LMFDB - Embedded newform 1008.2.ca.e.257.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(257,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.257"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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			257.19
Character	$\chi$	$=$	1008.257
Dual form			1008.2.ca.e.353.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32026 + 1.12112i) q^{3} +(1.38468 + 2.39834i) q^{5} +(1.42373 + 2.23002i) q^{7} +(0.486198 + 2.96034i) q^{9} +(-2.09513 - 1.20962i) q^{11} +(-0.0461613 - 0.0266512i) q^{13} +(-0.860670 + 4.71884i) q^{15} +(1.79727 + 3.11297i) q^{17} +(-3.96978 - 2.29195i) q^{19} +(-0.620412 + 4.54038i) q^{21} +(-0.0925928 + 0.0534585i) q^{23} +(-1.33469 + 2.31176i) q^{25} +(-2.67697 + 4.45352i) q^{27} +(6.57376 - 3.79536i) q^{29} -6.81563i q^{31} +(-1.41000 - 3.94590i) q^{33} +(-3.37694 + 6.50246i) q^{35} +(2.06198 - 3.57146i) q^{37} +(-0.0310660 - 0.0869389i) q^{39} +(-0.838974 + 1.45315i) q^{41} +(-1.74347 - 3.01978i) q^{43} +(-6.42667 + 5.26520i) q^{45} -13.1940 q^{47} +(-2.94599 + 6.34989i) q^{49} +(-1.11712 + 6.12489i) q^{51} +(5.27512 - 3.04559i) q^{53} -6.69977i q^{55} +(-2.67161 - 7.47657i) q^{57} +9.44833 q^{59} +2.65498i q^{61} +(-5.90941 + 5.29896i) q^{63} -0.147614i q^{65} +14.1871 q^{67} +(-0.182180 - 0.0332279i) q^{69} +1.40262i q^{71} +(5.54168 - 3.19949i) q^{73} +(-4.35390 + 1.55579i) q^{75} +(-0.285412 - 6.39435i) q^{77} -4.22133 q^{79} +(-8.52722 + 2.87862i) q^{81} +(6.86670 + 11.8935i) q^{83} +(-4.97731 + 8.62095i) q^{85} +(12.9341 + 2.35907i) q^{87} +(-5.71724 + 9.90254i) q^{89} +(-0.00628839 - 0.140885i) q^{91} +(7.64111 - 8.99843i) q^{93} -12.6945i q^{95} +(-14.3549 + 8.28778i) q^{97} +(2.56224 - 6.79040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Character values

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

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

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
$3$	1.32026	+	1.12112i	0.762255	+	0.647277i
$3$	1.32026	+	1.12112i	0.762255	+	0.647277i
$4$		0			0
$5$	1.38468	+	2.39834i	0.619249	+	1.07257i	0.989623	+	0.143688i	$0.0458962\pi$
$5$	1.38468	+	2.39834i	0.619249	+	1.07257i	−0.370374	+	0.928883i	$0.620770\pi$
$6$		0			0
$7$	1.42373	+	2.23002i	0.538119	+	0.842869i
$7$	1.42373	+	2.23002i	0.538119	+	0.842869i
$8$		0			0
$9$	0.486198	+	2.96034i	0.162066	+	0.986780i
$10$		0			0
$11$	−2.09513	−	1.20962i	−0.631704	−	0.364715i	0.149707	−	0.988730i	$-0.452167\pi$
$11$	−2.09513	−	1.20962i	−0.631704	−	0.364715i	−0.781412	+	0.624016i	$0.785500\pi$
$12$		0			0
$13$	−0.0461613	−	0.0266512i	−0.0128028	−	0.00739172i	0.493585	−	0.869698i	$-0.335686\pi$
$13$	−0.0461613	−	0.0266512i	−0.0128028	−	0.00739172i	−0.506388	+	0.862306i	$0.669020\pi$
$14$		0			0
$15$	−0.860670	+	4.71884i	−0.222224	+	1.21840i
$16$		0			0
$17$	1.79727	+	3.11297i	0.435903	+	0.755006i	0.997369	−	0.0724940i	$-0.0230958\pi$
$17$	1.79727	+	3.11297i	0.435903	+	0.755006i	−0.561466	+	0.827500i	$0.689762\pi$
$18$		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
$21$	−0.620412	+	4.54038i	−0.135385	+	0.990793i
$22$		0			0
$23$	−0.0925928	+	0.0534585i	−0.0193069	+	0.0111469i	−0.509622	−	0.860398i	$-0.670215\pi$
$23$	−0.0925928	+	0.0534585i	−0.0193069	+	0.0111469i	0.490315	+	0.871545i	$0.336882\pi$
$24$		0			0
$25$	−1.33469	+	2.31176i	−0.266939	+	0.462351i
$26$		0			0
$27$	−2.67697	+	4.45352i	−0.515184	+	0.857080i
$28$		0			0
$29$	6.57376	−	3.79536i	1.22072	−	0.704781i	0.255646	−	0.966770i	$-0.417712\pi$
$29$	6.57376	−	3.79536i	1.22072	−	0.704781i	0.965071	+	0.261989i	$0.0843785\pi$
$30$		0			0
$31$		−	6.81563i		−	1.22412i	−0.790810	−	0.612062i	$-0.790340\pi$
$31$		−	6.81563i		−	1.22412i	0.790810	−	0.612062i	$-0.209660\pi$
$32$		0			0
$33$	−1.41000	−	3.94590i	−0.245449	−	0.686893i
$34$		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
$39$	−0.0310660	−	0.0869389i	−0.00497454	−	0.0139214i
$40$		0			0
$41$	−0.838974	+	1.45315i	−0.131026	+	0.226943i	−0.924072	−	0.382218i	$-0.875160\pi$
$41$	−0.838974	+	1.45315i	−0.131026	+	0.226943i	0.793047	+	0.609161i	$0.208494\pi$
$42$		0			0
$43$	−1.74347	−	3.01978i	−0.265877	−	0.460513i	0.701916	−	0.712260i	$-0.252328\pi$
$43$	−1.74347	−	3.01978i	−0.265877	−	0.460513i	−0.967793	+	0.251747i	$0.918995\pi$
$44$		0			0
$45$	−6.42667	+	5.26520i	−0.958032	+	0.784890i
$46$		0			0
$47$	−13.1940			−1.92454			−0.962268	−	0.272104i	$-0.912280\pi$
$47$	−13.1940			−1.92454			−0.962268	+	0.272104i	$0.912280\pi$
$48$		0			0
$49$	−2.94599	+	6.34989i	−0.420855	+	0.907128i
$50$		0			0
$51$	−1.11712	+	6.12489i	−0.156428	+	0.857657i
$52$		0			0
$53$	5.27512	−	3.04559i	0.724593	−	0.418344i	−0.0918477	−	0.995773i	$-0.529277\pi$
$53$	5.27512	−	3.04559i	0.724593	−	0.418344i	0.816441	+	0.577429i	$0.195944\pi$
$54$		0			0
$55$		−	6.69977i		−	0.903397i
$56$		0			0
$57$	−2.67161	−	7.47657i	−0.353864	−	0.990295i
$58$		0			0
$59$	9.44833			1.23007			0.615034	−	0.788500i	$-0.289142\pi$
$59$	9.44833			1.23007			0.615034	+	0.788500i	$0.289142\pi$
$60$		0			0
$61$			2.65498i			0.339935i	0.985450	+	0.169967i	$0.0543663\pi$
$61$			2.65498i			0.339935i	−0.985450	+	0.169967i	$0.945634\pi$
$62$		0			0
$63$	−5.90941	+	5.29896i	−0.744515	+	0.667606i
$64$		0			0
$65$		−	0.147614i		−	0.0183093i
$66$		0			0
$67$	14.1871			1.73323			0.866616	−	0.498975i	$-0.166290\pi$
$67$	14.1871			1.73323			0.866616	+	0.498975i	$0.166290\pi$
$68$		0			0
$69$	−0.182180	−	0.0332279i	−0.0219319	−	0.00400017i
$70$		0			0
$71$			1.40262i			0.166460i	0.996530	+	0.0832300i	$0.0265236\pi$
$71$			1.40262i			0.166460i	−0.996530	+	0.0832300i	$0.973476\pi$
$72$		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
$75$	−4.35390	+	1.55579i	−0.502745	+	0.179647i
$76$		0			0
$77$	−0.285412	−	6.39435i	−0.0325257	−	0.728704i
$78$		0			0
$79$	−4.22133			−0.474937			−0.237469	−	0.971395i	$-0.576318\pi$
$79$	−4.22133			−0.474937			−0.237469	+	0.971395i	$0.576318\pi$
$80$		0			0
$81$	−8.52722	+	2.87862i	−0.947469	+	0.319847i
$82$		0			0
$83$	6.86670	+	11.8935i	0.753719	+	1.30548i	0.946009	+	0.324141i	$0.105075\pi$
$83$	6.86670	+	11.8935i	0.753719	+	1.30548i	−0.192290	+	0.981338i	$0.561591\pi$
$84$		0			0
$85$	−4.97731	+	8.62095i	−0.539865	+	0.935073i
$86$		0			0
$87$	12.9341	+	2.35907i	1.38669	+	0.252918i
$88$		0			0
$89$	−5.71724	+	9.90254i	−0.606026	+	1.04967i	0.385863	+	0.922556i	$0.373904\pi$
$89$	−5.71724	+	9.90254i	−0.606026	+	1.04967i	−0.991888	+	0.127111i	$0.959429\pi$
$90$		0			0
$91$	−0.00628839	−	0.140885i	−0.000659203	−	0.0147687i
$92$		0			0
$93$	7.64111	−	8.99843i	0.792346	−	0.933094i
$94$		0			0
$95$		−	12.6945i		−	1.30243i
$96$		0			0
$97$	−14.3549	+	8.28778i	−1.45751	+	0.841496i	−0.998889	−	0.0471333i	$-0.984991\pi$
$97$	−14.3549	+	8.28778i	−1.45751	+	0.841496i	−0.458626	+	0.888630i	$0.651658\pi$
$98$		0			0
$99$	2.56224	−	6.79040i	0.257515	−	0.682461i
$100$		0			0
$101$	−5.25000	+	9.09326i	−0.522394	+	0.904813i	0.477266	+	0.878759i	$0.341628\pi$
$101$	−5.25000	+	9.09326i	−0.522394	+	0.904813i	−0.999661	+	0.0260545i	$0.991706\pi$
$102$		0			0
$103$	13.3602	−	7.71349i	1.31642	−	0.760033i	0.333266	−	0.942833i	$-0.391849\pi$
$103$	13.3602	−	7.71349i	1.31642	−	0.760033i	0.983150	+	0.182800i	$0.0585160\pi$
$104$		0			0
$105$	−11.7485	+	4.79903i	−1.14653	+	0.468338i
$106$		0			0
$107$	9.76426	+	5.63740i	0.943946	+	0.544988i	0.891195	−	0.453620i	$-0.149868\pi$
$107$	9.76426	+	5.63740i	0.943946	+	0.544988i	0.0527511	+	0.998608i	$0.483201\pi$
$108$		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	0.937723	−	0.347384i	$-0.112930\pi$
$113$	11.7542	+	6.78629i	1.10574	+	0.638400i	0.168018	+	0.985784i	$0.446263\pi$
$114$		0			0
$115$	−0.256423	−	0.148046i	−0.0239116	−	0.0138054i
$116$		0			0
$117$	0.0564532	−	0.149611i	0.00521910	−	0.0138315i
$118$		0			0
$119$	−4.38315	+	8.43998i	−0.401803	+	0.773692i
$120$		0			0
$121$	−2.57363	−	4.45766i	−0.233966	−	0.405242i
$122$		0			0
$123$	−2.73681	+	0.977949i	−0.246770	+	0.0881787i
$124$		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
$129$	1.08368	−	5.94155i	0.0954129	−	0.523124i
$130$		0			0
$131$	1.59440	+	2.76158i	0.139303	+	0.241280i	0.927233	−	0.374485i	$-0.122180\pi$
$131$	1.59440	+	2.76158i	0.139303	+	0.241280i	−0.787930	+	0.615765i	$0.788847\pi$
$132$		0			0
$133$	−0.540789	−	12.1158i	−0.0468924	−	1.05057i
$134$		0			0
$135$	−14.3878	−	0.253588i	−1.23831	−	0.0218254i
$136$		0			0
$137$	4.87507	+	2.81462i	0.416505	+	0.240470i	0.693581	−	0.720379i	$-0.256032\pi$
$137$	4.87507	+	2.81462i	0.416505	+	0.240470i	−0.277076	+	0.960848i	$0.589365\pi$
$138$		0			0
$139$	−18.6739	−	10.7814i	−1.58390	−	0.914467i	−0.994282	−	0.106786i	$-0.965944\pi$
$139$	−18.6739	−	10.7814i	−1.58390	−	0.914467i	−0.589620	−	0.807680i	$-0.700723\pi$
$140$		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
$147$	−11.0085	+	5.08075i	−0.907962	+	0.419053i
$148$		0			0
$149$	16.5674	−	9.56517i	1.35725	−	0.783609i	0.367998	−	0.929826i	$-0.380043\pi$
$149$	16.5674	−	9.56517i	1.35725	−	0.783609i	0.989252	+	0.146217i	$0.0467099\pi$
$150$		0			0
$151$	−3.94050	+	6.82515i	−0.320673	+	0.555423i	−0.980627	−	0.195884i	$-0.937243\pi$
$151$	−3.94050	+	6.82515i	−0.320673	+	0.555423i	0.659954	+	0.751306i	$0.270576\pi$
$152$		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
$157$		−	19.9593i		−	1.59293i	−0.604687	−	0.796463i	$-0.706702\pi$
$157$		−	19.9593i		−	1.59293i	0.604687	−	0.796463i	$-0.293298\pi$
$158$		0			0
$159$	10.3790	+	1.89303i	0.823109	+	0.150127i
$160$		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
$165$	7.51122	−	8.84547i	0.584748	−	0.688619i
$166$		0			0
$167$	0.793686	−	1.37470i	0.0614172	−	0.106378i	−0.833682	−	0.552245i	$-0.813771\pi$
$167$	0.793686	−	1.37470i	0.0614172	−	0.106378i	0.895099	+	0.445867i	$0.147105\pi$
$168$		0			0
$169$	−6.49858	−	11.2559i	−0.499891	−	0.865836i
$170$		0			0
$171$	4.85486	−	12.8662i	0.371260	−	0.983906i
$172$		0			0
$173$	4.23711			0.322142			0.161071	−	0.986943i	$-0.448505\pi$
$173$	4.23711			0.322142			0.161071	+	0.986943i	$0.448505\pi$
$174$		0			0
$175$	−7.05551	+	0.314923i	−0.533346	+	0.0238059i
$176$		0			0
$177$	12.4743	+	10.5927i	0.937626	+	0.796194i
$178$		0			0
$179$	−3.38034	+	1.95164i	−0.252658	+	0.145872i	−0.620981	−	0.783826i	$-0.713266\pi$
$179$	−3.38034	+	1.95164i	−0.252658	+	0.145872i	0.368323	+	0.929698i	$0.379932\pi$
$180$		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
$185$	11.4208			0.839671
$186$		0			0
$187$		−	8.69608i		−	0.635921i
$188$		0			0
$189$	−13.7427	+	0.370896i	−0.999636	+	0.0269787i
$190$		0			0
$191$		−	2.63751i		−	0.190844i	−0.995437	−	0.0954219i	$-0.969580\pi$
$191$		−	2.63751i		−	0.190844i	0.995437	−	0.0954219i	$-0.0304200\pi$
$192$		0			0
$193$	−7.45930			−0.536932			−0.268466	−	0.963289i	$-0.586517\pi$
$193$	−7.45930			−0.536932			−0.268466	+	0.963289i	$0.586517\pi$
$194$		0			0
$195$	0.165492	−	0.194890i	0.0118512	−	0.0139563i
$196$		0			0
$197$		−	2.77770i		−	0.197903i	−0.995092	−	0.0989515i	$-0.968451\pi$
$197$		−	2.77770i		−	0.197903i	0.995092	−	0.0989515i	$-0.0315489\pi$
$198$		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
$201$	18.7308	+	15.9054i	1.32117	+	1.12188i
$202$		0			0
$203$	17.8230	+	9.25606i	1.25093	+	0.649648i
$204$		0			0
$205$	−4.64685			−0.324550
$206$		0			0
$207$	−0.203274	−	0.248115i	−0.0141285	−	0.0172452i
$208$		0			0
$209$	5.54479	+	9.60386i	0.383541	+	0.664313i
$210$		0			0
$211$	10.4855	−	18.1614i	0.721849	−	1.25028i	−0.238409	−	0.971165i	$-0.576626\pi$
$211$	10.4855	−	18.1614i	0.721849	−	1.25028i	0.960258	−	0.279115i	$-0.0900410\pi$
$212$		0			0
$213$	−1.57250	+	1.85183i	−0.107746	+	0.126885i
$214$		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
$219$	10.9035	+	1.98869i	0.736789	+	0.134383i
$220$		0			0
$221$		−	0.191598i		−	0.0128883i
$222$		0			0
$223$	−8.82344	+	5.09421i	−0.590861	+	0.341134i	−0.765438	−	0.643510i	$-0.777478\pi$
$223$	−8.82344	+	5.09421i	−0.590861	+	0.341134i	0.174577	+	0.984644i	$0.444144\pi$
$224$		0			0
$225$	−7.49251	−	2.82717i	−0.499501	−	0.188478i
$226$		0			0
$227$	5.03151	−	8.71483i	0.333953	−	0.578424i	−0.649330	−	0.760507i	$-0.724951\pi$
$227$	5.03151	−	8.71483i	0.333953	−	0.578424i	0.983283	+	0.182083i	$0.0582839\pi$
$228$		0			0
$229$	12.9518	−	7.47775i	0.855882	−	0.494144i	−0.00674926	−	0.999977i	$-0.502148\pi$
$229$	12.9518	−	7.47775i	0.855882	−	0.494144i	0.862631	+	0.505834i	$0.168815\pi$
$230$		0			0
$231$	6.79199	−	8.76221i	0.446880	−	0.576511i
$232$		0			0
$233$	−14.3200	−	8.26764i	−0.938133	−	0.541631i	−0.0487581	−	0.998811i	$-0.515526\pi$
$233$	−14.3200	−	8.26764i	−0.938133	−	0.541631i	−0.889374	+	0.457180i	$0.848860\pi$
$234$		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	0.178990	−	0.983851i	$-0.442717\pi$
$239$	−9.02155	−	5.20859i	−0.583555	−	0.336916i	−0.762545	+	0.646935i	$0.776050\pi$
$240$		0			0
$241$	−8.97668	−	5.18269i	−0.578239	−	0.333846i	0.182194	−	0.983263i	$-0.441680\pi$
$241$	−8.97668	−	5.18269i	−0.578239	−	0.333846i	−0.760433	+	0.649416i	$0.775013\pi$
$242$		0			0
$243$	−14.4855	−	5.75946i	−0.929243	−	0.369470i
$244$		0			0
$245$	−19.3085	+	1.72711i	−1.23357	+	0.110341i
$246$		0			0
$247$	0.122167	+	0.211599i	0.00777328	+	0.0134637i
$248$		0			0
$249$	−4.26810	+	23.4009i	−0.270480	+	1.48297i
$250$		0			0
$251$	−13.1006			−0.826903			−0.413452	−	0.910526i	$-0.635677\pi$
$251$	−13.1006			−0.826903			−0.413452	+	0.910526i	$0.635677\pi$
$252$		0			0
$253$	0.258658			0.0162617
$254$		0			0
$255$	−16.2364	+	5.80180i	−1.01677	+	0.363323i
$256$		0			0
$257$	0.443415	+	0.768018i	0.0276595	+	0.0479076i	0.879524	−	0.475855i	$-0.157861\pi$
$257$	0.443415	+	0.768018i	0.0276595	+	0.0479076i	−0.851864	+	0.523763i	$0.824528\pi$
$258$		0			0
$259$	10.9001	−	0.486527i	0.677301	−	0.0302313i
$260$		0			0
$261$	14.4317	+	17.6153i	0.893301	+	1.09036i
$262$		0			0
$263$	−6.17036	−	3.56246i	−0.380481	−	0.219671i	0.297547	−	0.954707i	$-0.403832\pi$
$263$	−6.17036	−	3.56246i	−0.380481	−	0.219671i	−0.678028	+	0.735037i	$0.737165\pi$
$264$		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	$-0.753217\pi$
$269$	−15.7987	−	27.3641i	−0.963261	−	1.66842i	−0.249045	−	0.968492i	$-0.580117\pi$
$270$		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
$273$	0.149646	−	0.193055i	0.00905698	−	0.0116842i
$274$		0			0
$275$	5.59270	−	3.22895i	0.337253	−	0.194713i
$276$		0			0
$277$	15.2845	−	26.4735i	0.918357	−	1.59064i	0.116447	−	0.993197i	$-0.462850\pi$
$277$	15.2845	−	26.4735i	0.918357	−	1.59064i	0.801910	−	0.597444i	$-0.203817\pi$
$278$		0			0
$279$	20.1766	−	3.31375i	1.20794	−	0.198389i
$280$		0			0
$281$	3.92237	−	2.26458i	0.233989	−	0.135094i	−0.378422	−	0.925633i	$-0.623533\pi$
$281$	3.92237	−	2.26458i	0.233989	−	0.135094i	0.612411	+	0.790540i	$0.290200\pi$
$282$		0			0
$283$		−	9.36150i		−	0.556484i	−0.960511	−	0.278242i	$-0.910248\pi$
$283$		−	9.36150i		−	0.556484i	0.960511	−	0.278242i	$-0.0897517\pi$
$284$		0			0
$285$	14.2320	−	16.7601i	0.843032	−	0.992784i
$286$		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
$291$	−28.2438	−	5.15139i	−1.65568	−	0.301980i
$292$		0			0
$293$	8.17267	−	14.1555i	0.477452	−	0.826972i	−0.522214	−	0.852815i	$-0.674894\pi$
$293$	8.17267	−	14.1555i	0.477452	−	0.826972i	0.999666	+	0.0258430i	$0.00822701\pi$
$294$		0			0
$295$	13.0829	+	22.6603i	0.761719	+	1.31934i
$296$		0			0
$297$	10.9957	−	6.09255i	0.638033	−	0.353526i
$298$		0			0
$299$	0.00569894			0.000329578
$300$		0			0
$301$	4.25195	−	8.18734i	0.245078	−	0.471910i
$302$		0			0
$303$	−17.1260	+	6.11966i	−0.983862	+	0.351565i
$304$		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
$311$	26.2604			1.48909			0.744545	−	0.667573i	$-0.232667\pi$
$311$	26.2604			1.48909			0.744545	+	0.667573i	$0.232667\pi$
$312$		0			0
$313$		−	14.5329i		−	0.821446i	−0.911760	−	0.410723i	$-0.865276\pi$
$313$		−	14.5329i		−	0.821446i	0.911760	−	0.410723i	$-0.134724\pi$
$314$		0			0
$315$	−20.8914	−	6.83540i	−1.17709	−	0.385131i
$316$		0			0
$317$			29.4620i			1.65475i	0.561649	+	0.827375i	$0.310167\pi$
$317$			29.4620i			1.65475i	−0.561649	+	0.827375i	$0.689833\pi$
$318$		0			0
$319$	−18.3638			−1.02818
$320$		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
$327$	5.01172	−	27.4780i	0.277149	−	1.51954i
$328$		0			0
$329$	−18.7846	−	29.4228i	−1.03563	−	1.62213i
$330$		0			0
$331$	5.82030			0.319913			0.159956	−	0.987124i	$-0.448865\pi$
$331$	5.82030			0.319913			0.159956	+	0.987124i	$0.448865\pi$
$332$		0			0
$333$	11.5753	+	4.36773i	0.634320	+	0.239350i
$334$		0			0
$335$	19.6447	+	34.0255i	1.07330	+	1.85901i
$336$		0			0
$337$	−11.4909	+	19.9028i	−0.625950	+	1.08418i	0.362407	+	0.932020i	$0.381955\pi$
$337$	−11.4909	+	19.9028i	−0.625950	+	1.08418i	−0.988356	+	0.152157i	$0.951378\pi$
$338$		0			0
$339$	7.91043	+	22.1375i	0.429636	+	1.20234i
$340$		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
$345$	−0.172570	−	0.482940i	−0.00929085	−	0.0260006i
$346$		0			0
$347$		−	14.9459i		−	0.802336i	−0.916005	−	0.401168i	$-0.868604\pi$
$347$		−	14.9459i		−	0.802336i	0.916005	−	0.401168i	$-0.131396\pi$
$348$		0			0
$349$	0.768588	−	0.443744i	0.0411416	−	0.0237531i	−0.479288	−	0.877658i	$-0.659105\pi$
$349$	0.768588	−	0.443744i	0.0411416	−	0.0237531i	0.520430	+	0.853905i	$0.325772\pi$
$350$		0			0
$351$	0.242264	−	0.134235i	0.0129311	−	0.00716496i
$352$		0			0
$353$	2.52498	−	4.37339i	0.134391	−	0.232772i	−0.790974	−	0.611850i	$-0.790426\pi$
$353$	2.52498	−	4.37339i	0.134391	−	0.232772i	0.925365	+	0.379078i	$0.123759\pi$
$354$		0			0
$355$	−3.36395	+	1.94218i	−0.178540	+	0.103080i
$356$		0			0
$357$	−15.2491	+	6.22899i	−0.807069	+	0.329673i
$358$		0			0
$359$	−30.2467	−	17.4629i	−1.59636	−	0.921659i	−0.992181	−	0.124810i	$-0.960168\pi$
$359$	−30.2467	−	17.4629i	−1.59636	−	0.921659i	−0.604179	−	0.796848i	$-0.706499\pi$
$360$		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
$367$	19.9959	+	11.5446i	1.04378	+	0.602625i	0.920901	−	0.389797i	$-0.127455\pi$
$367$	19.9959	+	11.5446i	1.04378	+	0.602625i	0.122876	+	0.992422i	$0.460788\pi$
$368$		0			0
$369$	−4.70971	−	1.77713i	−0.245178	−	0.0925137i
$370$		0			0
$371$	14.3021	+	7.42753i	0.742527	+	0.385618i
$372$		0			0
$373$	−0.899257	−	1.55756i	−0.0465617	−	0.0806473i	0.841805	−	0.539781i	$-0.181493\pi$
$373$	−0.899257	−	1.55756i	−0.0465617	−	0.0806473i	−0.888367	+	0.459134i	$0.848160\pi$
$374$		0			0
$375$	8.52141	+	7.23604i	0.440044	+	0.373668i
$376$		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
$381$	12.1868	+	10.3485i	0.624348	+	0.530171i
$382$		0			0
$383$	−0.989164	−	1.71328i	−0.0505439	−	0.0875447i	0.839647	−	0.543133i	$-0.182762\pi$
$383$	−0.989164	−	1.71328i	−0.0505439	−	0.0875447i	−0.890190	+	0.455589i	$0.849429\pi$
$384$		0			0
$385$	14.9406	−	9.53866i	0.761445	−	0.486135i
$386$		0			0
$387$	8.09191	−	6.62949i	0.411335	−	0.336996i
$388$		0			0
$389$	−30.2325	−	17.4547i	−1.53285	−	0.884990i	−0.999229	−	0.0392657i	$-0.987498\pi$
$389$	−30.2325	−	17.4547i	−1.53285	−	0.884990i	−0.533619	−	0.845725i	$-0.679169\pi$
$390$		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
$399$	12.8692	−	16.6024i	0.644268	−	0.831158i
$400$		0			0
$401$	−28.6041	+	16.5146i	−1.42842	+	0.824698i	−0.996996	−	0.0774514i	$-0.975322\pi$
$401$	−28.6041	+	16.5146i	−1.42842	+	0.824698i	−0.431423	+	0.902150i	$0.641988\pi$
$402$		0			0
$403$	−0.181645	+	0.314618i	−0.00904838	+	0.0156723i
$404$		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
$409$		−	1.07813i		−	0.0533099i	−0.999645	−	0.0266549i	$-0.991514\pi$
$409$		−	1.07813i		−	0.0533099i	0.999645	−	0.0266549i	$-0.00848553\pi$
$410$		0			0
$411$	3.28087	+	9.18157i	0.161833	+	0.452893i
$412$		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
$417$	−12.5673	−	35.1699i	−0.615425	−	1.72228i
$418$		0			0
$419$	−13.2799	+	23.0015i	−0.648768	+	1.12370i	0.334650	+	0.942343i	$0.391382\pi$
$419$	−13.2799	+	23.0015i	−0.648768	+	1.12370i	−0.983418	+	0.181356i	$0.941951\pi$
$420$		0			0
$421$	3.32791	+	5.76411i	0.162192	+	0.280925i	0.935655	−	0.352917i	$-0.114810\pi$
$421$	3.32791	+	5.76411i	0.162192	+	0.280925i	−0.773462	+	0.633842i	$0.781477\pi$
$422$		0			0
$423$	−6.41487	−	39.0586i	−0.311902	−	1.89909i
$424$		0			0
$425$	−9.59524			−0.465437
$426$		0			0
$427$	−5.92065	+	3.77997i	−0.286521	+	0.182926i
$428$		0			0
$429$	−0.0400759	+	0.219726i	−0.00193488	+	0.0106085i
$430$		0			0
$431$	13.2930	−	7.67471i	0.640300	−	0.369678i	−0.144430	−	0.989515i	$-0.546135\pi$
$431$	13.2930	−	7.67471i	0.640300	−	0.369678i	0.784730	+	0.619837i	$0.212801\pi$
$432$		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
$437$	0.490097			0.0234445
$438$		0			0
$439$			20.6424i			0.985207i	0.870254	+	0.492603i	$0.163955\pi$
$439$			20.6424i			0.985207i	−0.870254	+	0.492603i	$0.836045\pi$
$440$		0			0
$441$	−20.2302	−	5.63382i	−0.963342	−	0.268277i
$442$		0			0
$443$			1.45354i			0.0690595i	0.999404	+	0.0345298i	$0.0109934\pi$
$443$			1.45354i			0.0690595i	−0.999404	+	0.0345298i	$0.989007\pi$
$444$		0			0
$445$	−31.6662			−1.50112
$446$		0			0
$447$	32.5970	+	5.94537i	1.54178	+	0.281207i
$448$		0			0
$449$			9.09933i			0.429424i	0.976677	+	0.214712i	$0.0688813\pi$
$449$			9.09933i			0.429424i	−0.976677	+	0.214712i	$0.931119\pi$
$450$		0			0
$451$	3.51551	−	2.02968i	0.165539	−	0.0955740i
$452$		0			0
$453$	−12.8543	+	4.59324i	−0.603947	+	0.215809i
$454$		0			0
$455$	0.329182	−	0.210163i	0.0154323	−	0.00985257i
$456$		0			0
$457$	−14.4642			−0.676606			−0.338303	−	0.941037i	$-0.609853\pi$
$457$	−14.4642			−0.676606			−0.338303	+	0.941037i	$0.609853\pi$
$458$		0			0
$459$	−18.6749	−	0.329149i	−0.871670	−	0.0153634i
$460$		0			0
$461$	13.2769	+	22.9963i	0.618369	+	1.07105i	0.989783	+	0.142579i	$0.0455395\pi$
$461$	13.2769	+	22.9963i	0.618369	+	1.07105i	−0.371415	+	0.928467i	$0.621127\pi$
$462$		0			0
$463$	−15.4968	+	26.8412i	−0.720196	+	1.24742i	0.240725	+	0.970593i	$0.422615\pi$
$463$	−15.4968	+	26.8412i	−0.720196	+	1.24742i	−0.960921	+	0.276823i	$0.910718\pi$
$464$		0			0
$465$	32.1618	+	5.86601i	1.49147	+	0.272030i
$466$		0			0
$467$	−10.1348	+	17.5541i	−0.468985	+	0.812306i	−0.999371	−	0.0354503i	$-0.988713\pi$
$467$	−10.1348	+	17.5541i	−0.468985	+	0.812306i	0.530387	+	0.847756i	$0.322047\pi$
$468$		0			0
$469$	20.1986	+	31.6376i	0.932686	+	1.46089i
$470$		0			0
$471$	22.3767	−	26.3516i	1.03106	−	1.21422i
$472$		0			0
$473$			8.43577i			0.387877i
$474$		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
$479$	−8.01288	+	13.8787i	−0.366118	+	0.634135i	−0.988955	−	0.148217i	$-0.952647\pi$
$479$	−8.01288	+	13.8787i	−0.366118	+	0.634135i	0.622837	+	0.782352i	$0.285980\pi$
$480$		0			0
$481$	−0.190368	+	0.109909i	−0.00868001	+	0.00501141i
$482$		0			0
$483$	−0.185276	−	0.453573i	−0.00843036	−	0.0206383i
$484$		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	0.177798	−	0.984067i	$-0.443103\pi$
$491$	−12.9745	−	7.49082i	−0.585530	−	0.338056i	−0.763328	+	0.646011i	$0.776436\pi$
$492$		0			0
$493$	23.6297	+	13.6426i	1.06423	+	0.614432i
$494$		0			0
$495$	19.8336	−	3.25742i	0.891454	−	0.146410i
$496$		0			0
$497$	−3.12787	+	1.99695i	−0.140304	+	0.0895753i
$498$		0			0
$499$	12.6638	+	21.9343i	0.566910	+	0.981916i	0.996869	+	0.0790682i	$0.0251945\pi$
$499$	12.6638	+	21.9343i	0.566910	+	0.981916i	−0.429960	+	0.902848i	$0.641472\pi$
$500$		0			0
$501$	2.58908	−	0.925160i	0.115671	−	0.0413331i
$502$		0			0
$503$	−9.95401			−0.443827			−0.221914	−	0.975066i	$-0.571230\pi$
$503$	−9.95401			−0.443827			−0.221914	+	0.975066i	$0.571230\pi$
$504$		0			0
$505$	−29.0783			−1.29397
$506$		0			0
$507$	4.03929	−	22.1464i	0.179391	−	0.983556i
$508$		0			0
$509$	−5.82977	−	10.0975i	−0.258400	−	0.447562i	0.707413	−	0.706800i	$-0.249862\pi$
$509$	−5.82977	−	10.0975i	−0.258400	−	0.447562i	−0.965813	+	0.259238i	$0.916529\pi$
$510$		0			0
$511$	15.0248	+	7.80285i	0.664657	+	0.345178i
$512$		0			0
$513$	20.8342	−	11.5440i	0.919854	−	0.509679i
$514$		0			0
$515$	36.9992	+	21.3615i	1.63038	+	0.941300i
$516$		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	0.990546	−	0.137183i	$-0.0438048\pi$
$521$	8.59307	+	14.8836i	0.376469	+	0.652064i	−0.614077	+	0.789246i	$0.710471\pi$
$522$		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
$525$	−9.66821	−	7.49426i	−0.421955	−	0.327076i
$526$		0			0
$527$	21.2168	−	12.2495i	0.924220	−	0.533599i
$528$		0			0
$529$	−11.4943	+	19.9087i	−0.499751	+	0.865595i
$530$		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
$535$			31.2240i			1.34993i
$536$		0			0
$537$	−6.65095	−	1.21307i	−0.287010	−	0.0523478i
$538$		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
$543$	−17.2299	+	20.2905i	−0.739405	+	0.870749i
$544$		0			0
$545$	22.3296	−	38.6760i	0.956495	−	1.65670i
$546$		0			0
$547$	−17.0000	−	29.4449i	−0.726869	−	1.25897i	−0.958200	−	0.286099i	$-0.907642\pi$
$547$	−17.0000	−	29.4449i	−0.726869	−	1.25897i	0.231331	−	0.972875i	$-0.425692\pi$
$548$		0			0
$549$	−7.85963	+	1.29084i	−0.335441	+	0.0550919i
$550$		0			0
$551$	−34.7952			−1.48232
$552$		0			0
$553$	−6.01004	−	9.41366i	−0.255573	−	0.400310i
$554$		0			0
$555$	15.0784	+	12.8040i	0.640044	+	0.543500i
$556$		0			0
$557$	−1.88366	+	1.08753i	−0.0798133	+	0.0460802i	−0.539376	−	0.842065i	$-0.681340\pi$
$557$	−1.88366	+	1.08753i	−0.0798133	+	0.0460802i	0.459562	+	0.888146i	$0.348006\pi$
$558$		0			0
$559$			0.185863i			0.00786116i
$560$		0			0
$561$	9.74932	−	11.4811i	0.411617	−	0.484734i
$562$		0			0
$563$	4.49555			0.189465			0.0947324	−	0.995503i	$-0.469800\pi$
$563$	4.49555			0.189465			0.0947324	+	0.995503i	$0.469800\pi$
$564$		0			0
$565$			37.5874i			1.58131i
$566$		0			0
$567$	−18.5599	−	14.9175i	−0.779440	−	0.626476i
$568$		0			0
$569$		−	6.12306i		−	0.256692i	−0.991729	−	0.128346i	$-0.959033\pi$
$569$		−	6.12306i		−	0.256692i	0.991729	−	0.128346i	$-0.0409668\pi$
$570$		0			0
$571$	32.3658			1.35447			0.677233	−	0.735769i	$-0.263179\pi$
$571$	32.3658			1.35447			0.677233	+	0.735769i	$0.263179\pi$
$572$		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
$579$	−9.84825	−	8.36274i	−0.409279	−	0.347544i
$580$		0			0
$581$	−16.7464	+	32.2460i	−0.694757	+	1.33779i
$582$		0			0
$583$	−14.7361			−0.610305
$584$		0			0
$585$	0.436988	−	0.0717697i	0.0180672	−	0.00296731i
$586$		0			0
$587$	0.129711	+	0.224667i	0.00535376	+	0.00927298i	0.868690	−	0.495356i	$-0.164963\pi$
$587$	0.129711	+	0.224667i	0.00535376	+	0.00927298i	−0.863336	+	0.504629i	$0.831629\pi$
$588$		0			0
$589$	−15.6211	+	27.0565i	−0.643656	+	1.11485i
$590$		0			0
$591$	3.11412	−	3.66730i	0.128098	−	0.150853i
$592$		0			0
$593$	−3.13549	+	5.43083i	−0.128759	+	0.223017i	−0.923196	−	0.384329i	$-0.874433\pi$
$593$	−3.13549	+	5.43083i	−0.128759	+	0.223017i	0.794437	+	0.607347i	$0.207766\pi$
$594$		0			0
$595$	−26.3112	+	1.17440i	−1.07866	+	0.0481458i
$596$		0			0
$597$	6.88427	+	1.25563i	0.281754	+	0.0513893i
$598$		0			0
$599$		−	6.37396i		−	0.260433i	−0.991486	−	0.130217i	$-0.958433\pi$
$599$		−	6.37396i		−	0.260433i	0.991486	−	0.130217i	$-0.0415672\pi$
$600$		0			0
$601$	15.0862	−	8.71001i	0.615378	−	0.355289i	−0.159689	−	0.987167i	$-0.551049\pi$
$601$	15.0862	−	8.71001i	0.615378	−	0.355289i	0.775067	+	0.631879i	$0.217716\pi$
$602$		0			0
$603$	6.89775	+	41.9987i	0.280898	+	1.71032i
$604$		0			0
$605$	7.12732	−	12.3449i	0.289767	−	0.501891i
$606$		0			0
$607$	−1.56183	+	0.901722i	−0.0633927	+	0.0365998i	−0.531361	−	0.847145i	$-0.678319\pi$
$607$	−1.56183	+	0.901722i	−0.0633927	+	0.0365998i	0.467969	+	0.883745i	$0.344986\pi$
$608$		0			0
$609$	13.1540	+	32.2021i	0.533026	+	1.30489i
$610$		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	0.336162	−	0.941804i	$-0.390871\pi$
$617$	−7.73458	−	4.46556i	−0.311383	−	0.179777i	−0.647545	+	0.762027i	$0.724204\pi$
$618$		0			0
$619$	−33.3546	−	19.2573i	−1.34064	−	0.774016i	−0.353735	−	0.935346i	$-0.615088\pi$
$619$	−33.3546	−	19.2573i	−1.34064	−	0.774016i	−0.986901	+	0.161330i	$0.948422\pi$
$620$		0			0
$621$	0.00979028	−	0.555470i	0.000392870	−	0.0222903i
$622$		0			0
$623$	−30.2227	+	1.34899i	−1.21085	+	0.0540461i
$624$		0			0
$625$	15.6107	+	27.0384i	0.624426	+	1.08154i
$626$		0			0
$627$	−3.44645	+	18.8960i	−0.137638	+	0.754633i
$628$		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
$633$	34.2046	−	12.2224i	1.35951	−	0.485796i
$634$		0			0
$635$	12.7814	+	22.1380i	0.507214	+	0.878521i
$636$		0			0
$637$	0.305223	−	0.214605i	0.0120934	−	0.00850297i
$638$		0			0
$639$	−4.15222	+	0.681950i	−0.164259	+	0.0269775i
$640$		0			0
$641$	29.1635	+	16.8376i	1.15189	+	0.665044i	0.949347	−	0.314229i	$-0.101746\pi$
$641$	29.1635	+	16.8376i	1.15189	+	0.665044i	0.202543	+	0.979273i	$0.435079\pi$
$642$		0			0
$643$	2.02496	+	1.16911i	0.0798567	+	0.0461053i	0.539397	−	0.842052i	$-0.318652\pi$
$643$	2.02496	+	1.16911i	0.0798567	+	0.0461053i	−0.459540	+	0.888157i	$0.651986\pi$
$644$		0			0
$645$	15.7504	−	5.62812i	0.620172	−	0.221607i
$646$		0			0
$647$	1.89769	+	3.28689i	0.0746059	+	0.129221i	0.900915	−	0.433996i	$-0.142897\pi$
$647$	1.89769	+	3.28689i	0.0746059	+	0.129221i	−0.826309	+	0.563217i	$0.809563\pi$
$648$		0			0
$649$	−19.7955	−	11.4289i	−0.777040	−	0.448624i
$650$		0			0
$651$	30.9456	+	4.22850i	1.21285	+	0.165728i
$652$		0			0
$653$	10.1456	−	5.85755i	0.397027	−	0.229224i	−0.288173	−	0.957578i	$-0.593048\pi$
$653$	10.1456	−	5.85755i	0.397027	−	0.229224i	0.685200	+	0.728355i	$0.259715\pi$
$654$		0			0
$655$	−4.41547	+	7.64782i	−0.172527	+	0.298825i
$656$		0			0
$657$	12.1659	+	14.8497i	0.474638	+	0.579341i
$658$		0			0
$659$	−22.4962	+	12.9882i	−0.876329	+	0.505949i	−0.869446	−	0.494028i	$-0.835524\pi$
$659$	−22.4962	+	12.9882i	−0.876329	+	0.505949i	−0.00688257	+	0.999976i	$0.502191\pi$
$660$		0			0
$661$		−	6.86096i		−	0.266860i	−0.991058	−	0.133430i	$-0.957401\pi$
$661$		−	6.86096i		−	0.266860i	0.991058	−	0.133430i	$-0.0425992\pi$
$662$		0			0
$663$	0.214804	−	0.252960i	0.00834229	−	0.00982417i
$664$		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
$669$	−17.3605	−	3.16639i	−0.671195	−	0.122420i
$670$		0			0
$671$	3.21152	−	5.56251i	0.123979	−	0.214738i
$672$		0			0
$673$	−0.652179	−	1.12961i	−0.0251397	−	0.0435432i	0.853182	−	0.521614i	$-0.174670\pi$
$673$	−0.652179	−	1.12961i	−0.0251397	−	0.0435432i	−0.878322	+	0.478070i	$0.841336\pi$
$674$		0			0
$675$	−6.72251	−	12.1326i	−0.258749	−	0.466984i
$676$		0			0
$677$	−13.2303			−0.508483			−0.254241	−	0.967141i	$-0.581826\pi$
$677$	−13.2303			−0.508483			−0.254241	+	0.967141i	$0.581826\pi$
$678$		0			0
$679$	−38.9193	−	20.2121i	−1.49359	−	0.775668i
$680$		0			0
$681$	16.4133	−	5.86498i	0.628958	−	0.224747i
$682$		0			0
$683$	−1.49949	+	0.865733i	−0.0573765	+	0.0331264i	−0.528414	−	0.848987i	$-0.677213\pi$
$683$	−1.49949	+	0.865733i	−0.0573765	+	0.0331264i	0.471037	+	0.882113i	$0.343880\pi$
$684$		0			0
$685$			15.5894i			0.595642i
$686$		0			0
$687$	25.4833	+	4.64791i	0.972248	+	0.177329i
$688$		0			0
$689$	−0.324675			−0.0123691
$690$		0			0
$691$			8.40092i			0.319586i	0.987151	+	0.159793i	$0.0510827\pi$
$691$			8.40092i			0.319586i	−0.987151	+	0.159793i	$0.948917\pi$
$692$		0			0
$693$	18.7907	−	3.95384i	0.713799	−	0.150194i
$694$		0			0
$695$		−	59.7153i		−	2.26513i
$696$		0			0
$697$	−6.03146			−0.228458
$698$		0			0
$699$	−9.63717	−	26.9698i	−0.364511	−	1.02009i
$700$		0			0
$701$		−	21.3493i		−	0.806353i	−0.915122	−	0.403176i	$-0.867906\pi$
$701$		−	21.3493i		−	0.806353i	0.915122	−	0.403176i	$-0.132094\pi$
$702$		0			0
$703$	−16.3712	+	9.45193i	−0.617452	+	0.356486i
$704$		0			0
$705$	11.3556	−	62.2601i	0.427678	−	2.34485i
$706$		0			0
$707$	−27.7527	+	1.23874i	−1.04375	+	0.0465877i
$708$		0			0
$709$	−19.2617			−0.723390			−0.361695	−	0.932296i	$-0.617802\pi$
$709$	−19.2617			−0.723390			−0.361695	+	0.932296i	$0.617802\pi$
$710$		0			0
$711$	−2.05240	−	12.4966i	−0.0769712	−	0.468658i
$712$		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
$717$	−6.07139	−	16.9909i	−0.226740	−	0.634538i
$718$		0			0
$719$	−5.39920	+	9.35168i	−0.201356	+	0.348759i	−0.948966	−	0.315380i	$-0.897868\pi$
$719$	−5.39920	+	9.35168i	−0.201356	+	0.348759i	0.747610	+	0.664138i	$0.231201\pi$
$720$		0			0
$721$	36.2225	+	18.8115i	1.34900	+	0.700577i
$722$		0			0
$723$	−6.04120	−	16.9064i	−0.224675	−	0.628757i
$724$		0			0
$725$			20.2626i			0.752534i
$726$		0			0
$727$	25.9316	−	14.9716i	0.961751	−	0.555267i	0.0650393	−	0.997883i	$-0.479283\pi$
$727$	25.9316	−	14.9716i	0.961751	−	0.555267i	0.896711	+	0.442616i	$0.145949\pi$
$728$		0			0
$729$	−12.6676	−	23.8439i	−0.469171	−	0.883107i
$730$		0			0
$731$	6.26700	−	10.8548i	0.231793	−	0.401478i
$732$		0			0
$733$	−13.8872	+	8.01776i	−0.512934	+	0.296143i	−0.734039	−	0.679107i	$-0.762367\pi$
$733$	−13.8872	+	8.01776i	−0.512934	+	0.296143i	0.221105	+	0.975250i	$0.429034\pi$
$734$		0			0
$735$	−27.4286	−	19.3668i	−1.01172	−	0.714355i
$736$		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	−0.375609	−	0.926778i	$-0.622567\pi$
$743$	−37.2352	−	21.4978i	−1.36603	−	0.788676i	−0.990418	+	0.138102i	$0.955900\pi$
$744$		0			0
$745$	45.8811	+	26.4895i	1.68095	+	0.970498i
$746$		0			0
$747$	−31.8702	+	26.1104i	−1.16607	+	0.955328i
$748$		0			0
$749$	1.33015	+	29.8006i	0.0486026	+	1.08889i
$750$		0			0
$751$	17.6900	+	30.6400i	0.645518	+	1.11807i	0.984182	+	0.177162i	$0.0566917\pi$
$751$	17.6900	+	30.6400i	0.645518	+	1.11807i	−0.338664	+	0.940907i	$0.609975\pi$
$752$		0			0
$753$	−17.2963	−	14.6873i	−0.630311	−	0.535235i
$754$		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
$759$	0.341497	+	0.289986i	0.0123956	+	0.0105258i
$760$		0			0
$761$	6.89264	+	11.9384i	0.249858	+	0.432766i	0.963486	−	0.267758i	$-0.0862828\pi$
$761$	6.89264	+	11.9384i	0.249858	+	0.432766i	−0.713628	+	0.700525i	$0.752949\pi$
$762$		0			0
$763$	19.6641	−	37.8641i	0.711887	−	1.37077i
$764$		0			0
$765$	−27.9409	−	10.5430i	−1.01021	−	0.381184i
$766$		0			0
$767$	−0.436147	−	0.251810i	−0.0157484	−	0.00909233i
$768$		0			0
$769$	20.0352	+	11.5673i	0.722486	+	0.417128i	0.815667	−	0.578522i	$-0.196370\pi$
$769$	20.0352	+	11.5673i	0.722486	+	0.417128i	−0.0931808	+	0.995649i	$0.529703\pi$
$770$		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	$-0.764226\pi$
$773$	−26.5072	−	45.9118i	−0.953398	−	1.65133i	−0.215405	−	0.976525i	$-0.569107\pi$
$774$		0			0
$775$	15.7561	+	9.09678i	0.565975	+	0.326766i
$776$		0			0
$777$	14.9365	+	11.5780i	0.535844	+	0.415357i
$778$		0			0
$779$	6.66108	−	3.84578i	0.238658	−	0.137789i
$780$		0			0
$781$	1.69664	−	2.93866i	0.0607104	−	0.105154i
$782$		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
$787$			5.96329i			0.212568i	0.994336	+	0.106284i	$0.0338953\pi$
$787$			5.96329i			0.212568i	−0.994336	+	0.106284i	$0.966105\pi$
$788$		0			0
$789$	−4.15258	−	11.6211i	−0.147836	−	0.413722i
$790$		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
$795$	9.83150	+	27.5137i	0.348688	+	0.975809i
$796$		0			0
$797$	−5.28758	+	9.15836i	−0.187296	+	0.324406i	−0.944348	−	0.328949i	$-0.893306\pi$
$797$	−5.28758	+	9.15836i	−0.187296	+	0.324406i	0.757052	+	0.653355i	$0.226639\pi$
$798$		0			0
$799$	−23.7131	−	41.0724i	−0.838910	−	1.45304i
$800$		0			0
$801$	−32.0946	−	12.1104i	−1.13401	−	0.427899i
$802$		0			0
$803$	−15.4807			−0.546302
$804$		0			0
$805$	−0.0349316	−	0.782607i	−0.00123118	−	0.0275833i
$806$		0			0
$807$	9.81989	−	53.8400i	0.345677	−	1.89526i
$808$		0			0
$809$	32.1452	−	18.5591i	1.13017	−	0.652501i	0.186189	−	0.982514i	$-0.440386\pi$
$809$	32.1452	−	18.5591i	1.13017	−	0.652501i	0.943977	+	0.330012i	$0.107053\pi$
$810$		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
$815$	−66.6989			−2.33636
$816$		0			0
$817$			15.9838i			0.559203i
$818$		0			0
$819$	0.414010	−	0.0871137i	0.0144667	−	0.00304400i
$820$		0			0
$821$		−	21.4378i		−	0.748184i	−0.927392	−	0.374092i	$-0.877954\pi$
$821$		−	21.4378i		−	0.748184i	0.927392	−	0.374092i	$-0.122046\pi$
$822$		0			0
$823$	19.4491			0.677953			0.338977	−	0.940795i	$-0.389919\pi$
$823$	19.4491			0.677953			0.338977	+	0.940795i	$0.389919\pi$
$824$		0			0
$825$	11.0039	+	2.00700i	0.383106	+	0.0698748i
$826$		0			0
$827$		−	16.3789i		−	0.569549i	−0.958595	−	0.284774i	$-0.908081\pi$
$827$		−	16.3789i		−	0.569549i	0.958595	−	0.284774i	$-0.0919187\pi$
$828$		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
$831$	49.8595	−	17.8164i	1.72961	−	0.618043i
$832$		0			0
$833$	−25.0618	+	2.24173i	−0.868339	+	0.0776713i
$834$		0			0
$835$	4.39601			0.152130
$836$		0			0
$837$	30.3535	+	18.2453i	1.04917	+	0.630648i
$838$		0			0
$839$	0.260756	+	0.451642i	0.00900229	+	0.0155924i	0.870491	−	0.492184i	$-0.163801\pi$
$839$	0.260756	+	0.451642i	0.00900229	+	0.0155924i	−0.861489	+	0.507776i	$0.830468\pi$
$840$		0			0
$841$	14.3096	−	24.7849i	0.493433	−	0.854652i
$842$		0			0
$843$	7.71742	+	1.40758i	0.265802	+	0.0484798i
$844$		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
$849$	10.4953	−	12.3597i	0.360199	−	0.424183i
$850$		0			0
$851$			0.440921i			0.0151146i
$852$		0			0
$853$	−15.3460	+	8.85999i	−0.525436	+	0.303360i	−0.739156	−	0.673535i	$-0.764775\pi$
$853$	−15.3460	+	8.85999i	−0.525436	+	0.303360i	0.213720	+	0.976895i	$0.431442\pi$
$854$		0			0
$855$	37.5801	−	6.17205i	1.28521	−	0.211080i
$856$		0			0
$857$	−1.41363	+	2.44849i	−0.0482888	+	0.0836387i	−0.889160	−	0.457597i	$-0.848710\pi$
$857$	−1.41363	+	2.44849i	−0.0482888	+	0.0836387i	0.840871	+	0.541236i	$0.182043\pi$
$858$		0			0
$859$	−7.97741	+	4.60576i	−0.272186	+	0.157147i	−0.629881	−	0.776692i	$-0.716896\pi$
$859$	−7.97741	+	4.60576i	−0.272186	+	0.157147i	0.357695	+	0.933839i	$0.383563\pi$
$860$		0			0
$861$	−6.07733	−	4.71081i	−0.207115	−	0.160544i
$862$		0			0
$863$	−15.7016	−	9.06534i	−0.534490	−	0.308588i	0.208353	−	0.978054i	$-0.433190\pi$
$863$	−15.7016	−	9.06534i	−0.534490	−	0.308588i	−0.742843	+	0.669466i	$0.766523\pi$
$864$		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
$871$	−0.654896	−	0.378104i	−0.0221903	−	0.0128116i
$872$		0			0
$873$	−31.5139	−	38.4657i	−1.06659	−	1.30187i
$874$		0			0
$875$	9.18921	+	14.3933i	0.310652	+	0.486581i
$876$		0			0
$877$	−7.10432	−	12.3050i	−0.239896	−	0.415512i	0.720788	−	0.693155i	$-0.243780\pi$
$877$	−7.10432	−	12.3050i	−0.239896	−	0.415512i	−0.960684	+	0.277643i	$0.910447\pi$
$878$		0			0
$879$	26.6600	−	9.52647i	0.899220	−	0.321320i
$880$		0			0
$881$	−46.0649			−1.55197			−0.775984	−	0.630753i	$-0.782746\pi$
$881$	−46.0649			−1.55197			−0.775984	+	0.630753i	$0.782746\pi$
$882$		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
$885$	−8.13190	+	44.5851i	−0.273351	+	1.49871i
$886$		0			0
$887$	−13.5643	−	23.4941i	−0.455446	−	0.788856i	0.543267	−	0.839560i	$-0.317187\pi$
$887$	−13.5643	−	23.4941i	−0.455446	−	0.788856i	−0.998714	+	0.0507036i	$0.983854\pi$
$888$		0			0
$889$	13.1418	+	20.5843i	0.440763	+	0.690377i
$890$		0			0
$891$	21.3477	+	4.28364i	0.715173	+	0.143507i
$892$		0			0
$893$	52.3771	+	30.2399i	1.75273	+	1.01194i
$894$		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
$903$	14.7927	−	6.04253i	0.492269	−	0.201083i
$904$		0			0
$905$	−36.8589	+	21.2805i	−1.22523	+	0.707388i
$906$		0			0
$907$	−12.7926	+	22.1574i	−0.424770	+	0.735724i	−0.996399	−	0.0847887i	$-0.972978\pi$
$907$	−12.7926	+	22.1574i	−0.424770	+	0.735724i	0.571629	+	0.820512i	$0.306312\pi$
$908$		0			0
$909$	−29.4717	−	11.1206i	−0.977514	−	0.368849i
$910$		0			0
$911$	−4.57426	+	2.64095i	−0.151552	+	0.0874986i	−0.573858	−	0.818955i	$-0.694554\pi$
$911$	−4.57426	+	2.64095i	−0.151552	+	0.0874986i	0.422306	+	0.906453i	$0.361221\pi$
$912$		0			0
$913$		−	33.2245i		−	1.09957i
$914$		0			0
$915$	−12.5284	−	2.28506i	−0.414176	−	0.0755418i
$916$		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
$921$	1.10435	−	1.30051i	0.0363894	−	0.0428534i
$922$		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
$927$	29.3303	+	35.8003i	0.963332	+	1.17584i
$928$		0			0
$929$	−35.2009			−1.15490			−0.577452	−	0.816425i	$-0.695953\pi$
$929$	−35.2009			−1.15490			−0.577452	+	0.816425i	$0.695953\pi$
$930$		0			0
$931$	26.2486	−	18.4556i	0.860262	−	0.604858i
$932$		0			0
$933$	34.6706	+	29.4409i	1.13507	+	0.963853i
$934$		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
$941$	20.7603			0.676767			0.338384	−	0.941008i	$-0.390120\pi$
$941$	20.7603			0.676767			0.338384	+	0.941008i	$0.390120\pi$
$942$		0			0
$943$		−	0.179401i		−	0.00584210i
$944$		0			0
$945$	−19.9188	−	32.4462i	−0.647960	−	1.05547i
$946$		0			0
$947$		−	7.51326i		−	0.244148i	−0.992521	−	0.122074i	$-0.961045\pi$
$947$		−	7.51326i		−	0.244148i	0.992521	−	0.122074i	$-0.0389545\pi$
$948$		0			0
$949$	−0.341082			−0.0110720
$950$		0			0
$951$	−33.0303	+	38.8976i	−1.07108	+	1.26134i
$952$		0			0
$953$			53.6047i			1.73643i	0.496192	+	0.868213i	$0.334731\pi$
$953$			53.6047i			1.73643i	−0.496192	+	0.868213i	$0.665269\pi$
$954$		0			0
$955$	6.32566	−	3.65212i	0.204694	−	0.118180i
$956$		0			0
$957$	−24.2451	−	20.5880i	−0.783733	−	0.665514i
$958$		0			0
$959$	0.664114	+	14.8788i	0.0214454	+	0.480461i
$960$		0			0
$961$	−15.4528			−0.498477
$962$		0			0
$963$	−11.9412	+	31.6464i	−0.384801	+	1.01979i
$964$		0			0
$965$	−10.3288	−	17.8899i	−0.332495	−	0.575898i
$966$		0			0
$967$	5.72860	−	9.92223i	0.184220	−	0.319078i	−0.759094	−	0.650981i	$-0.774358\pi$
$967$	5.72860	−	9.92223i	0.184220	−	0.319078i	0.943313	+	0.331904i	$0.107691\pi$
$968$		0			0
$969$	18.4727	−	21.7541i	0.593429	−	0.698842i
$970$		0			0
$971$	−4.02601	+	6.97326i	−0.129201	+	0.223782i	−0.923367	−	0.383918i	$-0.874575\pi$
$971$	−4.02601	+	6.97326i	−0.129201	+	0.223782i	0.794166	+	0.607700i	$0.207908\pi$
$972$		0			0
$973$	−2.54388	−	56.9931i	−0.0815532	−	1.82711i
$974$		0			0
$975$	0.242445	+	0.0442197i	0.00776446	+	0.00141616i
$976$		0			0
$977$		−	47.8756i		−	1.53168i	−0.643034	−	0.765838i	$-0.722324\pi$
$977$		−	47.8756i		−	1.53168i	0.643034	−	0.765838i	$-0.277676\pi$
$978$		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
$983$	−1.18090	+	2.04538i	−0.0376648	+	0.0652374i	−0.884243	−	0.467027i	$-0.845325\pi$
$983$	−1.18090	+	2.04538i	−0.0376648	+	0.0652374i	0.846578	+	0.532264i	$0.178659\pi$
$984$		0			0
$985$	6.66187	−	3.84623i	0.212265	−	0.122551i
$986$		0			0
$987$	8.18568	−	59.9056i	0.260553	−	1.90682i
$988$		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
$997$	36.7446	+	21.2145i	1.16371	+	0.671869i	0.952191	−	0.305504i	$-0.0988250\pi$
$997$	36.7446	+	21.2145i	1.16371	+	0.671869i	0.211521	+	0.977373i	$0.432158\pi$
$998$		0			0
$999$	10.3857	+	18.7438i	0.328588	+	0.593027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.e.257.19		48
3.2	odd	2		3024.2.ca.e.2609.4		48
4.3	odd	2		504.2.bs.a.257.6	✓	48
7.3	odd	6		1008.2.df.e.689.11		48
9.2	odd	6		1008.2.df.e.929.11		48
9.7	even	3		3024.2.df.e.1601.4		48
12.11	even	2		1512.2.bs.a.1097.4		48
21.17	even	6		3024.2.df.e.17.4		48
28.3	even	6		504.2.cx.a.185.14	yes	48
36.7	odd	6		1512.2.cx.a.89.4		48
36.11	even	6		504.2.cx.a.425.14	yes	48
63.38	even	6	inner	1008.2.ca.e.353.19		48
63.52	odd	6		3024.2.ca.e.2033.4		48
84.59	odd	6		1512.2.cx.a.17.4		48
252.115	even	6		1512.2.bs.a.521.4		48
252.227	odd	6		504.2.bs.a.353.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.6	✓	48	4.3	odd	2
504.2.bs.a.353.6	yes	48	252.227	odd	6
504.2.cx.a.185.14	yes	48	28.3	even	6
504.2.cx.a.425.14	yes	48	36.11	even	6
1008.2.ca.e.257.19		48	1.1	even	1	trivial
1008.2.ca.e.353.19		48	63.38	even	6	inner
1008.2.df.e.689.11		48	7.3	odd	6
1008.2.df.e.929.11		48	9.2	odd	6
1512.2.bs.a.521.4		48	252.115	even	6
1512.2.bs.a.1097.4		48	12.11	even	2
1512.2.cx.a.17.4		48	84.59	odd	6
1512.2.cx.a.89.4		48	36.7	odd	6
3024.2.ca.e.2033.4		48	63.52	odd	6
3024.2.ca.e.2609.4		48	3.2	odd	2
3024.2.df.e.17.4		48	21.17	even	6
3024.2.df.e.1601.4		48	9.7	even	3

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.32026 + 1.12112i) q^{3} +(1.38468 + 2.39834i) q^{5} +(1.42373 + 2.23002i) q^{7} +(0.486198 + 2.96034i) q^{9} +(-2.09513 - 1.20962i) q^{11} +(-0.0461613 - 0.0266512i) q^{13} +(-0.860670 + 4.71884i) q^{15} +(1.79727 + 3.11297i) q^{17} +(-3.96978 - 2.29195i) q^{19} +(-0.620412 + 4.54038i) q^{21} +(-0.0925928 + 0.0534585i) q^{23} +(-1.33469 + 2.31176i) q^{25} +(-2.67697 + 4.45352i) q^{27} +(6.57376 - 3.79536i) q^{29} -6.81563i q^{31} +(-1.41000 - 3.94590i) q^{33} +(-3.37694 + 6.50246i) q^{35} +(2.06198 - 3.57146i) q^{37} +(-0.0310660 - 0.0869389i) q^{39} +(-0.838974 + 1.45315i) q^{41} +(-1.74347 - 3.01978i) q^{43} +(-6.42667 + 5.26520i) q^{45} -13.1940 q^{47} +(-2.94599 + 6.34989i) q^{49} +(-1.11712 + 6.12489i) q^{51} +(5.27512 - 3.04559i) q^{53} -6.69977i q^{55} +(-2.67161 - 7.47657i) q^{57} +9.44833 q^{59} +2.65498i q^{61} +(-5.90941 + 5.29896i) q^{63} -0.147614i q^{65} +14.1871 q^{67} +(-0.182180 - 0.0332279i) q^{69} +1.40262i q^{71} +(5.54168 - 3.19949i) q^{73} +(-4.35390 + 1.55579i) q^{75} +(-0.285412 - 6.39435i) q^{77} -4.22133 q^{79} +(-8.52722 + 2.87862i) q^{81} +(6.86670 + 11.8935i) q^{83} +(-4.97731 + 8.62095i) q^{85} +(12.9341 + 2.35907i) q^{87} +(-5.71724 + 9.90254i) q^{89} +(-0.00628839 - 0.140885i) q^{91} +(7.64111 - 8.99843i) q^{93} -12.6945i q^{95} +(-14.3549 + 8.28778i) q^{97} +(2.56224 - 6.79040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more