LMFDB - Embedded newform 1008.2.bf.f.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(31,1008)]

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, 2, 1]))

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

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

chi := DirichletCharacter("1008.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bf (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			31.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1008.31
Dual form			1008.2.bf.f.943.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{3} +0.717439i q^{5} +(1.62132 + 2.09077i) q^{7} +(1.50000 - 2.59808i) q^{9} -1.73205i q^{11} +(3.62132 + 2.09077i) q^{13} +(0.621320 + 1.07616i) q^{15} +(-2.74264 - 1.58346i) q^{17} +(0.500000 + 0.866025i) q^{19} +(4.24264 + 1.73205i) q^{21} +2.74666i q^{23} +4.48528 q^{25} -5.19615i q^{27} +(0.621320 + 1.07616i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-1.50000 - 2.59808i) q^{33} +(-1.50000 + 1.16320i) q^{35} +(1.62132 + 2.80821i) q^{37} +7.24264 q^{39} +(8.74264 + 5.04757i) q^{41} +(-5.74264 + 3.31552i) q^{43} +(1.86396 + 1.07616i) q^{45} +(4.24264 - 7.34847i) q^{47} +(-1.74264 + 6.77962i) q^{49} -5.48528 q^{51} +(-0.621320 + 1.07616i) q^{53} +1.24264 q^{55} +(1.50000 + 0.866025i) q^{57} +(-3.00000 - 5.19615i) q^{59} +(6.00000 + 3.46410i) q^{61} +(7.86396 - 1.07616i) q^{63} +(-1.50000 + 2.59808i) q^{65} +(2.37868 + 4.11999i) q^{69} -13.2621i q^{71} +(-7.50000 - 4.33013i) q^{73} +(6.72792 - 3.88437i) q^{75} +(3.62132 - 2.80821i) q^{77} +(1.75736 + 1.01461i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-5.74264 - 9.94655i) q^{83} +(1.13604 - 1.96768i) q^{85} +(1.86396 + 1.07616i) q^{87} +(-14.2279 + 8.21449i) q^{89} +(1.50000 + 10.9612i) q^{91} +(-6.00000 - 3.46410i) q^{93} +(-0.621320 + 0.358719i) q^{95} +(5.74264 - 3.31552i) q^{97} +(-4.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 2 q^{7} + 6 q^{9} + 6 q^{13} - 6 q^{15} + 6 q^{17} + 2 q^{19} - 16 q^{25} - 6 q^{29} - 8 q^{31} - 6 q^{33} - 6 q^{35} - 2 q^{37} + 12 q^{39} + 18 q^{41} - 6 q^{43} - 18 q^{45} + 10 q^{49}+ \cdots - 18 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 2 * q^7 + 6 * q^9 + 6 * q^13 - 6 * q^15 + 6 * q^17 + 2 * q^19 - 16 * q^25 - 6 * q^29 - 8 * q^31 - 6 * q^33 - 6 * q^35 - 2 * q^37 + 12 * q^39 + 18 * q^41 - 6 * q^43 - 18 * q^45 + 10 * q^49 + 12 * q^51 + 6 * q^53 - 12 * q^55 + 6 * q^57 - 12 * q^59 + 24 * q^61 + 6 * q^63 - 6 * q^65 + 18 * q^69 - 30 * q^73 - 24 * q^75 + 6 * q^77 + 24 * q^79 - 18 * q^81 - 6 * q^83 + 30 * q^85 - 18 * q^87 - 6 * q^89 + 6 * q^91 - 24 * q^93 + 6 * q^95 + 6 * q^97 - 18 * q^99

Character values

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

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

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
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$		0			0
$5$			0.717439i			0.320848i	0.987048	+	0.160424i	$0.0512862\pi$
$5$			0.717439i			0.320848i	−0.987048	+	0.160424i	$0.948714\pi$
$6$		0			0
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$		−	1.73205i		−	0.522233i	−0.965307	−	0.261116i	$-0.915909\pi$
$11$		−	1.73205i		−	0.522233i	0.965307	−	0.261116i	$-0.0840907\pi$
$12$		0			0
$13$	3.62132	+	2.09077i	1.00437	+	0.579875i	0.909539	−	0.415618i	$-0.136435\pi$
$13$	3.62132	+	2.09077i	1.00437	+	0.579875i	0.0948342	+	0.995493i	$0.469768\pi$
$14$		0			0
$15$	0.621320	+	1.07616i	0.160424	+	0.277863i
$16$		0			0
$17$	−2.74264	−	1.58346i	−0.665188	−	0.384047i	0.129063	−	0.991636i	$-0.458803\pi$
$17$	−2.74264	−	1.58346i	−0.665188	−	0.384047i	−0.794251	+	0.607590i	$0.792136\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	4.24264	+	1.73205i	0.925820	+	0.377964i
$22$		0			0
$23$			2.74666i			0.572719i	0.958122	+	0.286359i	$0.0924451\pi$
$23$			2.74666i			0.572719i	−0.958122	+	0.286359i	$0.907555\pi$
$24$		0			0
$25$	4.48528			0.897056
$26$		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
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		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	0.967967	−	0.251078i	$-0.0807851\pi$
$37$	1.62132	+	2.80821i	0.266543	+	0.461667i	−0.701423	+	0.712745i	$0.747452\pi$
$38$		0			0
$39$	7.24264			1.15975
$40$		0			0
$41$	8.74264	+	5.04757i	1.36537	+	0.788297i	0.990333	−	0.138712i	$-0.0442962\pi$
$41$	8.74264	+	5.04757i	1.36537	+	0.788297i	0.375038	+	0.927009i	$0.377630\pi$
$42$		0			0
$43$	−5.74264	+	3.31552i	−0.875744	+	0.505611i	−0.869253	−	0.494368i	$-0.835400\pi$
$43$	−5.74264	+	3.31552i	−0.875744	+	0.505611i	−0.00649156	+	0.999979i	$0.502066\pi$
$44$		0			0
$45$	1.86396	+	1.07616i	0.277863	+	0.160424i
$46$		0			0
$47$	4.24264	−	7.34847i	0.618853	−	1.07188i	−0.370843	−	0.928696i	$-0.620931\pi$
$47$	4.24264	−	7.34847i	0.618853	−	1.07188i	0.989695	−	0.143189i	$-0.0457356\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$		0			0
$51$	−5.48528			−0.768093
$52$		0			0
$53$	−0.621320	+	1.07616i	−0.0853449	+	0.147822i	−0.905538	−	0.424265i	$-0.860533\pi$
$53$	−0.621320	+	1.07616i	−0.0853449	+	0.147822i	0.820193	+	0.572087i	$0.193866\pi$
$54$		0			0
$55$	1.24264			0.167558
$56$		0			0
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$		0			0
$63$	7.86396	−	1.07616i	0.990766	−	0.135583i
$64$		0			0
$65$	−1.50000	+	2.59808i	−0.186052	+	0.322252i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$	2.37868	+	4.11999i	0.286359	+	0.495989i
$70$		0			0
$71$		−	13.2621i		−	1.57392i	−0.617006	−	0.786959i	$-0.711655\pi$
$71$		−	13.2621i		−	1.57392i	0.617006	−	0.786959i	$-0.288345\pi$
$72$		0			0
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.00787336	−	0.999969i	$-0.502506\pi$
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.869935	+	0.493166i	$0.835840\pi$
$74$		0			0
$75$	6.72792	−	3.88437i	0.776874	−	0.448528i
$76$		0			0
$77$	3.62132	−	2.80821i	0.412688	−	0.320025i
$78$		0			0
$79$	1.75736	+	1.01461i	0.197718	+	0.114153i	0.595591	−	0.803288i	$-0.296918\pi$
$79$	1.75736	+	1.01461i	0.197718	+	0.114153i	−0.397872	+	0.917441i	$0.630251\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		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	−0.508202	+	0.861238i	$0.669690\pi$
$89$	−14.2279	+	8.21449i	−1.50816	+	0.870735i	−0.999955	+	0.00949668i	$0.996977\pi$
$90$		0			0
$91$	1.50000	+	10.9612i	0.157243	+	1.14904i
$92$		0			0
$93$	−6.00000	−	3.46410i	−0.622171	−	0.359211i
$94$		0			0
$95$	−0.621320	+	0.358719i	−0.0637461	+	0.0368038i
$96$		0			0
$97$	5.74264	−	3.31552i	0.583077	−	0.336640i	−0.179278	−	0.983798i	$-0.557376\pi$
$97$	5.74264	−	3.31552i	0.583077	−	0.336640i	0.762355	+	0.647159i	$0.224043\pi$
$98$		0			0
$99$	−4.50000	−	2.59808i	−0.452267	−	0.261116i
$100$		0			0
$101$			4.18154i			0.416079i	0.978120	+	0.208039i	$0.0667082\pi$
$101$			4.18154i			0.416079i	−0.978120	+	0.208039i	$0.933292\pi$
$102$		0			0
$103$	−11.7279			−1.15559			−0.577793	−	0.816183i	$-0.696086\pi$
$103$	−11.7279			−1.15559			−0.577793	+	0.816183i	$0.696086\pi$
$104$		0			0
$105$	−1.24264	+	3.04384i	−0.121269	+	0.297048i
$106$		0			0
$107$	−9.98528	+	5.76500i	−0.965314	+	0.557324i	−0.897804	−	0.440395i	$-0.854839\pi$
$107$	−9.98528	+	5.76500i	−0.965314	+	0.557324i	−0.0675093	+	0.997719i	$0.521505\pi$
$108$		0			0
$109$	4.37868	−	7.58410i	0.419401	−	0.726425i	−0.576478	−	0.817113i	$-0.695573\pi$
$109$	4.37868	−	7.58410i	0.419401	−	0.726425i	0.995879	+	0.0906881i	$0.0289066\pi$
$110$		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
$115$	−1.97056			−0.183756
$116$		0			0
$117$	10.8640	−	6.27231i	1.00437	−	0.579875i
$118$		0			0
$119$	−1.13604	−	8.30153i	−0.104141	−	0.761000i
$120$		0			0
$121$	8.00000			0.727273
$122$		0			0
$123$	17.4853			1.57659
$124$		0			0
$125$			6.80511i			0.608668i
$126$		0			0
$127$		−	0.594346i		−	0.0527397i	−0.999652	−	0.0263698i	$-0.991605\pi$
$127$		−	0.594346i		−	0.0527397i	0.999652	−	0.0263698i	$-0.00839475\pi$
$128$		0			0
$129$	−5.74264	+	9.94655i	−0.505611	+	0.875744i
$130$		0			0
$131$	−17.4853			−1.52770			−0.763848	−	0.645396i	$-0.776692\pi$
$131$	−17.4853			−1.52770			−0.763848	+	0.645396i	$0.776692\pi$
$132$		0			0
$133$	−1.00000	+	2.44949i	−0.0867110	+	0.212398i
$134$		0			0
$135$	3.72792			0.320848
$136$		0			0
$137$	9.00000			0.768922			0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000			0.768922			0.384461	+	0.923141i	$0.374387\pi$
$138$		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
$147$	3.25736	+	11.6786i	0.268662	+	0.963234i
$148$		0			0
$149$	−19.2426			−1.57642			−0.788209	−	0.615407i	$-0.788992\pi$
$149$	−19.2426			−1.57642			−0.788209	+	0.615407i	$0.788992\pi$
$150$		0			0
$151$			23.7775i			1.93498i	0.252905	+	0.967491i	$0.418614\pi$
$151$			23.7775i			1.93498i	−0.252905	+	0.967491i	$0.581386\pi$
$152$		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
$157$	−1.75736	+	1.01461i	−0.140253	+	0.0809748i	−0.568484	−	0.822694i	$-0.692470\pi$
$157$	−1.75736	+	1.01461i	−0.140253	+	0.0809748i	0.428232	+	0.903669i	$0.359137\pi$
$158$		0			0
$159$			2.15232i			0.170690i
$160$		0			0
$161$	−5.74264	+	4.45322i	−0.452583	+	0.350963i
$162$		0			0
$163$	−0.257359	+	0.148586i	−0.0201579	+	0.0116382i	−0.510045	−	0.860148i	$-0.670371\pi$
$163$	−0.257359	+	0.148586i	−0.0201579	+	0.0116382i	0.489887	+	0.871786i	$0.337038\pi$
$164$		0			0
$165$	1.86396	−	1.07616i	0.145109	−	0.0837788i
$166$		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
$171$	3.00000			0.229416
$172$		0			0
$173$	−8.48528	−	4.89898i	−0.645124	−	0.372463i	0.141462	−	0.989944i	$-0.454820\pi$
$173$	−8.48528	−	4.89898i	−0.645124	−	0.372463i	−0.786586	+	0.617481i	$0.788153\pi$
$174$		0			0
$175$	7.27208	+	9.37769i	0.549717	+	0.708887i
$176$		0			0
$177$	−9.00000	−	5.19615i	−0.676481	−	0.390567i
$178$		0			0
$179$	−0.985281	−	0.568852i	−0.0736434	−	0.0425180i	0.462726	−	0.886501i	$-0.346871\pi$
$179$	−0.985281	−	0.568852i	−0.0736434	−	0.0425180i	−0.536370	+	0.843983i	$0.680205\pi$
$180$		0			0
$181$			13.2621i			0.985761i	0.870097	+	0.492881i	$0.164056\pi$
$181$			13.2621i			0.985761i	−0.870097	+	0.492881i	$0.835944\pi$
$182$		0			0
$183$	12.0000			0.887066
$184$		0			0
$185$	−2.01472	+	1.16320i	−0.148125	+	0.0855200i
$186$		0			0
$187$	−2.74264	+	4.75039i	−0.200562	+	0.347383i
$188$		0			0
$189$	10.8640	−	8.42463i	0.790237	−	0.612801i
$190$		0			0
$191$	15.7279	+	9.08052i	1.13803	+	0.657043i	0.945943	−	0.324334i	$-0.105140\pi$
$191$	15.7279	+	9.08052i	1.13803	+	0.657043i	0.192090	+	0.981377i	$0.438473\pi$
$192$		0			0
$193$	−10.4853	−	18.1610i	−0.754747	−	1.30726i	−0.945500	−	0.325622i	$-0.894426\pi$
$193$	−10.4853	−	18.1610i	−0.754747	−	1.30726i	0.190753	−	0.981638i	$-0.438907\pi$
$194$		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	−0.269493	−	0.963002i	$-0.586856\pi$
$199$	9.86396	−	17.0849i	0.699238	−	1.21112i	0.968731	−	0.248113i	$-0.0798104\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.24264	+	3.04384i	−0.0872163	+	0.213635i
$204$		0			0
$205$	−3.62132	+	6.27231i	−0.252924	+	0.438077i
$206$		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	−0.102295	−	0.994754i	$-0.532619\pi$
$211$	−14.7426	−	8.51167i	−1.01493	−	0.585967i	−0.912630	+	0.408787i	$0.865952\pi$
$212$		0			0
$213$	−11.4853	−	19.8931i	−0.786959	−	1.36305i
$214$		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
$219$	−15.0000			−1.01361
$220$		0			0
$221$	−6.62132	−	11.4685i	−0.445398	−	0.771452i
$222$		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
$227$	17.4853			1.16054			0.580269	−	0.814425i	$-0.302947\pi$
$227$	17.4853			1.16054			0.580269	+	0.814425i	$0.302947\pi$
$228$		0			0
$229$			20.0672i			1.32608i	0.748586	+	0.663038i	$0.230733\pi$
$229$			20.0672i			1.32608i	−0.748586	+	0.663038i	$0.769267\pi$
$230$		0			0
$231$	3.00000	−	7.34847i	0.197386	−	0.483494i
$232$		0			0
$233$	6.25736	+	10.8381i	0.409933	+	0.710025i	0.994882	−	0.101045i	$-0.0322187\pi$
$233$	6.25736	+	10.8381i	0.409933	+	0.710025i	−0.584949	+	0.811070i	$0.698885\pi$
$234$		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	0.496548	−	0.868009i	$-0.334601\pi$
$239$	−0.106602	−	0.0615465i	−0.00689549	−	0.00398111i	−0.503444	+	0.864028i	$0.667934\pi$
$240$		0			0
$241$		−	0.297173i		−	0.0191426i	−0.999954	−	0.00957130i	$-0.996953\pi$
$241$		−	0.297173i		−	0.0191426i	0.999954	−	0.00957130i	$-0.00304668\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$		0			0
$245$	−4.86396	−	1.25024i	−0.310747	−	0.0798748i
$246$		0			0
$247$			4.18154i			0.266065i
$248$		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
$255$		−	3.93535i		−	0.246441i
$256$		0			0
$257$		−	25.3864i		−	1.58356i	−0.610806	−	0.791781i	$-0.709154\pi$
$257$		−	25.3864i		−	1.58356i	0.610806	−	0.791781i	$-0.290846\pi$
$258$		0			0
$259$	−3.24264	+	7.94282i	−0.201488	+	0.493543i
$260$		0			0
$261$	3.72792			0.230753
$262$		0			0
$263$		−	13.9795i		−	0.862013i	−0.902349	−	0.431006i	$-0.858159\pi$
$263$		−	13.9795i		−	0.862013i	0.902349	−	0.431006i	$-0.141841\pi$
$264$		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	−0.223789	−	0.974638i	$-0.571843\pi$
$269$	−19.3492	−	11.1713i	−1.17974	−	0.681126i	−0.955955	+	0.293512i	$0.905176\pi$
$270$		0			0
$271$	5.86396	+	10.1567i	0.356210	+	0.616974i	0.987324	−	0.158716i	$-0.0507354\pi$
$271$	5.86396	+	10.1567i	0.356210	+	0.616974i	−0.631114	+	0.775690i	$0.717402\pi$
$272$		0			0
$273$	11.7426	+	15.1427i	0.710697	+	0.916478i
$274$		0			0
$275$		−	7.76874i		−	0.468472i
$276$		0			0
$277$	−11.7279			−0.704663			−0.352331	−	0.935875i	$-0.614611\pi$
$277$	−11.7279			−0.704663			−0.352331	+	0.935875i	$0.614611\pi$
$278$		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
$283$	−2.75736	−	4.77589i	−0.163908	−	0.283897i	0.772359	−	0.635186i	$-0.219077\pi$
$283$	−2.75736	−	4.77589i	−0.163908	−	0.283897i	−0.936267	+	0.351289i	$0.885743\pi$
$284$		0			0
$285$	−0.621320	+	1.07616i	−0.0368038	+	0.0637461i
$286$		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	0.00901553	−	0.999959i	$-0.497130\pi$
$293$	−14.5919	−	8.42463i	−0.852467	−	0.492172i	−0.861482	+	0.507787i	$0.830464\pi$
$294$		0			0
$295$	3.72792	−	2.15232i	0.217048	−	0.125313i
$296$		0			0
$297$	−9.00000			−0.522233
$298$		0			0
$299$	−5.74264	+	9.94655i	−0.332105	+	0.575224i
$300$		0			0
$301$	−16.2426	−	6.63103i	−0.936210	−	0.382206i
$302$		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
$311$	−11.4853	−	19.8931i	−0.651271	−	1.12803i	−0.982815	−	0.184594i	$-0.940903\pi$
$311$	−11.4853	−	19.8931i	−0.651271	−	1.12803i	0.331544	−	0.943440i	$-0.392430\pi$
$312$		0			0
$313$	−1.24264	−	0.717439i	−0.0702382	−	0.0405520i	0.464470	−	0.885589i	$-0.346245\pi$
$313$	−1.24264	−	0.717439i	−0.0702382	−	0.0405520i	−0.534708	+	0.845037i	$0.679578\pi$
$314$		0			0
$315$	0.772078	+	5.64191i	0.0435017	+	0.317886i
$316$		0			0
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$		0			0
$319$	1.86396	−	1.07616i	0.104362	−	0.0602533i
$320$		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
$327$		−	15.1682i		−	0.838803i
$328$		0			0
$329$	22.2426	−	3.04384i	1.22628	−	0.167812i
$330$		0			0
$331$	−9.51472	−	5.49333i	−0.522976	−	0.301940i	0.215175	−	0.976575i	$-0.430968\pi$
$331$	−9.51472	−	5.49333i	−0.522976	−	0.301940i	−0.738152	+	0.674635i	$0.764301\pi$
$332$		0			0
$333$	9.72792			0.533087
$334$		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
$339$		−	19.8931i		−	1.08044i
$340$		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
$347$	24.0000	−	13.8564i	1.28839	−	0.743851i	0.310021	−	0.950730i	$-0.399664\pi$
$347$	24.0000	−	13.8564i	1.28839	−	0.743851i	0.978367	+	0.206879i	$0.0663306\pi$
$348$		0			0
$349$	−2.37868	+	1.37333i	−0.127328	+	0.0735127i	−0.562311	−	0.826926i	$-0.690088\pi$
$349$	−2.37868	+	1.37333i	−0.127328	+	0.0735127i	0.434983	+	0.900439i	$0.356754\pi$
$350$		0			0
$351$	10.8640	−	18.8169i	0.579875	−	1.00437i
$352$		0			0
$353$			6.63103i			0.352934i	0.984307	+	0.176467i	$0.0564669\pi$
$353$			6.63103i			0.352934i	−0.984307	+	0.176467i	$0.943533\pi$
$354$		0			0
$355$	9.51472			0.504989
$356$		0			0
$357$	−8.89340	−	11.4685i	−0.470689	−	0.606975i
$358$		0			0
$359$	−5.37868	+	3.10538i	−0.283876	+	0.163896i	−0.635177	−	0.772367i	$-0.719073\pi$
$359$	−5.37868	+	3.10538i	−0.283876	+	0.163896i	0.351301	+	0.936263i	$0.385739\pi$
$360$		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
$367$	−6.27208			−0.327400			−0.163700	−	0.986510i	$-0.552343\pi$
$367$	−6.27208			−0.327400			−0.163700	+	0.986510i	$0.552343\pi$
$368$		0			0
$369$	26.2279	−	15.1427i	1.36537	−	0.788297i
$370$		0			0
$371$	−3.25736	+	0.445759i	−0.169114	+	0.0231427i
$372$		0			0
$373$	35.7279			1.84992			0.924961	−	0.380062i	$-0.124097\pi$
$373$	35.7279			1.84992			0.924961	+	0.380062i	$0.124097\pi$
$374$		0			0
$375$	5.89340	+	10.2077i	0.304334	+	0.527122i
$376$		0			0
$377$			5.19615i			0.267615i
$378$		0			0
$379$		−	2.02922i		−	0.104234i	−0.998641	−	0.0521171i	$-0.983403\pi$
$379$		−	2.02922i		−	0.104234i	0.998641	−	0.0521171i	$-0.0165969\pi$
$380$		0			0
$381$	−0.514719	−	0.891519i	−0.0263698	−	0.0456739i
$382$		0			0
$383$	−19.2426			−0.983253			−0.491627	−	0.870806i	$-0.663597\pi$
$383$	−19.2426			−0.983253			−0.491627	+	0.870806i	$0.663597\pi$
$384$		0			0
$385$	2.01472	+	2.59808i	0.102680	+	0.132410i
$386$		0			0
$387$			19.8931i			1.01122i
$388$		0			0
$389$	28.7574			1.45806			0.729028	−	0.684484i	$-0.239972\pi$
$389$	28.7574			1.45806			0.729028	+	0.684484i	$0.239972\pi$
$390$		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	−0.689608	+	0.724183i	$0.742217\pi$
$397$	−33.1066	+	19.1141i	−1.66157	+	0.959309i	−0.971965	+	0.235127i	$0.924450\pi$
$398$		0			0
$399$	0.621320	+	4.54026i	0.0311049	+	0.227297i
$400$		0			0
$401$	34.4558			1.72064			0.860321	−	0.509752i	$-0.170263\pi$
$401$	34.4558			1.72064			0.860321	+	0.509752i	$0.170263\pi$
$402$		0			0
$403$		−	16.7262i		−	0.833189i
$404$		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
$409$	−10.7574	+	6.21076i	−0.531917	+	0.307103i	−0.741797	−	0.670625i	$-0.766026\pi$
$409$	−10.7574	+	6.21076i	−0.531917	+	0.307103i	0.209880	+	0.977727i	$0.432693\pi$
$410$		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
$417$			22.5167i			1.10265i
$418$		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
$423$	−12.7279	−	22.0454i	−0.618853	−	1.07188i
$424$		0			0
$425$	−12.3015	−	7.10228i	−0.596711	−	0.344511i
$426$		0			0
$427$	2.48528	+	18.1610i	0.120271	+	0.878874i
$428$		0			0
$429$		−	12.5446i		−	0.605660i
$430$		0			0
$431$	33.8345	+	19.5344i	1.62975	+	0.940938i	0.984166	+	0.177250i	$0.0567200\pi$
$431$	33.8345	+	19.5344i	1.62975	+	0.940938i	0.645586	+	0.763688i	$0.276613\pi$
$432$		0			0
$433$		−	13.2621i		−	0.637334i	−0.947867	−	0.318667i	$-0.896765\pi$
$433$		−	13.2621i		−	0.637334i	0.947867	−	0.318667i	$-0.103235\pi$
$434$		0			0
$435$	−0.772078	+	1.33728i	−0.0370183	+	0.0641176i
$436$		0			0
$437$	−2.37868	+	1.37333i	−0.113788	+	0.0656953i
$438$		0			0
$439$	13.4853	−	23.3572i	0.643617	−	1.11478i	−0.341002	−	0.940063i	$-0.610766\pi$
$439$	13.4853	−	23.3572i	0.643617	−	1.11478i	0.984619	−	0.174715i	$-0.0559005\pi$
$440$		0			0
$441$	15.0000	+	14.6969i	0.714286	+	0.699854i
$442$		0			0
$443$	7.75736	+	4.47871i	0.368563	+	0.212790i	0.672831	−	0.739797i	$-0.265078\pi$
$443$	7.75736	+	4.47871i	0.368563	+	0.212790i	−0.304267	+	0.952587i	$0.598412\pi$
$444$		0			0
$445$	−5.89340	−	10.2077i	−0.279374	−	0.483890i
$446$		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
$455$	−7.86396	+	1.07616i	−0.368668	+	0.0504511i
$456$		0			0
$457$	19.4853	−	33.7495i	0.911483	−	1.57873i	0.0995126	−	0.995036i	$-0.468272\pi$
$457$	19.4853	−	33.7495i	0.911483	−	1.57873i	0.811970	−	0.583699i	$-0.198395\pi$
$458$		0			0
$459$	−8.22792	+	14.2512i	−0.384047	+	0.665188i
$460$		0			0
$461$	22.8640	−	13.2005i	1.06488	−	0.614809i	0.138102	−	0.990418i	$-0.455900\pi$
$461$	22.8640	−	13.2005i	1.06488	−	0.614809i	0.926778	+	0.375609i	$0.122566\pi$
$462$		0			0
$463$	11.3787	+	6.56948i	0.528812	+	0.305310i	0.740533	−	0.672020i	$-0.234573\pi$
$463$	11.3787	+	6.56948i	0.528812	+	0.305310i	−0.211720	+	0.977330i	$0.567907\pi$
$464$		0			0
$465$	2.48528	−	4.30463i	0.115252	−	0.199623i
$466$		0			0
$467$	11.7426	+	20.3389i	0.543385	+	0.941170i	0.998707	+	0.0508429i	$0.0161908\pi$
$467$	11.7426	+	20.3389i	0.543385	+	0.941170i	−0.455322	+	0.890327i	$0.650476\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.75736	+	3.04384i	−0.0809748	+	0.140253i
$472$		0			0
$473$	5.74264	+	9.94655i	0.264047	+	0.457343i
$474$		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
$479$	7.24264			0.330925			0.165462	−	0.986216i	$-0.447088\pi$
$479$	7.24264			0.330925			0.165462	+	0.986216i	$0.447088\pi$
$480$		0			0
$481$			13.5592i			0.618248i
$482$		0			0
$483$	−4.75736	+	11.6531i	−0.216467	+	0.530235i
$484$		0			0
$485$	2.37868	+	4.11999i	0.108010	+	0.187079i
$486$		0			0
$487$	11.8934	+	6.86666i	0.538941	+	0.311158i	0.744650	−	0.667455i	$-0.232617\pi$
$487$	11.8934	+	6.86666i	0.538941	+	0.311158i	−0.205708	+	0.978613i	$0.565950\pi$
$488$		0			0
$489$	−0.257359	+	0.445759i	−0.0116382	+	0.0201579i
$490$		0			0
$491$	12.9853	+	7.49706i	0.586018	+	0.338337i	0.763521	−	0.645783i	$-0.223469\pi$
$491$	12.9853	+	7.49706i	0.586018	+	0.338337i	−0.177504	+	0.984120i	$0.556802\pi$
$492$		0			0
$493$		−	3.93535i		−	0.177239i
$494$		0			0
$495$	1.86396	−	3.22848i	0.0837788	−	0.145109i
$496$		0			0
$497$	27.7279	−	21.5020i	1.24377	−	0.964499i
$498$		0			0
$499$		−	33.7495i		−	1.51083i	−0.655244	−	0.755417i	$-0.727434\pi$
$499$		−	33.7495i		−	1.51083i	0.655244	−	0.755417i	$-0.272566\pi$
$500$		0			0
$501$			27.2416i			1.21706i
$502$		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
$509$		−	8.48617i		−	0.376143i	−0.982155	−	0.188072i	$-0.939776\pi$
$509$		−	8.48617i		−	0.376143i	0.982155	−	0.188072i	$-0.0602237\pi$
$510$		0			0
$511$	−3.10660	−	22.7013i	−0.137428	−	1.00425i
$512$		0			0
$513$	4.50000	−	2.59808i	0.198680	−	0.114708i
$514$		0			0
$515$		−	8.41407i		−	0.370768i
$516$		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	0.655211	−	0.755446i	$-0.272580\pi$
$521$	7.50000	+	4.33013i	0.328581	+	0.189706i	−0.326630	+	0.945152i	$0.605913\pi$
$522$		0			0
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	0.854887	−	0.518815i	$-0.173627\pi$
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	−0.876750	+	0.480946i	$0.840293\pi$
$524$		0			0
$525$	19.0294	+	7.76874i	0.830513	+	0.339055i
$526$		0			0
$527$			12.6677i			0.551814i
$528$		0			0
$529$	15.4558			0.671993
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$	21.1066	+	36.5577i	0.914228	+	1.58349i
$534$		0			0
$535$	−4.13604	−	7.16383i	−0.178817	−	0.309719i
$536$		0			0
$537$	−1.97056			−0.0850361
$538$		0			0
$539$	11.7426	+	3.01834i	0.505791	+	0.130009i
$540$		0			0
$541$	22.1066	+	38.2898i	0.950437	+	1.64621i	0.744481	+	0.667644i	$0.232697\pi$
$541$	22.1066	+	38.2898i	0.950437	+	1.64621i	0.205956	+	0.978561i	$0.433969\pi$
$542$		0			0
$543$	11.4853	+	19.8931i	0.492881	+	0.853694i
$544$		0			0
$545$	5.44113	+	3.14144i	0.233072	+	0.134564i
$546$		0			0
$547$	23.2279	−	13.4106i	0.993154	−	0.573398i	0.0869386	−	0.996214i	$-0.472292\pi$
$547$	23.2279	−	13.4106i	0.993154	−	0.573398i	0.906216	+	0.422816i	$0.138958\pi$
$548$		0			0
$549$	18.0000	−	10.3923i	0.768221	−	0.443533i
$550$		0			0
$551$	−0.621320	+	1.07616i	−0.0264691	+	0.0458459i
$552$		0			0
$553$	0.727922	+	5.31925i	0.0309544	+	0.226197i
$554$		0			0
$555$	−2.01472	+	3.48960i	−0.0855200	+	0.148125i
$556$		0			0
$557$	9.10660	−	15.7731i	0.385859	−	0.668328i	−0.606029	−	0.795443i	$-0.707238\pi$
$557$	9.10660	−	15.7731i	0.385859	−	0.668328i	0.991888	+	0.127115i	$0.0405718\pi$
$558$		0			0
$559$	−27.7279			−1.17277
$560$		0			0
$561$			9.50079i			0.401124i
$562$		0			0
$563$	−0.514719	−	0.891519i	−0.0216928	−	0.0375730i	0.854975	−	0.518669i	$-0.173572\pi$
$563$	−0.514719	−	0.891519i	−0.0216928	−	0.0375730i	−0.876668	+	0.481096i	$0.840239\pi$
$564$		0			0
$565$	7.13604	+	4.11999i	0.300215	+	0.173329i
$566$		0			0
$567$	9.00000	−	22.0454i	0.377964	−	0.925820i
$568$		0			0
$569$	−11.4853	+	19.8931i	−0.481488	+	0.833962i	−0.999774	−	0.0212455i	$-0.993237\pi$
$569$	−11.4853	+	19.8931i	−0.481488	+	0.833962i	0.518286	+	0.855207i	$0.326570\pi$
$570$		0			0
$571$	27.9411	−	16.1318i	1.16930	−	0.675096i	0.215785	−	0.976441i	$-0.430769\pi$
$571$	27.9411	−	16.1318i	1.16930	−	0.675096i	0.953515	+	0.301345i	$0.0974357\pi$
$572$		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	0.230047	−	0.973180i	$-0.426112\pi$
$577$	−11.9558	−	6.90271i	−0.497728	−	0.287364i	−0.727775	+	0.685816i	$0.759445\pi$
$578$		0			0
$579$	−31.4558	−	18.1610i	−1.30726	−	0.754747i
$580$		0			0
$581$	11.4853	−	28.1331i	0.476490	−	1.16716i
$582$		0			0
$583$	1.86396	+	1.07616i	0.0771974	+	0.0445699i
$584$		0			0
$585$	4.50000	+	7.79423i	0.186052	+	0.322252i
$586$		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
$591$	−21.7279	+	12.5446i	−0.893767	+	0.516017i
$592$		0			0
$593$	−11.2279	+	6.48244i	−0.461075	+	0.266202i	−0.712496	−	0.701676i	$-0.752436\pi$
$593$	−11.2279	+	6.48244i	−0.461075	+	0.266202i	0.251421	+	0.967878i	$0.419102\pi$
$594$		0			0
$595$	5.95584	−	0.815039i	0.244166	−	0.0334133i
$596$		0			0
$597$		−	34.1698i		−	1.39848i
$598$		0			0
$599$	−6.51472	+	3.76127i	−0.266184	+	0.153682i	−0.627152	−	0.778897i	$-0.715780\pi$
$599$	−6.51472	+	3.76127i	−0.266184	+	0.153682i	0.360968	+	0.932578i	$0.382446\pi$
$600$		0			0
$601$	−21.9853	+	12.6932i	−0.896798	+	0.517767i	−0.876160	−	0.482020i	$-0.839903\pi$
$601$	−21.9853	+	12.6932i	−0.896798	+	0.517767i	−0.0206383	+	0.999787i	$0.506570\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$			5.73951i			0.233344i
$606$		0			0
$607$	34.6985			1.40837			0.704184	−	0.710018i	$-0.251313\pi$
$607$	34.6985			1.40837			0.704184	+	0.710018i	$0.251313\pi$
$608$		0			0
$609$	0.772078	+	5.64191i	0.0312862	+	0.228622i
$610$		0			0
$611$	30.7279	−	17.7408i	1.24312	−	0.717715i
$612$		0			0
$613$	−1.62132	+	2.80821i	−0.0654845	+	0.113423i	−0.896909	−	0.442216i	$-0.854193\pi$
$613$	−1.62132	+	2.80821i	−0.0654845	+	0.113423i	0.831424	+	0.555638i	$0.187526\pi$
$614$		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
$619$	2.02944			0.0815700			0.0407850	−	0.999168i	$-0.487014\pi$
$619$	2.02944			0.0815700			0.0407850	+	0.999168i	$0.487014\pi$
$620$		0			0
$621$	14.2721			0.572719
$622$		0			0
$623$	−40.2426	−	16.4290i	−1.61229	−	0.658214i
$624$		0			0
$625$	17.5442			0.701766
$626$		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	$-0.901555\pi$
$631$		−	15.2913i		−	0.608736i	0.952554	−	0.304368i	$-0.0984453\pi$
$632$		0			0
$633$	−29.4853			−1.17193
$634$		0			0
$635$	0.426407			0.0169214
$636$		0			0
$637$	−20.4853	+	20.9077i	−0.811656	+	0.828393i
$638$		0			0
$639$	−34.4558	−	19.8931i	−1.36305	−	0.786959i
$640$		0			0
$641$	36.9411			1.45909			0.729543	−	0.683935i	$-0.239733\pi$
$641$	36.9411			1.45909			0.729543	+	0.683935i	$0.239733\pi$
$642$		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	−0.978180	−	0.207760i	$-0.933383\pi$
$647$	−7.86396	+	13.6208i	−0.309164	+	0.535488i	0.669016	+	0.743248i	$0.266716\pi$
$648$		0			0
$649$	−9.00000	+	5.19615i	−0.353281	+	0.203967i
$650$		0			0
$651$	−2.48528	−	18.1610i	−0.0974059	−	0.711787i
$652$		0			0
$653$	−43.2426			−1.69222			−0.846108	−	0.533012i	$-0.821060\pi$
$653$	−43.2426			−1.69222			−0.846108	+	0.533012i	$0.821060\pi$
$654$		0			0
$655$		−	12.5446i		−	0.490159i
$656$		0			0
$657$	−22.5000	+	12.9904i	−0.877809	+	0.506803i
$658$		0			0
$659$	−21.4706	+	12.3960i	−0.836374	+	0.482881i	−0.856030	−	0.516926i	$-0.827076\pi$
$659$	−21.4706	+	12.3960i	−0.836374	+	0.482881i	0.0196558	+	0.999807i	$0.493743\pi$
$660$		0			0
$661$	37.4558	−	21.6251i	1.45686	−	0.841121i	0.458008	−	0.888948i	$-0.348563\pi$
$661$	37.4558	−	21.6251i	1.45686	−	0.841121i	0.998856	+	0.0478276i	$0.0152298\pi$
$662$		0			0
$663$	−19.8640	−	11.4685i	−0.771452	−	0.445398i
$664$		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
$675$		−	23.3062i		−	0.897056i
$676$		0			0
$677$	6.72792	+	3.88437i	0.258575	+	0.149288i	0.623684	−	0.781676i	$-0.285635\pi$
$677$	6.72792	+	3.88437i	0.258575	+	0.149288i	−0.365109	+	0.930965i	$0.618968\pi$
$678$		0			0
$679$	16.2426	+	6.63103i	0.623335	+	0.254476i
$680$		0			0
$681$	26.2279	−	15.1427i	1.00506	−	0.580269i
$682$		0			0
$683$	14.0147	+	8.09140i	0.536258	+	0.309609i	0.743561	−	0.668668i	$-0.233135\pi$
$683$	14.0147	+	8.09140i	0.536258	+	0.309609i	−0.207303	+	0.978277i	$0.566469\pi$
$684$		0			0
$685$			6.45695i			0.246707i
$686$		0			0
$687$	17.3787	+	30.1008i	0.663038	+	1.14842i
$688$		0			0
$689$	−4.50000	+	2.59808i	−0.171436	+	0.0989788i
$690$		0			0
$691$	11.9706	−	20.7336i	0.455382	−	0.788744i	−0.543328	−	0.839520i	$-0.682836\pi$
$691$	11.9706	−	20.7336i	0.455382	−	0.788744i	0.998710	+	0.0507761i	$0.0161695\pi$
$692$		0			0
$693$	−1.86396	−	13.6208i	−0.0708060	−	0.517411i
$694$		0			0
$695$	−8.07716	−	4.66335i	−0.306384	−	0.176891i
$696$		0			0
$697$	−15.9853	−	27.6873i	−0.605486	−	1.04873i
$698$		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
$705$	10.5442			0.397116
$706$		0			0
$707$	−8.74264	+	6.77962i	−0.328801	+	0.254974i
$708$		0			0
$709$	−14.2426	+	24.6690i	−0.534894	+	0.926463i	0.464275	+	0.885691i	$0.346315\pi$
$709$	−14.2426	+	24.6690i	−0.534894	+	0.926463i	−0.999168	+	0.0407717i	$0.987018\pi$
$710$		0			0
$711$	5.27208	−	3.04384i	0.197718	−	0.114153i
$712$		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
$717$	−0.213203			−0.00796223
$718$		0			0
$719$	24.6213	+	42.6454i	0.918220	+	1.59040i	0.802117	+	0.597167i	$0.203707\pi$
$719$	24.6213	+	42.6454i	0.918220	+	1.59040i	0.116103	+	0.993237i	$0.462960\pi$
$720$		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
$725$	2.78680	+	4.82687i	0.103499	+	0.179266i
$726$		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
$731$	21.0000			0.776713
$732$		0			0
$733$			44.3159i			1.63684i	0.574617	+	0.818422i	$0.305151\pi$
$733$			44.3159i			1.63684i	−0.574617	+	0.818422i	$0.694849\pi$
$734$		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	−0.0936386	−	0.995606i	$-0.529850\pi$
$739$	−27.2574	−	15.7370i	−1.00268	−	0.578897i	−0.909040	+	0.416710i	$0.863183\pi$
$740$		0			0
$741$	3.62132	+	6.27231i	0.133033	+	0.230419i
$742$		0			0
$743$	13.1360	+	7.58410i	0.481915	+	0.278233i	0.721214	−	0.692712i	$-0.243584\pi$
$743$	13.1360	+	7.58410i	0.481915	+	0.278233i	−0.239299	+	0.970946i	$0.576918\pi$
$744$		0			0
$745$		−	13.8054i		−	0.505791i
$746$		0			0
$747$	−34.4558			−1.26067
$748$		0			0
$749$	−28.2426	−	11.5300i	−1.03196	−	0.421297i
$750$		0			0
$751$		−	36.1990i		−	1.32092i	−0.750861	−	0.660460i	$-0.770361\pi$
$751$		−	36.1990i		−	1.32092i	0.750861	−	0.660460i	$-0.229639\pi$
$752$		0			0
$753$	−39.7279	+	22.9369i	−1.44777	+	0.835868i
$754$		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
$759$	7.13604	−	4.11999i	0.259022	−	0.149546i
$760$		0			0
$761$		−	23.9515i		−	0.868243i	−0.900854	−	0.434121i	$-0.857059\pi$
$761$		−	23.9515i		−	0.868243i	0.900854	−	0.434121i	$-0.142941\pi$
$762$		0			0
$763$	22.9558	−	3.14144i	0.831057	−	0.113728i
$764$		0			0
$765$	−3.40812	−	5.90303i	−0.123221	−	0.213425i
$766$		0			0
$767$		−	25.0892i		−	0.905920i
$768$		0			0
$769$	−25.1985	−	14.5484i	−0.908681	−	0.524627i	−0.0286742	−	0.999589i	$-0.509129\pi$
$769$	−25.1985	−	14.5484i	−0.908681	−	0.524627i	−0.880006	+	0.474962i	$0.842462\pi$
$770$		0			0
$771$	−21.9853	−	38.0796i	−0.791781	−	1.37140i
$772$		0			0
$773$	1.34924	+	0.778985i	0.0485289	+	0.0280182i	0.524068	−	0.851676i	$-0.324414\pi$
$773$	1.34924	+	0.778985i	0.0485289	+	0.0280182i	−0.475539	+	0.879694i	$0.657747\pi$
$774$		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
$779$			10.0951i			0.361696i
$780$		0			0
$781$	−22.9706			−0.821951
$782$		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
$787$	5.24264	+	9.08052i	0.186880	+	0.323686i	0.944208	−	0.329349i	$-0.106829\pi$
$787$	5.24264	+	9.08052i	0.186880	+	0.323686i	−0.757328	+	0.653034i	$0.773496\pi$
$788$		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
$795$	−1.54416			−0.0547656
$796$		0			0
$797$	−6.10660	−	3.52565i	−0.216307	−	0.124885i	0.387932	−	0.921688i	$-0.373189\pi$
$797$	−6.10660	−	3.52565i	−0.216307	−	0.124885i	−0.604239	+	0.796803i	$0.706523\pi$
$798$		0			0
$799$	−23.2721	+	13.4361i	−0.823307	+	0.475336i
$800$		0			0
$801$			49.2870i			1.74147i
$802$		0			0
$803$	−7.50000	+	12.9904i	−0.264669	+	0.458421i
$804$		0			0
$805$	−3.19491	−	4.11999i	−0.112606	−	0.145211i
$806$		0			0
$807$	−38.6985			−1.36225
$808$		0			0
$809$	15.9853	−	27.6873i	0.562013	−	0.973434i	−0.435308	−	0.900282i	$-0.643361\pi$
$809$	15.9853	−	27.6873i	0.562013	−	0.973434i	0.997321	−	0.0731528i	$-0.0233061\pi$
$810$		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
$815$	−0.106602	−	0.184640i	−0.00373410	−	0.00646764i
$816$		0			0
$817$	−5.74264	−	3.31552i	−0.200910	−	0.115995i
$818$		0			0
$819$	30.7279	+	12.5446i	1.07372	+	0.438345i
$820$		0			0
$821$	−24.7279	+	42.8300i	−0.863010	+	1.49478i	0.00599878	+	0.999982i	$0.498091\pi$
$821$	−24.7279	+	42.8300i	−0.863010	+	1.49478i	−0.869009	+	0.494796i	$0.835243\pi$
$822$		0			0
$823$	−42.2132	+	24.3718i	−1.47146	+	0.849548i	−0.999486	−	0.0320648i	$-0.989792\pi$
$823$	−42.2132	+	24.3718i	−1.47146	+	0.849548i	−0.471974	+	0.881612i	$0.656458\pi$
$824$		0			0
$825$	−6.72792	−	11.6531i	−0.234236	−	0.405709i
$826$		0			0
$827$			21.6251i			0.751980i	0.926624	+	0.375990i	$0.122697\pi$
$827$			21.6251i			0.751980i	−0.926624	+	0.375990i	$0.877303\pi$
$828$		0			0
$829$	−18.8345	−	10.8741i	−0.654150	−	0.377674i	0.135894	−	0.990723i	$-0.456609\pi$
$829$	−18.8345	−	10.8741i	−0.654150	−	0.377674i	−0.790044	+	0.613050i	$0.789943\pi$
$830$		0			0
$831$	−17.5919	+	10.1567i	−0.610256	+	0.352331i
$832$		0			0
$833$	15.5147	−	15.8346i	0.537553	−	0.548638i
$834$		0			0
$835$	−9.77208	−	5.64191i	−0.338177	−	0.195246i
$836$		0			0
$837$	−18.0000	+	10.3923i	−0.622171	+	0.359211i
$838$		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
$849$	−8.27208	−	4.77589i	−0.283897	−	0.163908i
$850$		0			0
$851$	−7.71320	+	4.45322i	−0.264405	+	0.152654i
$852$		0			0
$853$	−7.86396	+	4.54026i	−0.269257	+	0.155456i	−0.628550	−	0.777769i	$-0.716351\pi$
$853$	−7.86396	+	4.54026i	−0.269257	+	0.155456i	0.359293	+	0.933225i	$0.383018\pi$
$854$		0			0
$855$			2.15232i			0.0736077i
$856$		0			0
$857$			4.60181i			0.157195i	0.996906	+	0.0785974i	$0.0250441\pi$
$857$			4.60181i			0.157195i	−0.996906	+	0.0785974i	$0.974956\pi$
$858$		0			0
$859$	33.9706			1.15906			0.579530	−	0.814951i	$-0.303236\pi$
$859$	33.9706			1.15906			0.579530	+	0.814951i	$0.303236\pi$
$860$		0			0
$861$	28.3492	+	36.5577i	0.966140	+	1.24588i
$862$		0			0
$863$	−5.59188	+	3.22848i	−0.190350	+	0.109899i	−0.592146	−	0.805830i	$-0.701719\pi$
$863$	−5.59188	+	3.22848i	−0.190350	+	0.109899i	0.401796	+	0.915729i	$0.368386\pi$
$864$		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
$873$		−	19.8931i		−	0.673279i
$874$		0			0
$875$	−14.2279	+	11.0333i	−0.480992	+	0.372992i
$876$		0			0
$877$	−12.6985			−0.428797			−0.214399	−	0.976746i	$-0.568779\pi$
$877$	−12.6985			−0.428797			−0.214399	+	0.976746i	$0.568779\pi$
$878$		0			0
$879$	−29.1838			−0.984344
$880$		0			0
$881$			22.2195i			0.748594i	0.927309	+	0.374297i	$0.122116\pi$
$881$			22.2195i			0.748594i	−0.927309	+	0.374297i	$0.877884\pi$
$882$		0			0
$883$			4.89898i			0.164864i	0.996597	+	0.0824319i	$0.0262687\pi$
$883$			4.89898i			0.164864i	−0.996597	+	0.0824319i	$0.973731\pi$
$884$		0			0
$885$	3.72792	−	6.45695i	0.125313	−	0.217048i
$886$		0			0
$887$	−43.6690			−1.46626			−0.733132	−	0.680087i	$-0.761942\pi$
$887$	−43.6690			−1.46626			−0.733132	+	0.680087i	$0.761942\pi$
$888$		0			0
$889$	1.24264	−	0.963625i	0.0416768	−	0.0323189i
$890$		0			0
$891$	−13.5000	+	7.79423i	−0.452267	+	0.261116i
$892$		0			0
$893$	8.48528			0.283949
$894$		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
$903$	−30.1066	+	4.11999i	−1.00188	+	0.137105i
$904$		0			0
$905$	−9.51472			−0.316280
$906$		0			0
$907$			1.13770i			0.0377769i	0.999822	+	0.0188884i	$0.00601273\pi$
$907$			1.13770i			0.0377769i	−0.999822	+	0.0188884i	$0.993987\pi$
$908$		0			0
$909$	10.8640	+	6.27231i	0.360335	+	0.208039i
$910$		0			0
$911$	16.1360	−	9.31615i	0.534611	−	0.308658i	−0.208281	−	0.978069i	$-0.566787\pi$
$911$	16.1360	−	9.31615i	0.534611	−	0.308658i	0.742892	+	0.669411i	$0.233454\pi$
$912$		0			0
$913$	−17.2279	+	9.94655i	−0.570161	+	0.329183i
$914$		0			0
$915$			8.60927i			0.284614i
$916$		0			0
$917$	−28.3492	−	36.5577i	−0.936174	−	1.20724i
$918$		0			0
$919$	−4.13604	+	2.38794i	−0.136435	+	0.0787710i	−0.566664	−	0.823949i	$-0.691766\pi$
$919$	−4.13604	+	2.38794i	−0.136435	+	0.0787710i	0.430229	+	0.902720i	$0.358433\pi$
$920$		0			0
$921$	−27.7279	+	16.0087i	−0.913666	+	0.527505i
$922$		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
$929$	−41.4853	−	23.9515i	−1.36109	−	0.785824i	−0.371319	−	0.928505i	$-0.621094\pi$
$929$	−41.4853	−	23.9515i	−1.36109	−	0.785824i	−0.989769	+	0.142681i	$0.954428\pi$
$930$		0			0
$931$	−6.74264	+	1.88064i	−0.220981	+	0.0616354i
$932$		0			0
$933$	−34.4558	−	19.8931i	−1.12803	−	0.651271i
$934$		0			0
$935$	−3.40812	−	1.96768i	−0.111457	−	0.0643499i
$936$		0			0
$937$		−	52.4539i		−	1.71359i	−0.515654	−	0.856797i	$-0.672451\pi$
$937$		−	52.4539i		−	1.71359i	0.515654	−	0.856797i	$-0.327549\pi$
$938$		0			0
$939$	−2.48528			−0.0811041
$940$		0			0
$941$	31.4558	−	18.1610i	1.02543	−	0.592033i	0.109759	−	0.993958i	$-0.464992\pi$
$941$	31.4558	−	18.1610i	1.02543	−	0.592033i	0.915672	+	0.401925i	$0.131659\pi$
$942$		0			0
$943$	−13.8640	+	24.0131i	−0.451473	+	0.781974i
$944$		0			0
$945$	6.04416	+	7.79423i	0.196616	+	0.253546i
$946$		0			0
$947$	49.9706	+	28.8505i	1.62383	+	0.937516i	0.985884	+	0.167431i	$0.0535471\pi$
$947$	49.9706	+	28.8505i	1.62383	+	0.937516i	0.637941	+	0.770085i	$0.279786\pi$
$948$		0			0
$949$	−18.1066	−	31.3616i	−0.587765	−	1.01804i
$950$		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
$957$	1.86396	−	3.22848i	0.0602533	−	0.104362i
$958$		0			0
$959$	14.5919	+	18.8169i	0.471196	+	0.607630i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$			34.5900i			1.11465i
$964$		0			0
$965$	13.0294	−	7.52255i	0.419432	−	0.242159i
$966$		0			0
$967$	−32.5919	−	18.8169i	−1.04808	−	0.605112i	−0.125972	−	0.992034i	$-0.540205\pi$
$967$	−32.5919	−	18.8169i	−1.04808	−	0.605112i	−0.922112	+	0.386922i	$0.873538\pi$
$968$		0			0
$969$	−2.74264	−	4.75039i	−0.0881063	−	0.152605i
$970$		0			0
$971$	6.25736	+	10.8381i	0.200808	+	0.347810i	0.948789	−	0.315910i	$-0.102310\pi$
$971$	6.25736	+	10.8381i	0.200808	+	0.347810i	−0.747981	+	0.663720i	$0.768977\pi$
$972$		0			0
$973$	−34.0772	+	4.66335i	−1.09246	+	0.149500i
$974$		0			0
$975$	32.4853			1.04036
$976$		0			0
$977$	8.48528	+	14.6969i	0.271468	+	0.470197i	0.969238	−	0.246125i	$-0.0791575\pi$
$977$	8.48528	+	14.6969i	0.271468	+	0.470197i	−0.697770	+	0.716322i	$0.745824\pi$
$978$		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
$983$	−25.2426			−0.805115			−0.402558	−	0.915395i	$-0.631879\pi$
$983$	−25.2426			−0.805115			−0.402558	+	0.915395i	$0.631879\pi$
$984$		0			0
$985$		−	10.3923i		−	0.331126i
$986$		0			0
$987$	30.7279	−	23.8284i	0.978081	−	0.758468i
$988$		0			0
$989$	−9.10660	−	15.7731i	−0.289573	−	0.501555i
$990$		0			0
$991$	−25.1360	−	14.5123i	−0.798473	−	0.460998i	0.0444642	−	0.999011i	$-0.485842\pi$
$991$	−25.1360	−	14.5123i	−0.798473	−	0.460998i	−0.842937	+	0.538013i	$0.819175\pi$
$992$		0			0
$993$	−19.0294			−0.603881
$994$		0			0
$995$	12.2574	+	7.07679i	0.388584	+	0.224349i
$996$		0			0
$997$		−	9.08052i		−	0.287583i	−0.989608	−	0.143791i	$-0.954071\pi$
$997$		−	9.08052i		−	0.287583i	0.989608	−	0.143791i	$-0.0459295\pi$
$998$		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.bf.f.31.2	yes	4
3.2	odd	2		3024.2.bf.e.1711.1		4
4.3	odd	2		1008.2.bf.e.31.2	✓	4
7.5	odd	6		1008.2.cz.e.607.1	yes	4
9.2	odd	6		3024.2.cz.f.2719.2		4
9.7	even	3		1008.2.cz.f.367.1	yes	4
12.11	even	2		3024.2.bf.f.1711.1		4
21.5	even	6		3024.2.cz.e.1279.2		4
28.19	even	6		1008.2.cz.f.607.1	yes	4
36.7	odd	6		1008.2.cz.e.367.1	yes	4
36.11	even	6		3024.2.cz.e.2719.2		4
63.47	even	6		3024.2.bf.f.2287.2		4
63.61	odd	6		1008.2.bf.e.943.1	yes	4
84.47	odd	6		3024.2.cz.f.1279.2		4
252.47	odd	6		3024.2.bf.e.2287.2		4
252.187	even	6	inner	1008.2.bf.f.943.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.e.31.2	✓	4	4.3	odd	2
1008.2.bf.e.943.1	yes	4	63.61	odd	6
1008.2.bf.f.31.2	yes	4	1.1	even	1	trivial
1008.2.bf.f.943.1	yes	4	252.187	even	6	inner
1008.2.cz.e.367.1	yes	4	36.7	odd	6
1008.2.cz.e.607.1	yes	4	7.5	odd	6
1008.2.cz.f.367.1	yes	4	9.7	even	3
1008.2.cz.f.607.1	yes	4	28.19	even	6
3024.2.bf.e.1711.1		4	3.2	odd	2
3024.2.bf.e.2287.2		4	252.47	odd	6
3024.2.bf.f.1711.1		4	12.11	even	2
3024.2.bf.f.2287.2		4	63.47	even	6
3024.2.cz.e.1279.2		4	21.5	even	6
3024.2.cz.e.2719.2		4	36.11	even	6
3024.2.cz.f.1279.2		4	84.47	odd	6
3024.2.cz.f.2719.2		4	9.2	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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +0.717439i q^{5} +(1.62132 + 2.09077i) q^{7} +(1.50000 - 2.59808i) q^{9} -1.73205i q^{11} +(3.62132 + 2.09077i) q^{13} +(0.621320 + 1.07616i) q^{15} +(-2.74264 - 1.58346i) q^{17} +(0.500000 + 0.866025i) q^{19} +(4.24264 + 1.73205i) q^{21} +2.74666i q^{23} +4.48528 q^{25} -5.19615i q^{27} +(0.621320 + 1.07616i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-1.50000 - 2.59808i) q^{33} +(-1.50000 + 1.16320i) q^{35} +(1.62132 + 2.80821i) q^{37} +7.24264 q^{39} +(8.74264 + 5.04757i) q^{41} +(-5.74264 + 3.31552i) q^{43} +(1.86396 + 1.07616i) q^{45} +(4.24264 - 7.34847i) q^{47} +(-1.74264 + 6.77962i) q^{49} -5.48528 q^{51} +(-0.621320 + 1.07616i) q^{53} +1.24264 q^{55} +(1.50000 + 0.866025i) q^{57} +(-3.00000 - 5.19615i) q^{59} +(6.00000 + 3.46410i) q^{61} +(7.86396 - 1.07616i) q^{63} +(-1.50000 + 2.59808i) q^{65} +(2.37868 + 4.11999i) q^{69} -13.2621i q^{71} +(-7.50000 - 4.33013i) q^{73} +(6.72792 - 3.88437i) q^{75} +(3.62132 - 2.80821i) q^{77} +(1.75736 + 1.01461i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-5.74264 - 9.94655i) q^{83} +(1.13604 - 1.96768i) q^{85} +(1.86396 + 1.07616i) q^{87} +(-14.2279 + 8.21449i) q^{89} +(1.50000 + 10.9612i) q^{91} +(-6.00000 - 3.46410i) q^{93} +(-0.621320 + 0.358719i) q^{95} +(5.74264 - 3.31552i) q^{97} +(-4.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 2 q^{7} + 6 q^{9} + 6 q^{13} - 6 q^{15} + 6 q^{17} + 2 q^{19} - 16 q^{25} - 6 q^{29} - 8 q^{31} - 6 q^{33} - 6 q^{35} - 2 q^{37} + 12 q^{39} + 18 q^{41} - 6 q^{43} - 18 q^{45} + 10 q^{49}+ \cdots - 18 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 2 * q^7 + 6 * q^9 + 6 * q^13 - 6 * q^15 + 6 * q^17 + 2 * q^19 - 16 * q^25 - 6 * q^29 - 8 * q^31 - 6 * q^33 - 6 * q^35 - 2 * q^37 + 12 * q^39 + 18 * q^41 - 6 * q^43 - 18 * q^45 + 10 * q^49 + 12 * q^51 + 6 * q^53 - 12 * q^55 + 6 * q^57 - 12 * q^59 + 24 * q^61 + 6 * q^63 - 6 * q^65 + 18 * q^69 - 30 * q^73 - 24 * q^75 + 6 * q^77 + 24 * q^79 - 18 * q^81 - 6 * q^83 + 30 * q^85 - 18 * q^87 - 6 * q^89 + 6 * q^91 - 24 * q^93 + 6 * q^95 + 6 * q^97 - 18 * q^99

Introduction

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