LMFDB - Embedded newform 1008.2.cz.f.607.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.f.367.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205i q^{3} +(-0.621320 + 0.358719i) q^{5} +(1.00000 + 2.44949i) q^{7} -3.00000 q^{9} +O(q^{10})$	\(q+1.73205i q^{3} +(-0.621320 + 0.358719i) q^{5} +(1.00000 + 2.44949i) q^{7} -3.00000 q^{9} +(-1.50000 - 0.866025i) q^{11} +(-3.62132 - 2.09077i) q^{13} +(-0.621320 - 1.07616i) q^{15} +(-2.74264 + 1.58346i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-4.24264 + 1.73205i) q^{21} +(-2.37868 + 1.37333i) q^{23} +(-2.24264 + 3.88437i) q^{25} -5.19615i q^{27} +(0.621320 + 1.07616i) q^{29} +4.00000 q^{31} +(1.50000 - 2.59808i) q^{33} +(-1.50000 - 1.16320i) q^{35} +(1.62132 - 2.80821i) q^{37} +(3.62132 - 6.27231i) q^{39} +(-8.74264 - 5.04757i) q^{41} +(5.74264 - 3.31552i) q^{43} +(1.86396 - 1.07616i) q^{45} -8.48528 q^{47} +(-5.00000 + 4.89898i) q^{49} +(-2.74264 - 4.75039i) q^{51} +(-0.621320 - 1.07616i) q^{53} +1.24264 q^{55} +(1.50000 + 0.866025i) q^{57} +6.00000 q^{59} +6.92820i q^{61} +(-3.00000 - 7.34847i) q^{63} +3.00000 q^{65} +(-2.37868 - 4.11999i) q^{69} +13.2621i q^{71} +(-7.50000 + 4.33013i) q^{73} +(-6.72792 - 3.88437i) q^{75} +(0.621320 - 4.54026i) q^{77} +2.02922i q^{79} +9.00000 q^{81} +(-5.74264 - 9.94655i) q^{83} +(1.13604 - 1.96768i) q^{85} +(-1.86396 + 1.07616i) q^{87} +(-14.2279 - 8.21449i) q^{89} +(1.50000 - 10.9612i) q^{91} +6.92820i q^{93} +0.717439i q^{95} +(-5.74264 + 3.31552i) q^{97} +(4.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{5} + 4 q^{7} - 12 q^{9}+O(q^{10}) $ 4 * q + 6 * q^5 + 4 * q^7 - 12 * q^9	$ 4 q + 6 q^{5} + 4 q^{7} - 12 q^{9} - 6 q^{11} - 6 q^{13} + 6 q^{15} + 6 q^{17} + 2 q^{19} - 18 q^{23} + 8 q^{25} - 6 q^{29} + 16 q^{31} + 6 q^{33} - 6 q^{35} - 2 q^{37} + 6 q^{39} - 18 q^{41} + 6 q^{43} - 18 q^{45} - 20 q^{49} + 6 q^{51} + 6 q^{53} - 12 q^{55} + 6 q^{57} + 24 q^{59} - 12 q^{63} + 12 q^{65} - 18 q^{69} - 30 q^{73} + 24 q^{75} - 6 q^{77} + 36 q^{81} - 6 q^{83} + 30 q^{85} + 18 q^{87} - 6 q^{89} + 6 q^{91} - 6 q^{97} + 18 q^{99}+O(q^{100}) $ 4 * q + 6 * q^5 + 4 * q^7 - 12 * q^9 - 6 * q^11 - 6 * q^13 + 6 * q^15 + 6 * q^17 + 2 * q^19 - 18 * q^23 + 8 * q^25 - 6 * q^29 + 16 * q^31 + 6 * q^33 - 6 * q^35 - 2 * q^37 + 6 * q^39 - 18 * q^41 + 6 * q^43 - 18 * q^45 - 20 * q^49 + 6 * q^51 + 6 * q^53 - 12 * q^55 + 6 * q^57 + 24 * q^59 - 12 * q^63 + 12 * q^65 - 18 * q^69 - 30 * q^73 + 24 * q^75 - 6 * q^77 + 36 * q^81 - 6 * q^83 + 30 * q^85 + 18 * q^87 - 6 * q^89 + 6 * q^91 - 6 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$		0			0
$5$	−0.621320	+	0.358719i	−0.277863	+	0.160424i	−0.632456	−	0.774597i	$-0.717953\pi$
$5$	−0.621320	+	0.358719i	−0.277863	+	0.160424i	0.354593	+	0.935021i	$0.384620\pi$
$6$		0			0
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$8$		0			0
$9$	−3.00000			−1.00000
$10$		0			0
$11$	−1.50000	−	0.866025i	−0.452267	−	0.261116i	0.256520	−	0.966539i	$-0.417424\pi$
$11$	−1.50000	−	0.866025i	−0.452267	−	0.261116i	−0.708787	+	0.705422i	$0.750757\pi$
$12$		0			0
$13$	−3.62132	−	2.09077i	−1.00437	−	0.579875i	−0.0948342	−	0.995493i	$-0.530232\pi$
$13$	−3.62132	−	2.09077i	−1.00437	−	0.579875i	−0.909539	+	0.415618i	$0.863565\pi$
$14$		0			0
$15$	−0.621320	−	1.07616i	−0.160424	−	0.277863i
$16$		0			0
$17$	−2.74264	+	1.58346i	−0.665188	+	0.384047i	−0.794251	−	0.607590i	$-0.792136\pi$
$17$	−2.74264	+	1.58346i	−0.665188	+	0.384047i	0.129063	+	0.991636i	$0.458803\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$	−4.24264	+	1.73205i	−0.925820	+	0.377964i
$22$		0			0
$23$	−2.37868	+	1.37333i	−0.495989	+	0.286359i	−0.727056	−	0.686579i	$-0.759112\pi$
$23$	−2.37868	+	1.37333i	−0.495989	+	0.286359i	0.231067	+	0.972938i	$0.425778\pi$
$24$		0			0
$25$	−2.24264	+	3.88437i	−0.448528	+	0.776874i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	0.621320	+	1.07616i	0.115376	+	0.199838i	0.917930	−	0.396742i	$-0.129859\pi$
$29$	0.621320	+	1.07616i	0.115376	+	0.199838i	−0.802554	+	0.596580i	$0.796526\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$		0			0
$35$	−1.50000	−	1.16320i	−0.253546	−	0.196616i
$36$		0			0
$37$	1.62132	−	2.80821i	0.266543	−	0.461667i	−0.701423	−	0.712745i	$-0.747452\pi$
$37$	1.62132	−	2.80821i	0.266543	−	0.461667i	0.967967	+	0.251078i	$0.0807851\pi$
$38$		0			0
$39$	3.62132	−	6.27231i	0.579875	−	1.00437i
$40$		0			0
$41$	−8.74264	−	5.04757i	−1.36537	−	0.788297i	−0.375038	−	0.927009i	$-0.622370\pi$
$41$	−8.74264	−	5.04757i	−1.36537	−	0.788297i	−0.990333	+	0.138712i	$0.955704\pi$
$42$		0			0
$43$	5.74264	−	3.31552i	0.875744	−	0.505611i	0.00649156	−	0.999979i	$-0.497934\pi$
$43$	5.74264	−	3.31552i	0.875744	−	0.505611i	0.869253	+	0.494368i	$0.164600\pi$
$44$		0			0
$45$	1.86396	−	1.07616i	0.277863	−	0.160424i
$46$		0			0
$47$	−8.48528			−1.23771			−0.618853	−	0.785507i	$-0.712402\pi$
$47$	−8.48528			−1.23771			−0.618853	+	0.785507i	$0.712402\pi$
$48$		0			0
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$		0			0
$51$	−2.74264	−	4.75039i	−0.384047	−	0.665188i
$52$		0			0
$53$	−0.621320	−	1.07616i	−0.0853449	−	0.147822i	0.820193	−	0.572087i	$-0.193866\pi$
$53$	−0.621320	−	1.07616i	−0.0853449	−	0.147822i	−0.905538	+	0.424265i	$0.860533\pi$
$54$		0			0
$55$	1.24264			0.167558
$56$		0			0
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$		0			0
$59$	6.00000			0.781133			0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000			0.781133			0.390567	+	0.920575i	$0.372279\pi$
$60$		0			0
$61$			6.92820i			0.887066i	0.896258	+	0.443533i	$0.146275\pi$
$61$			6.92820i			0.887066i	−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$	−3.00000	−	7.34847i	−0.377964	−	0.925820i
$64$		0			0
$65$	3.00000			0.372104
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$	−2.37868	−	4.11999i	−0.286359	−	0.495989i
$70$		0			0
$71$			13.2621i			1.57392i	0.617006	+	0.786959i	$0.288345\pi$
$71$			13.2621i			1.57392i	−0.617006	+	0.786959i	$0.711655\pi$
$72$		0			0
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.869935	−	0.493166i	$-0.835840\pi$
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.00787336	+	0.999969i	$0.502506\pi$
$74$		0			0
$75$	−6.72792	−	3.88437i	−0.776874	−	0.448528i
$76$		0			0
$77$	0.621320	−	4.54026i	0.0708060	−	0.517411i
$78$		0			0
$79$			2.02922i			0.228306i	0.993463	+	0.114153i	$0.0364153\pi$
$79$			2.02922i			0.228306i	−0.993463	+	0.114153i	$0.963585\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	−5.74264	−	9.94655i	−0.630337	−	1.09178i	−0.987483	−	0.157727i	$-0.949584\pi$
$83$	−5.74264	−	9.94655i	−0.630337	−	1.09178i	0.357146	−	0.934049i	$-0.383750\pi$
$84$		0			0
$85$	1.13604	−	1.96768i	0.123221	−	0.213425i
$86$		0			0
$87$	−1.86396	+	1.07616i	−0.199838	+	0.115376i
$88$		0			0
$89$	−14.2279	−	8.21449i	−1.50816	−	0.870735i	−0.999955	−	0.00949668i	$-0.996977\pi$
$89$	−14.2279	−	8.21449i	−1.50816	−	0.870735i	−0.508202	−	0.861238i	$-0.669690\pi$
$90$		0			0
$91$	1.50000	−	10.9612i	0.157243	−	1.14904i
$92$		0			0
$93$			6.92820i			0.718421i
$94$		0			0
$95$			0.717439i			0.0736077i
$96$		0			0
$97$	−5.74264	+	3.31552i	−0.583077	+	0.336640i	−0.762355	−	0.647159i	$-0.775957\pi$
$97$	−5.74264	+	3.31552i	−0.583077	+	0.336640i	0.179278	+	0.983798i	$0.442624\pi$
$98$		0			0
$99$	4.50000	+	2.59808i	0.452267	+	0.261116i
$100$		0			0
$101$	3.62132	+	2.09077i	0.360335	+	0.208039i	0.669228	−	0.743057i	$-0.266625\pi$
$101$	3.62132	+	2.09077i	0.360335	+	0.208039i	−0.308893	+	0.951097i	$0.599958\pi$
$102$		0			0
$103$	5.86396	+	10.1567i	0.577793	+	1.00077i	0.995732	+	0.0922920i	$0.0294193\pi$
$103$	5.86396	+	10.1567i	0.577793	+	1.00077i	−0.417939	+	0.908475i	$0.637247\pi$
$104$		0			0
$105$	2.01472	−	2.59808i	0.196616	−	0.253546i
$106$		0			0
$107$	−9.98528	−	5.76500i	−0.965314	−	0.557324i	−0.0675093	−	0.997719i	$-0.521505\pi$
$107$	−9.98528	−	5.76500i	−0.965314	−	0.557324i	−0.897804	+	0.440395i	$0.854839\pi$
$108$		0			0
$109$	4.37868	+	7.58410i	0.419401	+	0.726425i	0.995879	−	0.0906881i	$-0.0289066\pi$
$109$	4.37868	+	7.58410i	0.419401	+	0.726425i	−0.576478	+	0.817113i	$0.695573\pi$
$110$		0			0
$111$	4.86396	+	2.80821i	0.461667	+	0.266543i
$112$		0			0
$113$	5.74264	−	9.94655i	0.540222	−	0.935692i	−0.458669	−	0.888607i	$-0.651674\pi$
$113$	5.74264	−	9.94655i	0.540222	−	0.935692i	0.998891	−	0.0470849i	$-0.0149931\pi$
$114$		0			0
$115$	0.985281	−	1.70656i	0.0918780	−	0.159137i
$116$		0			0
$117$	10.8640	+	6.27231i	1.00437	+	0.579875i
$118$		0			0
$119$	−6.62132	−	5.13461i	−0.606975	−	0.470689i
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		0			0
$123$	8.74264	−	15.1427i	0.788297	−	1.36537i
$124$		0			0
$125$		−	6.80511i		−	0.608668i
$126$		0			0
$127$			0.594346i			0.0527397i	0.999652	+	0.0263698i	$0.00839475\pi$
$127$			0.594346i			0.0527397i	−0.999652	+	0.0263698i	$0.991605\pi$
$128$		0			0
$129$	5.74264	+	9.94655i	0.505611	+	0.875744i
$130$		0			0
$131$	8.74264	+	15.1427i	0.763848	+	1.32302i	0.940853	+	0.338814i	$0.110026\pi$
$131$	8.74264	+	15.1427i	0.763848	+	1.32302i	−0.177005	+	0.984210i	$0.556641\pi$
$132$		0			0
$133$	2.62132	+	0.358719i	0.227297	+	0.0311049i
$134$		0			0
$135$	1.86396	+	3.22848i	0.160424	+	0.277863i
$136$		0			0
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$		0			0
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	0.446857	+	0.894606i	$0.352543\pi$
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	−0.998179	+	0.0603135i	$0.980790\pi$
$140$		0			0
$141$		−	14.6969i		−	1.23771i
$142$		0			0
$143$	3.62132	+	6.27231i	0.302830	+	0.524517i
$144$		0			0
$145$	−0.772078	−	0.445759i	−0.0641176	−	0.0370183i
$146$		0			0
$147$	−8.48528	−	8.66025i	−0.699854	−	0.714286i
$148$		0			0
$149$	9.62132	+	16.6646i	0.788209	+	1.36522i	0.927063	+	0.374906i	$0.122325\pi$
$149$	9.62132	+	16.6646i	0.788209	+	1.36522i	−0.138854	+	0.990313i	$0.544342\pi$
$150$		0			0
$151$	20.5919	+	11.8887i	1.67574	+	0.967491i	0.964324	+	0.264723i	$0.0852806\pi$
$151$	20.5919	+	11.8887i	1.67574	+	0.967491i	0.711419	+	0.702768i	$0.248053\pi$
$152$		0			0
$153$	8.22792	−	4.75039i	0.665188	−	0.384047i
$154$		0			0
$155$	−2.48528	+	1.43488i	−0.199623	+	0.115252i
$156$		0			0
$157$			2.02922i			0.161950i	0.996716	+	0.0809748i	$0.0258033\pi$
$157$			2.02922i			0.161950i	−0.996716	+	0.0809748i	$0.974197\pi$
$158$		0			0
$159$	1.86396	−	1.07616i	0.147822	−	0.0853449i
$160$		0			0
$161$	−5.74264	−	4.45322i	−0.452583	−	0.350963i
$162$		0			0
$163$	−0.257359	−	0.148586i	−0.0201579	−	0.0116382i	0.489887	−	0.871786i	$-0.337038\pi$
$163$	−0.257359	−	0.148586i	−0.0201579	−	0.0116382i	−0.510045	+	0.860148i	$0.670371\pi$
$164$		0			0
$165$			2.15232i			0.167558i
$166$		0			0
$167$	−7.86396	+	13.6208i	−0.608532	+	1.05401i	0.382951	+	0.923769i	$0.374908\pi$
$167$	−7.86396	+	13.6208i	−0.608532	+	1.05401i	−0.991483	+	0.130239i	$0.958426\pi$
$168$		0			0
$169$	2.24264	+	3.88437i	0.172511	+	0.298798i
$170$		0			0
$171$	−1.50000	+	2.59808i	−0.114708	+	0.198680i
$172$		0			0
$173$		−	9.79796i		−	0.744925i	−0.928047	−	0.372463i	$-0.878514\pi$
$173$		−	9.79796i		−	0.744925i	0.928047	−	0.372463i	$-0.121486\pi$
$174$		0			0
$175$	−11.7574	−	1.60896i	−0.888773	−	0.121626i
$176$		0			0
$177$			10.3923i			0.781133i
$178$		0			0
$179$	−0.985281	+	0.568852i	−0.0736434	+	0.0425180i	−0.536370	−	0.843983i	$-0.680205\pi$
$179$	−0.985281	+	0.568852i	−0.0736434	+	0.0425180i	0.462726	+	0.886501i	$0.346871\pi$
$180$		0			0
$181$		−	13.2621i		−	0.985761i	−0.870097	−	0.492881i	$-0.835944\pi$
$181$		−	13.2621i		−	0.985761i	0.870097	−	0.492881i	$-0.164056\pi$
$182$		0			0
$183$	−12.0000			−0.887066
$184$		0			0
$185$			2.32640i			0.171040i
$186$		0			0
$187$	5.48528			0.401124
$188$		0			0
$189$	12.7279	−	5.19615i	0.925820	−	0.377964i
$190$		0			0
$191$			18.1610i			1.31409i	0.753853	+	0.657043i	$0.228193\pi$
$191$			18.1610i			1.31409i	−0.753853	+	0.657043i	$0.771807\pi$
$192$		0			0
$193$	20.9706			1.50949			0.754747	−	0.656016i	$-0.227760\pi$
$193$	20.9706			1.50949			0.754747	+	0.656016i	$0.227760\pi$
$194$		0			0
$195$			5.19615i			0.372104i
$196$		0			0
$197$	−14.4853			−1.03203			−0.516017	−	0.856578i	$-0.672586\pi$
$197$	−14.4853			−1.03203			−0.516017	+	0.856578i	$0.672586\pi$
$198$		0			0
$199$	9.86396	+	17.0849i	0.699238	+	1.21112i	0.968731	+	0.248113i	$0.0798104\pi$
$199$	9.86396	+	17.0849i	0.699238	+	1.21112i	−0.269493	+	0.963002i	$0.586856\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.01472	+	2.59808i	−0.141406	+	0.182349i
$204$		0			0
$205$	7.24264			0.505848
$206$		0			0
$207$	7.13604	−	4.11999i	0.495989	−	0.286359i
$208$		0			0
$209$	−1.50000	+	0.866025i	−0.103757	+	0.0599042i
$210$		0			0
$211$	14.7426	+	8.51167i	1.01493	+	0.585967i	0.912630	−	0.408787i	$-0.134048\pi$
$211$	14.7426	+	8.51167i	1.01493	+	0.585967i	0.102295	+	0.994754i	$0.467381\pi$
$212$		0			0
$213$	−22.9706			−1.57392
$214$		0			0
$215$	−2.37868	+	4.11999i	−0.162225	+	0.280981i
$216$		0			0
$217$	4.00000	+	9.79796i	0.271538	+	0.665129i
$218$		0			0
$219$	−7.50000	−	12.9904i	−0.506803	−	0.877809i
$220$		0			0
$221$	13.2426			0.890796
$222$		0			0
$223$	2.62132	+	4.54026i	0.175537	+	0.304038i	0.940347	−	0.340217i	$-0.110501\pi$
$223$	2.62132	+	4.54026i	0.175537	+	0.304038i	−0.764810	+	0.644256i	$0.777167\pi$
$224$		0			0
$225$	6.72792	−	11.6531i	0.448528	−	0.776874i
$226$		0			0
$227$	−8.74264	+	15.1427i	−0.580269	+	1.00506i	0.415178	+	0.909740i	$0.363719\pi$
$227$	−8.74264	+	15.1427i	−0.580269	+	1.00506i	−0.995447	+	0.0953158i	$0.969614\pi$
$228$		0			0
$229$	−17.3787	+	10.0336i	−1.14842	+	0.663038i	−0.948501	−	0.316775i	$-0.897400\pi$
$229$	−17.3787	+	10.0336i	−1.14842	+	0.663038i	−0.199915	+	0.979813i	$0.564067\pi$
$230$		0			0
$231$	7.86396	+	1.07616i	0.517411	+	0.0708060i
$232$		0			0
$233$	6.25736	−	10.8381i	0.409933	−	0.710025i	−0.584949	−	0.811070i	$-0.698885\pi$
$233$	6.25736	−	10.8381i	0.409933	−	0.710025i	0.994882	+	0.101045i	$0.0322187\pi$
$234$		0			0
$235$	5.27208	−	3.04384i	0.343912	−	0.198558i
$236$		0			0
$237$	−3.51472			−0.228306
$238$		0			0
$239$	0.106602	+	0.0615465i	0.00689549	+	0.00398111i	0.503444	−	0.864028i	$-0.332066\pi$
$239$	0.106602	+	0.0615465i	0.00689549	+	0.00398111i	−0.496548	+	0.868009i	$0.665399\pi$
$240$		0			0
$241$	−0.257359	−	0.148586i	−0.0165780	−	0.00957130i	0.491688	−	0.870771i	$-0.336380\pi$
$241$	−0.257359	−	0.148586i	−0.0165780	−	0.00957130i	−0.508266	+	0.861200i	$0.669713\pi$
$242$		0			0
$243$			15.5885i			1.00000i
$244$		0			0
$245$	1.34924	−	4.83743i	0.0861999	−	0.309052i
$246$		0			0
$247$	−3.62132	+	2.09077i	−0.230419	+	0.133033i
$248$		0			0
$249$	17.2279	−	9.94655i	1.09178	−	0.630337i
$250$		0			0
$251$	−26.4853			−1.67174			−0.835868	−	0.548930i	$-0.815035\pi$
$251$	−26.4853			−1.67174			−0.835868	+	0.548930i	$0.815035\pi$
$252$		0			0
$253$	4.75736			0.299093
$254$		0			0
$255$	3.40812	+	1.96768i	0.213425	+	0.123221i
$256$		0			0
$257$	21.9853	−	12.6932i	1.37140	−	0.791781i	0.380299	−	0.924863i	$-0.375821\pi$
$257$	21.9853	−	12.6932i	1.37140	−	0.791781i	0.991105	+	0.133083i	$0.0424877\pi$
$258$		0			0
$259$	8.50000	+	1.16320i	0.528164	+	0.0722776i
$260$		0			0
$261$	−1.86396	−	3.22848i	−0.115376	−	0.199838i
$262$		0			0
$263$	−12.1066	−	6.98975i	−0.746525	−	0.431006i	0.0779119	−	0.996960i	$-0.475175\pi$
$263$	−12.1066	−	6.98975i	−0.746525	−	0.431006i	−0.824437	+	0.565954i	$0.808508\pi$
$264$		0			0
$265$	0.772078	+	0.445759i	0.0474284	+	0.0273828i
$266$		0			0
$267$	14.2279	−	24.6435i	0.870735	−	1.50816i
$268$		0			0
$269$	−19.3492	+	11.1713i	−1.17974	+	0.681126i	−0.955955	−	0.293512i	$-0.905176\pi$
$269$	−19.3492	+	11.1713i	−1.17974	+	0.681126i	−0.223789	+	0.974638i	$0.571843\pi$
$270$		0			0
$271$	5.86396	−	10.1567i	0.356210	−	0.616974i	−0.631114	−	0.775690i	$-0.717402\pi$
$271$	5.86396	−	10.1567i	0.356210	−	0.616974i	0.987324	+	0.158716i	$0.0507354\pi$
$272$		0			0
$273$	18.9853	+	2.59808i	1.14904	+	0.157243i
$274$		0			0
$275$	6.72792	−	3.88437i	0.405709	−	0.234236i
$276$		0			0
$277$	5.86396	−	10.1567i	0.352331	−	0.610256i	−0.634326	−	0.773066i	$-0.718722\pi$
$277$	5.86396	−	10.1567i	0.352331	−	0.610256i	0.986657	+	0.162810i	$0.0520557\pi$
$278$		0			0
$279$	−12.0000			−0.718421
$280$		0			0
$281$	15.9853	+	27.6873i	0.953602	+	1.65169i	0.737536	+	0.675308i	$0.235989\pi$
$281$	15.9853	+	27.6873i	0.953602	+	1.65169i	0.216066	+	0.976379i	$0.430677\pi$
$282$		0			0
$283$	5.51472			0.327816			0.163908	−	0.986476i	$-0.447590\pi$
$283$	5.51472			0.327816			0.163908	+	0.986476i	$0.447590\pi$
$284$		0			0
$285$	−1.24264			−0.0736077
$286$		0			0
$287$	3.62132	−	26.4626i	0.213760	−	1.56204i
$288$		0			0
$289$	−3.48528	+	6.03668i	−0.205017	+	0.355099i
$290$		0			0
$291$	−5.74264	−	9.94655i	−0.336640	−	0.583077i
$292$		0			0
$293$	14.5919	+	8.42463i	0.852467	+	0.492172i	0.861482	−	0.507787i	$-0.169536\pi$
$293$	14.5919	+	8.42463i	0.852467	+	0.492172i	−0.00901553	+	0.999959i	$0.502870\pi$
$294$		0			0
$295$	−3.72792	+	2.15232i	−0.217048	+	0.125313i
$296$		0			0
$297$	−4.50000	+	7.79423i	−0.261116	+	0.452267i
$298$		0			0
$299$	11.4853			0.664211
$300$		0			0
$301$	13.8640	+	10.7510i	0.799105	+	0.619679i
$302$		0			0
$303$	−3.62132	+	6.27231i	−0.208039	+	0.360335i
$304$		0			0
$305$	−2.48528	−	4.30463i	−0.142307	−	0.246483i
$306$		0			0
$307$	−18.4853			−1.05501			−0.527505	−	0.849552i	$-0.676873\pi$
$307$	−18.4853			−1.05501			−0.527505	+	0.849552i	$0.676873\pi$
$308$		0			0
$309$	−17.5919	+	10.1567i	−1.00077	+	0.577793i
$310$		0			0
$311$	22.9706			1.30254			0.651271	−	0.758846i	$-0.274236\pi$
$311$	22.9706			1.30254			0.651271	+	0.758846i	$0.274236\pi$
$312$		0			0
$313$		−	1.43488i		−	0.0811041i	−0.999177	−	0.0405520i	$-0.987088\pi$
$313$		−	1.43488i		−	0.0811041i	0.999177	−	0.0405520i	$-0.0129117\pi$
$314$		0			0
$315$	4.50000	+	3.48960i	0.253546	+	0.196616i
$316$		0			0
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$		0			0
$319$		−	2.15232i		−	0.120507i
$320$		0			0
$321$	9.98528	−	17.2950i	0.557324	−	0.965314i
$322$		0			0
$323$			3.16693i			0.176213i
$324$		0			0
$325$	16.2426	−	9.37769i	0.900980	−	0.520181i
$326$		0			0
$327$	−13.1360	+	7.58410i	−0.726425	+	0.419401i
$328$		0			0
$329$	−8.48528	−	20.7846i	−0.467809	−	1.14589i
$330$		0			0
$331$		−	10.9867i		−	0.603881i	−0.953327	−	0.301940i	$-0.902366\pi$
$331$		−	10.9867i		−	0.603881i	0.953327	−	0.301940i	$-0.0976344\pi$
$332$		0			0
$333$	−4.86396	+	8.42463i	−0.266543	+	0.461667i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	0.789865	+	0.613280i	$0.210150\pi$
$338$		0			0
$339$	17.2279	+	9.94655i	0.935692	+	0.540222i
$340$		0			0
$341$	−6.00000	−	3.46410i	−0.324918	−	0.187592i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$		0			0
$345$	2.95584	+	1.70656i	0.159137	+	0.0918780i
$346$		0			0
$347$		−	27.7128i		−	1.48770i	−0.668346	−	0.743851i	$-0.732997\pi$
$347$		−	27.7128i		−	1.48770i	0.668346	−	0.743851i	$-0.267003\pi$
$348$		0			0
$349$	2.37868	−	1.37333i	0.127328	−	0.0735127i	−0.434983	−	0.900439i	$-0.643246\pi$
$349$	2.37868	−	1.37333i	0.127328	−	0.0735127i	0.562311	+	0.826926i	$0.309912\pi$
$350$		0			0
$351$	−10.8640	+	18.8169i	−0.579875	+	1.00437i
$352$		0			0
$353$	5.74264	+	3.31552i	0.305650	+	0.176467i	0.644978	−	0.764201i	$-0.276866\pi$
$353$	5.74264	+	3.31552i	0.305650	+	0.176467i	−0.339328	+	0.940668i	$0.610200\pi$
$354$		0			0
$355$	−4.75736	−	8.23999i	−0.252494	−	0.437333i
$356$		0			0
$357$	8.89340	−	11.4685i	0.470689	−	0.606975i
$358$		0			0
$359$	−5.37868	−	3.10538i	−0.283876	−	0.163896i	0.351301	−	0.936263i	$-0.385739\pi$
$359$	−5.37868	−	3.10538i	−0.283876	−	0.163896i	−0.635177	+	0.772367i	$0.719073\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$		0			0
$363$	12.0000	−	6.92820i	0.629837	−	0.363636i
$364$		0			0
$365$	3.10660	−	5.38079i	0.162607	−	0.281644i
$366$		0			0
$367$	3.13604	−	5.43178i	0.163700	−	0.283537i	−0.772493	−	0.635023i	$-0.780990\pi$
$367$	3.13604	−	5.43178i	0.163700	−	0.283537i	0.936193	+	0.351487i	$0.114324\pi$
$368$		0			0
$369$	26.2279	+	15.1427i	1.36537	+	0.788297i
$370$		0			0
$371$	2.01472	−	2.59808i	0.104599	−	0.134885i
$372$		0			0
$373$	−17.8640	−	30.9413i	−0.924961	−	1.60208i	−0.791624	−	0.611008i	$-0.790764\pi$
$373$	−17.8640	−	30.9413i	−0.924961	−	1.60208i	−0.133337	−	0.991071i	$-0.542569\pi$
$374$		0			0
$375$	11.7868			0.608668
$376$		0			0
$377$		−	5.19615i		−	0.267615i
$378$		0			0
$379$			2.02922i			0.104234i	0.998641	+	0.0521171i	$0.0165969\pi$
$379$			2.02922i			0.104234i	−0.998641	+	0.0521171i	$0.983403\pi$
$380$		0			0
$381$	−1.02944			−0.0527397
$382$		0			0
$383$	9.62132	+	16.6646i	0.491627	+	0.851522i	0.999954	−	0.00964204i	$-0.00306920\pi$
$383$	9.62132	+	16.6646i	0.491627	+	0.851522i	−0.508327	+	0.861164i	$0.669736\pi$
$384$		0			0
$385$	1.24264	+	3.04384i	0.0633308	+	0.155128i
$386$		0			0
$387$	−17.2279	+	9.94655i	−0.875744	+	0.505611i
$388$		0			0
$389$	−14.3787	+	24.9046i	−0.729028	+	1.26271i	0.228266	+	0.973599i	$0.426694\pi$
$389$	−14.3787	+	24.9046i	−0.729028	+	1.26271i	−0.957294	+	0.289115i	$0.906639\pi$
$390$		0			0
$391$	4.34924	−	7.53311i	0.219951	−	0.380966i
$392$		0			0
$393$	−26.2279	+	15.1427i	−1.32302	+	0.763848i
$394$		0			0
$395$	−0.727922	−	1.26080i	−0.0366257	−	0.0634376i
$396$		0			0
$397$	−33.1066	−	19.1141i	−1.66157	−	0.959309i	−0.971965	−	0.235127i	$-0.924450\pi$
$397$	−33.1066	−	19.1141i	−1.66157	−	0.959309i	−0.689608	−	0.724183i	$-0.742217\pi$
$398$		0			0
$399$	−0.621320	+	4.54026i	−0.0311049	+	0.227297i
$400$		0			0
$401$	−17.2279	−	29.8396i	−0.860321	−	1.49012i	−0.871619	−	0.490184i	$-0.836930\pi$
$401$	−17.2279	−	29.8396i	−0.860321	−	1.49012i	0.0112975	−	0.999936i	$-0.496404\pi$
$402$		0			0
$403$	−14.4853	−	8.36308i	−0.721563	−	0.416595i
$404$		0			0
$405$	−5.59188	+	3.22848i	−0.277863	+	0.160424i
$406$		0			0
$407$	−4.86396	+	2.80821i	−0.241098	+	0.139198i
$408$		0			0
$409$			12.4215i			0.614205i	0.951676	+	0.307103i	$0.0993595\pi$
$409$			12.4215i			0.614205i	−0.951676	+	0.307103i	$0.900641\pi$
$410$		0			0
$411$	−13.5000	−	7.79423i	−0.665906	−	0.384461i
$412$		0			0
$413$	6.00000	+	14.6969i	0.295241	+	0.723189i
$414$		0			0
$415$	7.13604	+	4.11999i	0.350294	+	0.202243i
$416$		0			0
$417$	−19.5000	−	11.2583i	−0.954919	−	0.551323i
$418$		0			0
$419$	3.98528	−	6.90271i	0.194694	−	0.337219i	−0.752106	−	0.659042i	$-0.770962\pi$
$419$	3.98528	−	6.90271i	0.194694	−	0.337219i	0.946800	+	0.321822i	$0.104295\pi$
$420$		0			0
$421$	−6.86396	−	11.8887i	−0.334529	−	0.579421i	0.648865	−	0.760903i	$-0.275244\pi$
$421$	−6.86396	−	11.8887i	−0.334529	−	0.579421i	−0.983394	+	0.181482i	$0.941911\pi$
$422$		0			0
$423$	25.4558			1.23771
$424$		0			0
$425$		−	14.2046i		−	0.689023i
$426$		0			0
$427$	−16.9706	+	6.92820i	−0.821263	+	0.335279i
$428$		0			0
$429$	−10.8640	+	6.27231i	−0.524517	+	0.302830i
$430$		0			0
$431$	33.8345	−	19.5344i	1.62975	−	0.940938i	0.645586	−	0.763688i	$-0.276613\pi$
$431$	33.8345	−	19.5344i	1.62975	−	0.940938i	0.984166	−	0.177250i	$-0.0567200\pi$
$432$		0			0
$433$			13.2621i			0.637334i	0.947867	+	0.318667i	$0.103235\pi$
$433$			13.2621i			0.637334i	−0.947867	+	0.318667i	$0.896765\pi$
$434$		0			0
$435$	0.772078	−	1.33728i	0.0370183	−	0.0641176i
$436$		0			0
$437$			2.74666i			0.131391i
$438$		0			0
$439$	−26.9706			−1.28723			−0.643617	−	0.765347i	$-0.722567\pi$
$439$	−26.9706			−1.28723			−0.643617	+	0.765347i	$0.722567\pi$
$440$		0			0
$441$	15.0000	−	14.6969i	0.714286	−	0.699854i
$442$		0			0
$443$			8.95743i			0.425580i	0.977098	+	0.212790i	$0.0682551\pi$
$443$			8.95743i			0.425580i	−0.977098	+	0.212790i	$0.931745\pi$
$444$		0			0
$445$	11.7868			0.558748
$446$		0			0
$447$	−28.8640	+	16.6646i	−1.36522	+	0.788209i
$448$		0			0
$449$	−24.0000			−1.13263			−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000			−1.13263			−0.566315	+	0.824189i	$0.691631\pi$
$450$		0			0
$451$	8.74264	+	15.1427i	0.411675	+	0.713042i
$452$		0			0
$453$	−20.5919	+	35.6662i	−0.967491	+	1.67574i
$454$		0			0
$455$	3.00000	+	7.34847i	0.140642	+	0.344502i
$456$		0			0
$457$	−38.9706			−1.82297			−0.911483	−	0.411338i	$-0.865062\pi$
$457$	−38.9706			−1.82297			−0.911483	+	0.411338i	$0.865062\pi$
$458$		0			0
$459$	8.22792	+	14.2512i	0.384047	+	0.665188i
$460$		0			0
$461$	−22.8640	+	13.2005i	−1.06488	+	0.614809i	−0.926778	−	0.375609i	$-0.877434\pi$
$461$	−22.8640	+	13.2005i	−1.06488	+	0.614809i	−0.138102	+	0.990418i	$0.544100\pi$
$462$		0			0
$463$	−11.3787	−	6.56948i	−0.528812	−	0.305310i	0.211720	−	0.977330i	$-0.432093\pi$
$463$	−11.3787	−	6.56948i	−0.528812	−	0.305310i	−0.740533	+	0.672020i	$0.765427\pi$
$464$		0			0
$465$	−2.48528	−	4.30463i	−0.115252	−	0.199623i
$466$		0			0
$467$	11.7426	−	20.3389i	0.543385	−	0.941170i	−0.455322	−	0.890327i	$-0.650476\pi$
$467$	11.7426	−	20.3389i	0.543385	−	0.941170i	0.998707	−	0.0508429i	$-0.0161908\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−3.51472			−0.161950
$472$		0			0
$473$	−11.4853			−0.528094
$474$		0			0
$475$	2.24264	+	3.88437i	0.102899	+	0.178227i
$476$		0			0
$477$	1.86396	+	3.22848i	0.0853449	+	0.147822i
$478$		0			0
$479$	−3.62132	+	6.27231i	−0.165462	+	0.286589i	−0.936819	−	0.349813i	$-0.886245\pi$
$479$	−3.62132	+	6.27231i	−0.165462	+	0.286589i	0.771357	+	0.636403i	$0.219578\pi$
$480$		0			0
$481$	−11.7426	+	6.77962i	−0.535418	+	0.309124i
$482$		0			0
$483$	7.71320	−	9.94655i	0.350963	−	0.452583i
$484$		0			0
$485$	2.37868	−	4.11999i	0.108010	−	0.187079i
$486$		0			0
$487$	11.8934	−	6.86666i	0.538941	−	0.311158i	−0.205708	−	0.978613i	$-0.565950\pi$
$487$	11.8934	−	6.86666i	0.538941	−	0.311158i	0.744650	+	0.667455i	$0.232617\pi$
$488$		0			0
$489$	0.257359	−	0.445759i	0.0116382	−	0.0201579i
$490$		0			0
$491$	−12.9853	−	7.49706i	−0.586018	−	0.338337i	0.177504	−	0.984120i	$-0.443198\pi$
$491$	−12.9853	−	7.49706i	−0.586018	−	0.338337i	−0.763521	+	0.645783i	$0.776531\pi$
$492$		0			0
$493$	−3.40812	−	1.96768i	−0.153494	−	0.0886197i
$494$		0			0
$495$	−3.72792			−0.167558
$496$		0			0
$497$	−32.4853	+	13.2621i	−1.45716	+	0.594885i
$498$		0			0
$499$	29.2279	−	16.8747i	1.30842	−	0.755417i	0.326589	−	0.945167i	$-0.394101\pi$
$499$	29.2279	−	16.8747i	1.30842	−	0.755417i	0.981833	+	0.189749i	$0.0607674\pi$
$500$		0			0
$501$	−23.5919	−	13.6208i	−1.05401	−	0.608532i
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−3.00000			−0.133498
$506$		0			0
$507$	−6.72792	+	3.88437i	−0.298798	+	0.172511i
$508$		0			0
$509$	7.34924	−	4.24309i	0.325749	−	0.188072i	−0.328203	−	0.944607i	$-0.606443\pi$
$509$	7.34924	−	4.24309i	0.325749	−	0.188072i	0.653952	+	0.756536i	$0.273110\pi$
$510$		0			0
$511$	−18.1066	−	14.0410i	−0.800989	−	0.621139i
$512$		0			0
$513$	−4.50000	−	2.59808i	−0.198680	−	0.114708i
$514$		0			0
$515$	−7.28680	−	4.20703i	−0.321095	−	0.185384i
$516$		0			0
$517$	12.7279	+	7.34847i	0.559773	+	0.323185i
$518$		0			0
$519$	16.9706			0.744925
$520$		0			0
$521$	7.50000	−	4.33013i	0.328581	−	0.189706i	−0.326630	−	0.945152i	$-0.605913\pi$
$521$	7.50000	−	4.33013i	0.328581	−	0.189706i	0.655211	+	0.755446i	$0.272580\pi$
$522$		0			0
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	−0.876750	−	0.480946i	$-0.840293\pi$
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	0.854887	+	0.518815i	$0.173627\pi$
$524$		0			0
$525$	2.78680	−	20.3643i	0.121626	−	0.888773i
$526$		0			0
$527$	−10.9706	+	6.33386i	−0.477885	+	0.275907i
$528$		0			0
$529$	−7.72792	+	13.3852i	−0.335997	+	0.581963i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$	21.1066	+	36.5577i	0.914228	+	1.58349i
$534$		0			0
$535$	8.27208			0.357633
$536$		0			0
$537$	−0.985281	−	1.70656i	−0.0425180	−	0.0736434i
$538$		0			0
$539$	11.7426	−	3.01834i	0.505791	−	0.130009i
$540$		0			0
$541$	22.1066	−	38.2898i	0.950437	−	1.64621i	0.205956	−	0.978561i	$-0.433969\pi$
$541$	22.1066	−	38.2898i	0.950437	−	1.64621i	0.744481	−	0.667644i	$-0.232697\pi$
$542$		0			0
$543$	22.9706			0.985761
$544$		0			0
$545$	−5.44113	−	3.14144i	−0.233072	−	0.134564i
$546$		0			0
$547$	−23.2279	+	13.4106i	−0.993154	+	0.573398i	−0.906216	−	0.422816i	$-0.861042\pi$
$547$	−23.2279	+	13.4106i	−0.993154	+	0.573398i	−0.0869386	+	0.996214i	$0.527708\pi$
$548$		0			0
$549$		−	20.7846i		−	0.887066i
$550$		0			0
$551$	1.24264			0.0529383
$552$		0			0
$553$	−4.97056	+	2.02922i	−0.211370	+	0.0862914i
$554$		0			0
$555$	−4.02944			−0.171040
$556$		0			0
$557$	9.10660	+	15.7731i	0.385859	+	0.668328i	0.991888	−	0.127115i	$-0.0405718\pi$
$557$	9.10660	+	15.7731i	0.385859	+	0.668328i	−0.606029	+	0.795443i	$0.707238\pi$
$558$		0			0
$559$	−27.7279			−1.17277
$560$		0			0
$561$			9.50079i			0.401124i
$562$		0			0
$563$	1.02944			0.0433856			0.0216928	−	0.999765i	$-0.493094\pi$
$563$	1.02944			0.0433856			0.0216928	+	0.999765i	$0.493094\pi$
$564$		0			0
$565$			8.23999i			0.346659i
$566$		0			0
$567$	9.00000	+	22.0454i	0.377964	+	0.925820i
$568$		0			0
$569$	22.9706			0.962976			0.481488	−	0.876453i	$-0.340096\pi$
$569$	22.9706			0.962976			0.481488	+	0.876453i	$0.340096\pi$
$570$		0			0
$571$		−	32.2636i		−	1.35019i	−0.737730	−	0.675096i	$-0.764102\pi$
$571$		−	32.2636i		−	1.35019i	0.737730	−	0.675096i	$-0.235898\pi$
$572$		0			0
$573$	−31.4558			−1.31409
$574$		0			0
$575$		−	12.3196i		−	0.513761i
$576$		0			0
$577$	−11.9558	+	6.90271i	−0.497728	+	0.287364i	−0.727775	−	0.685816i	$-0.759445\pi$
$577$	−11.9558	+	6.90271i	−0.497728	+	0.287364i	0.230047	+	0.973180i	$0.426112\pi$
$578$		0			0
$579$			36.3221i			1.50949i
$580$		0			0
$581$	18.6213	−	24.0131i	0.772543	−	0.996231i
$582$		0			0
$583$			2.15232i			0.0891399i
$584$		0			0
$585$	−9.00000			−0.372104
$586$		0			0
$587$	9.98528	+	17.2950i	0.412137	+	0.713842i	0.995123	−	0.0986402i	$-0.0314493\pi$
$587$	9.98528	+	17.2950i	0.412137	+	0.713842i	−0.582986	+	0.812482i	$0.698116\pi$
$588$		0			0
$589$	2.00000	−	3.46410i	0.0824086	−	0.142736i
$590$		0			0
$591$		−	25.0892i		−	1.03203i
$592$		0			0
$593$	−11.2279	−	6.48244i	−0.461075	−	0.266202i	0.251421	−	0.967878i	$-0.419102\pi$
$593$	−11.2279	−	6.48244i	−0.461075	−	0.266202i	−0.712496	+	0.701676i	$0.752436\pi$
$594$		0			0
$595$	5.95584	+	0.815039i	0.244166	+	0.0334133i
$596$		0			0
$597$	−29.5919	+	17.0849i	−1.21112	+	0.699238i
$598$		0			0
$599$			7.52255i			0.307363i	0.988120	+	0.153682i	$0.0491130\pi$
$599$			7.52255i			0.307363i	−0.988120	+	0.153682i	$0.950887\pi$
$600$		0			0
$601$	21.9853	−	12.6932i	0.896798	−	0.517767i	0.0206383	−	0.999787i	$-0.493430\pi$
$601$	21.9853	−	12.6932i	0.896798	−	0.517767i	0.876160	+	0.482020i	$0.160097\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.97056	+	2.86976i	0.202082	+	0.116672i
$606$		0			0
$607$	−17.3492	−	30.0498i	−0.704184	−	1.21968i	−0.966985	−	0.254833i	$-0.917980\pi$
$607$	−17.3492	−	30.0498i	−0.704184	−	1.21968i	0.262801	−	0.964850i	$-0.415354\pi$
$608$		0			0
$609$	−4.50000	−	3.48960i	−0.182349	−	0.141406i
$610$		0			0
$611$	30.7279	+	17.7408i	1.24312	+	0.717715i
$612$		0			0
$613$	−1.62132	−	2.80821i	−0.0654845	−	0.113423i	0.831424	−	0.555638i	$-0.187526\pi$
$613$	−1.62132	−	2.80821i	−0.0654845	−	0.113423i	−0.896909	+	0.442216i	$0.854193\pi$
$614$		0			0
$615$			12.5446i			0.505848i
$616$		0			0
$617$	−2.74264	+	4.75039i	−0.110415	+	0.191244i	−0.915937	−	0.401321i	$-0.868551\pi$
$617$	−2.74264	+	4.75039i	−0.110415	+	0.191244i	0.805523	+	0.592565i	$0.201885\pi$
$618$		0			0
$619$	−1.01472	+	1.75754i	−0.0407850	+	0.0706417i	−0.885697	−	0.464263i	$-0.846319\pi$
$619$	−1.01472	+	1.75754i	−0.0407850	+	0.0706417i	0.844912	+	0.534905i	$0.179653\pi$
$620$		0			0
$621$	7.13604	+	12.3600i	0.286359	+	0.495989i
$622$		0			0
$623$	5.89340	−	43.0656i	0.236114	−	1.72539i
$624$		0			0
$625$	−8.77208	−	15.1937i	−0.350883	−	0.607747i
$626$		0			0
$627$	−1.50000	−	2.59808i	−0.0599042	−	0.103757i
$628$		0			0
$629$			10.2692i			0.409460i
$630$		0			0
$631$			15.2913i			0.608736i	0.952554	+	0.304368i	$0.0984453\pi$
$631$			15.2913i			0.608736i	−0.952554	+	0.304368i	$0.901555\pi$
$632$		0			0
$633$	−14.7426	+	25.5350i	−0.585967	+	1.01493i
$634$		0			0
$635$	−0.213203	−	0.369279i	−0.00846072	−	0.0146544i
$636$		0			0
$637$	28.3492	−	7.28692i	1.12324	−	0.288718i
$638$		0			0
$639$		−	39.7862i		−	1.57392i
$640$		0			0
$641$	−18.4706	+	31.9920i	−0.729543	+	1.26361i	0.227533	+	0.973770i	$0.426934\pi$
$641$	−18.4706	+	31.9920i	−0.729543	+	1.26361i	−0.957076	+	0.289836i	$0.906399\pi$
$642$		0			0
$643$	−12.2279	+	21.1794i	−0.482222	+	0.835233i	−0.999792	−	0.0204078i	$-0.993504\pi$
$643$	−12.2279	+	21.1794i	−0.482222	+	0.835233i	0.517570	+	0.855641i	$0.326837\pi$
$644$		0			0
$645$	−7.13604	−	4.11999i	−0.280981	−	0.162225i
$646$		0			0
$647$	−7.86396	−	13.6208i	−0.309164	−	0.535488i	0.669016	−	0.743248i	$-0.266716\pi$
$647$	−7.86396	−	13.6208i	−0.309164	−	0.535488i	−0.978180	+	0.207760i	$0.933383\pi$
$648$		0			0
$649$	−9.00000	−	5.19615i	−0.353281	−	0.203967i
$650$		0			0
$651$	−16.9706	+	6.92820i	−0.665129	+	0.271538i
$652$		0			0
$653$	21.6213	+	37.4492i	0.846108	+	1.46550i	0.884656	+	0.466245i	$0.154393\pi$
$653$	21.6213	+	37.4492i	0.846108	+	1.46550i	−0.0385482	+	0.999257i	$0.512273\pi$
$654$		0			0
$655$	−10.8640	−	6.27231i	−0.424490	−	0.245079i
$656$		0			0
$657$	22.5000	−	12.9904i	0.877809	−	0.506803i
$658$		0			0
$659$	21.4706	−	12.3960i	0.836374	−	0.482881i	−0.0196558	−	0.999807i	$-0.506257\pi$
$659$	21.4706	−	12.3960i	0.836374	−	0.482881i	0.856030	+	0.516926i	$0.172924\pi$
$660$		0			0
$661$		−	43.2503i		−	1.68224i	−0.540848	−	0.841121i	$-0.681896\pi$
$661$		−	43.2503i		−	1.68224i	0.540848	−	0.841121i	$-0.318104\pi$
$662$		0			0
$663$			22.9369i			0.890796i
$664$		0			0
$665$	−1.75736	+	0.717439i	−0.0681475	+	0.0278211i
$666$		0			0
$667$	−2.95584	−	1.70656i	−0.114451	−	0.0660782i
$668$		0			0
$669$	−7.86396	+	4.54026i	−0.304038	+	0.175537i
$670$		0			0
$671$	6.00000	−	10.3923i	0.231627	−	0.401190i
$672$		0			0
$673$	−11.9853	−	20.7591i	−0.461999	−	0.800205i	0.537062	−	0.843543i	$-0.319534\pi$
$673$	−11.9853	−	20.7591i	−0.461999	−	0.800205i	−0.999060	+	0.0433378i	$0.986201\pi$
$674$		0			0
$675$	20.1838	+	11.6531i	0.776874	+	0.448528i
$676$		0			0
$677$			7.76874i			0.298577i	0.988794	+	0.149288i	$0.0476983\pi$
$677$			7.76874i			0.298577i	−0.988794	+	0.149288i	$0.952302\pi$
$678$		0			0
$679$	−13.8640	−	10.7510i	−0.532050	−	0.412586i
$680$		0			0
$681$	−26.2279	−	15.1427i	−1.00506	−	0.580269i
$682$		0			0
$683$	14.0147	−	8.09140i	0.536258	−	0.309609i	−0.207303	−	0.978277i	$-0.566469\pi$
$683$	14.0147	−	8.09140i	0.536258	−	0.309609i	0.743561	+	0.668668i	$0.233135\pi$
$684$		0			0
$685$		−	6.45695i		−	0.246707i
$686$		0			0
$687$	−17.3787	−	30.1008i	−0.663038	−	1.14842i
$688$		0			0
$689$			5.19615i			0.197958i
$690$		0			0
$691$	−23.9411			−0.910763			−0.455382	−	0.890296i	$-0.650497\pi$
$691$	−23.9411			−0.910763			−0.455382	+	0.890296i	$0.650497\pi$
$692$		0			0
$693$	−1.86396	+	13.6208i	−0.0708060	+	0.517411i
$694$		0			0
$695$		−	9.32671i		−	0.353782i
$696$		0			0
$697$	31.9706			1.21097
$698$		0			0
$699$	18.7721	+	10.8381i	0.710025	+	0.409933i
$700$		0			0
$701$	1.02944			0.0388813			0.0194407	−	0.999811i	$-0.493811\pi$
$701$	1.02944			0.0388813			0.0194407	+	0.999811i	$0.493811\pi$
$702$		0			0
$703$	−1.62132	−	2.80821i	−0.0611493	−	0.105914i
$704$		0			0
$705$	5.27208	+	9.13151i	0.198558	+	0.343912i
$706$		0			0
$707$	−1.50000	+	10.9612i	−0.0564133	+	0.412237i
$708$		0			0
$709$	28.4853			1.06979			0.534894	−	0.844919i	$-0.320352\pi$
$709$	28.4853			1.06979			0.534894	+	0.844919i	$0.320352\pi$
$710$		0			0
$711$		−	6.08767i		−	0.228306i
$712$		0			0
$713$	−9.51472	+	5.49333i	−0.356329	+	0.205727i
$714$		0			0
$715$	−4.50000	−	2.59808i	−0.168290	−	0.0971625i
$716$		0			0
$717$	−0.106602	+	0.184640i	−0.00398111	+	0.00689549i
$718$		0			0
$719$	24.6213	−	42.6454i	0.918220	−	1.59040i	0.116103	−	0.993237i	$-0.462960\pi$
$719$	24.6213	−	42.6454i	0.918220	−	1.59040i	0.802117	−	0.597167i	$-0.203707\pi$
$720$		0			0
$721$	−19.0147	+	24.5204i	−0.708145	+	0.913187i
$722$		0			0
$723$	0.257359	−	0.445759i	0.00957130	−	0.0165780i
$724$		0			0
$725$	−5.57359			−0.206998
$726$		0			0
$727$	−21.3492	−	36.9780i	−0.791800	−	1.37144i	−0.924852	−	0.380328i	$-0.875811\pi$
$727$	−21.3492	−	36.9780i	−0.791800	−	1.37144i	0.133052	−	0.991109i	$-0.457522\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−10.5000	+	18.1865i	−0.388357	+	0.672653i
$732$		0			0
$733$	−38.3787	+	22.1579i	−1.41755	+	0.818422i	−0.996083	−	0.0884221i	$-0.971818\pi$
$733$	−38.3787	+	22.1579i	−1.41755	+	0.818422i	−0.421466	+	0.906844i	$0.638484\pi$
$734$		0			0
$735$	8.37868	+	2.33696i	0.309052	+	0.0861999i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−27.2574	+	15.7370i	−1.00268	+	0.578897i	−0.909040	−	0.416710i	$-0.863183\pi$
$739$	−27.2574	+	15.7370i	−1.00268	+	0.578897i	−0.0936386	+	0.995606i	$0.529850\pi$
$740$		0			0
$741$	−3.62132	−	6.27231i	−0.133033	−	0.230419i
$742$		0			0
$743$	−13.1360	−	7.58410i	−0.481915	−	0.278233i	0.239299	−	0.970946i	$-0.423082\pi$
$743$	−13.1360	−	7.58410i	−0.481915	−	0.278233i	−0.721214	+	0.692712i	$0.756416\pi$
$744$		0			0
$745$	−11.9558	−	6.90271i	−0.438028	−	0.252896i
$746$		0			0
$747$	17.2279	+	29.8396i	0.630337	+	1.09178i
$748$		0			0
$749$	4.13604	−	30.2238i	0.151128	−	1.10436i
$750$		0			0
$751$	31.3492	−	18.0995i	1.14395	−	0.660460i	0.196544	−	0.980495i	$-0.437028\pi$
$751$	31.3492	−	18.0995i	1.14395	−	0.660460i	0.947406	+	0.320035i	$0.103695\pi$
$752$		0			0
$753$		−	45.8739i		−	1.67174i
$754$		0			0
$755$	−17.0589			−0.620836
$756$		0			0
$757$	23.9411			0.870155			0.435078	−	0.900393i	$-0.356721\pi$
$757$	23.9411			0.870155			0.435078	+	0.900393i	$0.356721\pi$
$758$		0			0
$759$			8.23999i			0.299093i
$760$		0			0
$761$	20.7426	−	11.9758i	0.751920	−	0.434121i	−0.0744671	−	0.997223i	$-0.523726\pi$
$761$	20.7426	−	11.9758i	0.751920	−	0.434121i	0.826387	+	0.563102i	$0.190392\pi$
$762$		0			0
$763$	−14.1985	+	18.3096i	−0.514020	+	0.662853i
$764$		0			0
$765$	−3.40812	+	5.90303i	−0.123221	+	0.213425i
$766$		0			0
$767$	−21.7279	−	12.5446i	−0.784550	−	0.452960i
$768$		0			0
$769$	25.1985	+	14.5484i	0.908681	+	0.524627i	0.880006	−	0.474962i	$-0.157538\pi$
$769$	25.1985	+	14.5484i	0.908681	+	0.524627i	0.0286742	+	0.999589i	$0.490871\pi$
$770$		0			0
$771$	21.9853	+	38.0796i	0.791781	+	1.37140i
$772$		0			0
$773$	1.34924	−	0.778985i	0.0485289	−	0.0280182i	−0.475539	−	0.879694i	$-0.657747\pi$
$773$	1.34924	−	0.778985i	0.0485289	−	0.0280182i	0.524068	+	0.851676i	$0.324414\pi$
$774$		0			0
$775$	−8.97056	+	15.5375i	−0.322232	+	0.558122i
$776$		0			0
$777$	−2.01472	+	14.7224i	−0.0722776	+	0.528164i
$778$		0			0
$779$	−8.74264	+	5.04757i	−0.313238	+	0.180848i
$780$		0			0
$781$	11.4853	−	19.8931i	0.410976	−	0.711831i
$782$		0			0
$783$	5.59188	−	3.22848i	0.199838	−	0.115376i
$784$		0			0
$785$	−0.727922	−	1.26080i	−0.0259807	−	0.0449998i
$786$		0			0
$787$	−10.4853			−0.373760			−0.186880	−	0.982383i	$-0.559838\pi$
$787$	−10.4853			−0.373760			−0.186880	+	0.982383i	$0.559838\pi$
$788$		0			0
$789$	12.1066	−	20.9692i	0.431006	−	0.746525i
$790$		0			0
$791$	30.1066	+	4.11999i	1.07047	+	0.146490i
$792$		0			0
$793$	14.4853	−	25.0892i	0.514387	−	0.890945i
$794$		0			0
$795$	−0.772078	+	1.33728i	−0.0273828	+	0.0474284i
$796$		0			0
$797$	6.10660	+	3.52565i	0.216307	+	0.124885i	0.604239	−	0.796803i	$-0.293477\pi$
$797$	6.10660	+	3.52565i	0.216307	+	0.124885i	−0.387932	+	0.921688i	$0.626811\pi$
$798$		0			0
$799$	23.2721	−	13.4361i	0.823307	−	0.475336i
$800$		0			0
$801$	42.6838	+	24.6435i	1.50816	+	0.870735i
$802$		0			0
$803$	15.0000			0.529339
$804$		0			0
$805$	5.16548	+	0.706879i	0.182059	+	0.0249142i
$806$		0			0
$807$	−19.3492	−	33.5139i	−0.681126	−	1.17974i
$808$		0			0
$809$	15.9853	+	27.6873i	0.562013	+	0.973434i	0.997321	+	0.0731528i	$0.0233061\pi$
$809$	15.9853	+	27.6873i	0.562013	+	0.973434i	−0.435308	+	0.900282i	$0.643361\pi$
$810$		0			0
$811$	37.9411			1.33229			0.666147	−	0.745821i	$-0.267943\pi$
$811$	37.9411			1.33229			0.666147	+	0.745821i	$0.267943\pi$
$812$		0			0
$813$	17.5919	+	10.1567i	0.616974	+	0.356210i
$814$		0			0
$815$	0.213203			0.00746819
$816$		0			0
$817$		−	6.63103i		−	0.231990i
$818$		0			0
$819$	−4.50000	+	32.8835i	−0.157243	+	1.14904i
$820$		0			0
$821$	49.4558			1.72602			0.863010	−	0.505186i	$-0.168576\pi$
$821$	49.4558			1.72602			0.863010	+	0.505186i	$0.168576\pi$
$822$		0			0
$823$			48.7436i			1.69910i	0.527512	+	0.849548i	$0.323125\pi$
$823$			48.7436i			1.69910i	−0.527512	+	0.849548i	$0.676875\pi$
$824$		0			0
$825$	6.72792	+	11.6531i	0.234236	+	0.405709i
$826$		0			0
$827$		−	21.6251i		−	0.751980i	−0.926624	−	0.375990i	$-0.877303\pi$
$827$		−	21.6251i		−	0.751980i	0.926624	−	0.375990i	$-0.122697\pi$
$828$		0			0
$829$	−18.8345	+	10.8741i	−0.654150	+	0.377674i	−0.790044	−	0.613050i	$-0.789943\pi$
$829$	−18.8345	+	10.8741i	−0.654150	+	0.377674i	0.135894	+	0.990723i	$0.456609\pi$
$830$		0			0
$831$	17.5919	+	10.1567i	0.610256	+	0.352331i
$832$		0			0
$833$	5.95584	−	21.3535i	0.206358	−	0.739854i
$834$		0			0
$835$		−	11.2838i		−	0.390493i
$836$		0			0
$837$		−	20.7846i		−	0.718421i
$838$		0			0
$839$	9.62132	+	16.6646i	0.332165	+	0.575326i	0.982936	−	0.183947i	$-0.0588876\pi$
$839$	9.62132	+	16.6646i	0.332165	+	0.575326i	−0.650771	+	0.759274i	$0.725554\pi$
$840$		0			0
$841$	13.7279	−	23.7775i	0.473377	−	0.819912i
$842$		0			0
$843$	−47.9558	+	27.6873i	−1.65169	+	0.953602i
$844$		0			0
$845$	−2.78680	−	1.60896i	−0.0958687	−	0.0553498i
$846$		0			0
$847$	12.9706	−	16.7262i	0.445674	−	0.574718i
$848$		0			0
$849$			9.55177i			0.327816i
$850$		0			0
$851$			8.90644i			0.305309i
$852$		0			0
$853$	7.86396	−	4.54026i	0.269257	−	0.155456i	−0.359293	−	0.933225i	$-0.616982\pi$
$853$	7.86396	−	4.54026i	0.269257	−	0.155456i	0.628550	+	0.777769i	$0.283649\pi$
$854$		0			0
$855$		−	2.15232i		−	0.0736077i
$856$		0			0
$857$	3.98528	+	2.30090i	0.136135	+	0.0785974i	0.566521	−	0.824048i	$-0.308289\pi$
$857$	3.98528	+	2.30090i	0.136135	+	0.0785974i	−0.430386	+	0.902645i	$0.641623\pi$
$858$		0			0
$859$	−16.9853	−	29.4194i	−0.579530	−	1.00378i	−0.995533	−	0.0944126i	$-0.969903\pi$
$859$	−16.9853	−	29.4194i	−0.579530	−	1.00378i	0.416003	−	0.909363i	$-0.363431\pi$
$860$		0			0
$861$	45.8345	+	6.27231i	1.56204	+	0.213760i
$862$		0			0
$863$	−5.59188	−	3.22848i	−0.190350	−	0.109899i	0.401796	−	0.915729i	$-0.368386\pi$
$863$	−5.59188	−	3.22848i	−0.190350	−	0.109899i	−0.592146	+	0.805830i	$0.701719\pi$
$864$		0			0
$865$	3.51472	+	6.08767i	0.119504	+	0.206987i
$866$		0			0
$867$	−10.4558	−	6.03668i	−0.355099	−	0.205017i
$868$		0			0
$869$	1.75736	−	3.04384i	0.0596143	−	0.103255i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	17.2279	−	9.94655i	0.583077	−	0.336640i
$874$		0			0
$875$	16.6690	−	6.80511i	0.563517	−	0.230055i
$876$		0			0
$877$	6.34924	+	10.9972i	0.214399	+	0.371349i	0.953086	−	0.302698i	$-0.0978875\pi$
$877$	6.34924	+	10.9972i	0.214399	+	0.371349i	−0.738688	+	0.674048i	$0.764554\pi$
$878$		0			0
$879$	−14.5919	+	25.2739i	−0.492172	+	0.852467i
$880$		0			0
$881$		−	22.2195i		−	0.748594i	−0.927309	−	0.374297i	$-0.877884\pi$
$881$		−	22.2195i		−	0.748594i	0.927309	−	0.374297i	$-0.122116\pi$
$882$		0			0
$883$		−	4.89898i		−	0.164864i	−0.996597	−	0.0824319i	$-0.973731\pi$
$883$		−	4.89898i		−	0.164864i	0.996597	−	0.0824319i	$-0.0262687\pi$
$884$		0			0
$885$	−3.72792	−	6.45695i	−0.125313	−	0.217048i
$886$		0			0
$887$	21.8345	+	37.8185i	0.733132	+	1.26982i	0.955538	+	0.294867i	$0.0952754\pi$
$887$	21.8345	+	37.8185i	0.733132	+	1.26982i	−0.222407	+	0.974954i	$0.571391\pi$
$888$		0			0
$889$	−1.45584	+	0.594346i	−0.0488274	+	0.0199337i
$890$		0			0
$891$	−13.5000	−	7.79423i	−0.452267	−	0.261116i
$892$		0			0
$893$	−4.24264	+	7.34847i	−0.141975	+	0.245907i
$894$		0			0
$895$	0.408117	−	0.706879i	0.0136418	−	0.0236284i
$896$		0			0
$897$			19.8931i			0.664211i
$898$		0			0
$899$	2.48528	+	4.30463i	0.0828888	+	0.143568i
$900$		0			0
$901$	3.40812	+	1.96768i	0.113541	+	0.0655528i
$902$		0			0
$903$	−18.6213	+	24.0131i	−0.619679	+	0.799105i
$904$		0			0
$905$	4.75736	+	8.23999i	0.158140	+	0.273906i
$906$		0			0
$907$	0.985281	+	0.568852i	0.0327157	+	0.0188884i	0.516269	−	0.856427i	$-0.327321\pi$
$907$	0.985281	+	0.568852i	0.0327157	+	0.0188884i	−0.483553	+	0.875315i	$0.660654\pi$
$908$		0			0
$909$	−10.8640	−	6.27231i	−0.360335	−	0.208039i
$910$		0			0
$911$	−16.1360	+	9.31615i	−0.534611	+	0.308658i	−0.742892	−	0.669411i	$-0.766546\pi$
$911$	−16.1360	+	9.31615i	−0.534611	+	0.308658i	0.208281	+	0.978069i	$0.433213\pi$
$912$		0			0
$913$			19.8931i			0.658365i
$914$		0			0
$915$	7.45584	−	4.30463i	0.246483	−	0.142307i
$916$		0			0
$917$	−28.3492	+	36.5577i	−0.936174	+	1.20724i
$918$		0			0
$919$	−4.13604	−	2.38794i	−0.136435	−	0.0787710i	0.430229	−	0.902720i	$-0.358433\pi$
$919$	−4.13604	−	2.38794i	−0.136435	−	0.0787710i	−0.566664	+	0.823949i	$0.691766\pi$
$920$		0			0
$921$		−	32.0174i		−	1.05501i
$922$		0			0
$923$	27.7279	−	48.0262i	0.912676	−	1.58080i
$924$		0			0
$925$	7.27208	+	12.5956i	0.239104	+	0.414141i
$926$		0			0
$927$	−17.5919	−	30.4700i	−0.577793	−	1.00077i
$928$		0			0
$929$		−	47.9031i		−	1.57165i	−0.618450	−	0.785824i	$-0.712239\pi$
$929$		−	47.9031i		−	1.57165i	0.618450	−	0.785824i	$-0.287761\pi$
$930$		0			0
$931$	1.74264	+	6.77962i	0.0571127	+	0.222193i
$932$		0			0
$933$			39.7862i			1.30254i
$934$		0			0
$935$	−3.40812	+	1.96768i	−0.111457	+	0.0643499i
$936$		0			0
$937$			52.4539i			1.71359i	0.515654	+	0.856797i	$0.327549\pi$
$937$			52.4539i			1.71359i	−0.515654	+	0.856797i	$0.672451\pi$
$938$		0			0
$939$	2.48528			0.0811041
$940$		0			0
$941$		−	36.3221i		−	1.18407i	−0.805914	−	0.592033i	$-0.798326\pi$
$941$		−	36.3221i		−	1.18407i	0.805914	−	0.592033i	$-0.201674\pi$
$942$		0			0
$943$	27.7279			0.902945
$944$		0			0
$945$	−6.04416	+	7.79423i	−0.196616	+	0.253546i
$946$		0			0
$947$			57.7010i			1.87503i	0.347943	+	0.937516i	$0.386880\pi$
$947$			57.7010i			1.87503i	−0.347943	+	0.937516i	$0.613120\pi$
$948$		0			0
$949$	36.2132			1.17553
$950$		0			0
$951$			31.1769i			1.01098i
$952$		0			0
$953$	27.5147			0.891289			0.445645	−	0.895210i	$-0.352975\pi$
$953$	27.5147			0.891289			0.445645	+	0.895210i	$0.352975\pi$
$954$		0			0
$955$	−6.51472	−	11.2838i	−0.210811	−	0.365136i
$956$		0			0
$957$	3.72792			0.120507
$958$		0			0
$959$	−23.5919	−	3.22848i	−0.761822	−	0.104253i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	29.9558	+	17.2950i	0.965314	+	0.557324i
$964$		0			0
$965$	−13.0294	+	7.52255i	−0.419432	+	0.242159i
$966$		0			0
$967$	32.5919	+	18.8169i	1.04808	+	0.605112i	0.922112	−	0.386922i	$-0.126462\pi$
$967$	32.5919	+	18.8169i	1.04808	+	0.605112i	0.125972	+	0.992034i	$0.459795\pi$
$968$		0			0
$969$	−5.48528			−0.176213
$970$		0			0
$971$	6.25736	−	10.8381i	0.200808	−	0.347810i	−0.747981	−	0.663720i	$-0.768977\pi$
$971$	6.25736	−	10.8381i	0.200808	−	0.347810i	0.948789	+	0.315910i	$0.102310\pi$
$972$		0			0
$973$	−34.0772	−	4.66335i	−1.09246	−	0.149500i
$974$		0			0
$975$	16.2426	+	28.1331i	0.520181	+	0.900980i
$976$		0			0
$977$	−16.9706			−0.542936			−0.271468	−	0.962447i	$-0.587509\pi$
$977$	−16.9706			−0.542936			−0.271468	+	0.962447i	$0.587509\pi$
$978$		0			0
$979$	14.2279	+	24.6435i	0.454726	+	0.787609i
$980$		0			0
$981$	−13.1360	−	22.7523i	−0.419401	−	0.726425i
$982$		0			0
$983$	12.6213	−	21.8608i	0.402558	−	0.697250i	−0.591476	−	0.806322i	$-0.701455\pi$
$983$	12.6213	−	21.8608i	0.402558	−	0.697250i	0.994034	+	0.109072i	$0.0347880\pi$
$984$		0			0
$985$	9.00000	−	5.19615i	0.286764	−	0.165563i
$986$		0			0
$987$	36.0000	−	14.6969i	1.14589	−	0.467809i
$988$		0			0
$989$	−9.10660	+	15.7731i	−0.289573	+	0.501555i
$990$		0			0
$991$	−25.1360	+	14.5123i	−0.798473	+	0.460998i	−0.842937	−	0.538013i	$-0.819175\pi$
$991$	−25.1360	+	14.5123i	−0.798473	+	0.460998i	0.0444642	+	0.999011i	$0.485842\pi$
$992$		0			0
$993$	19.0294			0.603881
$994$		0			0
$995$	−12.2574	−	7.07679i	−0.388584	−	0.224349i
$996$		0			0
$997$	−7.86396	−	4.54026i	−0.249054	−	0.143791i	0.370277	−	0.928921i	$-0.379263\pi$
$997$	−7.86396	−	4.54026i	−0.249054	−	0.143791i	−0.619331	+	0.785130i	$0.712596\pi$
$998$		0			0
$999$	−14.5919	−	8.42463i	−0.461667	−	0.266543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.f.607.1	yes	4
3.2	odd	2		3024.2.cz.f.1279.2		4
4.3	odd	2		1008.2.cz.e.607.1	yes	4
7.3	odd	6		1008.2.bf.e.31.2	✓	4
9.2	odd	6		3024.2.bf.e.2287.2		4
9.7	even	3		1008.2.bf.f.943.1	yes	4
12.11	even	2		3024.2.cz.e.1279.2		4
21.17	even	6		3024.2.bf.f.1711.1		4
28.3	even	6		1008.2.bf.f.31.2	yes	4
36.7	odd	6		1008.2.bf.e.943.1	yes	4
36.11	even	6		3024.2.bf.f.2287.2		4
63.38	even	6		3024.2.cz.e.2719.2		4
63.52	odd	6		1008.2.cz.e.367.1	yes	4
84.59	odd	6		3024.2.bf.e.1711.1		4
252.115	even	6	inner	1008.2.cz.f.367.1	yes	4
252.227	odd	6		3024.2.cz.f.2719.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.e.31.2	✓	4	7.3	odd	6
1008.2.bf.e.943.1	yes	4	36.7	odd	6
1008.2.bf.f.31.2	yes	4	28.3	even	6
1008.2.bf.f.943.1	yes	4	9.7	even	3
1008.2.cz.e.367.1	yes	4	63.52	odd	6
1008.2.cz.e.607.1	yes	4	4.3	odd	2
1008.2.cz.f.367.1	yes	4	252.115	even	6	inner
1008.2.cz.f.607.1	yes	4	1.1	even	1	trivial
3024.2.bf.e.1711.1		4	84.59	odd	6
3024.2.bf.e.2287.2		4	9.2	odd	6
3024.2.bf.f.1711.1		4	21.17	even	6
3024.2.bf.f.2287.2		4	36.11	even	6
3024.2.cz.e.1279.2		4	12.11	even	2
3024.2.cz.e.2719.2		4	63.38	even	6
3024.2.cz.f.1279.2		4	3.2	odd	2
3024.2.cz.f.2719.2		4	252.227	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.73205i q^{3} +(-0.621320 + 0.358719i) q^{5} +(1.00000 + 2.44949i) q^{7} -3.00000 q^{9} +O(q^{10})\)	\(q+1.73205i q^{3} +(-0.621320 + 0.358719i) q^{5} +(1.00000 + 2.44949i) q^{7} -3.00000 q^{9} +(-1.50000 - 0.866025i) q^{11} +(-3.62132 - 2.09077i) q^{13} +(-0.621320 - 1.07616i) q^{15} +(-2.74264 + 1.58346i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-4.24264 + 1.73205i) q^{21} +(-2.37868 + 1.37333i) q^{23} +(-2.24264 + 3.88437i) q^{25} -5.19615i q^{27} +(0.621320 + 1.07616i) q^{29} +4.00000 q^{31} +(1.50000 - 2.59808i) q^{33} +(-1.50000 - 1.16320i) q^{35} +(1.62132 - 2.80821i) q^{37} +(3.62132 - 6.27231i) q^{39} +(-8.74264 - 5.04757i) q^{41} +(5.74264 - 3.31552i) q^{43} +(1.86396 - 1.07616i) q^{45} -8.48528 q^{47} +(-5.00000 + 4.89898i) q^{49} +(-2.74264 - 4.75039i) q^{51} +(-0.621320 - 1.07616i) q^{53} +1.24264 q^{55} +(1.50000 + 0.866025i) q^{57} +6.00000 q^{59} +6.92820i q^{61} +(-3.00000 - 7.34847i) q^{63} +3.00000 q^{65} +(-2.37868 - 4.11999i) q^{69} +13.2621i q^{71} +(-7.50000 + 4.33013i) q^{73} +(-6.72792 - 3.88437i) q^{75} +(0.621320 - 4.54026i) q^{77} +2.02922i q^{79} +9.00000 q^{81} +(-5.74264 - 9.94655i) q^{83} +(1.13604 - 1.96768i) q^{85} +(-1.86396 + 1.07616i) q^{87} +(-14.2279 - 8.21449i) q^{89} +(1.50000 - 10.9612i) q^{91} +6.92820i q^{93} +0.717439i q^{95} +(-5.74264 + 3.31552i) q^{97} +(4.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{5} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) 4 * q + 6 * q^5 + 4 * q^7 - 12 * q^9	\( 4 q + 6 q^{5} + 4 q^{7} - 12 q^{9} - 6 q^{11} - 6 q^{13} + 6 q^{15} + 6 q^{17} + 2 q^{19} - 18 q^{23} + 8 q^{25} - 6 q^{29} + 16 q^{31} + 6 q^{33} - 6 q^{35} - 2 q^{37} + 6 q^{39} - 18 q^{41} + 6 q^{43} - 18 q^{45} - 20 q^{49} + 6 q^{51} + 6 q^{53} - 12 q^{55} + 6 q^{57} + 24 q^{59} - 12 q^{63} + 12 q^{65} - 18 q^{69} - 30 q^{73} + 24 q^{75} - 6 q^{77} + 36 q^{81} - 6 q^{83} + 30 q^{85} + 18 q^{87} - 6 q^{89} + 6 q^{91} - 6 q^{97} + 18 q^{99}+O(q^{100}) \) 4 * q + 6 * q^5 + 4 * q^7 - 12 * q^9 - 6 * q^11 - 6 * q^13 + 6 * q^15 + 6 * q^17 + 2 * q^19 - 18 * q^23 + 8 * q^25 - 6 * q^29 + 16 * q^31 + 6 * q^33 - 6 * q^35 - 2 * q^37 + 6 * q^39 - 18 * q^41 + 6 * q^43 - 18 * q^45 - 20 * q^49 + 6 * q^51 + 6 * q^53 - 12 * q^55 + 6 * q^57 + 24 * q^59 - 12 * q^63 + 12 * q^65 - 18 * q^69 - 30 * q^73 + 24 * q^75 - 6 * q^77 + 36 * q^81 - 6 * q^83 + 30 * q^85 + 18 * q^87 - 6 * q^89 + 6 * q^91 - 6 * q^97 + 18 * q^99

Introduction

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