LMFDB - Embedded newform 1008.2.df.e.929.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(689,1008)]

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([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("1008.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			929.11
Character	$\chi$	$=$	1008.929
Dual form			1008.2.df.e.689.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.310783 - 1.70394i) q^{3} +2.76937 q^{5} +(1.21939 - 2.34800i) q^{7} +(-2.80683 + 1.05911i) q^{9} +O(q^{10})$	\(q+(-0.310783 - 1.70394i) q^{3} +2.76937 q^{5} +(1.21939 - 2.34800i) q^{7} +(-2.80683 + 1.05911i) q^{9} -2.41924i q^{11} +(0.0461613 - 0.0266512i) q^{13} +(-0.860670 - 4.71884i) q^{15} +(-1.79727 - 3.11297i) q^{17} +(-3.96978 - 2.29195i) q^{19} +(-4.37981 - 1.34805i) q^{21} +0.106917i q^{23} +2.66939 q^{25} +(2.67697 + 4.45352i) q^{27} +(6.57376 + 3.79536i) q^{29} +(5.90251 + 3.40781i) q^{31} +(-4.12225 + 0.751859i) q^{33} +(3.37694 - 6.50246i) q^{35} +(2.06198 - 3.57146i) q^{37} +(-0.0597583 - 0.0703734i) q^{39} +(0.838974 + 1.45315i) q^{41} +(-1.74347 + 3.01978i) q^{43} +(-7.77313 + 2.93306i) q^{45} +(-6.59698 - 11.4263i) q^{47} +(-4.02618 - 5.72625i) q^{49} +(-4.74575 + 4.02990i) q^{51} +(-5.27512 + 3.04559i) q^{53} -6.69977i q^{55} +(-2.67161 + 7.47657i) q^{57} +(4.72417 - 8.18250i) q^{59} +(2.29928 - 1.32749i) q^{61} +(-0.935832 + 7.88189i) q^{63} +(0.127838 - 0.0738070i) q^{65} +(-7.09356 + 12.2864i) q^{67} +(0.182180 - 0.0332279i) q^{69} -1.40262i q^{71} +(5.54168 - 3.19949i) q^{73} +(-0.829599 - 4.54848i) q^{75} +(-5.68038 - 2.95000i) q^{77} +(2.11067 + 3.65578i) q^{79} +(6.75657 - 5.94548i) q^{81} +(-6.86670 + 11.8935i) q^{83} +(-4.97731 - 8.62095i) q^{85} +(4.42406 - 12.3808i) q^{87} +(5.71724 - 9.90254i) q^{89} +(-0.00628839 - 0.140885i) q^{91} +(3.97232 - 11.1166i) q^{93} +(-10.9938 - 6.34726i) q^{95} +(14.3549 + 8.28778i) q^{97} +(2.56224 + 6.79040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9}+O(q^{10}) $ 48 * q + 2 * q^9	$ 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} + 32 q^{63} - 36 q^{65} - 12 q^{77} - 6 q^{79} + 6 q^{81} + 54 q^{87} - 18 q^{89} - 6 q^{91} + 4 q^{93} + 54 q^{95} + 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.310783	−	1.70394i	−0.179430	−	0.983771i
$3$	−0.310783	−	1.70394i	−0.179430	−	0.983771i
$4$		0			0
$5$	2.76937			1.23850			0.619249	−	0.785195i	$-0.287437\pi$
$5$	2.76937			1.23850			0.619249	+	0.785195i	$0.287437\pi$
$6$		0			0
$7$	1.21939	−	2.34800i	0.460886	−	0.887459i
$7$	1.21939	−	2.34800i	0.460886	−	0.887459i
$8$		0			0
$9$	−2.80683	+	1.05911i	−0.935609	+	0.353037i
$10$		0			0
$11$		−	2.41924i		−	0.729429i	−0.931119	−	0.364715i	$-0.881167\pi$
$11$		−	2.41924i		−	0.729429i	0.931119	−	0.364715i	$-0.118833\pi$
$12$		0			0
$13$	0.0461613	−	0.0266512i	0.0128028	−	0.00739172i	−0.493585	−	0.869698i	$-0.664314\pi$
$13$	0.0461613	−	0.0266512i	0.0128028	−	0.00739172i	0.506388	+	0.862306i	$0.330980\pi$
$14$		0			0
$15$	−0.860670	−	4.71884i	−0.222224	−	1.21840i
$16$		0			0
$17$	−1.79727	−	3.11297i	−0.435903	−	0.755006i	0.561466	−	0.827500i	$-0.310238\pi$
$17$	−1.79727	−	3.11297i	−0.435903	−	0.755006i	−0.997369	+	0.0724940i	$0.976904\pi$
$18$		0			0
$19$	−3.96978	−	2.29195i	−0.910730	−	0.525810i	−0.0300639	−	0.999548i	$-0.509571\pi$
$19$	−3.96978	−	2.29195i	−0.910730	−	0.525810i	−0.880666	+	0.473738i	$0.842904\pi$
$20$		0			0
$21$	−4.37981	−	1.34805i	−0.955753	−	0.294169i
$22$		0			0
$23$			0.106917i			0.0222937i	0.999938	+	0.0111469i	$0.00354823\pi$
$23$			0.106917i			0.0222937i	−0.999938	+	0.0111469i	$0.996452\pi$
$24$		0			0
$25$	2.66939			0.533877
$26$		0			0
$27$	2.67697	+	4.45352i	0.515184	+	0.857080i
$28$		0			0
$29$	6.57376	+	3.79536i	1.22072	+	0.704781i	0.965071	−	0.261989i	$-0.0843785\pi$
$29$	6.57376	+	3.79536i	1.22072	+	0.704781i	0.255646	+	0.966770i	$0.417712\pi$
$30$		0			0
$31$	5.90251	+	3.40781i	1.06012	+	0.612062i	0.925466	−	0.378831i	$-0.123674\pi$
$31$	5.90251	+	3.40781i	1.06012	+	0.612062i	0.134656	+	0.990892i	$0.457007\pi$
$32$		0			0
$33$	−4.12225	+	0.751859i	−0.717591	+	0.130882i
$34$		0			0
$35$	3.37694	−	6.50246i	0.570807	−	1.09912i
$36$		0			0
$37$	2.06198	−	3.57146i	0.338988	−	0.587144i	−0.645255	−	0.763967i	$-0.723249\pi$
$37$	2.06198	−	3.57146i	0.338988	−	0.587144i	0.984243	+	0.176823i	$0.0565821\pi$
$38$		0			0
$39$	−0.0597583	−	0.0703734i	−0.00956898	−	0.0112688i
$40$		0			0
$41$	0.838974	+	1.45315i	0.131026	+	0.226943i	0.924072	−	0.382218i	$-0.124840\pi$
$41$	0.838974	+	1.45315i	0.131026	+	0.226943i	−0.793047	+	0.609161i	$0.791506\pi$
$42$		0			0
$43$	−1.74347	+	3.01978i	−0.265877	+	0.460513i	−0.967793	−	0.251747i	$-0.918995\pi$
$43$	−1.74347	+	3.01978i	−0.265877	+	0.460513i	0.701916	+	0.712260i	$0.252328\pi$
$44$		0			0
$45$	−7.77313	+	2.93306i	−1.15875	+	0.437235i
$46$		0			0
$47$	−6.59698	−	11.4263i	−0.962268	−	1.66670i	−0.716783	−	0.697296i	$-0.754386\pi$
$47$	−6.59698	−	11.4263i	−0.962268	−	1.66670i	−0.245484	−	0.969401i	$-0.578947\pi$
$48$		0			0
$49$	−4.02618	−	5.72625i	−0.575168	−	0.818035i
$50$		0			0
$51$	−4.74575	+	4.02990i	−0.664538	+	0.564299i
$52$		0			0
$53$	−5.27512	+	3.04559i	−0.724593	+	0.418344i	−0.816441	−	0.577429i	$-0.804056\pi$
$53$	−5.27512	+	3.04559i	−0.724593	+	0.418344i	0.0918477	+	0.995773i	$0.470723\pi$
$54$		0			0
$55$		−	6.69977i		−	0.903397i
$56$		0			0
$57$	−2.67161	+	7.47657i	−0.353864	+	0.990295i
$58$		0			0
$59$	4.72417	−	8.18250i	0.615034	−	1.06527i	−0.375344	−	0.926885i	$-0.622476\pi$
$59$	4.72417	−	8.18250i	0.615034	−	1.06527i	0.990379	−	0.138385i	$-0.0441911\pi$
$60$		0			0
$61$	2.29928	−	1.32749i	0.294392	−	0.169967i	−0.345529	−	0.938408i	$-0.612300\pi$
$61$	2.29928	−	1.32749i	0.294392	−	0.169967i	0.639921	+	0.768441i	$0.278967\pi$
$62$		0			0
$63$	−0.935832	+	7.88189i	−0.117904	+	0.993025i
$64$		0			0
$65$	0.127838	−	0.0738070i	0.0158563	−	0.00915464i
$66$		0			0
$67$	−7.09356	+	12.2864i	−0.866616	+	1.50102i	−0.00118266	+	0.999999i	$0.500376\pi$
$67$	−7.09356	+	12.2864i	−0.866616	+	1.50102i	−0.865433	+	0.501024i	$0.832957\pi$
$68$		0			0
$69$	0.182180	−	0.0332279i	0.0219319	−	0.00400017i
$70$		0			0
$71$		−	1.40262i		−	0.166460i	−0.996530	−	0.0832300i	$-0.973476\pi$
$71$		−	1.40262i		−	0.166460i	0.996530	−	0.0832300i	$-0.0265236\pi$
$72$		0			0
$73$	5.54168	−	3.19949i	0.648605	−	0.374472i	−0.139317	−	0.990248i	$-0.544491\pi$
$73$	5.54168	−	3.19949i	0.648605	−	0.374472i	0.787921	+	0.615776i	$0.211157\pi$
$74$		0			0
$75$	−0.829599	−	4.54848i	−0.0957938	−	0.525213i
$76$		0			0
$77$	−5.68038	−	2.95000i	−0.647339	−	0.336184i
$78$		0			0
$79$	2.11067	+	3.65578i	0.237469	+	0.411308i	0.959987	−	0.280044i	$-0.0903490\pi$
$79$	2.11067	+	3.65578i	0.237469	+	0.411308i	−0.722519	+	0.691351i	$0.757016\pi$
$80$		0			0
$81$	6.75657	−	5.94548i	0.750730	−	0.660609i
$82$		0			0
$83$	−6.86670	+	11.8935i	−0.753719	+	1.30548i	0.192290	+	0.981338i	$0.438409\pi$
$83$	−6.86670	+	11.8935i	−0.753719	+	1.30548i	−0.946009	+	0.324141i	$0.894925\pi$
$84$		0			0
$85$	−4.97731	−	8.62095i	−0.539865	−	0.935073i
$86$		0			0
$87$	4.42406	−	12.3808i	0.474309	−	1.32736i
$88$		0			0
$89$	5.71724	−	9.90254i	0.606026	−	1.04967i	−0.385863	−	0.922556i	$-0.626096\pi$
$89$	5.71724	−	9.90254i	0.606026	−	1.04967i	0.991888	−	0.127111i	$-0.0405705\pi$
$90$		0			0
$91$	−0.00628839	−	0.140885i	−0.000659203	−	0.0147687i
$92$		0			0
$93$	3.97232	−	11.1166i	0.411910	−	1.15274i
$94$		0			0
$95$	−10.9938	−	6.34726i	−1.12794	−	0.651215i
$96$		0			0
$97$	14.3549	+	8.28778i	1.45751	+	0.841496i	0.998889	−	0.0471333i	$-0.0150086\pi$
$97$	14.3549	+	8.28778i	1.45751	+	0.841496i	0.458626	+	0.888630i	$0.348342\pi$
$98$		0			0
$99$	2.56224	+	6.79040i	0.257515	+	0.682461i
$100$		0			0
$101$	−10.5000			−1.04479			−0.522394	−	0.852704i	$-0.674961\pi$
$101$	−10.5000			−1.04479			−0.522394	+	0.852704i	$0.674961\pi$
$102$		0			0
$103$			15.4270i			1.52007i	0.649884	+	0.760033i	$0.274817\pi$
$103$			15.4270i			1.52007i	−0.649884	+	0.760033i	$0.725183\pi$
$104$		0			0
$105$	−12.1293	−	3.73325i	−1.18370	−	0.364328i
$106$		0			0
$107$	−9.76426	−	5.63740i	−0.943946	−	0.544988i	−0.0527511	−	0.998608i	$-0.516799\pi$
$107$	−9.76426	−	5.63740i	−0.943946	−	0.544988i	−0.891195	+	0.453620i	$0.850132\pi$
$108$		0			0
$109$	−8.06307	−	13.9657i	−0.772302	−	1.33767i	−0.936298	−	0.351206i	$-0.885772\pi$
$109$	−8.06307	−	13.9657i	−0.772302	−	1.33767i	0.163996	−	0.986461i	$-0.447562\pi$
$110$		0			0
$111$	−6.72638	−	2.40355i	−0.638440	−	0.228135i
$112$		0			0
$113$	11.7542	−	6.78629i	1.10574	−	0.638400i	0.168018	−	0.985784i	$-0.446263\pi$
$113$	11.7542	−	6.78629i	1.10574	−	0.638400i	0.937723	+	0.347384i	$0.112930\pi$
$114$		0			0
$115$			0.296092i			0.0276107i
$116$		0			0
$117$	−0.101340	+	0.123695i	−0.00936891	+	0.0114356i
$118$		0			0
$119$	−9.50082	+	0.424069i	−0.870938	+	0.0388743i
$120$		0			0
$121$	5.14726			0.467933
$122$		0			0
$123$	2.21533	−	1.88117i	0.199750	−	0.169620i
$124$		0			0
$125$	−6.45432			−0.577292
$126$		0			0
$127$	9.23056			0.819080			0.409540	−	0.912292i	$-0.365689\pi$
$127$	9.23056			0.819080			0.409540	+	0.912292i	$0.365689\pi$
$128$		0			0
$129$	5.68737	+	2.03228i	0.500745	+	0.178932i
$130$		0			0
$131$	3.18879			0.278606			0.139303	−	0.990250i	$-0.455514\pi$
$131$	3.18879			0.278606			0.139303	+	0.990250i	$0.455514\pi$
$132$		0			0
$133$	−10.2222	+	6.52624i	−0.886378	+	0.565897i
$134$		0			0
$135$	7.41352	+	12.3334i	0.638054	+	1.06149i
$136$		0			0
$137$			5.62925i			0.480939i	0.970657	+	0.240470i	$0.0773014\pi$
$137$			5.62925i			0.480939i	−0.970657	+	0.240470i	$0.922699\pi$
$138$		0			0
$139$	18.6739	−	10.7814i	1.58390	−	0.914467i	0.589620	−	0.807680i	$-0.299277\pi$
$139$	18.6739	−	10.7814i	1.58390	−	0.914467i	0.994282	−	0.106786i	$-0.0340560\pi$
$140$		0			0
$141$	−17.4195	+	14.7919i	−1.46699	+	1.24571i
$142$		0			0
$143$	−0.0644758	−	0.111675i	−0.00539174	−	0.00933877i
$144$		0			0
$145$	18.2052	+	10.5107i	1.51186	+	0.872870i
$146$		0			0
$147$	−8.50592	+	8.63998i	−0.701557	+	0.712614i
$148$		0			0
$149$		−	19.1303i		−	1.56722i	−0.621254	−	0.783609i	$-0.713377\pi$
$149$		−	19.1303i		−	1.56722i	0.621254	−	0.783609i	$-0.286623\pi$
$150$		0			0
$151$	7.88100			0.641347			0.320673	−	0.947190i	$-0.396091\pi$
$151$	7.88100			0.641347			0.320673	+	0.947190i	$0.396091\pi$
$152$		0			0
$153$	8.34161	+	6.83406i	0.674380	+	0.552501i
$154$		0			0
$155$	16.3462	+	9.43748i	1.31296	+	0.758037i
$156$		0			0
$157$	17.2853	+	9.97966i	1.37952	+	0.796463i	0.992101	−	0.125442i	$-0.0400350\pi$
$157$	17.2853	+	9.97966i	1.37952	+	0.796463i	0.387414	+	0.921906i	$0.373368\pi$
$158$		0			0
$159$	6.82892	+	8.04197i	0.541569	+	0.637770i
$160$		0			0
$161$	0.251041	+	0.130373i	0.0197848	+	0.0102749i
$162$		0			0
$163$	−12.0423	+	20.8578i	−0.943223	+	1.63371i	−0.183951	+	0.982935i	$0.558889\pi$
$163$	−12.0423	+	20.8578i	−0.943223	+	1.63371i	−0.759271	+	0.650774i	$0.774444\pi$
$164$		0			0
$165$	−11.4160	+	2.08217i	−0.888735	+	0.162097i
$166$		0			0
$167$	−0.793686	−	1.37470i	−0.0614172	−	0.106378i	0.833682	−	0.552245i	$-0.186229\pi$
$167$	−0.793686	−	1.37470i	−0.0614172	−	0.106378i	−0.895099	+	0.445867i	$0.852895\pi$
$168$		0			0
$169$	−6.49858	+	11.2559i	−0.499891	+	0.865836i
$170$		0			0
$171$	13.5699	+	2.22869i	1.03772	+	0.170432i
$172$		0			0
$173$	2.11856	+	3.66945i	0.161071	+	0.278983i	0.935253	−	0.353980i	$-0.115172\pi$
$173$	2.11856	+	3.66945i	0.161071	+	0.278983i	−0.774182	+	0.632963i	$0.781839\pi$
$174$		0			0
$175$	3.25502	−	6.26771i	0.246057	−	0.473794i
$176$		0			0
$177$	−15.4107	−	5.50672i	−1.15834	−	0.413911i
$178$		0			0
$179$	3.38034	−	1.95164i	0.252658	−	0.145872i	−0.368323	−	0.929698i	$-0.620068\pi$
$179$	3.38034	−	1.95164i	0.252658	−	0.145872i	0.620981	+	0.783826i	$0.286734\pi$
$180$		0			0
$181$			15.3685i			1.14233i	0.820835	+	0.571166i	$0.193509\pi$
$181$			15.3685i			1.14233i	−0.820835	+	0.571166i	$0.806491\pi$
$182$		0			0
$183$	−2.97654	−	3.50527i	−0.220032	−	0.259117i
$184$		0			0
$185$	5.71038	−	9.89067i	0.419836	−	0.727177i
$186$		0			0
$187$	−7.53103	+	4.34804i	−0.550723	+	0.317960i
$188$		0			0
$189$	13.7211	−	0.854952i	0.998064	−	0.0621886i
$190$		0			0
$191$	2.28415	−	1.31876i	0.165276	−	0.0954219i	−0.415081	−	0.909785i	$-0.636247\pi$
$191$	2.28415	−	1.31876i	0.165276	−	0.0954219i	0.580356	+	0.814363i	$0.302913\pi$
$192$		0			0
$193$	3.72965	−	6.45994i	0.268466	−	0.464997i	−0.700000	−	0.714143i	$-0.746817\pi$
$193$	3.72965	−	6.45994i	0.268466	−	0.464997i	0.968466	+	0.249146i	$0.0801499\pi$
$194$		0			0
$195$	−0.165492	−	0.194890i	−0.0118512	−	0.0139563i
$196$		0			0
$197$			2.77770i			0.197903i	0.995092	+	0.0989515i	$0.0315489\pi$
$197$			2.77770i			0.197903i	−0.995092	+	0.0989515i	$0.968451\pi$
$198$		0			0
$199$	3.49892	−	2.02010i	0.248032	−	0.143201i	−0.370831	−	0.928700i	$-0.620927\pi$
$199$	3.49892	−	2.02010i	0.248032	−	0.143201i	0.618863	+	0.785499i	$0.287594\pi$
$200$		0			0
$201$	23.1399	+	8.26860i	1.63216	+	0.583222i
$202$		0			0
$203$	16.9275	−	10.8071i	1.18808	−	0.758513i
$204$		0			0
$205$	2.32343	+	4.02429i	0.162275	+	0.281069i
$206$		0			0
$207$	−0.113237	−	0.300097i	−0.00787050	−	0.0208582i
$208$		0			0
$209$	−5.54479	+	9.60386i	−0.383541	+	0.664313i
$210$		0			0
$211$	10.4855	+	18.1614i	0.721849	+	1.25028i	0.960258	+	0.279115i	$0.0900410\pi$
$211$	10.4855	+	18.1614i	0.721849	+	1.25028i	−0.238409	+	0.971165i	$0.576626\pi$
$212$		0			0
$213$	−2.38998	+	0.435909i	−0.163758	+	0.0298680i
$214$		0			0
$215$	−4.82831	+	8.36289i	−0.329288	+	0.570344i
$216$		0			0
$217$	15.1990	−	9.70361i	1.03178	−	0.658724i
$218$		0			0
$219$	−7.17400	−	8.44835i	−0.484774	−	0.570887i
$220$		0			0
$221$	−0.165929	−	0.0957991i	−0.0111616	−	0.00644415i
$222$		0			0
$223$	8.82344	+	5.09421i	0.590861	+	0.341134i	0.765438	−	0.643510i	$-0.222522\pi$
$223$	8.82344	+	5.09421i	0.590861	+	0.341134i	−0.174577	+	0.984644i	$0.555856\pi$
$224$		0			0
$225$	−7.49251	+	2.82717i	−0.499501	+	0.188478i
$226$		0			0
$227$	10.0630			0.667906			0.333953	−	0.942590i	$-0.391617\pi$
$227$	10.0630			0.667906			0.333953	+	0.942590i	$0.391617\pi$
$228$		0			0
$229$			14.9555i			0.988287i	0.869380	+	0.494144i	$0.164518\pi$
$229$			14.9555i			0.988287i	−0.869380	+	0.494144i	$0.835482\pi$
$230$		0			0
$231$	−3.26127	+	10.5958i	−0.214576	+	0.697155i
$232$		0			0
$233$	14.3200	+	8.26764i	0.938133	+	0.541631i	0.889374	−	0.457180i	$-0.151140\pi$
$233$	14.3200	+	8.26764i	0.938133	+	0.541631i	0.0487581	+	0.998811i	$0.484474\pi$
$234$		0			0
$235$	−18.2694	−	31.6436i	−1.19177	−	2.06420i
$236$		0			0
$237$	5.57328	−	4.73260i	0.362023	−	0.307416i
$238$		0			0
$239$	−9.02155	+	5.20859i	−0.583555	+	0.336916i	−0.762545	−	0.646935i	$-0.776050\pi$
$239$	−9.02155	+	5.20859i	−0.583555	+	0.336916i	0.178990	+	0.983851i	$0.442717\pi$
$240$		0			0
$241$			10.3654i			0.667693i	0.942627	+	0.333846i	$0.108347\pi$
$241$			10.3654i			0.667693i	−0.942627	+	0.333846i	$0.891653\pi$
$242$		0			0
$243$	−12.2306	−	9.66505i	−0.784591	−	0.620013i
$244$		0			0
$245$	−11.1500	−	15.8581i	−0.712344	−	1.01314i
$246$		0			0
$247$	−0.244334			−0.0155466
$248$		0			0
$249$	22.3998	+	8.00417i	1.41953	+	0.507244i
$250$		0			0
$251$	13.1006			0.826903			0.413452	−	0.910526i	$-0.364323\pi$
$251$	13.1006			0.826903			0.413452	+	0.910526i	$0.364323\pi$
$252$		0			0
$253$	0.258658			0.0162617
$254$		0			0
$255$	−13.1427	+	11.1603i	−0.823029	+	0.698884i
$256$		0			0
$257$	0.886831			0.0553190			0.0276595	−	0.999617i	$-0.491195\pi$
$257$	0.886831			0.0553190			0.0276595	+	0.999617i	$0.491195\pi$
$258$		0			0
$259$	−5.87141	−	9.19653i	−0.364832	−	0.571444i
$260$		0			0
$261$	−22.4711	−	3.69060i	−1.39093	−	0.228442i
$262$		0			0
$263$		−	7.12492i		−	0.439342i	−0.975574	−	0.219671i	$-0.929502\pi$
$263$		−	7.12492i		−	0.439342i	0.975574	−	0.219671i	$-0.0704983\pi$
$264$		0			0
$265$	−14.6087	+	8.43436i	−0.897407	+	0.518118i
$266$		0			0
$267$	−18.6502	−	6.66429i	−1.14137	−	0.407848i
$268$		0			0
$269$	15.7987	+	27.3641i	0.963261	+	1.66842i	0.714216	+	0.699925i	$0.246783\pi$
$269$	15.7987	+	27.3641i	0.963261	+	1.66842i	0.249045	+	0.968492i	$0.419883\pi$
$270$		0			0
$271$	15.8215	+	9.13455i	0.961088	+	0.554884i	0.896508	−	0.443028i	$-0.146096\pi$
$271$	15.8215	+	9.13455i	0.961088	+	0.554884i	0.0645803	+	0.997913i	$0.479429\pi$
$272$		0			0
$273$	−0.238105	+	0.0544996i	−0.0144108	+	0.00329847i
$274$		0			0
$275$		−	6.45790i		−	0.389426i
$276$		0			0
$277$	−30.5690			−1.83671			−0.918357	−	0.395753i	$-0.870484\pi$
$277$	−30.5690			−1.83671			−0.918357	+	0.395753i	$0.870484\pi$
$278$		0			0
$279$	−20.1766	−	3.31375i	−1.20794	−	0.198389i
$280$		0			0
$281$	3.92237	+	2.26458i	0.233989	+	0.135094i	0.612411	−	0.790540i	$-0.290200\pi$
$281$	3.92237	+	2.26458i	0.233989	+	0.135094i	−0.378422	+	0.925633i	$0.623533\pi$
$282$		0			0
$283$	8.10730	+	4.68075i	0.481929	+	0.278242i	0.721220	−	0.692706i	$-0.243582\pi$
$283$	8.10730	+	4.68075i	0.481929	+	0.278242i	−0.239291	+	0.970948i	$0.576915\pi$
$284$		0			0
$285$	−7.39868	+	20.7053i	−0.438260	+	1.22648i
$286$		0			0
$287$	4.43502	−	0.197957i	0.261791	−	0.0116850i
$288$		0			0
$289$	2.03962	−	3.53272i	0.119977	−	0.207807i
$290$		0			0
$291$	9.66064	−	27.0355i	0.566317	−	1.58485i
$292$		0			0
$293$	−8.17267	−	14.1555i	−0.477452	−	0.826972i	0.522214	−	0.852815i	$-0.325106\pi$
$293$	−8.17267	−	14.1555i	−0.477452	−	0.826972i	−0.999666	+	0.0258430i	$0.991773\pi$
$294$		0			0
$295$	13.0829	−	22.6603i	0.761719	−	1.31934i
$296$		0			0
$297$	10.7741	−	6.47625i	0.625179	−	0.375790i
$298$		0			0
$299$	0.00284947	+	0.00493542i	0.000164789	+	0.000285423i
$300$		0			0
$301$	4.96447	+	7.77596i	0.286147	+	0.448199i
$302$		0			0
$303$	3.26321	+	17.8914i	0.187467	+	1.02783i
$304$		0			0
$305$	6.36754	−	3.67630i	0.364604	−	0.210504i
$306$		0			0
$307$		−	0.985041i		−	0.0562193i	−0.999605	−	0.0281096i	$-0.991051\pi$
$307$		−	0.985041i		−	0.0562193i	0.999605	−	0.0281096i	$-0.00894875\pi$
$308$		0			0
$309$	26.2867	−	4.79444i	1.49540	−	0.272746i
$310$		0			0
$311$	13.1302	−	22.7422i	0.744545	−	1.28959i	−0.205863	−	0.978581i	$-0.566000\pi$
$311$	13.1302	−	22.7422i	0.744545	−	1.28959i	0.950407	−	0.311008i	$-0.100667\pi$
$312$		0			0
$313$	−12.5858	+	7.26643i	−0.711393	+	0.410723i	−0.811576	−	0.584246i	$-0.801390\pi$
$313$	−12.5858	+	7.26643i	−0.711393	+	0.410723i	0.100184	+	0.994969i	$0.468057\pi$
$314$		0			0
$315$	−2.59166	+	21.8278i	−0.146024	+	1.22986i
$316$		0			0
$317$	−25.5148	+	14.7310i	−1.43306	+	0.827375i	−0.997353	−	0.0727147i	$-0.976834\pi$
$317$	−25.5148	+	14.7310i	−1.43306	+	0.827375i	−0.435704	+	0.900090i	$0.643500\pi$
$318$		0			0
$319$	9.18191	−	15.9035i	0.514088	−	0.890427i
$320$		0			0
$321$	−6.57123	+	18.3897i	−0.366770	+	1.02641i
$322$		0			0
$323$			16.4771i			0.916808i
$324$		0			0
$325$	0.123222	−	0.0711425i	0.00683515	−	0.00394627i
$326$		0			0
$327$	−21.2908	+	18.0793i	−1.17738	+	0.999787i
$328$		0			0
$329$	−34.8732	+	1.55656i	−1.92262	+	0.0858162i
$330$		0			0
$331$	−2.91015	−	5.04053i	−0.159956	−	0.277052i	0.774896	−	0.632088i	$-0.217802\pi$
$331$	−2.91015	−	5.04053i	−0.159956	−	0.277052i	−0.934853	+	0.355036i	$0.884469\pi$
$332$		0			0
$333$	−2.00506	+	12.2083i	−0.109877	+	0.669013i
$334$		0			0
$335$	−19.6447	+	34.0255i	−1.07330	+	1.85901i
$336$		0			0
$337$	−11.4909	−	19.9028i	−0.625950	−	1.08418i	−0.988356	−	0.152157i	$-0.951378\pi$
$337$	−11.4909	−	19.9028i	−0.625950	−	1.08418i	0.362407	−	0.932020i	$-0.381955\pi$
$338$		0			0
$339$	−15.2164	−	17.9194i	−0.826443	−	0.973248i
$340$		0			0
$341$	8.24433	−	14.2796i	0.446456	−	0.773284i
$342$		0			0
$343$	−18.3547	+	2.47092i	−0.991060	+	0.133417i
$344$		0			0
$345$	0.504523	−	0.0920202i	0.0271626	−	0.00495420i
$346$		0			0
$347$	−12.9435	−	7.47293i	−0.694843	−	0.401168i	0.110581	−	0.993867i	$-0.464729\pi$
$347$	−12.9435	−	7.47293i	−0.694843	−	0.401168i	−0.805424	+	0.592699i	$0.798062\pi$
$348$		0			0
$349$	−0.768588	−	0.443744i	−0.0411416	−	0.0237531i	0.479288	−	0.877658i	$-0.340895\pi$
$349$	−0.768588	−	0.443744i	−0.0411416	−	0.0237531i	−0.520430	+	0.853905i	$0.674228\pi$
$350$		0			0
$351$	0.242264	+	0.134235i	0.0129311	+	0.00716496i
$352$		0			0
$353$	5.04996			0.268782			0.134391	−	0.990928i	$-0.457092\pi$
$353$	5.04996			0.268782			0.134391	+	0.990928i	$0.457092\pi$
$354$		0			0
$355$		−	3.88436i		−	0.206160i
$356$		0			0
$357$	3.67528	+	16.0570i	0.194516	+	0.849828i
$358$		0			0
$359$	30.2467	+	17.4629i	1.59636	+	0.921659i	0.992181	+	0.124810i	$0.0398322\pi$
$359$	30.2467	+	17.4629i	1.59636	+	0.921659i	0.604179	+	0.796848i	$0.293501\pi$
$360$		0			0
$361$	1.00610	+	1.74261i	0.0529524	+	0.0917163i
$362$		0			0
$363$	−1.59968	−	8.77063i	−0.0839614	−	0.460339i
$364$		0			0
$365$	15.3469	−	8.86056i	0.803296	−	0.463783i
$366$		0			0
$367$		−	23.0893i		−	1.20525i	−0.798025	−	0.602625i	$-0.794122\pi$
$367$		−	23.0893i		−	1.20525i	0.798025	−	0.602625i	$-0.205878\pi$
$368$		0			0
$369$	−3.89390	−	3.19016i	−0.202708	−	0.166073i
$370$		0			0
$371$	0.718611	+	16.0997i	0.0373084	+	0.835856i
$372$		0			0
$373$	1.79851			0.0931235			0.0465617	−	0.998915i	$-0.485174\pi$
$373$	1.79851			0.0931235			0.0465617	+	0.998915i	$0.485174\pi$
$374$		0			0
$375$	2.00589	+	10.9978i	0.103584	+	0.567923i
$376$		0			0
$377$	0.404605			0.0208382
$378$		0			0
$379$	3.34605			0.171875			0.0859375	−	0.996301i	$-0.472611\pi$
$379$	3.34605			0.171875			0.0859375	+	0.996301i	$0.472611\pi$
$380$		0			0
$381$	−2.86870	−	15.7283i	−0.146968	−	0.805787i
$382$		0			0
$383$	−1.97833			−0.101088			−0.0505439	−	0.998722i	$-0.516095\pi$
$383$	−1.97833			−0.101088			−0.0505439	+	0.998722i	$0.516095\pi$
$384$		0			0
$385$	−15.7310	−	8.16963i	−0.801728	−	0.416363i
$386$		0			0
$387$	1.69535	−	10.3225i	0.0861793	−	0.524724i
$388$		0			0
$389$		−	34.9095i		−	1.76998i	−0.465609	−	0.884990i	$-0.654165\pi$
$389$		−	34.9095i		−	1.76998i	0.465609	−	0.884990i	$-0.345835\pi$
$390$		0			0
$391$	0.332829	−	0.192159i	0.0168319	−	0.00971789i
$392$		0			0
$393$	−0.991021	−	5.43352i	−0.0499904	−	0.274085i
$394$		0			0
$395$	5.84521	+	10.1242i	0.294104	+	0.509404i
$396$		0			0
$397$	2.73751	+	1.58050i	0.137392	+	0.0793231i	0.567120	−	0.823635i	$-0.308057\pi$
$397$	2.73751	+	1.58050i	0.137392	+	0.0793231i	−0.429729	+	0.902958i	$0.641391\pi$
$398$		0			0
$399$	14.2972	+	15.3898i	0.715756	+	0.770453i
$400$		0			0
$401$			33.0291i			1.64940i	0.565573	+	0.824698i	$0.308655\pi$
$401$			33.0291i			1.64940i	−0.565573	+	0.824698i	$0.691345\pi$
$402$		0			0
$403$	0.363290			0.0180968
$404$		0			0
$405$	18.7114	−	16.4652i	0.929778	−	0.818163i
$406$		0			0
$407$	−8.64023	−	4.98844i	−0.428280	−	0.247268i
$408$		0			0
$409$	0.933684	+	0.539063i	0.0461677	+	0.0266549i	0.522906	−	0.852390i	$-0.324848\pi$
$409$	0.933684	+	0.539063i	0.0461677	+	0.0266549i	−0.476739	+	0.879045i	$0.658181\pi$
$410$		0			0
$411$	9.59190	−	1.74947i	0.473134	−	0.0862951i
$412$		0			0
$413$	−13.4519	−	21.0700i	−0.661923	−	1.03679i
$414$		0			0
$415$	−19.0164	+	32.9374i	−0.933479	+	1.61683i
$416$		0			0
$417$	−24.1744	−	28.4686i	−1.18383	−	1.39411i
$418$		0			0
$419$	13.2799	+	23.0015i	0.648768	+	1.12370i	0.983418	+	0.181356i	$0.0580486\pi$
$419$	13.2799	+	23.0015i	0.648768	+	1.12370i	−0.334650	+	0.942343i	$0.608618\pi$
$420$		0			0
$421$	3.32791	−	5.76411i	0.162192	−	0.280925i	−0.773462	−	0.633842i	$-0.781477\pi$
$421$	3.32791	−	5.76411i	0.162192	−	0.280925i	0.935655	+	0.352917i	$0.114810\pi$
$422$		0			0
$423$	30.6183	+	25.0847i	1.48871	+	1.21966i
$424$		0			0
$425$	−4.79762	−	8.30972i	−0.232719	−	0.403081i
$426$		0			0
$427$	−0.313223	−	7.01742i	−0.0151579	−	0.339597i
$428$		0			0
$429$	−0.170250	+	0.144570i	−0.00821976	+	0.00697989i
$430$		0			0
$431$	−13.2930	+	7.67471i	−0.640300	+	0.369678i	−0.784730	−	0.619837i	$-0.787199\pi$
$431$	−13.2930	+	7.67471i	−0.640300	+	0.369678i	0.144430	+	0.989515i	$0.453865\pi$
$432$		0			0
$433$		−	15.9407i		−	0.766060i	−0.923736	−	0.383030i	$-0.874881\pi$
$433$		−	15.9407i		−	0.766060i	0.923736	−	0.383030i	$-0.125119\pi$
$434$		0			0
$435$	12.2519	−	34.2871i	0.587431	−	1.64394i
$436$		0			0
$437$	0.245049	−	0.424436i	0.0117223	−	0.0203036i
$438$		0			0
$439$	17.8768	−	10.3212i	0.853214	−	0.492603i	−0.00852006	−	0.999964i	$-0.502712\pi$
$439$	17.8768	−	10.3212i	0.853214	−	0.492603i	0.861734	+	0.507360i	$0.169379\pi$
$440$		0			0
$441$	17.3655	+	11.8084i	0.826929	+	0.562306i
$442$		0			0
$443$	−1.25880	+	0.726768i	−0.0598073	+	0.0345298i	−0.529605	−	0.848244i	$-0.677660\pi$
$443$	−1.25880	+	0.726768i	−0.0598073	+	0.0345298i	0.469798	+	0.882774i	$0.344327\pi$
$444$		0			0
$445$	15.8331	−	27.4238i	0.750562	−	1.30001i
$446$		0			0
$447$	−32.5970	+	5.94537i	−1.54178	+	0.281207i
$448$		0			0
$449$		−	9.09933i		−	0.429424i	−0.976677	−	0.214712i	$-0.931119\pi$
$449$		−	9.09933i		−	0.429424i	0.976677	−	0.214712i	$-0.0688813\pi$
$450$		0			0
$451$	3.51551	−	2.02968i	0.165539	−	0.0955740i
$452$		0			0
$453$	−2.44928	−	13.4288i	−0.115077	−	0.630938i
$454$		0			0
$455$	−0.0174149	−	0.390162i	−0.000816421	−	0.0182911i
$456$		0			0
$457$	7.23209	+	12.5264i	0.338303	+	0.585958i	0.984114	−	0.177540i	$-0.0568138\pi$
$457$	7.23209	+	12.5264i	0.338303	+	0.585958i	−0.645811	+	0.763498i	$0.723480\pi$
$458$		0			0
$459$	9.05240	−	16.3375i	0.422530	−	0.762570i
$460$		0			0
$461$	−13.2769	+	22.9963i	−0.618369	+	1.07105i	0.371415	+	0.928467i	$0.378873\pi$
$461$	−13.2769	+	22.9963i	−0.618369	+	1.07105i	−0.989783	+	0.142579i	$0.954461\pi$
$462$		0			0
$463$	−15.4968	−	26.8412i	−0.720196	−	1.24742i	−0.960921	−	0.276823i	$-0.910718\pi$
$463$	−15.4968	−	26.8412i	−0.720196	−	1.24742i	0.240725	−	0.970593i	$-0.422615\pi$
$464$		0			0
$465$	11.0008	−	30.7860i	0.510150	−	1.42767i
$466$		0			0
$467$	10.1348	−	17.5541i	0.468985	−	0.812306i	−0.530387	−	0.847756i	$-0.677953\pi$
$467$	10.1348	−	17.5541i	0.468985	−	0.812306i	0.999371	+	0.0354503i	$0.0112865\pi$
$468$		0			0
$469$	20.1986	+	31.6376i	0.932686	+	1.46089i
$470$		0			0
$471$	11.6328	−	32.5546i	0.536010	−	1.50004i
$472$		0			0
$473$	7.30559	+	4.21789i	0.335911	+	0.193939i
$474$		0			0
$475$	−10.5969	−	6.11811i	−0.486218	−	0.280718i
$476$		0			0
$477$	11.5807	−	14.1354i	0.530245	−	0.647215i
$478$		0			0
$479$	−16.0258			−0.732236			−0.366118	−	0.930568i	$-0.619313\pi$
$479$	−16.0258			−0.732236			−0.366118	+	0.930568i	$0.619313\pi$
$480$		0			0
$481$		−	0.219817i		−	0.0100228i
$482$		0			0
$483$	0.144130	−	0.468276i	0.00655812	−	0.0213073i
$484$		0			0
$485$	39.7538	+	22.9519i	1.80513	+	1.04219i
$486$		0			0
$487$	−8.54048	−	14.7925i	−0.387006	−	0.670314i	0.605039	−	0.796196i	$-0.293157\pi$
$487$	−8.54048	−	14.7925i	−0.387006	−	0.670314i	−0.992045	+	0.125881i	$0.959824\pi$
$488$		0			0
$489$	39.2830	+	14.0371i	1.77644	+	0.634778i
$490$		0			0
$491$	−12.9745	+	7.49082i	−0.585530	+	0.338056i	−0.763328	−	0.646011i	$-0.776436\pi$
$491$	−12.9745	+	7.49082i	−0.585530	+	0.338056i	0.177798	+	0.984067i	$0.443103\pi$
$492$		0			0
$493$		−	27.2852i		−	1.22886i
$494$		0			0
$495$	7.09579	+	18.8051i	0.318932	+	0.845227i
$496$		0			0
$497$	−3.29334	−	1.71034i	−0.147726	−	0.0767191i
$498$		0			0
$499$	−25.3276			−1.13382			−0.566910	−	0.823780i	$-0.691861\pi$
$499$	−25.3276			−1.13382			−0.566910	+	0.823780i	$0.691861\pi$
$500$		0			0
$501$	−2.09575	+	1.77963i	−0.0936312	+	0.0795079i
$502$		0			0
$503$	9.95401			0.443827			0.221914	−	0.975066i	$-0.428770\pi$
$503$	9.95401			0.443827			0.221914	+	0.975066i	$0.428770\pi$
$504$		0			0
$505$	−29.0783			−1.29397
$506$		0			0
$507$	21.1990	+	7.57507i	0.941480	+	0.336421i
$508$		0			0
$509$	−11.6595			−0.516800			−0.258400	−	0.966038i	$-0.583195\pi$
$509$	−11.6595			−0.516800			−0.258400	+	0.966038i	$0.583195\pi$
$510$		0			0
$511$	−0.754924	−	16.9133i	−0.0333959	−	0.748199i
$512$		0			0
$513$	−0.419744	−	23.8150i	−0.0185321	−	1.05146i
$514$		0			0
$515$			42.7230i			1.88260i
$516$		0			0
$517$	−27.6430	+	15.9597i	−1.21574	+	0.701906i
$518$		0			0
$519$	5.59411	−	4.75029i	0.245554	−	0.208515i
$520$		0			0
$521$	−8.59307	−	14.8836i	−0.376469	−	0.652064i	0.614077	−	0.789246i	$-0.289529\pi$
$521$	−8.59307	−	14.8836i	−0.376469	−	0.652064i	−0.990546	+	0.137183i	$0.956195\pi$
$522$		0			0
$523$	38.1175	+	22.0071i	1.66676	+	0.962305i	0.969367	+	0.245616i	$0.0789903\pi$
$523$	38.1175	+	22.0071i	1.66676	+	0.962305i	0.697394	+	0.716688i	$0.254343\pi$
$524$		0			0
$525$	−11.6914	−	3.59847i	−0.510255	−	0.157050i
$526$		0			0
$527$		−	24.4991i		−	1.06720i
$528$		0			0
$529$	22.9886			0.999503
$530$		0			0
$531$	−4.59376	+	27.9703i	−0.199352	+	1.21381i
$532$		0			0
$533$	0.0774562	+	0.0447194i	0.00335500	+	0.00193701i
$534$		0			0
$535$	−27.0408	−	15.6120i	−1.16908	−	0.674966i
$536$		0			0
$537$	−4.37602	−	5.15336i	−0.188839	−	0.222384i
$538$		0			0
$539$	−13.8532	+	9.74030i	−0.596699	+	0.419544i
$540$		0			0
$541$	−5.06580	+	8.77423i	−0.217796	+	0.377234i	−0.954134	−	0.299380i	$-0.903220\pi$
$541$	−5.06580	+	8.77423i	−0.217796	+	0.377234i	0.736338	+	0.676614i	$0.236553\pi$
$542$		0			0
$543$	26.1870	−	4.77626i	1.12379	−	0.204969i
$544$		0			0
$545$	−22.3296	−	38.6760i	−0.956495	−	1.65670i
$546$		0			0
$547$	−17.0000	+	29.4449i	−0.726869	+	1.25897i	0.231331	+	0.972875i	$0.425692\pi$
$547$	−17.0000	+	29.4449i	−0.726869	+	1.25897i	−0.958200	+	0.286099i	$0.907642\pi$
$548$		0			0
$549$	−5.04772	+	6.16122i	−0.215431	+	0.262954i
$550$		0			0
$551$	−17.3976	−	30.1335i	−0.741162	−	1.28373i
$552$		0			0
$553$	11.1575	−	0.498014i	0.474465	−	0.0211777i
$554$		0			0
$555$	−18.6278	−	6.65631i	−0.790706	−	0.282544i
$556$		0			0
$557$	1.88366	−	1.08753i	0.0798133	−	0.0460802i	−0.459562	−	0.888146i	$-0.651994\pi$
$557$	1.88366	−	1.08753i	0.0798133	−	0.0460802i	0.539376	+	0.842065i	$0.318660\pi$
$558$		0			0
$559$			0.185863i			0.00786116i
$560$		0			0
$561$	9.74932	+	11.4811i	0.411617	+	0.484734i
$562$		0			0
$563$	2.24777	−	3.89326i	0.0947324	−	0.164081i	−0.814765	−	0.579792i	$-0.803134\pi$
$563$	2.24777	−	3.89326i	0.0947324	−	0.164081i	0.909497	+	0.415711i	$0.136467\pi$
$564$		0			0
$565$	32.5517	−	18.7937i	1.36946	−	0.790657i
$566$		0			0
$567$	−5.72107	−	23.1143i	−0.240262	−	0.970708i
$568$		0			0
$569$	5.30272	−	3.06153i	0.222302	−	0.128346i	−0.384714	−	0.923036i	$-0.625700\pi$
$569$	5.30272	−	3.06153i	0.222302	−	0.128346i	0.607016	+	0.794690i	$0.292367\pi$
$570$		0			0
$571$	−16.1829	+	28.0296i	−0.677233	+	1.17300i	0.298578	+	0.954385i	$0.403488\pi$
$571$	−16.1829	+	28.0296i	−0.677233	+	1.17300i	−0.975811	+	0.218616i	$0.929846\pi$
$572$		0			0
$573$	−2.95696	−	3.48222i	−0.123529	−	0.145472i
$574$		0			0
$575$			0.285403i			0.0119021i
$576$		0			0
$577$	−34.2034	+	19.7473i	−1.42390	+	0.822092i	−0.996630	−	0.0820304i	$-0.973860\pi$
$577$	−34.2034	+	19.7473i	−1.42390	+	0.822092i	−0.427274	+	0.904122i	$0.640526\pi$
$578$		0			0
$579$	−12.1665	−	4.34747i	−0.505621	−	0.180675i
$580$		0			0
$581$	19.5527	+	30.6258i	0.811181	+	1.27057i
$582$		0			0
$583$	7.36803	+	12.7618i	0.305152	+	0.528540i
$584$		0			0
$585$	−0.280648	+	0.342558i	−0.0116034	+	0.0141630i
$586$		0			0
$587$	−0.129711	+	0.224667i	−0.00535376	+	0.00927298i	−0.868690	−	0.495356i	$-0.835037\pi$
$587$	−0.129711	+	0.224667i	−0.00535376	+	0.00927298i	0.863336	+	0.504629i	$0.168371\pi$
$588$		0			0
$589$	−15.6211	−	27.0565i	−0.643656	−	1.11485i
$590$		0			0
$591$	4.73304	−	0.863261i	0.194691	−	0.0355098i
$592$		0			0
$593$	3.13549	−	5.43083i	0.128759	−	0.223017i	−0.794437	−	0.607347i	$-0.792234\pi$
$593$	3.13549	−	5.43083i	0.128759	−	0.223017i	0.923196	+	0.384329i	$0.125567\pi$
$594$		0			0
$595$	−26.3112	+	1.17440i	−1.07866	+	0.0481458i
$596$		0			0
$597$	−4.52954	−	5.33414i	−0.185382	−	0.218312i
$598$		0			0
$599$	−5.52001	−	3.18698i	−0.225542	−	0.130217i	0.382972	−	0.923760i	$-0.374901\pi$
$599$	−5.52001	−	3.18698i	−0.225542	−	0.130217i	−0.608514	+	0.793543i	$0.708234\pi$
$600$		0			0
$601$	−15.0862	−	8.71001i	−0.615378	−	0.355289i	0.159689	−	0.987167i	$-0.448951\pi$
$601$	−15.0862	−	8.71001i	−0.615378	−	0.355289i	−0.775067	+	0.631879i	$0.782284\pi$
$602$		0			0
$603$	6.89775	−	41.9987i	0.280898	−	1.71032i
$604$		0			0
$605$	14.2546			0.579534
$606$		0			0
$607$		−	1.80344i		−	0.0731996i	−0.999330	−	0.0365998i	$-0.988347\pi$
$607$		−	1.80344i		−	0.0731996i	0.999330	−	0.0365998i	$-0.0116527\pi$
$608$		0			0
$609$	−23.6755	−	25.4848i	−0.959380	−	1.03269i
$610$		0			0
$611$	−0.609050	−	0.351635i	−0.0246395	−	0.0142256i
$612$		0			0
$613$	−17.6290	−	30.5343i	−0.712028	−	1.23327i	−0.964095	−	0.265559i	$-0.914443\pi$
$613$	−17.6290	−	30.5343i	−0.712028	−	1.23327i	0.252066	−	0.967710i	$-0.418890\pi$
$614$		0			0
$615$	6.13507	−	5.20966i	0.247390	−	0.210074i
$616$		0			0
$617$	−7.73458	+	4.46556i	−0.311383	+	0.179777i	−0.647545	−	0.762027i	$-0.724204\pi$
$617$	−7.73458	+	4.46556i	−0.311383	+	0.179777i	0.336162	+	0.941804i	$0.390871\pi$
$618$		0			0
$619$			38.5146i			1.54803i	0.633166	+	0.774016i	$0.281755\pi$
$619$			38.5146i			1.54803i	−0.633166	+	0.774016i	$0.718245\pi$
$620$		0			0
$621$	−0.476156	+	0.286214i	−0.0191075	+	0.0114854i
$622$		0			0
$623$	−16.2796	−	25.4991i	−0.652228	−	1.02160i
$624$		0			0
$625$	−31.2213			−1.24885
$626$		0			0
$627$	18.0876	+	6.46329i	0.722351	+	0.258119i
$628$		0			0
$629$	−14.8238			−0.591063
$630$		0			0
$631$	24.5826			0.978616			0.489308	−	0.872111i	$-0.337249\pi$
$631$	24.5826			0.978616			0.489308	+	0.872111i	$0.337249\pi$
$632$		0			0
$633$	27.6872	−	23.5108i	1.10047	−	0.934472i
$634$		0			0
$635$	25.5628			1.01443
$636$		0			0
$637$	−0.338465	−	0.157028i	−0.0134105	−	0.00622169i
$638$		0			0
$639$	1.48553	+	3.93690i	0.0587665	+	0.155742i
$640$		0			0
$641$			33.6752i			1.33009i	0.746804	+	0.665044i	$0.231587\pi$
$641$			33.6752i			1.33009i	−0.746804	+	0.665044i	$0.768413\pi$
$642$		0			0
$643$	−2.02496	+	1.16911i	−0.0798567	+	0.0461053i	−0.539397	−	0.842052i	$-0.681348\pi$
$643$	−2.02496	+	1.16911i	−0.0798567	+	0.0461053i	0.459540	+	0.888157i	$0.348014\pi$
$644$		0			0
$645$	15.7504	+	5.62812i	0.620172	+	0.221607i
$646$		0			0
$647$	−1.89769	−	3.28689i	−0.0746059	−	0.129221i	0.826309	−	0.563217i	$-0.190437\pi$
$647$	−1.89769	−	3.28689i	−0.0746059	−	0.129221i	−0.900915	+	0.433996i	$0.857103\pi$
$648$		0			0
$649$	−19.7955	−	11.4289i	−0.777040	−	0.448624i
$650$		0			0
$651$	−21.2580	−	22.8825i	−0.833165	−	0.896835i
$652$		0			0
$653$		−	11.7151i		−	0.458447i	−0.973374	−	0.229224i	$-0.926381\pi$
$653$		−	11.7151i		−	0.458447i	0.973374	−	0.229224i	$-0.0736187\pi$
$654$		0			0
$655$	8.83094			0.345053
$656$		0			0
$657$	−12.1659	+	14.8497i	−0.474638	+	0.579341i
$658$		0			0
$659$	−22.4962	−	12.9882i	−0.876329	−	0.505949i	−0.00688257	−	0.999976i	$-0.502191\pi$
$659$	−22.4962	−	12.9882i	−0.876329	−	0.505949i	−0.869446	+	0.494028i	$0.835524\pi$
$660$		0			0
$661$	5.94177	+	3.43048i	0.231108	+	0.133430i	0.611083	−	0.791566i	$-0.290734\pi$
$661$	5.94177	+	3.43048i	0.231108	+	0.133430i	−0.379975	+	0.924997i	$0.624067\pi$
$662$		0			0
$663$	−0.111668	+	0.312506i	−0.00433683	+	0.0121367i
$664$		0			0
$665$	−28.3090	+	18.0736i	−1.09778	+	0.700862i
$666$		0			0
$667$	−0.405789	+	0.702846i	−0.0157122	+	0.0272143i
$668$		0			0
$669$	5.93807	−	16.6178i	0.229579	−	0.642482i
$670$		0			0
$671$	−3.21152	−	5.56251i	−0.123979	−	0.214738i
$672$		0			0
$673$	−0.652179	+	1.12961i	−0.0251397	+	0.0435432i	−0.878322	−	0.478070i	$-0.841336\pi$
$673$	−0.652179	+	1.12961i	−0.0251397	+	0.0435432i	0.853182	+	0.521614i	$0.174670\pi$
$674$		0			0
$675$	7.14588	+	11.8882i	0.275045	+	0.457575i
$676$		0			0
$677$	−6.61516	−	11.4578i	−0.254241	−	0.440359i	0.710448	−	0.703750i	$-0.248492\pi$
$677$	−6.61516	−	11.4578i	−0.254241	−	0.440359i	−0.964689	+	0.263391i	$0.915159\pi$
$678$		0			0
$679$	36.9638	−	23.5991i	1.41854	−	0.905651i
$680$		0			0
$681$	−3.12741	−	17.1468i	−0.119843	−	0.657067i
$682$		0			0
$683$	1.49949	−	0.865733i	0.0573765	−	0.0331264i	−0.471037	−	0.882113i	$-0.656120\pi$
$683$	1.49949	−	0.865733i	0.0573765	−	0.0331264i	0.528414	+	0.848987i	$0.322787\pi$
$684$		0			0
$685$			15.5894i			0.595642i
$686$		0			0
$687$	25.4833	−	4.64791i	0.972248	−	0.177329i
$688$		0			0
$689$	−0.162338	+	0.281177i	−0.00618457	+	0.0107120i
$690$		0			0
$691$	7.27541	−	4.20046i	0.276770	−	0.159793i	−0.355190	−	0.934794i	$-0.615584\pi$
$691$	7.27541	−	4.20046i	0.276770	−	0.159793i	0.631960	+	0.775001i	$0.282251\pi$
$692$		0			0
$693$	19.0682	+	2.26401i	0.724342	+	0.0860024i
$694$		0			0
$695$	51.7150	−	29.8576i	1.96166	−	1.13256i
$696$		0			0
$697$	3.01573	−	5.22340i	0.114229	−	0.197850i
$698$		0			0
$699$	9.63717	−	26.9698i	0.364511	−	1.02009i
$700$		0			0
$701$			21.3493i			0.806353i	0.915122	+	0.403176i	$0.132094\pi$
$701$			21.3493i			0.806353i	−0.915122	+	0.403176i	$0.867906\pi$
$702$		0			0
$703$	−16.3712	+	9.45193i	−0.617452	+	0.356486i
$704$		0			0
$705$	−48.2410	+	40.9643i	−1.81686	+	1.54281i
$706$		0			0
$707$	−12.8036	+	24.6539i	−0.481528	+	0.927207i
$708$		0			0
$709$	9.63087	+	16.6812i	0.361695	+	0.626474i	0.988240	−	0.152911i	$-0.0488648\pi$
$709$	9.63087	+	16.6812i	0.361695	+	0.626474i	−0.626545	+	0.779385i	$0.715532\pi$
$710$		0			0
$711$	−9.79616	−	8.02573i	−0.367385	−	0.300988i
$712$		0			0
$713$	−0.364353	+	0.631078i	−0.0136451	+	0.0236341i
$714$		0			0
$715$	−0.178557	−	0.309270i	−0.00667766	−	0.0115660i
$716$		0			0
$717$	11.6789	+	13.7534i	0.436155	+	0.513632i
$718$		0			0
$719$	5.39920	−	9.35168i	0.201356	−	0.348759i	−0.747610	−	0.664138i	$-0.768799\pi$
$719$	5.39920	−	9.35168i	0.201356	−	0.348759i	0.948966	+	0.315380i	$0.102132\pi$
$720$		0			0
$721$	36.2225	+	18.8115i	1.34900	+	0.700577i
$722$		0			0
$723$	17.6620	−	3.22138i	0.656857	−	0.119804i
$724$		0			0
$725$	17.5479	+	10.1313i	0.651713	+	0.376267i
$726$		0			0
$727$	−25.9316	−	14.9716i	−0.961751	−	0.555267i	−0.0650393	−	0.997883i	$-0.520717\pi$
$727$	−25.9316	−	14.9716i	−0.961751	−	0.555267i	−0.896711	+	0.442616i	$0.854051\pi$
$728$		0			0
$729$	−12.6676	+	23.8439i	−0.469171	+	0.883107i
$730$		0			0
$731$	12.5340			0.463586
$732$		0			0
$733$		−	16.0355i		−	0.592286i	−0.955144	−	0.296143i	$-0.904300\pi$
$733$		−	16.0355i		−	0.592286i	0.955144	−	0.296143i	$-0.0957004\pi$
$734$		0			0
$735$	−23.5560	+	23.9273i	−0.868876	+	0.882571i
$736$		0			0
$737$	29.7238	+	17.1610i	1.09489	+	0.632135i
$738$		0			0
$739$	−11.5186	−	19.9508i	−0.423719	−	0.733903i	0.572581	−	0.819848i	$-0.305942\pi$
$739$	−11.5186	−	19.9508i	−0.423719	−	0.733903i	−0.996300	+	0.0859453i	$0.972609\pi$
$740$		0			0
$741$	0.0759346	+	0.416330i	0.00278953	+	0.0152943i
$742$		0			0
$743$	−37.2352	+	21.4978i	−1.36603	+	0.788676i	−0.990418	−	0.138102i	$-0.955900\pi$
$743$	−37.2352	+	21.4978i	−1.36603	+	0.788676i	−0.375609	+	0.926778i	$0.622567\pi$
$744$		0			0
$745$		−	52.9789i		−	1.94100i
$746$		0			0
$747$	6.67716	−	40.6556i	0.244304	−	1.48751i
$748$		0			0
$749$	−25.1430	+	16.0523i	−0.918706	+	0.586537i
$750$		0			0
$751$	−35.3800			−1.29104			−0.645518	−	0.763745i	$-0.723358\pi$
$751$	−35.3800			−1.29104			−0.645518	+	0.763745i	$0.723358\pi$
$752$		0			0
$753$	−4.07144	−	22.3227i	−0.148372	−	0.813483i
$754$		0			0
$755$	21.8254			0.794307
$756$		0			0
$757$	−24.6138			−0.894604			−0.447302	−	0.894383i	$-0.647615\pi$
$757$	−24.6138			−0.894604			−0.447302	+	0.894383i	$0.647615\pi$
$758$		0			0
$759$	−0.0803864	−	0.440738i	−0.00291784	−	0.0159978i
$760$		0			0
$761$	13.7853			0.499716			0.249858	−	0.968283i	$-0.419616\pi$
$761$	13.7853			0.499716			0.249858	+	0.968283i	$0.419616\pi$
$762$		0			0
$763$	−42.6233	+	1.90249i	−1.54307	+	0.0688748i
$764$		0			0
$765$	23.1010	+	18.9260i	0.835218	+	0.684271i
$766$		0			0
$767$		−	0.503620i		−	0.0181847i
$768$		0			0
$769$	−20.0352	+	11.5673i	−0.722486	+	0.417128i	−0.815667	−	0.578522i	$-0.803630\pi$
$769$	−20.0352	+	11.5673i	−0.722486	+	0.417128i	0.0931808	+	0.995649i	$0.470297\pi$
$770$		0			0
$771$	−0.275611	−	1.51111i	−0.00992591	−	0.0544212i
$772$		0			0
$773$	26.5072	+	45.9118i	0.953398	+	1.65133i	0.737993	+	0.674808i	$0.235774\pi$
$773$	26.5072	+	45.9118i	0.953398	+	1.65133i	0.215405	+	0.976525i	$0.430893\pi$
$774$		0			0
$775$	15.7561	+	9.09678i	0.565975	+	0.326766i
$776$		0			0
$777$	−13.8456	+	12.8627i	−0.496708	+	0.461445i
$778$		0			0
$779$		−	7.69155i		−	0.275578i
$780$		0			0
$781$	−3.39327			−0.121421
$782$		0			0
$783$	0.695075	+	39.4364i	0.0248400	+	1.40934i
$784$		0			0
$785$	47.8693	+	27.6373i	1.70853	+	0.986418i
$786$		0			0
$787$	−5.16436	−	2.98164i	−0.184089	−	0.106284i	0.405123	−	0.914262i	$-0.367229\pi$
$787$	−5.16436	−	2.98164i	−0.184089	−	0.106284i	−0.589213	+	0.807978i	$0.700562\pi$
$788$		0			0
$789$	−12.1404	+	2.21430i	−0.432211	+	0.0788312i
$790$		0			0
$791$	−1.60123	−	35.8739i	−0.0569333	−	1.27553i
$792$		0			0
$793$	0.0707584	−	0.122557i	0.00251271	−	0.00435213i
$794$		0			0
$795$	18.9118	+	22.2712i	0.670732	+	0.789877i
$796$		0			0
$797$	5.28758	+	9.15836i	0.187296	+	0.324406i	0.944348	−	0.328949i	$-0.106694\pi$
$797$	5.28758	+	9.15836i	0.187296	+	0.324406i	−0.757052	+	0.653355i	$0.773361\pi$
$798$		0			0
$799$	−23.7131	+	41.0724i	−0.838910	+	1.45304i
$800$		0			0
$801$	−5.55942	+	33.8499i	−0.196432	+	1.19603i
$802$		0			0
$803$	−7.74035	−	13.4067i	−0.273151	−	0.473111i
$804$		0			0
$805$	0.695223	+	0.361052i	0.0245034	+	0.0127254i
$806$		0			0
$807$	41.7168	−	35.4243i	1.46850	−	1.24699i
$808$		0			0
$809$	−32.1452	+	18.5591i	−1.13017	+	0.652501i	−0.943977	−	0.330012i	$-0.892947\pi$
$809$	−32.1452	+	18.5591i	−1.13017	+	0.652501i	−0.186189	+	0.982514i	$0.559614\pi$
$810$		0			0
$811$		−	7.02945i		−	0.246837i	−0.992355	−	0.123419i	$-0.960614\pi$
$811$		−	7.02945i		−	0.246837i	0.992355	−	0.123419i	$-0.0393858\pi$
$812$		0			0
$813$	10.6477	−	29.7978i	0.373431	−	1.04505i
$814$		0			0
$815$	−33.3494	+	57.7629i	−1.16818	+	2.02335i
$816$		0			0
$817$	13.8424	−	7.99192i	0.484284	−	0.279602i
$818$		0			0
$819$	0.166863	+	0.388779i	0.00583066	+	0.0135851i
$820$		0			0
$821$	18.5657	−	10.7189i	0.647947	−	0.374092i	−0.139722	−	0.990191i	$-0.544621\pi$
$821$	18.5657	−	10.7189i	0.647947	−	0.374092i	0.787669	+	0.616099i	$0.211288\pi$
$822$		0			0
$823$	−9.72455	+	16.8434i	−0.338977	+	0.587125i	−0.984240	−	0.176835i	$-0.943414\pi$
$823$	−9.72455	+	16.8434i	−0.338977	+	0.587125i	0.645264	+	0.763960i	$0.276747\pi$
$824$		0			0
$825$	−11.0039	+	2.00700i	−0.383106	+	0.0698748i
$826$		0			0
$827$			16.3789i			0.569549i	0.958595	+	0.284774i	$0.0919187\pi$
$827$			16.3789i			0.569549i	−0.958595	+	0.284774i	$0.908081\pi$
$828$		0			0
$829$	−13.5517	+	7.82408i	−0.470670	+	0.271741i	−0.716520	−	0.697566i	$-0.754266\pi$
$829$	−13.5517	+	7.82408i	−0.470670	+	0.271741i	0.245850	+	0.969308i	$0.420933\pi$
$830$		0			0
$831$	9.50032	+	52.0878i	0.329562	+	1.80691i
$832$		0			0
$833$	−10.5895	+	22.8250i	−0.366904	+	0.790839i
$834$		0			0
$835$	−2.19801	−	3.80706i	−0.0760651	−	0.131749i
$836$		0			0
$837$	0.624100	+	35.4095i	0.0215721	+	1.22393i
$838$		0			0
$839$	−0.260756	+	0.451642i	−0.00900229	+	0.0155924i	−0.870491	−	0.492184i	$-0.836199\pi$
$839$	−0.260756	+	0.451642i	−0.00900229	+	0.0155924i	0.861489	+	0.507776i	$0.169532\pi$
$840$		0			0
$841$	14.3096	+	24.7849i	0.493433	+	0.854652i
$842$		0			0
$843$	2.63971	−	7.38728i	0.0909164	−	0.254431i
$844$		0			0
$845$	−17.9969	+	31.1716i	−0.619114	+	1.07234i
$846$		0			0
$847$	6.27652	−	12.0858i	0.215664	−	0.415271i
$848$		0			0
$849$	5.45612	−	15.2691i	0.187253	−	0.524033i
$850$		0			0
$851$	0.381849	+	0.220461i	0.0130896	+	0.00755730i
$852$		0			0
$853$	15.3460	+	8.85999i	0.525436	+	0.303360i	0.739156	−	0.673535i	$-0.235225\pi$
$853$	15.3460	+	8.85999i	0.525436	+	0.303360i	−0.213720	+	0.976895i	$0.568558\pi$
$854$		0			0
$855$	37.5801	+	6.17205i	1.28521	+	0.211080i
$856$		0			0
$857$	−2.82727			−0.0965777			−0.0482888	−	0.998833i	$-0.515377\pi$
$857$	−2.82727			−0.0965777			−0.0482888	+	0.998833i	$0.515377\pi$
$858$		0			0
$859$		−	9.21152i		−	0.314293i	−0.987575	−	0.157147i	$-0.949770\pi$
$859$		−	9.21152i		−	0.314293i	0.987575	−	0.157147i	$-0.0502295\pi$
$860$		0			0
$861$	−1.71563	−	7.49548i	−0.0584686	−	0.255445i
$862$		0			0
$863$	15.7016	+	9.06534i	0.534490	+	0.308588i	0.742843	−	0.669466i	$-0.233477\pi$
$863$	15.7016	+	9.06534i	0.534490	+	0.308588i	−0.208353	+	0.978054i	$0.566810\pi$
$864$		0			0
$865$	5.86705	+	10.1620i	0.199486	+	0.345520i
$866$		0			0
$867$	−6.65342	−	2.37748i	−0.225962	−	0.0807434i
$868$		0			0
$869$	8.84423	−	5.10622i	0.300020	−	0.173217i
$870$		0			0
$871$			0.756208i			0.0256231i
$872$		0			0
$873$	−49.0693	−	8.05900i	−1.66074	−	0.272756i
$874$		0			0
$875$	−7.87033	+	15.1547i	−0.266066	+	0.512323i
$876$		0			0
$877$	14.2086			0.479792			0.239896	−	0.970799i	$-0.422887\pi$
$877$	14.2086			0.479792			0.239896	+	0.970799i	$0.422887\pi$
$878$		0			0
$879$	−21.5802	+	18.3250i	−0.727881	+	0.618087i
$880$		0			0
$881$	46.0649			1.55197			0.775984	−	0.630753i	$-0.217254\pi$
$881$	46.0649			1.55197			0.775984	+	0.630753i	$0.217254\pi$
$882$		0			0
$883$	−8.16154			−0.274658			−0.137329	−	0.990526i	$-0.543852\pi$
$883$	−8.16154			−0.274658			−0.137329	+	0.990526i	$0.543852\pi$
$884$		0			0
$885$	−42.6778	−	15.2501i	−1.43460	−	0.512628i
$886$		0			0
$887$	−27.1287			−0.910893			−0.455446	−	0.890263i	$-0.650520\pi$
$887$	−27.1287			−0.910893			−0.455446	+	0.890263i	$0.650520\pi$
$888$		0			0
$889$	11.2557	−	21.6733i	0.377503	−	0.726900i
$890$		0			0
$891$	−14.3836	−	16.3458i	−0.481868	−	0.547605i
$892$		0			0
$893$			60.4798i			2.02388i
$894$		0			0
$895$	9.36139	−	5.40480i	0.312917	−	0.180662i
$896$		0			0
$897$	0.00752410	−	0.00638917i	0.000251223	−	0.000213328i
$898$		0			0
$899$	25.8678	+	44.8043i	0.862739	+	1.49431i
$900$		0			0
$901$	18.9617	+	10.9475i	0.631704	+	0.364715i
$902$		0			0
$903$	11.7069	−	10.8758i	0.389582	−	0.361924i
$904$		0			0
$905$			42.5610i			1.41478i
$906$		0			0
$907$	25.5851			0.849541			0.424770	−	0.905301i	$-0.360355\pi$
$907$	25.5851			0.849541			0.424770	+	0.905301i	$0.360355\pi$
$908$		0			0
$909$	29.4717	−	11.1206i	0.977514	−	0.368849i
$910$		0			0
$911$	−4.57426	−	2.64095i	−0.151552	−	0.0874986i	0.422306	−	0.906453i	$-0.361221\pi$
$911$	−4.57426	−	2.64095i	−0.151552	−	0.0874986i	−0.573858	+	0.818955i	$0.694554\pi$
$912$		0			0
$913$	28.7732	+	16.6122i	0.952255	+	0.549785i
$914$		0			0
$915$	−8.24312	−	9.70738i	−0.272509	−	0.320916i
$916$		0			0
$917$	3.88838	−	7.48728i	0.128406	−	0.247252i
$918$		0			0
$919$	27.7214	−	48.0149i	0.914445	−	1.58387i	0.106733	−	0.994288i	$-0.465961\pi$
$919$	27.7214	−	48.0149i	0.914445	−	1.58387i	0.807712	−	0.589578i	$-0.200706\pi$
$920$		0			0
$921$	−1.67845	+	0.306133i	−0.0553069	+	0.0100874i
$922$		0			0
$923$	−0.0373815	−	0.0647466i	−0.00123043	−	0.00213116i
$924$		0			0
$925$	5.50423	−	9.53360i	0.180978	−	0.313463i
$926$		0			0
$927$	−16.3389	−	43.3009i	−0.536639	−	1.42219i
$928$		0			0
$929$	−17.6004	−	30.4849i	−0.577452	−	1.00018i	−0.995770	−	0.0918756i	$-0.970714\pi$
$929$	−17.6004	−	30.4849i	−0.577452	−	1.00018i	0.418319	−	0.908300i	$-0.362620\pi$
$930$		0			0
$931$	2.85874	+	31.9597i	0.0936914	+	1.04744i
$932$		0			0
$933$	−42.8319	−	15.3052i	−1.40225	−	0.501070i
$934$		0			0
$935$	−20.8562	+	12.0413i	−0.682070	+	0.393793i
$936$		0			0
$937$		−	47.6315i		−	1.55605i	−0.628231	−	0.778027i	$-0.716221\pi$
$937$		−	47.6315i		−	1.55605i	0.628231	−	0.778027i	$-0.283779\pi$
$938$		0			0
$939$	16.2930	+	19.1872i	0.531702	+	0.626151i
$940$		0			0
$941$	10.3802	−	17.9790i	0.338384	−	0.586098i	−0.645745	−	0.763553i	$-0.723453\pi$
$941$	10.3802	−	17.9790i	0.338384	−	0.586098i	0.984129	+	0.177455i	$0.0567865\pi$
$942$		0			0
$943$	−0.155366	+	0.0897005i	−0.00505941	+	0.00292105i
$944$		0			0
$945$	37.9988	−	2.36767i	1.23610	−	0.0770205i
$946$		0			0
$947$	6.50667	−	3.75663i	0.211438	−	0.122074i	−0.390541	−	0.920585i	$-0.627712\pi$
$947$	6.50667	−	3.75663i	0.211438	−	0.122074i	0.601980	+	0.798511i	$0.294379\pi$
$948$		0			0
$949$	0.170541	−	0.295385i	0.00553599	−	0.00958861i
$950$		0			0
$951$	33.0303	+	38.8976i	1.07108	+	1.26134i
$952$		0			0
$953$		−	53.6047i		−	1.73643i	−0.496192	−	0.868213i	$-0.665269\pi$
$953$		−	53.6047i		−	1.73643i	0.496192	−	0.868213i	$-0.334731\pi$
$954$		0			0
$955$	6.32566	−	3.65212i	0.204694	−	0.118180i
$956$		0			0
$957$	−29.9523	−	10.7029i	−0.968219	−	0.345975i
$958$		0			0
$959$	13.2175	+	6.86425i	0.426814	+	0.221658i
$960$		0			0
$961$	7.72640	+	13.3825i	0.249239	+	0.431694i
$962$		0			0
$963$	33.3772	+	5.48178i	1.07557	+	0.176648i
$964$		0			0
$965$	10.3288	−	17.8899i	0.332495	−	0.575898i
$966$		0			0
$967$	5.72860	+	9.92223i	0.184220	+	0.319078i	0.943313	−	0.331904i	$-0.107691\pi$
$967$	5.72860	+	9.92223i	0.184220	+	0.319078i	−0.759094	+	0.650981i	$0.774358\pi$
$968$		0			0
$969$	28.0759	−	5.12078i	0.901929	−	0.164503i
$970$		0			0
$971$	4.02601	−	6.97326i	0.129201	−	0.223782i	−0.794166	−	0.607700i	$-0.792092\pi$
$971$	4.02601	−	6.97326i	0.129201	−	0.223782i	0.923367	+	0.383918i	$0.125425\pi$
$972$		0			0
$973$	−2.54388	−	56.9931i	−0.0815532	−	1.82711i
$974$		0			0
$975$	−0.159518	−	0.187854i	−0.00510866	−	0.00601614i
$976$		0			0
$977$	−41.4615	−	23.9378i	−1.32647	−	0.765838i	−0.341718	−	0.939802i	$-0.611009\pi$
$977$	−41.4615	−	23.9378i	−1.32647	−	0.765838i	−0.984752	+	0.173965i	$0.944342\pi$
$978$		0			0
$979$	−23.9567	−	13.8314i	−0.765658	−	0.442053i
$980$		0			0
$981$	37.4228	+	30.6595i	1.19482	+	0.978883i
$982$		0			0
$983$	−2.36180			−0.0753297			−0.0376648	−	0.999290i	$-0.511992\pi$
$983$	−2.36180			−0.0753297			−0.0376648	+	0.999290i	$0.511992\pi$
$984$		0			0
$985$			7.69247i			0.245102i
$986$		0			0
$987$	13.4903	+	58.9381i	0.429400	+	1.87602i
$988$		0			0
$989$	−0.322866	−	0.186407i	−0.0102665	−	0.00592739i
$990$		0			0
$991$	11.8241	+	20.4800i	0.375606	+	0.650568i	0.990417	−	0.138106i	$-0.0441014\pi$
$991$	11.8241	+	20.4800i	0.375606	+	0.650568i	−0.614812	+	0.788674i	$0.710768\pi$
$992$		0			0
$993$	−7.68434	+	6.52523i	−0.243855	+	0.207072i
$994$		0			0
$995$	9.68979	−	5.59440i	0.307187	−	0.177355i
$996$		0			0
$997$		−	42.4290i		−	1.34374i	−0.740670	−	0.671869i	$-0.765492\pi$
$997$		−	42.4290i		−	1.34374i	0.740670	−	0.671869i	$-0.234508\pi$
$998$		0			0
$999$	21.4254	−	0.377627i	0.677870	−	0.0119476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.e.929.11		48
3.2	odd	2		3024.2.df.e.1601.4		48
4.3	odd	2		504.2.cx.a.425.14	yes	48
7.3	odd	6		1008.2.ca.e.353.19		48
9.4	even	3		3024.2.ca.e.2609.4		48
9.5	odd	6		1008.2.ca.e.257.19		48
12.11	even	2		1512.2.cx.a.89.4		48
21.17	even	6		3024.2.ca.e.2033.4		48
28.3	even	6		504.2.bs.a.353.6	yes	48
36.23	even	6		504.2.bs.a.257.6	✓	48
36.31	odd	6		1512.2.bs.a.1097.4		48
63.31	odd	6		3024.2.df.e.17.4		48
63.59	even	6	inner	1008.2.df.e.689.11		48
84.59	odd	6		1512.2.bs.a.521.4		48
252.31	even	6		1512.2.cx.a.17.4		48
252.59	odd	6		504.2.cx.a.185.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.6	✓	48	36.23	even	6
504.2.bs.a.353.6	yes	48	28.3	even	6
504.2.cx.a.185.14	yes	48	252.59	odd	6
504.2.cx.a.425.14	yes	48	4.3	odd	2
1008.2.ca.e.257.19		48	9.5	odd	6
1008.2.ca.e.353.19		48	7.3	odd	6
1008.2.df.e.689.11		48	63.59	even	6	inner
1008.2.df.e.929.11		48	1.1	even	1	trivial
1512.2.bs.a.521.4		48	84.59	odd	6
1512.2.bs.a.1097.4		48	36.31	odd	6
1512.2.cx.a.17.4		48	252.31	even	6
1512.2.cx.a.89.4		48	12.11	even	2
3024.2.ca.e.2033.4		48	21.17	even	6
3024.2.ca.e.2609.4		48	9.4	even	3
3024.2.df.e.17.4		48	63.31	odd	6
3024.2.df.e.1601.4		48	3.2	odd	2

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.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.310783 - 1.70394i) q^{3} +2.76937 q^{5} +(1.21939 - 2.34800i) q^{7} +(-2.80683 + 1.05911i) q^{9} +O(q^{10})\)	\(q+(-0.310783 - 1.70394i) q^{3} +2.76937 q^{5} +(1.21939 - 2.34800i) q^{7} +(-2.80683 + 1.05911i) q^{9} -2.41924i q^{11} +(0.0461613 - 0.0266512i) q^{13} +(-0.860670 - 4.71884i) q^{15} +(-1.79727 - 3.11297i) q^{17} +(-3.96978 - 2.29195i) q^{19} +(-4.37981 - 1.34805i) q^{21} +0.106917i q^{23} +2.66939 q^{25} +(2.67697 + 4.45352i) q^{27} +(6.57376 + 3.79536i) q^{29} +(5.90251 + 3.40781i) q^{31} +(-4.12225 + 0.751859i) q^{33} +(3.37694 - 6.50246i) q^{35} +(2.06198 - 3.57146i) q^{37} +(-0.0597583 - 0.0703734i) q^{39} +(0.838974 + 1.45315i) q^{41} +(-1.74347 + 3.01978i) q^{43} +(-7.77313 + 2.93306i) q^{45} +(-6.59698 - 11.4263i) q^{47} +(-4.02618 - 5.72625i) q^{49} +(-4.74575 + 4.02990i) q^{51} +(-5.27512 + 3.04559i) q^{53} -6.69977i q^{55} +(-2.67161 + 7.47657i) q^{57} +(4.72417 - 8.18250i) q^{59} +(2.29928 - 1.32749i) q^{61} +(-0.935832 + 7.88189i) q^{63} +(0.127838 - 0.0738070i) q^{65} +(-7.09356 + 12.2864i) q^{67} +(0.182180 - 0.0332279i) q^{69} -1.40262i q^{71} +(5.54168 - 3.19949i) q^{73} +(-0.829599 - 4.54848i) q^{75} +(-5.68038 - 2.95000i) q^{77} +(2.11067 + 3.65578i) q^{79} +(6.75657 - 5.94548i) q^{81} +(-6.86670 + 11.8935i) q^{83} +(-4.97731 - 8.62095i) q^{85} +(4.42406 - 12.3808i) q^{87} +(5.71724 - 9.90254i) q^{89} +(-0.00628839 - 0.140885i) q^{91} +(3.97232 - 11.1166i) q^{93} +(-10.9938 - 6.34726i) q^{95} +(14.3549 + 8.28778i) q^{97} +(2.56224 + 6.79040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9}+O(q^{10}) \) 48 * q + 2 * q^9	\( 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} + 32 q^{63} - 36 q^{65} - 12 q^{77} - 6 q^{79} + 6 q^{81} + 54 q^{87} - 18 q^{89} - 6 q^{91} + 4 q^{93} + 54 q^{95} + 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Introduction

L-functions

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