	0.578689i
$544$		0			0
$545$	1.66652	+	2.88650i	0.0713858	+	0.123644i
$546$		0			0
$547$	−19.0910	+	33.0666i	−0.816272	+	1.41382i	0.0921387	+	0.995746i	$0.470630\pi$
$547$	−19.0910	+	33.0666i	−0.816272	+	1.41382i	−0.908411	+	0.418079i	$0.862704\pi$
$548$		0			0
$549$	−4.48771	−	14.9050i	−0.191531	−	0.636131i
$550$		0			0
$551$	−4.53808	+	7.86019i	−0.193329	+	0.334855i
$552$		0			0
$553$	4.06538	+	7.04144i	0.172877	+	0.299433i
$554$		0			0
$555$	−0.501341	−	0.372625i	−0.0212808	−	0.0158171i
$556$		0			0
$557$	36.8404			1.56098			0.780490	−	0.625169i	$-0.214970\pi$
$557$	36.8404			1.56098			0.780490	+	0.625169i	$0.214970\pi$
$558$		0			0
$559$	1.19906			0.0507150
$560$		0			0
$561$	−0.463501	+	3.99261i	−0.0195690	+	0.168568i
$562$		0			0
$563$	−9.56265	−	16.5630i	−0.403018	−	0.698047i	0.591071	−	0.806620i	$-0.298705\pi$
$563$	−9.56265	−	16.5630i	−0.403018	−	0.698047i	−0.994089	+	0.108572i	$0.965372\pi$
$564$		0			0
$565$	−2.63083	+	4.55672i	−0.110680	+	0.191703i
$566$		0			0
$567$	−8.05531	−	4.01398i	−0.338291	−	0.168571i
$568$		0			0
$569$	12.9576	−	22.4433i	0.543212	−	0.940871i	−0.455505	−	0.890233i	$-0.650541\pi$
$569$	12.9576	−	22.4433i	0.543212	−	0.940871i	0.998717	−	0.0506376i	$-0.0161253\pi$
$570$		0			0
$571$	19.5679	+	33.8925i	0.818889	+	1.41836i	0.906501	+	0.422203i	$0.138743\pi$
$571$	19.5679	+	33.8925i	0.818889	+	1.41836i	−0.0876117	+	0.996155i	$0.527923\pi$
$572$		0			0
$573$	4.03842	−	34.7871i	0.168707	−	1.45325i
$574$		0			0
$575$	−8.57985			−0.357805
$576$		0			0
$577$	9.72008			0.404652			0.202326	−	0.979318i	$-0.435150\pi$
$577$	9.72008			0.404652			0.202326	+	0.979318i	$0.435150\pi$
$578$		0			0
$579$	−24.7296	−	18.3804i	−1.02773	−	0.763865i
$580$		0			0
$581$	−2.78959	−	4.83171i	−0.115732	−	0.200453i
$582$		0			0
$583$	−7.41981	+	12.8515i	−0.307297	+	0.532254i
$584$		0			0
$585$	0.171590	+	0.569900i	0.00709436	+	0.0235625i
$586$		0			0
$587$	−6.91088	+	11.9700i	−0.285242	+	0.494054i	−0.972668	−	0.232200i	$-0.925407\pi$
$587$	−6.91088	+	11.9700i	−0.285242	+	0.494054i	0.687425	+	0.726255i	$0.258741\pi$
$588$		0			0
$589$	12.4067	+	21.4891i	0.511211	+	0.885444i
$590$		0			0
$591$	12.7849	−	5.52673i	0.525899	−	0.227339i
$592$		0			0
$593$	−22.1361			−0.909022			−0.454511	−	0.890741i	$-0.650186\pi$
$593$	−22.1361			−0.909022			−0.454511	+	0.890741i	$0.650186\pi$
$594$		0			0
$595$	0.870718			0.0356960
$596$		0			0
$597$	22.3109	−	9.64470i	0.913123	−	0.394731i
$598$		0			0
$599$	−2.28059	−	3.95010i	−0.0931824	−	0.161397i	0.815666	−	0.578523i	$-0.196371\pi$
$599$	−2.28059	−	3.95010i	−0.0931824	−	0.161397i	−0.908849	+	0.417126i	$0.863037\pi$
$600$		0			0
$601$	−10.2116	+	17.6870i	−0.416541	+	0.721469i	−0.995589	−	0.0938238i	$-0.970091\pi$
$601$	−10.2116	+	17.6870i	−0.416541	+	0.721469i	0.579048	+	0.815293i	$0.303424\pi$
$602$		0			0
$603$	34.4858	+	8.11627i	1.40437	+	0.330520i
$604$		0			0
$605$	2.53375	−	4.38858i	0.103012	−	0.178421i
$606$		0			0
$607$	−7.11206	−	12.3184i	−0.288670	−	0.499990i	0.684823	−	0.728710i	$-0.259880\pi$
$607$	−7.11206	−	12.3184i	−0.288670	−	0.499990i	−0.973492	+	0.228719i	$0.926546\pi$
$608$		0			0
$609$	4.89187	+	3.63591i	0.198229	+	0.147335i
$610$		0			0
$611$	1.29154			0.0522499
$612$		0			0
$613$	−31.3892			−1.26780			−0.633899	−	0.773416i	$-0.718546\pi$
$613$	−31.3892			−1.26780			−0.633899	+	0.773416i	$0.718546\pi$
$614$		0			0
$615$	−0.794126	+	6.84063i	−0.0320222	+	0.275841i
$616$		0			0
$617$	−2.51767	−	4.36073i	−0.101357	−	0.175556i	0.810887	−	0.585203i	$-0.198985\pi$
$617$	−2.51767	−	4.36073i	−0.101357	−	0.175556i	−0.912244	+	0.409647i	$0.865652\pi$
$618$		0			0
$619$	19.1803	−	33.2212i	0.770920	−	1.33527i	−0.166140	−	0.986102i	$-0.553130\pi$
$619$	19.1803	−	33.2212i	0.770920	−	1.33527i	0.937060	−	0.349170i	$-0.113536\pi$
$620$		0			0
$621$	−9.45964	+	1.69091i	−0.379602	+	0.0678539i
$622$		0			0
$623$	−1.91535	+	3.31748i	−0.0767367	+	0.132912i
$624$		0			0
$625$	−9.86020	−	17.0784i	−0.394408	−	0.683135i
$626$		0			0
$627$	0.824508	−	7.10234i	0.0329277	−	0.283640i
$628$		0			0
$629$	−0.870718			−0.0347178
$630$		0			0
$631$	24.0768			0.958480			0.479240	−	0.877684i	$-0.340912\pi$
$631$	24.0768			0.958480			0.479240	+	0.877684i	$0.340912\pi$
$632$		0			0
$633$	−20.3688	−	15.1392i	−0.809586	−	0.601730i
$634$		0			0
$635$	3.34863	+	5.79999i	0.132886	+	0.230166i
$636$		0			0
$637$	−0.165178	+	0.286096i	−0.00654457	+	0.0113355i
$638$		0			0
$639$	−8.59060	+	9.13412i	−0.339839	+	0.361340i
$640$		0			0
$641$	−20.7800	+	35.9920i	−0.820760	+	1.42160i	0.0843567	+	0.996436i	$0.473116\pi$
$641$	−20.7800	+	35.9920i	−0.820760	+	1.42160i	−0.905117	+	0.425163i	$0.860217\pi$
$642$		0			0
$643$	0.924345	+	1.60101i	0.0364526	+	0.0631378i	0.883676	−	0.468099i	$-0.155061\pi$
$643$	0.924345	+	1.60101i	0.0364526	+	0.0631378i	−0.847224	+	0.531237i	$0.821728\pi$
$644$		0			0
$645$	3.46545	−	1.49807i	0.136452	−	0.0589863i
$646$		0			0
$647$	−38.8480			−1.52727			−0.763637	−	0.645646i	$-0.776588\pi$
$647$	−38.8480			−1.52727			−0.763637	+	0.645646i	$0.776588\pi$
$648$		0			0
$649$	22.1987			0.871374
$650$		0			0
$651$	15.2955	−	6.61206i	0.599479	−	0.259147i
$652$		0			0
$653$	−20.3225	−	35.1996i	−0.795281	−	1.37747i	−0.922661	−	0.385613i	$-0.873990\pi$
$653$	−20.3225	−	35.1996i	−0.795281	−	1.37747i	0.127380	−	0.991854i	$-0.459343\pi$
$654$		0			0
$655$	1.56135	−	2.70435i	0.0610072	−	0.105668i
$656$		0			0
$657$	8.50833	−	9.04664i	0.331942	−	0.352943i
$658$		0			0
$659$	−19.2140	+	33.2796i	−0.748471	+	1.29639i	0.200084	+	0.979779i	$0.435879\pi$
$659$	−19.2140	+	33.2796i	−0.748471	+	1.29639i	−0.948555	+	0.316612i	$0.897455\pi$
$660$		0			0
$661$	5.72841	+	9.92190i	0.222809	+	0.385917i	0.955660	−	0.294472i	$-0.0951439\pi$
$661$	5.72841	+	9.92190i	0.222809	+	0.385917i	−0.732851	+	0.680390i	$0.761811\pi$
$662$		0			0
$663$	0.665846	+	0.494894i	0.0258593	+	0.0192201i
$664$		0			0
$665$	−1.54889			−0.0600635
$666$		0			0
$667$	6.50793			0.251988
$668$		0			0
$669$	2.80701	−	24.1797i	0.108525	−	0.934842i
$670$		0			0
$671$	−4.15231	−	7.19202i	−0.160298	−	0.277645i
$672$		0			0
$673$	−23.4933	+	40.6916i	−0.905601	+	1.56855i	−0.0854925	+	0.996339i	$0.527246\pi$
$673$	−23.4933	+	40.6916i	−0.905601	+	1.56855i	−0.820108	+	0.572208i	$0.806087\pi$
$674$		0			0
$675$	−15.5389	−	18.4304i	−0.598092	−	0.709388i
$676$		0			0
$677$	8.03942	−	13.9247i	0.308980	−	0.535169i	−0.669159	−	0.743119i	$-0.733346\pi$
$677$	8.03942	−	13.9247i	0.308980	−	0.535169i	0.978140	+	0.207950i	$0.0666790\pi$
$678$		0			0
$679$	−0.974782	−	1.68837i	−0.0374087	−	0.0647938i
$680$		0			0
$681$	−0.961113	+	8.27906i	−0.0368299	+	0.317254i
$682$		0			0
$683$	−5.20464			−0.199150			−0.0995750	−	0.995030i	$-0.531748\pi$
$683$	−5.20464			−0.199150			−0.0995750	+	0.995030i	$0.531748\pi$
$684$		0			0
$685$	5.27750			0.201643
$686$		0			0
$687$	−4.68247	−	3.48027i	−0.178647	−	0.132781i
$688$		0			0
$689$	1.53147	+	2.65258i	0.0583444	+	0.101055i
$690$		0			0
$691$	−0.783381	+	1.35686i	−0.0298012	+	0.0516172i	−0.880541	−	0.473969i	$-0.842821\pi$
$691$	−0.783381	+	1.35686i	−0.0298012	+	0.0516172i	0.850740	+	0.525587i	$0.176154\pi$
$692$		0			0
$693$	−4.67391	−	1.10001i	−0.177547	−	0.0417859i
$694$		0			0
$695$	2.70802	−	4.69043i	0.102721	−	0.177918i
$696$		0			0
$697$	4.79966	+	8.31326i	0.181800	+	0.314887i
$698$		0			0
$699$	33.2498	−	14.3735i	1.25762	−	0.543654i
$700$		0			0
$701$	5.94479			0.224532			0.112266	−	0.993678i	$-0.464189\pi$
$701$	5.94479			0.224532			0.112266	+	0.993678i	$0.464189\pi$
$702$		0			0
$703$	1.54889			0.0584176
$704$		0			0
$705$	3.73270	−	1.61360i	0.140582	−	0.0607716i
$706$		0			0
$707$	8.79520	+	15.2337i	0.330777	+	0.572923i
$708$		0			0
$709$	6.53916	−	11.3262i	0.245583	−	0.425362i	−0.716712	−	0.697369i	$-0.754354\pi$
$709$	6.53916	−	11.3262i	0.245583	−	0.425362i	0.962295	+	0.272007i	$0.0876872\pi$
$710$		0			0
$711$	7.03237	+	23.3566i	0.263734	+	0.875939i
$712$		0			0
$713$	8.89607	−	15.4084i	0.333160	−	0.577051i
$714$		0			0
$715$	0.158766	+	0.274990i	0.00593749	+	0.0102840i
$716$		0			0
$717$	−26.7075	−	19.8505i	−0.997411	−	0.741332i
$718$		0			0
$719$	−10.5600			−0.393821			−0.196910	−	0.980422i	$-0.563091\pi$
$719$	−10.5600			−0.393821			−0.196910	+	0.980422i	$0.563091\pi$
$720$		0			0
$721$	10.6109			0.395172
$722$		0			0
$723$	3.55088	−	30.5874i	0.132059	−	1.13756i
$724$		0			0
$725$	8.16297	+	14.1387i	0.303165	+	0.525097i
$726$		0			0
$727$	5.08052	−	8.79972i	0.188426	−	0.326364i	−0.756300	−	0.654226i	$-0.772995\pi$
$727$	5.08052	−	8.79972i	0.188426	−	0.326364i	0.944726	+	0.327862i	$0.106328\pi$
$728$		0			0
$729$	−20.7645	−	17.2579i	−0.769056	−	0.639182i
$730$		0			0
$731$	2.63129	−	4.55753i	0.0973218	−	0.168566i
$732$		0			0
$733$	−13.2280	−	22.9116i	−0.488589	−	0.846260i	0.511325	−	0.859387i	$-0.329155\pi$
$733$	−13.2280	−	22.9116i	−0.488589	−	0.846260i	−0.999914	+	0.0131270i	$0.995821\pi$
$734$		0			0
$735$	−0.119946	+	1.03322i	−0.00442428	+	0.0381109i
$736$		0			0
$737$	18.9013			0.696237
$738$		0			0
$739$	24.3880			0.897127			0.448563	−	0.893751i	$-0.351936\pi$
$739$	24.3880			0.897127			0.448563	+	0.893751i	$0.351936\pi$
$740$		0			0
$741$	−1.18445	−	0.880352i	−0.0435120	−	0.0323405i
$742$		0			0
$743$	−8.21961	−	14.2368i	−0.301548	−	0.522297i	0.674939	−	0.737874i	$-0.264170\pi$
$743$	−8.21961	−	14.2368i	−0.301548	−	0.522297i	−0.976487	+	0.215577i	$0.930837\pi$
$744$		0			0
$745$	0.315654	−	0.546728i	0.0115647	−	0.0200306i
$746$		0			0
$747$	−4.82549	−	16.0269i	−0.176555	−	0.586392i
$748$		0			0
$749$	−1.71974	+	2.97869i	−0.0628381	+	0.108839i
$750$		0			0
$751$	0.0653789	+	0.113240i	0.00238571	+	0.00413217i	0.867216	−	0.497932i	$-0.165907\pi$
$751$	0.0653789	+	0.113240i	0.00238571	+	0.00413217i	−0.864830	+	0.502065i	$0.832574\pi$
$752$		0			0
$753$	32.6765	−	14.1256i	1.19080	−	0.514766i
$754$		0			0
$755$	−7.79415			−0.283658
$756$		0			0
$757$	36.1017			1.31214			0.656069	−	0.754701i	$-0.272218\pi$
$757$	36.1017			1.31214			0.656069	+	0.754701i	$0.272218\pi$
$758$		0			0
$759$	−4.70594	+	2.03432i	−0.170815	+	0.0738410i
$760$		0			0
$761$	4.61027	+	7.98523i	0.167122	+	0.289464i	0.937407	−	0.348236i	$-0.113219\pi$
$761$	4.61027	+	7.98523i	0.167122	+	0.289464i	−0.770285	+	0.637700i	$0.779886\pi$
$762$		0			0
$763$	−2.77505	+	4.80653i	−0.100464	+	0.174008i
$764$		0			0
$765$	2.54268	+	0.598423i	0.0919309	+	0.0216360i
$766$		0			0
$767$	2.29093	−	3.96801i	0.0827208	−	0.143277i
$768$		0			0
$769$	22.8660	+	39.6050i	0.824568	+	1.42819i	0.902249	+	0.431216i	$0.141915\pi$
$769$	22.8660	+	39.6050i	0.824568	+	1.42819i	−0.0776802	+	0.996978i	$0.524751\pi$
$770$		0			0
$771$	35.2933	+	26.2319i	1.27106	+	0.944721i
$772$		0			0
$773$	25.9709			0.934109			0.467054	−	0.884229i	$-0.345315\pi$
$773$	25.9709			0.934109			0.467054	+	0.884229i	$0.345315\pi$
$774$		0			0
$775$	44.6338			1.60329
$776$		0			0
$777$	0.119946	−	1.03322i	0.00430305	−	0.0370666i
$778$		0			0
$779$	−8.53797	−	14.7882i	−0.305905	−	0.529842i
$780$		0			0
$781$	−3.34490	+	5.79353i	−0.119690	+	0.207309i
$782$		0			0
$783$	11.7864	+	13.9797i	0.421213	+	0.499594i
$784$		0			0
$785$	5.92549	−	10.2632i	0.211490	−	0.366311i
$786$		0			0
$787$	−25.3821	−	43.9630i	−0.904773	−	1.56711i	−0.821222	−	0.570609i	$-0.806707\pi$
$787$	−25.3821	−	43.9630i	−0.904773	−	1.56711i	−0.0835512	−	0.996503i	$-0.526626\pi$
$788$		0			0
$789$	6.13404	−	52.8389i	0.218378	−	1.88111i
$790$		0			0
$791$	−8.76158			−0.311526
$792$		0			0
$793$	−1.71410			−0.0608694
$794$		0			0
$795$	7.74019	+	5.75294i	0.274516	+	0.204036i
$796$		0			0
$797$	−13.2977	−	23.0322i	−0.471027	−	0.815843i	0.528424	−	0.848981i	$-0.322783\pi$
$797$	−13.2977	−	23.0322i	−0.471027	−	0.815843i	−0.999451	+	0.0331379i	$0.989450\pi$
$798$		0			0
$799$	2.83422	−	4.90901i	0.100267	−	0.173668i
$800$		0			0
$801$	−7.87324	+	8.37137i	−0.278187	+	0.295788i
$802$		0			0
$803$	3.31286	−	5.73805i	0.116908	−	0.202491i
$804$		0			0
$805$	0.555305	+	0.961817i	0.0195719	+	0.0338996i
$806$		0			0
$807$	21.8450	−	9.44332i	0.768981	−	0.332421i
$808$		0			0
$809$	−21.1540			−0.743735			−0.371867	−	0.928286i	$-0.621282\pi$
$809$	−21.1540			−0.743735			−0.371867	+	0.928286i	$0.621282\pi$
$810$		0			0
$811$	−15.4615			−0.542927			−0.271464	−	0.962449i	$-0.587508\pi$
$811$	−15.4615			−0.542927			−0.271464	+	0.962449i	$0.587508\pi$
$812$		0			0
$813$	12.1621	−	5.25750i	0.426542	−	0.184388i
$814$		0			0
$815$	6.88258	+	11.9210i	0.241086	+	0.417573i
$816$		0			0
$817$	−4.68072	+	8.10725i	−0.163758	+	0.283637i
$818$		0			0
$819$	−0.678981	+	0.721939i	−0.0237255	+	0.0252266i
$820$		0			0
$821$	−13.2843	+	23.0091i	−0.463626	+	0.803024i	−0.999138	−	0.0415036i	$-0.986785\pi$
$821$	−13.2843	+	23.0091i	−0.463626	+	0.803024i	0.535512	+	0.844527i	$0.320119\pi$
$822$		0			0
$823$	12.5469	+	21.7318i	0.437357	+	0.757524i	0.997485	−	0.0708819i	$-0.0225813\pi$
$823$	12.5469	+	21.7318i	0.437357	+	0.757524i	−0.560128	+	0.828406i	$0.689248\pi$
$824$		0			0
$825$	−10.3223	−	7.67214i	−0.359378	−	0.267110i
$826$		0			0
$827$	12.8156			0.445642			0.222821	−	0.974859i	$-0.428474\pi$
$827$	12.8156			0.445642			0.222821	+	0.974859i	$0.428474\pi$
$828$		0			0
$829$	37.9832			1.31921			0.659605	−	0.751613i	$-0.270724\pi$
$829$	37.9832			1.31921			0.659605	+	0.751613i	$0.270724\pi$
$830$		0			0
$831$	1.67445	−	14.4237i	0.0580859	−	0.500354i
$832$		0			0
$833$	0.724950	+	1.25565i	0.0251180	+	0.0435057i
$834$		0			0
$835$	−0.969913	+	1.67994i	−0.0335652	+	0.0581367i
$836$		0			0
$837$	49.2105	−	8.79639i	1.70097	−	0.304048i
$838$		0			0
$839$	2.95638	−	5.12060i	0.102065	−	0.176783i	−0.810470	−	0.585780i	$-0.800788\pi$
$839$	2.95638	−	5.12060i	0.102065	−	0.176783i	0.912535	+	0.408998i	$0.134122\pi$
$840$		0			0
$841$	8.30829	+	14.3904i	0.286493	+	0.496220i
$842$		0			0
$843$	5.10460	−	43.9712i	0.175812	−	1.51445i
$844$		0			0
$845$	−7.74144			−0.266313
$846$		0			0
$847$	8.43828			0.289943
$848$		0			0
$849$	−15.1838	−	11.2855i	−0.521108	−	0.387317i
$850$		0			0
$851$	−0.555305	−	0.961817i	−0.0190356	−	0.0329707i
$852$		0			0
$853$	9.72609	−	16.8461i	0.333015	−	0.576799i	−0.650087	−	0.759860i	$-0.725267\pi$
$853$	9.72609	−	16.8461i	0.333015	−	0.576799i	0.983101	+	0.183061i	$0.0586007\pi$
$854$		0			0
$855$	−4.52310	−	1.06452i	−0.154687	−	0.0364057i
$856$		0			0
$857$	3.42502	−	5.93231i	0.116996	−	0.202644i	−0.801580	−	0.597888i	$-0.796007\pi$
$857$	3.42502	−	5.93231i	0.116996	−	0.202644i	0.918576	+	0.395244i	$0.129340\pi$
$858$		0			0
$859$	−3.04742	−	5.27828i	−0.103977	−	0.180093i	0.809343	−	0.587336i	$-0.199823\pi$
$859$	−3.04742	−	5.27828i	−0.103977	−	0.180093i	−0.913320	+	0.407244i	$0.866490\pi$
$860$		0			0
$861$	−10.5260	+	4.55023i	−0.358724	+	0.155072i
$862$		0			0
$863$	−33.6568			−1.14569			−0.572846	−	0.819663i	$-0.694161\pi$
$863$	−33.6568			−1.14569			−0.572846	+	0.819663i	$0.694161\pi$
$864$		0			0
$865$	8.50423			0.289152
$866$		0			0
$867$	−23.6854	+	10.2389i	−0.804398	+	0.347731i
$868$		0			0
$869$	6.50679	+	11.2701i	0.220728	+	0.382312i
$870$		0			0
$871$	1.95064	−	3.37860i	0.0660948	−	0.114480i
$872$		0			0
$873$	−1.68620	−	5.60035i	−0.0570691	−	0.189543i
$874$		0			0
$875$	−2.89439	+	5.01324i	−0.0978483	+	0.169478i
$876$		0			0
$877$	−8.18905	−	14.1839i	−0.276525	−	0.478955i	0.693994	−	0.719981i	$-0.255849\pi$
$877$	−8.18905	−	14.1839i	−0.276525	−	0.478955i	−0.970519	+	0.241026i	$0.922516\pi$
$878$		0			0
$879$	−38.9219	−	28.9289i	−1.31280	−	0.975749i
$880$		0			0
$881$	22.0864			0.744108			0.372054	−	0.928211i	$-0.378654\pi$
$881$	22.0864			0.744108			0.372054	+	0.928211i	$0.378654\pi$
$882$		0			0
$883$	13.1872			0.443784			0.221892	−	0.975071i	$-0.428777\pi$
$883$	13.1872			0.443784			0.221892	+	0.975071i	$0.428777\pi$
$884$		0			0
$885$	1.66360	−	14.3303i	0.0559211	−	0.481707i
$886$		0			0
$887$	−14.7174	−	25.4912i	−0.494160	−	0.855911i	0.505817	−	0.862641i	$-0.331191\pi$
$887$	−14.7174	−	25.4912i	−0.494160	−	0.855911i	−0.999977	+	0.00672982i	$0.997858\pi$
$888$		0			0
$889$	−5.57606	+	9.65801i	−0.187015	+	0.323919i
$890$		0			0
$891$	−12.8928	−	6.42453i	−0.431925	−	0.215230i
$892$		0			0
$893$	−5.04170	+	8.73249i	−0.168714	+	0.292222i
$894$		0			0
$895$	−2.12227	−	3.67587i	−0.0709395	−	0.122871i
$896$		0			0
$897$	−0.122025	+	1.05113i	−0.00407431	+	0.0350963i
$898$		0			0
$899$	−33.8553			−1.12914
$900$		0			0
$901$	13.4430			0.447850
$902$		0			0
$903$	5.04563	+	3.75020i	0.167908	+	0.124799i
$904$		0			0
$905$	5.89147	+	10.2043i	0.195839	+	0.339203i
$906$		0			0
$907$	−9.03916	+	15.6563i	−0.300140	+	0.519858i	−0.976167	−	0.217018i	$-0.930367\pi$
$907$	−9.03916	+	15.6563i	−0.300140	+	0.519858i	0.676027	+	0.736877i	$0.263700\pi$
$908$		0			0
$909$	15.2141	+	50.5305i	0.504620	+	1.67599i
$910$		0			0
$911$	−4.24050	+	7.34475i	−0.140494	+	0.243343i	−0.927683	−	0.373369i	$-0.878202\pi$
$911$	−4.24050	+	7.34475i	−0.140494	+	0.243343i	0.787189	+	0.616712i	$0.211536\pi$
$912$		0			0
$913$	−4.46484	−	7.73333i	−0.147765	−	0.255936i
$914$		0			0
$915$	−4.95396	+	2.14153i	−0.163773	+	0.0707969i
$916$		0			0
$917$	5.19987			0.171715
$918$		0			0
$919$	22.0092			0.726017			0.363008	−	0.931786i	$-0.381750\pi$
$919$	22.0092			0.726017			0.363008	+	0.931786i	$0.381750\pi$
$920$		0			0
$921$	−52.5065	+	22.6979i	−1.73015	+	0.747920i
$922$		0			0
$923$	0.690396	+	1.19580i	0.0227247	+	0.0393603i
$924$		0			0
$925$	1.39305	−	2.41284i	0.0458032	−	0.0793336i
$926$		0			0
$927$	30.9862	+	7.29264i	1.01772	+	0.239522i
$928$		0			0
$929$	−21.4107	+	37.0845i	−0.702464	+	1.21670i	0.265135	+	0.964211i	$0.414583\pi$
$929$	−21.4107	+	37.0845i	−0.702464	+	1.21670i	−0.967599	+	0.252492i	$0.918750\pi$
$930$		0			0
$931$	−1.28959	−	2.23364i	−0.0422646	−	0.0732045i
$932$		0			0
$933$	36.1832	+	26.8934i	1.18458	+	0.880450i
$934$		0			0
$935$	1.39362			0.0455761
$936$		0			0
$937$	8.65749			0.282828			0.141414	−	0.989951i	$-0.454835\pi$
$937$	8.65749			0.282828			0.141414	+	0.989951i	$0.454835\pi$
$938$		0			0
$939$	2.18354	−	18.8091i	0.0712572	−	0.613812i
$940$		0			0
$941$	−25.9474	−	44.9421i	−0.845859	−	1.46507i	−0.884873	−	0.465833i	$-0.845755\pi$
$941$	−25.9474	−	44.9421i	−0.845859	−	1.46507i	0.0390132	−	0.999239i	$-0.487579\pi$
$942$		0			0
$943$	−6.12203	+	10.6037i	−0.199361	+	0.345303i
$944$		0			0
$945$	−1.06038	+	2.93479i	−0.0344940	+	0.0954687i
$946$		0			0
$947$	11.5394	−	19.9869i	0.374981	−	0.649486i	−0.615343	−	0.788259i	$-0.710983\pi$
$947$	11.5394	−	19.9869i	0.374981	−	0.649486i	0.990324	+	0.138773i	$0.0443159\pi$
$948$		0			0
$949$	−0.683784	−	1.18435i	−0.0221966	−	0.0384456i
$950$		0			0
$951$	2.39116	−	20.5975i	0.0775387	−	0.667921i
$952$		0			0
$953$	−22.9656			−0.743927			−0.371964	−	0.928247i	$-0.621315\pi$
$953$	−22.9656			−0.743927			−0.371964	+	0.928247i	$0.621315\pi$
$954$		0			0
$955$	−12.1424			−0.392918
$956$		0			0
$957$	7.82962	+	5.81941i	0.253096	+	0.188115i
$958$		0			0
$959$	4.39399	+	7.61062i	0.141889	+	0.245760i
$960$		0			0
$961$	−30.7788	+	53.3104i	−0.992864	+	1.71969i
$962$		0			0
$963$	−7.06920	+	7.51646i	−0.227802	+	0.242215i
$964$		0			0
$965$	−5.34161	+	9.25194i	−0.171953	+	0.297830i
$966$		0			0
$967$	−29.4696	−	51.0429i	−0.947680	−	1.64143i	−0.750294	−	0.661104i	$-0.770088\pi$
$967$	−29.4696	−	51.0429i	−0.947680	−	1.64143i	−0.197386	−	0.980326i	$-0.563245\pi$
$968$		0			0
$969$	−5.94537	+	2.57010i	−0.190993	+	0.0825637i
$970$		0			0
$971$	25.8074			0.828198			0.414099	−	0.910232i	$-0.364097\pi$
$971$	25.8074			0.828198			0.414099	+	0.910232i	$0.364097\pi$
$972$		0			0
$973$	9.01867			0.289125
$974$		0			0
$975$	−2.43667	+	1.05334i	−0.0780360	+	0.0337340i
$976$		0			0
$977$	22.4774	+	38.9321i	0.719117	+	1.24555i	0.961350	+	0.275329i	$0.0887868\pi$
$977$	22.4774	+	38.9321i	0.719117	+	1.24555i	−0.242233	+	0.970218i	$0.577880\pi$
$978$		0			0
$979$	−3.06558	+	5.30974i	−0.0979764	+	0.169700i
$980$		0			0
$981$	−11.4071	+	12.1289i	−0.364202	+	0.387245i
$982$		0			0
$983$	4.33576	−	7.50976i	0.138289	−	0.239524i	−0.788560	−	0.614958i	$-0.789173\pi$
$983$	4.33576	−	7.50976i	0.138289	−	0.239524i	0.926849	+	0.375434i	$0.122506\pi$
$984$		0			0
$985$	−2.41461	−	4.18222i	−0.0769358	−	0.133257i
$986$		0			0
$987$	5.43476	+	4.03942i	0.172990	+	0.128576i
$988$		0			0
$989$	6.71248			0.213445
$990$		0			0
$991$	−3.39241			−0.107763			−0.0538817	−	0.998547i	$-0.517159\pi$
$991$	−3.39241			−0.107763			−0.0538817	+	0.998547i	$0.517159\pi$
$992$		0			0
$993$	−4.64081	+	39.9761i	−0.147272	+	1.26860i
$994$		0			0
$995$	−4.21374	−	7.29841i	−0.133584	−	0.231375i
$996$		0			0
$997$	−14.0201	+	24.2836i	−0.444023	+	0.769070i	−0.997984	−	0.0634730i	$-0.979782\pi$
$997$	−14.0201	+	24.2836i	−0.444023	+	0.769070i	0.553961	+	0.832543i	$0.313116\pi$
$998$		0			0
$999$	1.06038	−	2.93479i	0.0335488	−	0.0928527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.r.e.169.4	✓	8
3.2	odd	2		1512.2.r.e.505.3		8
4.3	odd	2		1008.2.r.l.673.1		8
9.2	odd	6		4536.2.a.y.1.2		4
9.4	even	3	inner	504.2.r.e.337.4	yes	8
9.5	odd	6		1512.2.r.e.1009.3		8
9.7	even	3		4536.2.a.z.1.3		4
12.11	even	2		3024.2.r.m.2017.3		8
36.7	odd	6		9072.2.a.cj.1.3		4
36.11	even	6		9072.2.a.cg.1.2		4
36.23	even	6		3024.2.r.m.1009.3		8
36.31	odd	6		1008.2.r.l.337.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.e.169.4	✓	8	1.1	even	1	trivial
504.2.r.e.337.4	yes	8	9.4	even	3	inner
1008.2.r.l.337.1		8	36.31	odd	6
1008.2.r.l.673.1		8	4.3	odd	2
1512.2.r.e.505.3		8	3.2	odd	2
1512.2.r.e.1009.3		8	9.5	odd	6
3024.2.r.m.1009.3		8	36.23	even	6
3024.2.r.m.2017.3		8	12.11	even	2
4536.2.a.y.1.2		4	9.2	odd	6
4536.2.a.z.1.3		4	9.7	even	3
9072.2.a.cg.1.2		4	36.11	even	6
9072.2.a.cj.1.3		4	36.7	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58986 - 0.687275i) q^{3} +(-0.300268 - 0.520080i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.05531 - 2.18534i) q^{9} +O(q^{10})\)	\(q+(1.58986 - 0.687275i) q^{3} +(-0.300268 - 0.520080i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.05531 - 2.18534i) q^{9} +(0.800268 - 1.38611i) q^{11} +(-0.165178 - 0.286096i) q^{13} +(-0.834822 - 0.620487i) q^{15} -1.44990 q^{17} +2.57918 q^{19} +(0.199732 - 1.72050i) q^{21} +(-0.924682 - 1.60160i) q^{23} +(2.31968 - 4.01780i) q^{25} +(1.76571 - 4.88695i) q^{27} +(-1.75950 + 3.04755i) q^{29} +(4.81034 + 8.33176i) q^{31} +(0.319678 - 2.75372i) q^{33} -0.600537 q^{35} +0.600537 q^{37} +(-0.459236 - 0.341330i) q^{39} +(-3.31034 - 5.73368i) q^{41} +(-1.81481 + 3.14334i) q^{43} +(-1.75370 - 0.412734i) q^{45} +(-1.95477 + 3.38576i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.30514 + 0.996481i) q^{51} -9.27166 q^{53} -0.961181 q^{55} +(4.10054 - 1.77261i) q^{57} +(6.93476 + 12.0113i) q^{59} +(2.59433 - 4.49351i) q^{61} +(-0.864909 - 2.87262i) q^{63} +(-0.0991952 + 0.171811i) q^{65} +(5.90467 + 10.2272i) q^{67} +(-2.57085 - 1.91080i) q^{69} -4.17972 q^{71} +4.13969 q^{73} +(0.926627 - 7.98199i) q^{75} +(-0.800268 - 1.38611i) q^{77} +(-4.06538 + 7.04144i) q^{79} +(-0.551441 - 8.98309i) q^{81} +(2.78959 - 4.83171i) q^{83} +(0.435359 + 0.754064i) q^{85} +(-0.702858 + 6.05444i) q^{87} -3.83069 q^{89} -0.330355 q^{91} +(13.3740 + 9.94029i) q^{93} +(-0.774447 - 1.34138i) q^{95} +(0.974782 - 1.68837i) q^{97} +(-1.38432 - 4.59773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} - 3 q^{5} + 4 q^{7} - q^{9}+O(q^{10}) \) 8 * q - q^3 - 3 * q^5 + 4 * q^7 - q^9	\( 8 q - q^{3} - 3 q^{5} + 4 q^{7} - q^{9} + 7 q^{11} + 3 q^{13} - 11 q^{15} + 6 q^{17} - 8 q^{19} + q^{21} + 2 q^{23} - 5 q^{25} + 11 q^{27} - 9 q^{29} + 3 q^{31} - 21 q^{33} - 6 q^{35} + 6 q^{37} + 2 q^{39} + 9 q^{41} + 8 q^{43} + 7 q^{45} + 3 q^{47} - 4 q^{49} - 18 q^{51} + 12 q^{53} - 56 q^{55} + 34 q^{57} + 10 q^{59} + 20 q^{61} - 2 q^{63} + q^{65} + 11 q^{67} - 17 q^{69} - 6 q^{71} - 48 q^{73} + 52 q^{75} - 7 q^{77} + 21 q^{79} - 25 q^{81} + 8 q^{83} + 9 q^{85} - 15 q^{87} + 12 q^{89} + 6 q^{91} + 29 q^{93} + 36 q^{95} + 16 q^{97} + 18 q^{99}+O(q^{100}) \) 8 * q - q^3 - 3 * q^5 + 4 * q^7 - q^9 + 7 * q^11 + 3 * q^13 - 11 * q^15 + 6 * q^17 - 8 * q^19 + q^21 + 2 * q^23 - 5 * q^25 + 11 * q^27 - 9 * q^29 + 3 * q^31 - 21 * q^33 - 6 * q^35 + 6 * q^37 + 2 * q^39 + 9 * q^41 + 8 * q^43 + 7 * q^45 + 3 * q^47 - 4 * q^49 - 18 * q^51 + 12 * q^53 - 56 * q^55 + 34 * q^57 + 10 * q^59 + 20 * q^61 - 2 * q^63 + q^65 + 11 * q^67 - 17 * q^69 - 6 * q^71 - 48 * q^73 + 52 * q^75 - 7 * q^77 + 21 * q^79 - 25 * q^81 + 8 * q^83 + 9 * q^85 - 15 * q^87 + 12 * q^89 + 6 * q^91 + 29 * q^93 + 36 * q^95 + 16 * q^97 + 18 * q^99

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