LMFDB - Embedded newform 1008.2.cz.i.607.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(367,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.367"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0] 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.6
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.i.367.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.891691 - 1.48489i) q^{3} +(2.03373 - 1.17418i) q^{5} +(1.63327 - 2.08145i) q^{7} +(-1.40978 + 2.64812i) q^{9} +(0.383599 + 0.221471i) q^{11} +(1.96099 + 1.13218i) q^{13} +(-3.55698 - 1.97286i) q^{15} +(4.01950 - 2.32066i) q^{17} +(3.30879 - 5.73100i) q^{19} +(-4.54709 - 0.569213i) q^{21} +(0.984190 - 0.568223i) q^{23} +(0.257380 - 0.445795i) q^{25} +(5.18924 - 0.267947i) q^{27} +(4.37712 + 7.58140i) q^{29} -4.64068 q^{31} +(-0.0131924 - 0.767085i) q^{33} +(0.877649 - 6.15086i) q^{35} +(-1.41316 + 2.44767i) q^{37} +(-0.0674408 - 3.92140i) q^{39} +(-4.55283 - 2.62858i) q^{41} +(-3.81500 + 2.20259i) q^{43} +(0.242252 + 7.04089i) q^{45} -5.34726 q^{47} +(-1.66485 - 6.79914i) q^{49} +(-7.03007 - 3.89919i) q^{51} +(-1.54428 - 2.67478i) q^{53} +1.04018 q^{55} +(-11.4603 + 0.197096i) q^{57} -1.37914 q^{59} -10.2608i q^{61} +(3.20938 + 7.25947i) q^{63} +5.31751 q^{65} +2.43388i q^{67} +(-1.72134 - 0.954732i) q^{69} -7.20644i q^{71} +(3.17824 - 1.83496i) q^{73} +(-0.891458 + 0.0153314i) q^{75} +(1.08750 - 0.436720i) q^{77} -8.38938i q^{79} +(-5.02507 - 7.46650i) q^{81} +(7.87941 + 13.6475i) q^{83} +(5.44973 - 9.43920i) q^{85} +(7.35448 - 13.2598i) q^{87} +(5.32537 + 3.07461i) q^{89} +(5.55940 - 2.23255i) q^{91} +(4.13805 + 6.89088i) q^{93} -15.5404i q^{95} +(-14.9489 + 8.63074i) q^{97} +(-1.12727 + 0.703592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85}+ \cdots + 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.891691	−	1.48489i	−0.514818	−	0.857300i
$3$	−0.891691	−	1.48489i	−0.514818	−	0.857300i
$4$		0			0
$5$	2.03373	−	1.17418i	0.909513	−	0.525108i	0.0292386	−	0.999572i	$-0.490692\pi$
$5$	2.03373	−	1.17418i	0.909513	−	0.525108i	0.880274	+	0.474465i	$0.157358\pi$
$6$		0			0
$7$	1.63327	−	2.08145i	0.617318	−	0.786713i
$7$	1.63327	−	2.08145i	0.617318	−	0.786713i
$8$		0			0
$9$	−1.40978	+	2.64812i	−0.469925	+	0.882706i
$10$		0			0
$11$	0.383599	+	0.221471i	0.115660	+	0.0667761i	0.556714	−	0.830704i	$-0.312062\pi$
$11$	0.383599	+	0.221471i	0.115660	+	0.0667761i	−0.441054	+	0.897480i	$0.645395\pi$
$12$		0			0
$13$	1.96099	+	1.13218i	0.543881	+	0.314010i	0.746650	−	0.665217i	$-0.231661\pi$
$13$	1.96099	+	1.13218i	0.543881	+	0.314010i	−0.202769	+	0.979226i	$0.564994\pi$
$14$		0			0
$15$	−3.55698	−	1.97286i	−0.918408	−	0.509390i
$16$		0			0
$17$	4.01950	−	2.32066i	0.974872	−	0.562843i	0.0741541	−	0.997247i	$-0.476374\pi$
$17$	4.01950	−	2.32066i	0.974872	−	0.562843i	0.900718	+	0.434404i	$0.143041\pi$
$18$		0			0
$19$	3.30879	−	5.73100i	0.759089	−	1.31478i	−0.184227	−	0.982884i	$-0.558978\pi$
$19$	3.30879	−	5.73100i	0.759089	−	1.31478i	0.943316	−	0.331897i	$-0.107689\pi$
$20$		0			0
$21$	−4.54709	−	0.569213i	−0.992256	−	0.124213i
$22$		0			0
$23$	0.984190	−	0.568223i	0.205218	−	0.118483i	−0.393869	−	0.919167i	$-0.628864\pi$
$23$	0.984190	−	0.568223i	0.205218	−	0.118483i	0.599087	+	0.800684i	$0.295530\pi$
$24$		0			0
$25$	0.257380	−	0.445795i	0.0514760	−	0.0891590i
$26$		0			0
$27$	5.18924	−	0.267947i	0.998670	−	0.0515664i
$28$		0			0
$29$	4.37712	+	7.58140i	0.812811	+	1.40783i	0.910889	+	0.412652i	$0.135397\pi$
$29$	4.37712	+	7.58140i	0.812811	+	1.40783i	−0.0980775	+	0.995179i	$0.531269\pi$
$30$		0			0
$31$	−4.64068			−0.833490			−0.416745	−	0.909023i	$-0.636829\pi$
$31$	−4.64068			−0.833490			−0.416745	+	0.909023i	$0.636829\pi$
$32$		0			0
$33$	−0.0131924	−	0.767085i	−0.00229651	−	0.133532i
$34$		0			0
$35$	0.877649	−	6.15086i	0.148350	−	1.03968i
$36$		0			0
$37$	−1.41316	+	2.44767i	−0.232323	+	0.402395i	−0.958491	−	0.285122i	$-0.907966\pi$
$37$	−1.41316	+	2.44767i	−0.232323	+	0.402395i	0.726169	+	0.687517i	$0.241299\pi$
$38$		0			0
$39$	−0.0674408	−	3.92140i	−0.0107992	−	0.627927i
$40$		0			0
$41$	−4.55283	−	2.62858i	−0.711032	−	0.410515i	0.100411	−	0.994946i	$-0.467984\pi$
$41$	−4.55283	−	2.62858i	−0.711032	−	0.410515i	−0.811443	+	0.584431i	$0.801318\pi$
$42$		0			0
$43$	−3.81500	+	2.20259i	−0.581782	+	0.335892i	−0.761841	−	0.647764i	$-0.775704\pi$
$43$	−3.81500	+	2.20259i	−0.581782	+	0.335892i	0.180059	+	0.983656i	$0.442371\pi$
$44$		0			0
$45$	0.242252	+	7.04089i	0.0361128	+	1.04959i
$46$		0			0
$47$	−5.34726			−0.779979			−0.389989	−	0.920819i	$-0.627521\pi$
$47$	−5.34726			−0.779979			−0.389989	+	0.920819i	$0.627521\pi$
$48$		0			0
$49$	−1.66485	−	6.79914i	−0.237836	−	0.971305i
$50$		0			0
$51$	−7.03007	−	3.89919i	−0.984406	−	0.545996i
$52$		0			0
$53$	−1.54428	−	2.67478i	−0.212124	−	0.367409i	0.740255	−	0.672326i	$-0.234705\pi$
$53$	−1.54428	−	2.67478i	−0.212124	−	0.367409i	−0.952379	+	0.304917i	$0.901371\pi$
$54$		0			0
$55$	1.04018			0.140259
$56$		0			0
$57$	−11.4603	+	0.197096i	−1.51795	+	0.0261060i
$58$		0			0
$59$	−1.37914			−0.179549			−0.0897743	−	0.995962i	$-0.528615\pi$
$59$	−1.37914			−0.179549			−0.0897743	+	0.995962i	$0.528615\pi$
$60$		0			0
$61$		−	10.2608i		−	1.31375i	−0.753997	−	0.656877i	$-0.771877\pi$
$61$		−	10.2608i		−	1.31375i	0.753997	−	0.656877i	$-0.228123\pi$
$62$		0			0
$63$	3.20938	+	7.25947i	0.404344	+	0.914607i
$64$		0			0
$65$	5.31751			0.659556
$66$		0			0
$67$			2.43388i			0.297346i	0.988886	+	0.148673i	$0.0475001\pi$
$67$			2.43388i			0.297346i	−0.988886	+	0.148673i	$0.952500\pi$
$68$		0			0
$69$	−1.72134	−	0.954732i	−0.207225	−	0.114936i
$70$		0			0
$71$		−	7.20644i		−	0.855247i	−0.903957	−	0.427623i	$-0.859351\pi$
$71$		−	7.20644i		−	0.855247i	0.903957	−	0.427623i	$-0.140649\pi$
$72$		0			0
$73$	3.17824	−	1.83496i	0.371984	−	0.214765i	−0.302341	−	0.953200i	$-0.597768\pi$
$73$	3.17824	−	1.83496i	0.371984	−	0.214765i	0.674325	+	0.738435i	$0.264435\pi$
$74$		0			0
$75$	−0.891458	+	0.0153314i	−0.102937	+	0.00177032i
$76$		0			0
$77$	1.08750	−	0.436720i	0.123932	−	0.0497688i
$78$		0			0
$79$		−	8.38938i		−	0.943879i	−0.881631	−	0.471939i	$-0.843554\pi$
$79$		−	8.38938i		−	0.943879i	0.881631	−	0.471939i	$-0.156446\pi$
$80$		0			0
$81$	−5.02507	−	7.46650i	−0.558341	−	0.829612i
$82$		0			0
$83$	7.87941	+	13.6475i	0.864878	+	1.49801i	0.867168	+	0.498015i	$0.165938\pi$
$83$	7.87941	+	13.6475i	0.864878	+	1.49801i	−0.00229000	+	0.999997i	$0.500729\pi$
$84$		0			0
$85$	5.44973	−	9.43920i	0.591106	−	1.02383i
$86$		0			0
$87$	7.35448	−	13.2598i	0.788483	−	1.42160i
$88$		0			0
$89$	5.32537	+	3.07461i	0.564488	+	0.325908i	0.754945	−	0.655788i	$-0.227664\pi$
$89$	5.32537	+	3.07461i	0.564488	+	0.325908i	−0.190457	+	0.981696i	$0.560997\pi$
$90$		0			0
$91$	5.55940	−	2.23255i	0.582783	−	0.234034i
$92$		0			0
$93$	4.13805	+	6.89088i	0.429096	+	0.714551i
$94$		0			0
$95$		−	15.5404i		−	1.59441i
$96$		0			0
$97$	−14.9489	+	8.63074i	−1.51783	+	0.876319i	−0.518049	+	0.855351i	$0.673341\pi$
$97$	−14.9489	+	8.63074i	−1.51783	+	0.876319i	−0.999780	+	0.0209677i	$0.993325\pi$
$98$		0			0
$99$	−1.12727	+	0.703592i	−0.113295	+	0.0707137i
$100$		0			0
$101$	15.0400	+	8.68337i	1.49654	+	0.864028i	0.999992	−	0.00398168i	$-0.00126741\pi$
$101$	15.0400	+	8.68337i	1.49654	+	0.864028i	0.496548	+	0.868009i	$0.334601\pi$
$102$		0			0
$103$	−4.61944	−	8.00111i	−0.455167	−	0.788373i	0.543531	−	0.839389i	$-0.317087\pi$
$103$	−4.61944	−	8.00111i	−0.455167	−	0.788373i	−0.998698	+	0.0510167i	$0.983754\pi$
$104$		0			0
$105$	−9.91592	+	4.18145i	−0.967694	+	0.408068i
$106$		0			0
$107$	−7.76296	−	4.48195i	−0.750474	−	0.433286i	0.0753911	−	0.997154i	$-0.475979\pi$
$107$	−7.76296	−	4.48195i	−0.750474	−	0.433286i	−0.825865	+	0.563868i	$0.809313\pi$
$108$		0			0
$109$	−6.46206	−	11.1926i	−0.618953	−	1.07206i	−0.989677	−	0.143315i	$-0.954224\pi$
$109$	−6.46206	−	11.1926i	−0.618953	−	1.07206i	0.370724	−	0.928743i	$-0.379110\pi$
$110$		0			0
$111$	4.89462	−	0.0841783i	0.464577	−	0.00798985i
$112$		0			0
$113$	−2.12502	+	3.68064i	−0.199905	+	0.346246i	−0.948497	−	0.316785i	$-0.897397\pi$
$113$	−2.12502	+	3.68064i	−0.199905	+	0.346246i	0.748592	+	0.663031i	$0.230730\pi$
$114$		0			0
$115$	1.33439	−	2.31123i	0.124432	−	0.215523i
$116$		0			0
$117$	−5.76270	+	3.59682i	−0.532762	+	0.332526i
$118$		0			0
$119$	1.73460	−	12.1566i	0.159010	−	1.11440i
$120$		0			0
$121$	−5.40190	−	9.35637i	−0.491082	−	0.850579i
$122$		0			0
$123$	0.156577	+	9.10431i	0.0141181	+	0.820908i
$124$		0			0
$125$			10.5329i			0.942094i
$126$		0			0
$127$			19.6660i			1.74507i	0.488549	+	0.872536i	$0.337526\pi$
$127$			19.6660i			1.74507i	−0.488549	+	0.872536i	$0.662474\pi$
$128$		0			0
$129$	6.67240	+	3.70081i	0.587472	+	0.325838i
$130$		0			0
$131$	8.53684	+	14.7862i	0.745867	+	1.29188i	0.949789	+	0.312892i	$0.101298\pi$
$131$	8.53684	+	14.7862i	0.745867	+	1.29188i	−0.203922	+	0.978987i	$0.565369\pi$
$132$		0			0
$133$	−6.52462	−	16.2473i	−0.565756	−	1.40882i
$134$		0			0
$135$	10.2389	−	6.63801i	0.881225	−	0.571309i
$136$		0			0
$137$	1.75681	−	3.04288i	0.150094	−	0.259971i	−0.781168	−	0.624321i	$-0.785376\pi$
$137$	1.75681	−	3.04288i	0.150094	−	0.259971i	0.931262	+	0.364351i	$0.118709\pi$
$138$		0			0
$139$	−8.66086	+	15.0011i	−0.734605	+	1.27237i	0.220292	+	0.975434i	$0.429299\pi$
$139$	−8.66086	+	15.0011i	−0.734605	+	1.27237i	−0.954896	+	0.296939i	$0.904034\pi$
$140$		0			0
$141$	4.76811	+	7.94008i	0.401547	+	0.668675i
$142$		0			0
$143$	0.501490	+	0.868606i	0.0419367	+	0.0726365i
$144$		0			0
$145$	17.8038	+	10.2790i	1.47853	+	0.853627i
$146$		0			0
$147$	−8.61141	+	8.53485i	−0.710257	+	0.703942i
$148$		0			0
$149$	3.04266	+	5.27005i	0.249265	+	0.431739i	0.963322	−	0.268348i	$-0.0864777\pi$
$149$	3.04266	+	5.27005i	0.249265	+	0.431739i	−0.714057	+	0.700087i	$0.753144\pi$
$150$		0			0
$151$	−2.26256	−	1.30629i	−0.184125	−	0.106304i	0.405105	−	0.914270i	$-0.367235\pi$
$151$	−2.26256	−	1.30629i	−0.184125	−	0.106304i	−0.589229	+	0.807966i	$0.700568\pi$
$152$		0			0
$153$	0.478791	+	13.9157i	0.0387079	+	1.12502i
$154$		0			0
$155$	−9.43790	+	5.44897i	−0.758070	+	0.437672i
$156$		0			0
$157$		−	18.7922i		−	1.49978i	−0.661560	−	0.749892i	$-0.730105\pi$
$157$		−	18.7922i		−	1.49978i	0.661560	−	0.749892i	$-0.269895\pi$
$158$		0			0
$159$	−2.59472	+	4.67816i	−0.205775	+	0.371002i
$160$		0			0
$161$	0.424723	−	2.97660i	0.0334729	−	0.234589i
$162$		0			0
$163$	2.90466	+	1.67700i	0.227510	+	0.131353i	0.609423	−	0.792845i	$-0.291401\pi$
$163$	2.90466	+	1.67700i	0.227510	+	0.131353i	−0.381913	+	0.924198i	$0.624734\pi$
$164$		0			0
$165$	−0.927523	−	1.54456i	−0.0722076	−	0.120244i
$166$		0			0
$167$	4.58344	−	7.93876i	0.354678	−	0.614320i	−0.632385	−	0.774654i	$-0.717924\pi$
$167$	4.58344	−	7.93876i	0.354678	−	0.614320i	0.987063	+	0.160335i	$0.0512573\pi$
$168$		0			0
$169$	−3.93635	−	6.81795i	−0.302796	−	0.524458i
$170$		0			0
$171$	10.5117	+	16.8415i	0.803850	+	1.28790i
$172$		0			0
$173$			22.6519i			1.72219i	0.508441	+	0.861097i	$0.330222\pi$
$173$			22.6519i			1.72219i	−0.508441	+	0.861097i	$0.669778\pi$
$174$		0			0
$175$	−0.507528	−	1.26383i	−0.0383655	−	0.0955363i
$176$		0			0
$177$	1.22977	+	2.04786i	0.0924348	+	0.153927i
$178$		0			0
$179$	−19.2752	+	11.1285i	−1.44069	+	0.831785i	−0.997896	−	0.0648357i	$-0.979348\pi$
$179$	−19.2752	+	11.1285i	−1.44069	+	0.831785i	−0.442799	+	0.896621i	$0.646014\pi$
$180$		0			0
$181$		−	4.33319i		−	0.322084i	−0.986948	−	0.161042i	$-0.948515\pi$
$181$		−	4.33319i		−	0.322084i	0.986948	−	0.161042i	$-0.0514854\pi$
$182$		0			0
$183$	−15.2361	+	9.14942i	−1.12628	+	0.676344i
$184$		0			0
$185$			6.63721i			0.487978i
$186$		0			0
$187$	2.05584			0.150338
$188$		0			0
$189$	7.91771	−	11.2388i	0.575929	−	0.817500i
$190$		0			0
$191$			24.9010i			1.80177i	0.434058	+	0.900885i	$0.357081\pi$
$191$			24.9010i			1.80177i	−0.434058	+	0.900885i	$0.642919\pi$
$192$		0			0
$193$	21.3254			1.53503			0.767517	−	0.641029i	$-0.221492\pi$
$193$	21.3254			1.53503			0.767517	+	0.641029i	$0.221492\pi$
$194$		0			0
$195$	−4.74157	−	7.89589i	−0.339551	−	0.565437i
$196$		0			0
$197$	18.5315			1.32032			0.660158	−	0.751127i	$-0.270489\pi$
$197$	18.5315			1.32032			0.660158	+	0.751127i	$0.270489\pi$
$198$		0			0
$199$	−0.918721	−	1.59127i	−0.0651264	−	0.112802i	0.831624	−	0.555340i	$-0.187412\pi$
$199$	−0.918721	−	1.59127i	−0.0651264	−	0.112802i	−0.896750	+	0.442537i	$0.854078\pi$
$200$		0			0
$201$	3.61403	−	2.17027i	0.254914	−	0.153079i
$202$		0			0
$203$	22.9293	+	3.27172i	1.60932	+	0.229630i
$204$		0			0
$205$	−12.3457			−0.862258
$206$		0			0
$207$	0.117234	+	3.40732i	0.00814831	+	0.236825i
$208$		0			0
$209$	2.53850	−	1.46560i	0.175592	−	0.101378i
$210$		0			0
$211$	17.5295	+	10.1207i	1.20678	+	0.696735i	0.962054	−	0.272858i	$-0.0879689\pi$
$211$	17.5295	+	10.1207i	1.20678	+	0.696735i	0.244725	+	0.969592i	$0.421302\pi$
$212$		0			0
$213$	−10.7007	+	6.42591i	−0.733203	+	0.440296i
$214$		0			0
$215$	−5.17246	+	8.95897i	−0.352759	+	0.610997i
$216$		0			0
$217$	−7.57948	+	9.65933i	−0.514529	+	0.655718i
$218$		0			0
$219$	−5.55870	−	3.08311i	−0.375622	−	0.208337i
$220$		0			0
$221$	10.5096			0.706952
$222$		0			0
$223$	−0.492098	−	0.852339i	−0.0329533	−	0.0570768i	0.849078	−	0.528267i	$-0.177158\pi$
$223$	−0.492098	−	0.852339i	−0.0329533	−	0.0570768i	−0.882032	+	0.471190i	$0.843825\pi$
$224$		0			0
$225$	0.817670	+	1.31004i	0.0545113	+	0.0873362i
$226$		0			0
$227$	−6.59642	+	11.4253i	−0.437820	+	0.758326i	−0.997521	−	0.0703684i	$-0.977583\pi$
$227$	−6.59642	+	11.4253i	−0.437820	+	0.758326i	0.559701	+	0.828694i	$0.310916\pi$
$228$		0			0
$229$	−4.91871	+	2.83982i	−0.325037	+	0.187660i	−0.653636	−	0.756809i	$-0.726757\pi$
$229$	−4.91871	+	2.83982i	−0.325037	+	0.187660i	0.328598	+	0.944470i	$0.393424\pi$
$230$		0			0
$231$	−1.61820	−	1.22540i	−0.106469	−	0.0806253i
$232$		0			0
$233$	7.42995	−	12.8691i	0.486752	−	0.843080i	−0.513132	−	0.858310i	$-0.671515\pi$
$233$	7.42995	−	12.8691i	0.486752	−	0.843080i	0.999884	+	0.0152301i	$0.00484808\pi$
$234$		0			0
$235$	−10.8749	+	6.27863i	−0.709401	+	0.409573i
$236$		0			0
$237$	−12.4573	+	7.48073i	−0.809187	+	0.485926i
$238$		0			0
$239$	15.6484	+	9.03459i	1.01221	+	0.584399i	0.911837	−	0.410551i	$-0.134664\pi$
$239$	15.6484	+	9.03459i	1.01221	+	0.584399i	0.100371	+	0.994950i	$0.467997\pi$
$240$		0			0
$241$	17.9703	+	10.3751i	1.15757	+	0.668322i	0.950720	−	0.310051i	$-0.100346\pi$
$241$	17.9703	+	10.3751i	1.15757	+	0.668322i	0.206848	+	0.978373i	$0.433680\pi$
$242$		0			0
$243$	−6.60611	+	14.1195i	−0.423782	+	0.905764i
$244$		0			0
$245$	−11.3693	−	11.8728i	−0.726355	−	0.758525i
$246$		0			0
$247$	12.9770	−	7.49228i	0.825708	−	0.476723i
$248$		0			0
$249$	13.2391	−	23.8694i	0.838991	−	1.51266i
$250$		0			0
$251$	9.53037			0.601552			0.300776	−	0.953695i	$-0.402754\pi$
$251$	9.53037			0.601552			0.300776	+	0.953695i	$0.402754\pi$
$252$		0			0
$253$	0.503380			0.0316472
$254$		0			0
$255$	−18.8756	+	0.324625i	−1.18204	+	0.0203288i
$256$		0			0
$257$	−9.86829	+	5.69746i	−0.615567	+	0.355398i	−0.775141	−	0.631788i	$-0.782321\pi$
$257$	−9.86829	+	5.69746i	−0.615567	+	0.355398i	0.159574	+	0.987186i	$0.448988\pi$
$258$		0			0
$259$	2.78662	+	6.93914i	0.173152	+	0.431177i
$260$		0			0
$261$	−26.2472	+	0.903073i	−1.62466	+	0.0558988i
$262$		0			0
$263$	−5.40199	−	3.11884i	−0.333101	−	0.192316i	0.324116	−	0.946017i	$-0.394933\pi$
$263$	−5.40199	−	3.11884i	−0.333101	−	0.192316i	−0.657217	+	0.753701i	$0.728266\pi$
$264$		0			0
$265$	−6.28132	−	3.62652i	−0.385859	−	0.222776i
$266$		0			0
$267$	−0.183146	−	10.6492i	−0.0112083	−	0.651719i
$268$		0			0
$269$	22.5563	−	13.0229i	1.37528	−	0.794018i	0.383693	−	0.923461i	$-0.374652\pi$
$269$	22.5563	−	13.0229i	1.37528	−	0.794018i	0.991587	+	0.129443i	$0.0413188\pi$
$270$		0			0
$271$	10.3180	−	17.8713i	0.626775	−	1.08561i	−0.361420	−	0.932403i	$-0.617708\pi$
$271$	10.3180	−	17.8713i	0.626775	−	1.08561i	0.988195	−	0.153203i	$-0.0489589\pi$
$272$		0			0
$273$	−8.27234	−	6.26433i	−0.500665	−	0.379135i
$274$		0			0
$275$	0.197461	−	0.114004i	0.0119074	−	0.00687472i
$276$		0			0
$277$	6.03611	−	10.4549i	0.362675	−	0.628171i	−0.625725	−	0.780044i	$-0.715197\pi$
$277$	6.03611	−	10.4549i	0.362675	−	0.628171i	0.988400	+	0.151872i	$0.0485302\pi$
$278$		0			0
$279$	6.54231	−	12.2891i	0.391678	−	0.735727i
$280$		0			0
$281$	−3.67299	−	6.36180i	−0.219112	−	0.379513i	0.735425	−	0.677606i	$-0.236983\pi$
$281$	−3.67299	−	6.36180i	−0.219112	−	0.379513i	−0.954537	+	0.298093i	$0.903649\pi$
$282$		0			0
$283$	17.3063			1.02875			0.514376	−	0.857565i	$-0.328023\pi$
$283$	17.3063			1.02875			0.514376	+	0.857565i	$0.328023\pi$
$284$		0			0
$285$	−23.0758	+	13.8572i	−1.36689	+	0.820833i
$286$		0			0
$287$	−12.9072	+	5.18330i	−0.761891	+	0.305961i
$288$		0			0
$289$	2.27092	−	3.93336i	0.133584	−	0.231374i
$290$		0			0
$291$	26.1454	+	14.5014i	1.53267	+	0.850089i
$292$		0			0
$293$	−0.965862	−	0.557641i	−0.0564263	−	0.0325777i	0.471521	−	0.881855i	$-0.343705\pi$
$293$	−0.965862	−	0.557641i	−0.0564263	−	0.0325777i	−0.527948	+	0.849277i	$0.677038\pi$
$294$		0			0
$295$	−2.80480	+	1.61935i	−0.163302	+	0.0942823i
$296$		0			0
$297$	2.04993	+	1.04648i	0.118949	+	0.0607231i
$298$		0			0
$299$	2.57332			0.148819
$300$		0			0
$301$	−1.64635	+	11.5382i	−0.0948940	+	0.665048i
$302$		0			0
$303$	−0.517245	−	30.0756i	−0.0297149	−	1.72780i
$304$		0			0
$305$	−12.0479	−	20.8676i	−0.689863	−	1.19488i
$306$		0			0
$307$	−30.5465			−1.74338			−0.871690	−	0.490058i	$-0.836975\pi$
$307$	−30.5465			−1.74338			−0.871690	+	0.490058i	$0.836975\pi$
$308$		0			0
$309$	−7.76162	+	13.9939i	−0.441543	+	0.796083i
$310$		0			0
$311$	6.89599			0.391036			0.195518	−	0.980700i	$-0.437361\pi$
$311$	6.89599			0.391036			0.195518	+	0.980700i	$0.437361\pi$
$312$		0			0
$313$			14.0173i			0.792305i	0.918185	+	0.396153i	$0.129655\pi$
$313$			14.0173i			0.792305i	−0.918185	+	0.396153i	$0.870345\pi$
$314$		0			0
$315$	15.0509	+	10.9954i	0.848023	+	0.619523i
$316$		0			0
$317$	−20.1774			−1.13328			−0.566638	−	0.823967i	$-0.691756\pi$
$317$	−20.1774			−1.13328			−0.566638	+	0.823967i	$0.691756\pi$
$318$		0			0
$319$			3.87763i			0.217105i
$320$		0			0
$321$	0.266978	+	15.5236i	0.0149012	+	0.866445i
$322$		0			0
$323$		−	30.7143i		−	1.70899i
$324$		0			0
$325$	1.00944	−	0.582800i	0.0559936	−	0.0323279i
$326$		0			0
$327$	−10.8576	+	19.5758i	−0.600427	+	1.08254i
$328$		0			0
$329$	−8.73353	+	11.1301i	−0.481495	+	0.613620i
$330$		0			0
$331$			32.2973i			1.77522i	0.460597	+	0.887609i	$0.347635\pi$
$331$			32.2973i			1.77522i	−0.460597	+	0.887609i	$0.652365\pi$
$332$		0			0
$333$	−4.48948	−	7.19289i	−0.246022	−	0.394168i
$334$		0			0
$335$	2.85780	+	4.94986i	0.156138	+	0.270440i
$336$		0			0
$337$	−10.1378	+	17.5591i	−0.552239	+	0.956506i	0.445873	+	0.895096i	$0.352893\pi$
$337$	−10.1378	+	17.5591i	−0.552239	+	0.956506i	−0.998113	+	0.0614102i	$0.980440\pi$
$338$		0			0
$339$	7.36020	−	0.126582i	0.399751	−	0.00687497i
$340$		0			0
$341$	−1.78016	−	1.02778i	−0.0964011	−	0.0556572i
$342$		0			0
$343$	−16.8712	−	7.63953i	−0.910960	−	0.412496i
$344$		0			0
$345$	−4.62177	+	0.0794858i	−0.248828	+	0.00427937i
$346$		0			0
$347$		−	4.19316i		−	0.225101i	−0.993646	−	0.112550i	$-0.964098\pi$
$347$		−	4.19316i		−	0.225101i	0.993646	−	0.112550i	$-0.0359020\pi$
$348$		0			0
$349$	6.54079	−	3.77632i	0.350120	−	0.202142i	−0.314618	−	0.949218i	$-0.601876\pi$
$349$	6.54079	−	3.77632i	0.350120	−	0.202142i	0.664738	+	0.747076i	$0.268543\pi$
$350$		0			0
$351$	10.4794	+	5.34970i	0.559350	+	0.285546i
$352$		0			0
$353$	15.1910	+	8.77050i	0.808533	+	0.466807i	0.846446	−	0.532474i	$-0.178738\pi$
$353$	15.1910	+	8.77050i	0.808533	+	0.466807i	−0.0379134	+	0.999281i	$0.512071\pi$
$354$		0			0
$355$	−8.46163	−	14.6560i	−0.449097	−	0.777858i
$356$		0			0
$357$	−19.5980	+	8.26429i	−1.03723	+	0.437392i
$358$		0			0
$359$	−18.3430	−	10.5904i	−0.968108	−	0.558937i	−0.0694490	−	0.997586i	$-0.522124\pi$
$359$	−18.3430	−	10.5904i	−0.968108	−	0.558937i	−0.898659	+	0.438648i	$0.855457\pi$
$360$		0			0
$361$	−12.3962	−	21.4709i	−0.652432	−	1.13005i
$362$		0			0
$363$	−9.07632	+	16.3642i	−0.476383	+	0.858898i
$364$		0			0
$365$	4.30912	−	7.46362i	0.225550	−	0.390664i
$366$		0			0
$367$	−1.11068	+	1.92375i	−0.0579768	+	0.100419i	−0.893557	−	0.448950i	$-0.851798\pi$
$367$	−1.11068	+	1.92375i	−0.0579768	+	0.100419i	0.835580	+	0.549368i	$0.185132\pi$
$368$		0			0
$369$	13.3793	−	8.35073i	0.696496	−	0.434722i
$370$		0			0
$371$	−8.08965	−	1.15429i	−0.419994	−	0.0599278i
$372$		0			0
$373$	3.80709	+	6.59408i	0.197124	+	0.341428i	0.947595	−	0.319475i	$-0.103507\pi$
$373$	3.80709	+	6.59408i	0.197124	+	0.341428i	−0.750471	+	0.660904i	$0.770173\pi$
$374$		0			0
$375$	15.6402	−	9.39211i	0.807656	−	0.485007i
$376$		0			0
$377$			19.8227i			1.02092i
$378$		0			0
$379$			4.06894i			0.209007i	0.994525	+	0.104504i	$0.0333254\pi$
$379$			4.06894i			0.209007i	−0.994525	+	0.104504i	$0.966675\pi$
$380$		0			0
$381$	29.2017	−	17.5360i	1.49605	−	0.898395i
$382$		0			0
$383$	1.02127	+	1.76888i	0.0521842	+	0.0903858i	0.890938	−	0.454126i	$-0.150048\pi$
$383$	1.02127	+	1.76888i	0.0521842	+	0.0903858i	−0.838753	+	0.544512i	$0.816715\pi$
$384$		0			0
$385$	1.69890	−	2.16509i	0.0865841	−	0.110343i
$386$		0			0
$387$	−0.454431	−	13.2077i	−0.0231000	−	0.671387i
$388$		0			0
$389$	12.1793	−	21.0952i	0.617517	−	1.06957i	−0.372421	−	0.928064i	$-0.621472\pi$
$389$	12.1793	−	21.0952i	0.617517	−	1.06957i	0.989937	−	0.141506i	$-0.0451945\pi$
$390$		0			0
$391$	2.63730	−	4.56794i	0.133374	−	0.231011i
$392$		0			0
$393$	14.3437	−	25.8610i	0.723542	−	1.30451i
$394$		0			0
$395$	−9.85061	−	17.0618i	−0.495638	−	0.858470i
$396$		0			0
$397$	−12.6996	−	7.33213i	−0.637375	−	0.367989i	0.146227	−	0.989251i	$-0.453287\pi$
$397$	−12.6996	−	7.33213i	−0.637375	−	0.367989i	−0.783603	+	0.621262i	$0.786620\pi$
$398$		0			0
$399$	−18.3075	+	24.1759i	−0.916523	+	1.21031i
$400$		0			0
$401$	−6.78892	−	11.7588i	−0.339022	−	0.587204i	0.645227	−	0.763991i	$-0.276763\pi$
$401$	−6.78892	−	11.7588i	−0.339022	−	0.587204i	−0.984249	+	0.176787i	$0.943430\pi$
$402$		0			0
$403$	−9.10032	−	5.25407i	−0.453319	−	0.261724i
$404$		0			0
$405$	−18.9866	−	9.28456i	−0.943454	−	0.461354i
$406$		0			0
$407$	−1.08418	+	0.625950i	−0.0537407	+	0.0310272i
$408$		0			0
$409$			6.58600i			0.325657i	0.986654	+	0.162828i	$0.0520617\pi$
$409$			6.58600i			0.325657i	−0.986654	+	0.162828i	$0.947938\pi$
$410$		0			0
$411$	−6.08486	+	0.104648i	−0.300144	+	0.00516192i
$412$		0			0
$413$	−2.25251	+	2.87061i	−0.110839	+	0.141253i
$414$		0			0
$415$	32.0493	+	18.5036i	1.57324	+	0.908308i
$416$		0			0
$417$	29.9977	−	0.515904i	1.46899	−	0.0252639i
$418$		0			0
$419$	11.4919	−	19.9046i	0.561416	−	0.972401i	−0.435957	−	0.899967i	$-0.643590\pi$
$419$	11.4919	−	19.9046i	0.561416	−	0.972401i	0.997373	−	0.0724336i	$-0.0230765\pi$
$420$		0			0
$421$	−1.00338	−	1.73790i	−0.0489017	−	0.0847003i	0.840538	−	0.541752i	$-0.182239\pi$
$421$	−1.00338	−	1.73790i	−0.0489017	−	0.0847003i	−0.889440	+	0.457052i	$0.848905\pi$
$422$		0			0
$423$	7.53844	−	14.1602i	0.366532	−	0.688492i
$424$		0			0
$425$		−	2.38916i		−	0.115891i
$426$		0			0
$427$	−21.3572	−	16.7586i	−1.03355	−	0.811005i
$428$		0			0
$429$	0.842607	−	1.51918i	0.0406814	−	0.0733468i
$430$		0			0
$431$	28.7684	−	16.6095i	1.38573	−	0.800049i	0.392896	−	0.919583i	$-0.371473\pi$
$431$	28.7684	−	16.6095i	1.38573	−	0.800049i	0.992830	+	0.119534i	$0.0381399\pi$
$432$		0			0
$433$			35.6573i			1.71358i	0.515663	+	0.856791i	$0.327546\pi$
$433$			35.6573i			1.71358i	−0.515663	+	0.856791i	$0.672454\pi$
$434$		0			0
$435$	−0.612294	−	35.6023i	−0.0293572	−	1.70700i
$436$		0			0
$437$		−	7.52052i		−	0.359755i
$438$		0			0
$439$	8.59226			0.410086			0.205043	−	0.978753i	$-0.434267\pi$
$439$	8.59226			0.410086			0.205043	+	0.978753i	$0.434267\pi$
$440$		0			0
$441$	20.3520	+	5.17652i	0.969142	+	0.246501i
$442$		0			0
$443$			36.4264i			1.73067i	0.501194	+	0.865335i	$0.332894\pi$
$443$			36.4264i			1.73067i	−0.501194	+	0.865335i	$0.667106\pi$
$444$		0			0
$445$	14.4405			0.684546
$446$		0			0
$447$	5.11231	−	9.21726i	0.241804	−	0.435962i
$448$		0			0
$449$	−12.2858			−0.579801			−0.289900	−	0.957057i	$-0.593622\pi$
$449$	−12.2858			−0.579801			−0.289900	+	0.957057i	$0.593622\pi$
$450$		0			0
$451$	−1.16431	−	2.01664i	−0.0548251	−	0.0949599i
$452$		0			0
$453$	0.0778121	+	4.52445i	0.00365593	+	0.212577i
$454$		0			0
$455$	8.68493	−	11.0681i	0.407156	−	0.518881i
$456$		0			0
$457$	−7.29349			−0.341175			−0.170587	−	0.985343i	$-0.554567\pi$
$457$	−7.29349			−0.341175			−0.170587	+	0.985343i	$0.554567\pi$
$458$		0			0
$459$	20.2363	−	13.1195i	0.944551	−	0.612365i
$460$		0			0
$461$	−7.33329	+	4.23388i	−0.341545	+	0.197191i	−0.660955	−	0.750425i	$-0.729849\pi$
$461$	−7.33329	+	4.23388i	−0.341545	+	0.197191i	0.319410	+	0.947617i	$0.396515\pi$
$462$		0			0
$463$	−4.53400	−	2.61771i	−0.210713	−	0.121655i	0.390930	−	0.920421i	$-0.372154\pi$
$463$	−4.53400	−	2.61771i	−0.210713	−	0.121655i	−0.601643	+	0.798765i	$0.705487\pi$
$464$		0			0
$465$	16.5068	+	9.15541i	0.765484	+	0.424572i
$466$		0			0
$467$	9.96542	−	17.2606i	0.461145	−	0.798726i	−0.537874	−	0.843025i	$-0.680772\pi$
$467$	9.96542	−	17.2606i	0.461145	−	0.798726i	0.999018	+	0.0442995i	$0.0141056\pi$
$468$		0			0
$469$	5.06599	+	3.97518i	0.233926	+	0.183557i
$470$		0			0
$471$	−27.9043	+	16.7569i	−1.28576	+	0.772116i
$472$		0			0
$473$	−1.95124			−0.0897182
$474$		0			0
$475$	−1.70323	−	2.95008i	−0.0781497	−	0.135359i
$476$		0			0
$477$	9.26023	−	0.318611i	0.423997	−	0.0145882i
$478$		0			0
$479$	−14.5123	+	25.1360i	−0.663083	+	1.14849i	0.316718	+	0.948520i	$0.397419\pi$
$479$	−14.5123	+	25.1360i	−0.663083	+	1.14849i	−0.979801	+	0.199974i	$0.935914\pi$
$480$		0			0
$481$	−5.54240	+	3.19991i	−0.252712	+	0.145903i
$482$		0			0
$483$	−4.79864	+	2.02354i	−0.218346	+	0.0920744i
$484$		0			0
$485$	−20.2680	+	35.1052i	−0.920323	+	1.59405i
$486$		0			0
$487$	−11.9472	+	6.89770i	−0.541378	+	0.312565i	−0.745637	−	0.666352i	$-0.767855\pi$
$487$	−11.9472	+	6.89770i	−0.541378	+	0.312565i	0.204259	+	0.978917i	$0.434521\pi$
$488$		0			0
$489$	−0.0998946	−	5.80845i	−0.00451739	−	0.262667i
$490$		0			0
$491$	−14.6069	−	8.43329i	−0.659200	−	0.380589i	0.132772	−	0.991147i	$-0.457612\pi$
$491$	−14.6069	−	8.43329i	−0.659200	−	0.380589i	−0.791972	+	0.610557i	$0.790945\pi$
$492$		0			0
$493$	35.1877	+	20.3156i	1.58477	+	0.914970i
$494$		0			0
$495$	−1.46643	+	2.75453i	−0.0659110	+	0.123807i
$496$		0			0
$497$	−14.9998	−	11.7701i	−0.672834	−	0.527959i
$498$		0			0
$499$	14.5193	−	8.38271i	0.649972	−	0.375262i	−0.138473	−	0.990366i	$-0.544220\pi$
$499$	14.5193	−	8.38271i	0.649972	−	0.375262i	0.788446	+	0.615104i	$0.210886\pi$
$500$		0			0
$501$	−15.8752	+	0.273023i	−0.709250	+	0.0121978i
$502$		0			0
$503$	−36.2366			−1.61571			−0.807856	−	0.589380i	$-0.799372\pi$
$503$	−36.2366			−1.61571			−0.807856	+	0.589380i	$0.799372\pi$
$504$		0			0
$505$	40.7832			1.81483
$506$		0			0
$507$	−6.61388	+	11.9245i	−0.293733	+	0.529587i
$508$		0			0
$509$	25.1838	−	14.5399i	1.11625	−	0.644468i	0.175811	−	0.984424i	$-0.443745\pi$
$509$	25.1838	−	14.5399i	1.11625	−	0.644468i	0.940441	+	0.339956i	$0.110412\pi$
$510$		0			0
$511$	1.37155	−	9.61231i	0.0606740	−	0.425224i
$512$		0			0
$513$	15.6345	−	30.6261i	0.690280	−	1.35217i
$514$		0			0
$515$	−18.7894	−	10.8481i	−0.827961	−	0.478023i
$516$		0			0
$517$	−2.05121	−	1.18427i	−0.0902120	−	0.0520839i
$518$		0			0
$519$	33.6355	−	20.1985i	1.47644	−	0.886616i
$520$		0			0
$521$	−31.1742	+	17.9984i	−1.36576	+	0.788524i	−0.990384	−	0.138346i	$-0.955821\pi$
$521$	−31.1742	+	17.9984i	−1.36576	+	0.788524i	−0.375381	+	0.926871i	$0.622488\pi$
$522$		0			0
$523$	17.0333	−	29.5026i	0.744816	−	1.29006i	−0.205465	−	0.978664i	$-0.565871\pi$
$523$	17.0333	−	29.5026i	0.744816	−	1.29006i	0.950281	−	0.311394i	$-0.100796\pi$
$524$		0			0
$525$	−1.42408	+	1.88056i	−0.0621520	+	0.0820745i
$526$		0			0
$527$	−18.6532	+	10.7694i	−0.812546	+	0.469124i
$528$		0			0
$529$	−10.8542	+	18.8001i	−0.471924	+	0.817396i
$530$		0			0
$531$	1.94428	−	3.65212i	0.0843744	−	0.158489i
$532$		0			0
$533$	−5.95203	−	10.3092i	−0.257811	−	0.446542i
$534$		0			0
$535$	−21.0504			−0.910088
$536$		0			0
$537$	33.7121	+	18.6982i	1.45478	+	0.806889i
$538$		0			0
$539$	0.867176	−	2.97686i	0.0373519	−	0.128223i
$540$		0			0
$541$	−4.04194	+	7.00084i	−0.173777	+	0.300990i	−0.939737	−	0.341898i	$-0.888930\pi$
$541$	−4.04194	+	7.00084i	−0.173777	+	0.300990i	0.765961	+	0.642887i	$0.222264\pi$
$542$		0			0
$543$	−6.43430	+	3.86387i	−0.276122	+	0.165814i
$544$		0			0
$545$	−26.2842	−	15.1752i	−1.12589	−	0.650034i
$546$		0			0
$547$	22.5917	−	13.0433i	0.965950	−	0.557691i	0.0679508	−	0.997689i	$-0.478354\pi$
$547$	22.5917	−	13.0433i	0.965950	−	0.557691i	0.897999	+	0.439997i	$0.145021\pi$
$548$		0			0
$549$	27.1717	+	14.4654i	1.15966	+	0.617366i
$550$		0			0
$551$	57.9320			2.46798
$552$		0			0
$553$	−17.4621	−	13.7021i	−0.742562	−	0.582674i
$554$		0			0
$555$	9.85551	−	5.91834i	0.418343	−	0.251220i
$556$		0			0
$557$	6.12408	+	10.6072i	0.259486	+	0.449442i	0.966104	−	0.258152i	$-0.0831137\pi$
$557$	6.12408	+	10.6072i	0.259486	+	0.449442i	−0.706619	+	0.707595i	$0.749780\pi$
$558$		0			0
$559$	−9.97491			−0.421894
$560$		0			0
$561$	−1.83317	−	3.05268i	−0.0773965	−	0.128884i
$562$		0			0
$563$	22.8504			0.963029			0.481515	−	0.876438i	$-0.340087\pi$
$563$	22.8504			0.963029			0.481515	+	0.876438i	$0.340087\pi$
$564$		0			0
$565$			9.98059i			0.419887i
$566$		0			0
$567$	−23.7484	−	1.73541i	−0.997341	−	0.0728802i
$568$		0			0
$569$	−5.73797			−0.240548			−0.120274	−	0.992741i	$-0.538377\pi$
$569$	−5.73797			−0.240548			−0.120274	+	0.992741i	$0.538377\pi$
$570$		0			0
$571$			24.9596i			1.04453i	0.852784	+	0.522264i	$0.174912\pi$
$571$			24.9596i			1.04453i	−0.852784	+	0.522264i	$0.825088\pi$
$572$		0			0
$573$	36.9751	−	22.2039i	1.54466	−	0.927583i
$574$		0			0
$575$		−	0.584996i		−	0.0243960i
$576$		0			0
$577$	−18.7652	+	10.8341i	−0.781206	+	0.451030i	−0.836858	−	0.547421i	$-0.815610\pi$
$577$	−18.7652	+	10.8341i	−0.781206	+	0.451030i	0.0556514	+	0.998450i	$0.482276\pi$
$578$		0			0
$579$	−19.0156	−	31.6658i	−0.790263	−	1.31598i
$580$		0			0
$581$	41.2759	+	5.88954i	1.71241	+	0.244339i
$582$		0			0
$583$		−	1.36806i		−	0.0566592i
$584$		0			0
$585$	−7.49649	+	14.0814i	−0.309942	+	0.582194i
$586$		0			0
$587$	−14.7121	−	25.4821i	−0.607233	−	1.05176i	−0.991694	−	0.128617i	$-0.958946\pi$
$587$	−14.7121	−	25.4821i	−0.607233	−	1.05176i	0.384461	−	0.923141i	$-0.374387\pi$
$588$		0			0
$589$	−15.3550	+	26.5957i	−0.632693	+	1.09586i
$590$		0			0
$591$	−16.5244	−	27.5172i	−0.679722	−	1.13191i
$592$		0			0
$593$	−25.5917	−	14.7754i	−1.05092	−	0.606752i	−0.128017	−	0.991772i	$-0.540861\pi$
$593$	−25.5917	−	14.7754i	−1.05092	−	0.606752i	−0.922908	+	0.385020i	$0.874194\pi$
$594$		0			0
$595$	−10.7463	−	26.7601i	−0.440557	−	1.09706i
$596$		0			0
$597$	−1.54364	+	2.78312i	−0.0631771	+	0.113905i
$598$		0			0
$599$		−	39.7332i		−	1.62345i	−0.584038	−	0.811727i	$-0.698528\pi$
$599$		−	39.7332i		−	1.62345i	0.584038	−	0.811727i	$-0.301472\pi$
$600$		0			0
$601$	−9.64604	+	5.56915i	−0.393470	+	0.227170i	−0.683663	−	0.729798i	$-0.739614\pi$
$601$	−9.64604	+	5.56915i	−0.393470	+	0.227170i	0.290192	+	0.956968i	$0.406281\pi$
$602$		0			0
$603$	−6.44520	−	3.43122i	−0.262469	−	0.139730i
$604$		0			0
$605$	−21.9720	−	12.6856i	−0.893291	−	0.515742i
$606$		0			0
$607$	−17.3314	−	30.0189i	−0.703461	−	1.21843i	−0.967244	−	0.253848i	$-0.918304\pi$
$607$	−17.3314	−	30.0189i	−0.703461	−	1.21843i	0.263783	−	0.964582i	$-0.415030\pi$
$608$		0			0
$609$	−15.5877	−	36.9648i	−0.631646	−	1.49789i
$610$		0			0
$611$	−10.4859	−	6.05406i	−0.424215	−	0.244921i
$612$		0			0
$613$	−16.1482	−	27.9695i	−0.652219	−	1.12968i	−0.982583	−	0.185823i	$-0.940505\pi$
$613$	−16.1482	−	27.9695i	−0.652219	−	1.12968i	0.330365	−	0.943853i	$-0.392828\pi$
$614$		0			0
$615$	11.0085	+	18.3319i	0.443906	+	0.739213i
$616$		0			0
$617$	−22.0343	+	38.1645i	−0.887067	+	1.53644i	−0.0437400	+	0.999043i	$0.513927\pi$
$617$	−22.0343	+	38.1645i	−0.887067	+	1.53644i	−0.843327	+	0.537401i	$0.819406\pi$
$618$		0			0
$619$	−4.65157	+	8.05675i	−0.186962	+	0.323828i	−0.944236	−	0.329270i	$-0.893198\pi$
$619$	−4.65157	+	8.05675i	−0.186962	+	0.323828i	0.757274	+	0.653098i	$0.226531\pi$
$620$		0			0
$621$	4.95495	−	3.21235i	0.198835	−	0.128907i
$622$		0			0
$623$	15.0974	−	6.06283i	0.604865	−	0.242902i
$624$		0			0
$625$	13.6544	+	23.6501i	0.546176	+	0.946005i
$626$		0			0
$627$	−4.43981	−	2.46252i	−0.177309	−	0.0983436i
$628$		0			0
$629$			13.1179i			0.523044i
$630$		0			0
$631$		−	28.6463i		−	1.14039i	−0.821509	−	0.570196i	$-0.806867\pi$
$631$		−	28.6463i		−	1.14039i	0.821509	−	0.570196i	$-0.193133\pi$
$632$		0			0
$633$	−0.602860	−	35.0538i	−0.0239615	−	1.39326i
$634$		0			0
$635$	23.0913	+	39.9953i	0.916351	+	1.58717i
$636$		0			0
$637$	4.43307	−	15.2180i	0.175645	−	0.602957i
$638$		0			0
$639$	19.0835	+	10.1595i	0.754932	+	0.401902i
$640$		0			0
$641$	−1.01626	+	1.76021i	−0.0401397	+	0.0695241i	−0.885397	−	0.464835i	$-0.846114\pi$
$641$	−1.01626	+	1.76021i	−0.0401397	+	0.0695241i	0.845258	+	0.534359i	$0.179447\pi$
$642$		0			0
$643$	14.7575	−	25.5608i	0.581980	−	1.00802i	−0.413265	−	0.910611i	$-0.635612\pi$
$643$	14.7575	−	25.5608i	0.581980	−	1.00802i	0.995245	−	0.0974077i	$-0.0310551\pi$
$644$		0			0
$645$	17.9153	−	0.308110i	0.705414	−	0.0121318i
$646$		0			0
$647$	−8.18434	−	14.1757i	−0.321759	−	0.557304i	0.659092	−	0.752063i	$-0.270941\pi$
$647$	−8.18434	−	14.1757i	−0.321759	−	0.557304i	−0.980851	+	0.194759i	$0.937608\pi$
$648$		0			0
$649$	−0.529037	−	0.305440i	−0.0207665	−	0.0119896i
$650$		0			0
$651$	21.1016	+	2.64154i	0.827035	+	0.103530i
$652$		0			0
$653$	−0.0892626	−	0.154607i	−0.00349312	−	0.00605026i	0.864274	−	0.503022i	$-0.167779\pi$
$653$	−0.0892626	−	0.154607i	−0.00349312	−	0.00605026i	−0.867767	+	0.496972i	$0.834445\pi$
$654$		0			0
$655$	34.7233	+	20.0475i	1.35675	+	0.783321i
$656$		0			0
$657$	0.378582	+	11.0032i	0.0147699	+	0.429276i
$658$		0			0
$659$	−17.4428	+	10.0706i	−0.679474	+	0.392294i	−0.799657	−	0.600457i	$-0.794985\pi$
$659$	−17.4428	+	10.0706i	−0.679474	+	0.392294i	0.120183	+	0.992752i	$0.461652\pi$
$660$		0			0
$661$			8.76781i			0.341028i	0.985355	+	0.170514i	$0.0545429\pi$
$661$			8.76781i			0.341028i	−0.985355	+	0.170514i	$0.945457\pi$
$662$		0			0
$663$	−9.37131	−	15.6056i	−0.363952	−	0.606070i
$664$		0			0
$665$	−32.3466	−	25.3817i	−1.25435	−	0.984261i
$666$		0			0
$667$	8.61584	+	4.97436i	0.333607	+	0.192608i
$668$		0			0
$669$	−0.826827	+	1.49073i	−0.0319670	+	0.0576350i
$670$		0			0
$671$	2.27246	−	3.93602i	0.0877274	−	0.151948i
$672$		0			0
$673$	−1.04120	−	1.80341i	−0.0401353	−	0.0695164i	0.845260	−	0.534355i	$-0.179446\pi$
$673$	−1.04120	−	1.80341i	−0.0401353	−	0.0695164i	−0.885395	+	0.464839i	$0.846112\pi$
$674$		0			0
$675$	1.21616	−	2.38230i	0.0468099	−	0.0916948i
$676$		0			0
$677$		−	13.9421i		−	0.535839i	−0.963441	−	0.267919i	$-0.913664\pi$
$677$		−	13.9421i		−	0.535839i	0.963441	−	0.267919i	$-0.0863361\pi$
$678$		0			0
$679$	−6.45113	+	45.2117i	−0.247572	+	1.73506i
$680$		0			0
$681$	22.8473	−	0.392931i	0.875510	−	0.0150571i
$682$		0			0
$683$	13.5049	−	7.79708i	0.516752	−	0.298347i	−0.218853	−	0.975758i	$-0.570231\pi$
$683$	13.5049	−	7.79708i	0.516752	−	0.298347i	0.735605	+	0.677411i	$0.236898\pi$
$684$		0			0
$685$		−	8.25120i		−	0.315262i
$686$		0			0
$687$	8.60278	+	4.77149i	0.328216	+	0.182044i
$688$		0			0
$689$		−	6.99362i		−	0.266436i
$690$		0			0
$691$	1.97347			0.0750743			0.0375371	−	0.999295i	$-0.488049\pi$
$691$	1.97347			0.0750743			0.0375371	+	0.999295i	$0.488049\pi$
$692$		0			0
$693$	−0.376648	+	3.49551i	−0.0143077	+	0.132784i
$694$		0			0
$695$			40.6775i			1.54299i
$696$		0			0
$697$	−24.4001			−0.924221
$698$		0			0
$699$	−25.7343	+	0.442582i	−0.973361	+	0.0167400i
$700$		0			0
$701$	−3.57171			−0.134902			−0.0674508	−	0.997723i	$-0.521487\pi$
$701$	−3.57171			−0.134902			−0.0674508	+	0.997723i	$0.521487\pi$
$702$		0			0
$703$	9.35173	+	16.1977i	0.352707	+	0.610907i
$704$		0			0
$705$	19.0201	+	10.5494i	0.716339	+	0.397314i
$706$		0			0
$707$	42.6384	−	17.1228i	1.60358	−	0.643968i
$708$		0			0
$709$	25.2557			0.948499			0.474250	−	0.880390i	$-0.342719\pi$
$709$	25.2557			0.948499			0.474250	+	0.880390i	$0.342719\pi$
$710$		0			0
$711$	22.2161	+	11.8271i	0.833168	+	0.443552i
$712$		0			0
$713$	−4.56731	+	2.63694i	−0.171047	+	0.0987541i
$714$		0			0
$715$	2.03979	+	1.17767i	0.0762839	+	0.0440425i
$716$		0			0
$717$	−0.538166	−	31.2921i	−0.0200982	−	1.16862i
$718$		0			0
$719$	−19.0045	+	32.9168i	−0.708749	+	1.22759i	0.256572	+	0.966525i	$0.417407\pi$
$719$	−19.0045	+	32.9168i	−0.708749	+	1.22759i	−0.965321	+	0.261065i	$0.915926\pi$
$720$		0			0
$721$	−24.1987	−	3.45285i	−0.901206	−	0.128591i
$722$		0			0
$723$	−0.618019	−	35.9353i	−0.0229844	−	1.33645i
$724$		0			0
$725$	4.50633			0.167361
$726$		0			0
$727$	−8.14853	−	14.1137i	−0.302212	−	0.523447i	0.674424	−	0.738344i	$-0.264392\pi$
$727$	−8.14853	−	14.1137i	−0.302212	−	0.523447i	−0.976637	+	0.214897i	$0.931059\pi$
$728$		0			0
$729$	26.8564	−	2.78088i	0.994682	−	0.102996i
$730$		0			0
$731$	−10.2229	+	17.7066i	−0.378109	+	0.654904i
$732$		0			0
$733$	−11.0088	+	6.35596i	−0.406621	+	0.234763i	−0.689337	−	0.724441i	$-0.742098\pi$
$733$	−11.0088	+	6.35596i	−0.406621	+	0.234763i	0.282716	+	0.959204i	$0.408765\pi$
$734$		0			0
$735$	−7.49190	+	27.4689i	−0.276343	+	1.01321i
$736$		0			0
$737$	−0.539034	+	0.933634i	−0.0198556	+	0.0343909i
$738$		0			0
$739$	−21.2467	+	12.2668i	−0.781574	+	0.451242i	−0.836988	−	0.547222i	$-0.815685\pi$
$739$	−21.2467	+	12.2668i	−0.781574	+	0.451242i	0.0554141	+	0.998463i	$0.482352\pi$
$740$		0			0
$741$	−22.6967	−	12.5886i	−0.833783	−	0.462454i
$742$		0			0
$743$	−25.5305	−	14.7400i	−0.936624	−	0.540760i	−0.0477233	−	0.998861i	$-0.515197\pi$
$743$	−25.5305	−	14.7400i	−0.936624	−	0.540760i	−0.888900	+	0.458101i	$0.848530\pi$
$744$		0			0
$745$	12.3759	+	7.14525i	0.453419	+	0.261782i
$746$		0			0
$747$	−47.2485	+	1.62565i	−1.72873	+	0.0594796i
$748$		0			0
$749$	−22.0080	+	8.83797i	−0.804154	+	0.322932i
$750$		0			0
$751$	34.4188	−	19.8717i	1.25596	−	0.725129i	0.283673	−	0.958921i	$-0.408447\pi$
$751$	34.4188	−	19.8717i	1.25596	−	0.725129i	0.972287	+	0.233792i	$0.0751135\pi$
$752$		0			0
$753$	−8.49815	−	14.1515i	−0.309690	−	0.515710i
$754$		0			0
$755$	−6.13526			−0.223285
$756$		0			0
$757$	−3.23130			−0.117444			−0.0587218	−	0.998274i	$-0.518702\pi$
$757$	−3.23130			−0.117444			−0.0587218	+	0.998274i	$0.518702\pi$
$758$		0			0
$759$	−0.448859	−	0.747462i	−0.0162926	−	0.0271311i
$760$		0			0
$761$	31.9261	−	18.4325i	1.15732	−	0.668178i	0.206659	−	0.978413i	$-0.433741\pi$
$761$	31.9261	−	18.4325i	1.15732	−	0.668178i	0.950660	+	0.310235i	$0.100408\pi$
$762$		0			0
$763$	−33.8511	−	4.83013i	−1.22549	−	0.174862i
$764$		0			0
$765$	17.3132	+	27.7387i	0.625962	+	1.00289i
$766$		0			0
$767$	−2.70448	−	1.56143i	−0.0976530	−	0.0563800i
$768$		0			0
$769$	21.3838	+	12.3460i	0.771120	+	0.445206i	0.833274	−	0.552860i	$-0.186464\pi$
$769$	21.3838	+	12.3460i	0.771120	+	0.445206i	−0.0621539	+	0.998067i	$0.519797\pi$
$770$		0			0
$771$	17.2595	+	9.57292i	0.621587	+	0.344760i
$772$		0			0
$773$	−18.1598	+	10.4846i	−0.653164	+	0.377104i	−0.789667	−	0.613535i	$-0.789747\pi$
$773$	−18.1598	+	10.4846i	−0.653164	+	0.377104i	0.136503	+	0.990640i	$0.456414\pi$
$774$		0			0
$775$	−1.19442	+	2.06879i	−0.0429047	+	0.0743131i
$776$		0			0
$777$	7.81902	−	10.3254i	0.280506	−	0.370421i
$778$		0			0
$779$	−30.1287	+	17.3948i	−1.07947	+	0.623234i
$780$		0			0
$781$	1.59602	−	2.76438i	0.0571100	−	0.0989175i
$782$		0			0
$783$	24.7454	+	38.1689i	0.884327	+	1.36404i
$784$		0			0
$785$	−22.0654	−	38.2184i	−0.787548	−	1.36407i
$786$		0			0
$787$	14.8884			0.530713			0.265356	−	0.964150i	$-0.414510\pi$
$787$	14.8884			0.530713			0.265356	+	0.964150i	$0.414510\pi$
$788$		0			0
$789$	0.185781	+	10.8024i	0.00661397	+	0.384575i
$790$		0			0
$791$	4.19033	+	10.4346i	0.148991	+	0.371012i
$792$		0			0
$793$	11.6170	−	20.1212i	0.412532	−	0.714526i
$794$		0			0
$795$	0.216022	+	12.5608i	0.00766151	+	0.445485i
$796$		0			0
$797$	−17.5335	−	10.1230i	−0.621068	−	0.358574i	0.156216	−	0.987723i	$-0.450070\pi$
$797$	−17.5335	−	10.1230i	−0.621068	−	0.358574i	−0.777285	+	0.629149i	$0.783404\pi$
$798$		0			0
$799$	−21.4933	+	12.4092i	−0.760380	+	0.439005i
$800$		0			0
$801$	−15.6495	+	9.76772i	−0.552948	+	0.345125i
$802$		0			0
$803$	1.62556			0.0573647
$804$		0			0
$805$	−2.63128	−	6.55231i	−0.0927405	−	0.230939i
$806$		0			0
$807$	−39.4507	−	21.8811i	−1.38873	−	0.770252i
$808$		0			0
$809$	−17.2300	−	29.8433i	−0.605775	−	1.04923i	−0.991928	−	0.126799i	$-0.959530\pi$
$809$	−17.2300	−	29.8433i	−0.605775	−	1.04923i	0.386153	−	0.922435i	$-0.373804\pi$
$810$		0			0
$811$	49.5905			1.74136			0.870679	−	0.491852i	$-0.163680\pi$
$811$	49.5905			1.74136			0.870679	+	0.491852i	$0.163680\pi$
$812$		0			0
$813$	−35.7374	+	0.614616i	−1.25336	+	0.0215555i
$814$		0			0
$815$	7.87639			0.275898
$816$		0			0
$817$			29.1517i			1.01989i
$818$		0			0
$819$	−1.92545	+	17.8693i	−0.0672808	+	0.624405i
$820$		0			0
$821$	39.1601			1.36670			0.683349	−	0.730092i	$-0.260523\pi$
$821$	39.1601			1.36670			0.683349	+	0.730092i	$0.260523\pi$
$822$		0			0
$823$			38.8786i			1.35522i	0.735420	+	0.677612i	$0.236985\pi$
$823$			38.8786i			1.35522i	−0.735420	+	0.677612i	$0.763015\pi$
$824$		0			0
$825$	−0.345358	−	0.191551i	−0.0120238	−	0.00666895i
$826$		0			0
$827$			41.0227i			1.42650i	0.700909	+	0.713250i	$0.252778\pi$
$827$			41.0227i			1.42650i	−0.700909	+	0.713250i	$0.747222\pi$
$828$		0			0
$829$	−11.4951	+	6.63672i	−0.399242	+	0.230503i	−0.686157	−	0.727453i	$-0.740704\pi$
$829$	−11.4951	+	6.63672i	−0.399242	+	0.230503i	0.286915	+	0.957956i	$0.407370\pi$
$830$		0			0
$831$	−20.9066	+	0.359555i	−0.725243	+	0.0124728i
$832$		0			0
$833$	−22.4704	−	23.4656i	−0.778552	−	0.813034i
$834$		0			0
$835$		−	21.5271i		−	0.744975i
$836$		0			0
$837$	−24.0816	+	1.24346i	−0.832381	+	0.0429801i
$838$		0			0
$839$	−15.9028	−	27.5445i	−0.549025	−	0.950940i	−0.998342	−	0.0575672i	$-0.981666\pi$
$839$	−15.9028	−	27.5445i	−0.549025	−	0.950940i	0.449316	−	0.893373i	$-0.351668\pi$
$840$		0			0
$841$	−23.8184	+	41.2547i	−0.821325	+	1.42258i
$842$		0			0
$843$	−6.17138	+	11.1267i	−0.212554	+	0.383225i
$844$		0			0
$845$	−16.0110	−	9.24393i	−0.550793	−	0.318001i
$846$		0			0
$847$	−28.2976	−	4.03770i	−0.972316	−	0.138737i
$848$		0			0
$849$	−15.4319	−	25.6979i	−0.529620	−	0.881949i
$850$		0			0
$851$			3.21197i			0.110105i
$852$		0			0
$853$	0.551551	−	0.318438i	0.0188847	−	0.0109031i	−0.490528	−	0.871425i	$-0.663196\pi$
$853$	0.551551	−	0.318438i	0.0188847	−	0.0109031i	0.509413	+	0.860522i	$0.329863\pi$
$854$		0			0
$855$	41.1529	+	21.9085i	1.40740	+	0.749255i
$856$		0			0
$857$	−3.94028	−	2.27492i	−0.134597	−	0.0777098i	0.431189	−	0.902261i	$-0.358094\pi$
$857$	−3.94028	−	2.27492i	−0.134597	−	0.0777098i	−0.565787	+	0.824552i	$0.691427\pi$
$858$		0			0
$859$	6.78168	+	11.7462i	0.231388	+	0.400775i	0.958217	−	0.286043i	$-0.0923401\pi$
$859$	6.78168	+	11.7462i	0.231388	+	0.400775i	−0.726829	+	0.686819i	$0.759007\pi$
$860$		0			0
$861$	19.2059	+	14.5439i	0.654535	+	0.495655i
$862$		0			0
$863$	14.1996	+	8.19817i	0.483361	+	0.279069i	0.721816	−	0.692085i	$-0.243308\pi$
$863$	14.1996	+	8.19817i	0.483361	+	0.279069i	−0.238455	+	0.971154i	$0.576641\pi$
$864$		0			0
$865$	26.5973	+	46.0680i	0.904337	+	1.56636i
$866$		0			0
$867$	−7.86555	+	0.135273i	−0.267128	+	0.00459410i
$868$		0			0
$869$	1.85801	−	3.21816i	0.0630285	−	0.109169i
$870$		0			0
$871$	−2.75558	+	4.77281i	−0.0933694	+	0.161721i
$872$		0			0
$873$	−1.78066	−	51.7538i	−0.0602664	−	1.75160i
$874$		0			0
$875$	21.9237	+	17.2031i	0.741158	+	0.581572i
$876$		0			0
$877$	24.7595	+	42.8847i	0.836068	+	1.44811i	0.893158	+	0.449743i	$0.148484\pi$
$877$	24.7595	+	42.8847i	0.836068	+	1.44811i	−0.0570903	+	0.998369i	$0.518182\pi$
$878$		0			0
$879$	0.0332171	+	1.93144i	0.00112039	+	0.0651458i
$880$		0			0
$881$			16.2659i			0.548012i	0.961728	+	0.274006i	$0.0883488\pi$
$881$			16.2659i			0.548012i	−0.961728	+	0.274006i	$0.911651\pi$
$882$		0			0
$883$			26.6667i			0.897404i	0.893681	+	0.448702i	$0.148114\pi$
$883$			26.6667i			0.897404i	−0.893681	+	0.448702i	$0.851886\pi$
$884$		0			0
$885$	4.90557	+	2.72085i	0.164899	+	0.0914603i
$886$		0			0
$887$	26.9978	+	46.7616i	0.906499	+	1.57010i	0.818892	+	0.573947i	$0.194589\pi$
$887$	26.9978	+	46.7616i	0.906499	+	1.57010i	0.0876066	+	0.996155i	$0.472078\pi$
$888$		0			0
$889$	40.9337	+	32.1199i	1.37287	+	1.07727i
$890$		0			0
$891$	−0.273997	−	3.97705i	−0.00917924	−	0.133236i
$892$		0			0
$893$	−17.6930	+	30.6452i	−0.592073	+	1.02550i
$894$		0			0
$895$	−26.1337	+	45.2649i	−0.873554	+	1.51304i
$896$		0			0
$897$	−2.29460	−	3.82108i	−0.0766146	−	0.127582i
$898$		0			0
$899$	−20.3128	−	35.1828i	−0.677470	−	1.17341i
$900$		0			0
$901$	−12.4145	−	7.16752i	−0.413587	−	0.238785i
$902$		0			0
$903$	18.6009	−	7.84383i	0.618999	−	0.261026i
$904$		0			0
$905$	−5.08793	−	8.81255i	−0.169129	−	0.292939i
$906$		0			0
$907$	−39.4433	−	22.7726i	−1.30969	−	0.756151i	−0.327648	−	0.944800i	$-0.606256\pi$
$907$	−39.4433	−	22.7726i	−1.30969	−	0.756151i	−0.982045	+	0.188649i	$0.939589\pi$
$908$		0			0
$909$	−44.1977	+	27.5862i	−1.46594	+	0.914977i
$910$		0			0
$911$	−10.7265	+	6.19296i	−0.355385	+	0.205182i	−0.667055	−	0.745009i	$-0.732445\pi$
$911$	−10.7265	+	6.19296i	−0.355385	+	0.205182i	0.311669	+	0.950191i	$0.399112\pi$
$912$		0			0
$913$			6.98025i			0.231013i
$914$		0			0
$915$	−20.2430	+	36.4973i	−0.669214	+	1.20656i
$916$		0			0
$917$	44.7198	+	6.38094i	1.47678	+	0.210717i
$918$		0			0
$919$	38.9097	+	22.4645i	1.28351	+	0.741037i	0.977489	−	0.210987i	$-0.0676678\pi$
$919$	38.9097	+	22.4645i	1.28351	+	0.741037i	0.306024	+	0.952024i	$0.401001\pi$
$920$		0			0
$921$	27.2380	+	45.3580i	0.897523	+	1.49460i
$922$		0			0
$923$	8.15897	−	14.1318i	0.268556	−	0.465152i
$924$		0			0
$925$	0.727439	+	1.25996i	0.0239181	+	0.0414273i
$926$		0			0
$927$	27.7003	−	0.953067i	0.909796	−	0.0313028i
$928$		0			0
$929$			25.5365i			0.837825i	0.908027	+	0.418912i	$0.137589\pi$
$929$			25.5365i			0.837825i	−0.908027	+	0.418912i	$0.862411\pi$
$930$		0			0
$931$	−44.4745	−	12.9557i	−1.45759	−	0.424605i
$932$		0			0
$933$	−6.14909	−	10.2398i	−0.201312	−	0.335235i
$934$		0			0
$935$	4.18102	−	2.41392i	0.136734	−	0.0789435i
$936$		0			0
$937$		−	29.7933i		−	0.973304i	−0.873596	−	0.486652i	$-0.838218\pi$
$937$		−	29.7933i		−	0.973304i	0.873596	−	0.486652i	$-0.161782\pi$
$938$		0			0
$939$	20.8141	−	12.4991i	0.679243	−	0.407893i
$940$		0			0
$941$		−	38.0234i		−	1.23953i	−0.784789	−	0.619763i	$-0.787229\pi$
$941$		−	38.0234i		−	1.23953i	0.784789	−	0.619763i	$-0.212771\pi$
$942$		0			0
$943$	−5.97447			−0.194555
$944$		0			0
$945$	2.90623	−	32.1534i	0.0945396	−	1.04595i
$946$		0			0
$947$		−	27.6471i		−	0.898409i	−0.893429	−	0.449205i	$-0.851707\pi$
$947$		−	27.6471i		−	0.898409i	0.893429	−	0.449205i	$-0.148293\pi$
$948$		0			0
$949$	8.30998			0.269754
$950$		0			0
$951$	17.9920	+	29.9612i	0.583431	+	0.971557i
$952$		0			0
$953$	38.4588			1.24580			0.622901	−	0.782301i	$-0.285954\pi$
$953$	38.4588			1.24580			0.622901	+	0.782301i	$0.285954\pi$
$954$		0			0
$955$	29.2381	+	50.6419i	0.946123	+	1.63873i
$956$		0			0
$957$	5.75784	−	3.45764i	0.186124	−	0.111770i
$958$		0			0
$959$	−3.46425	−	8.62655i	−0.111867	−	0.278566i
$960$		0			0
$961$	−9.46412			−0.305294
$962$		0			0
$963$	22.8128	−	14.2387i	0.735131	−	0.458836i
$964$		0			0
$965$	43.3701	−	25.0397i	1.39613	−	0.806058i
$966$		0			0
$967$	1.40644	+	0.812009i	0.0452281	+	0.0261125i	0.522444	−	0.852674i	$-0.325021\pi$
$967$	1.40644	+	0.812009i	0.0452281	+	0.0261125i	−0.477215	+	0.878786i	$0.658354\pi$
$968$		0			0
$969$	−45.6073	+	27.3877i	−1.46512	+	0.879819i
$970$		0			0
$971$	19.2966	−	33.4227i	0.619257	−	1.07258i	−0.370365	−	0.928886i	$-0.620767\pi$
$971$	19.2966	−	33.4227i	0.619257	−	1.07258i	0.989622	−	0.143698i	$-0.0458994\pi$
$972$		0			0
$973$	17.0784	+	42.5279i	0.547508	+	1.36338i
$974$		0			0
$975$	−1.76550	−	0.979224i	−0.0565412	−	0.0313603i
$976$		0			0
$977$	12.4008			0.396735			0.198368	−	0.980128i	$-0.436436\pi$
$977$	12.4008			0.396735			0.198368	+	0.980128i	$0.436436\pi$
$978$		0			0
$979$	1.36187	+	2.35883i	0.0435257	+	0.0753886i
$980$		0			0
$981$	38.7494	−	1.33323i	1.23717	−	0.0425668i
$982$		0			0
$983$	8.49837	−	14.7196i	0.271056	−	0.469483i	−0.698077	−	0.716023i	$-0.745960\pi$
$983$	8.49837	−	14.7196i	0.271056	−	0.469483i	0.969133	+	0.246540i	$0.0792938\pi$
$984$		0			0
$985$	37.6881	−	21.7593i	1.20084	−	0.693308i
$986$		0			0
$987$	24.3145	+	3.04373i	0.773938	+	0.0968831i
$988$		0			0
$989$	−2.50313	+	4.33554i	−0.0795947	+	0.137862i
$990$		0			0
$991$	−39.0008	+	22.5171i	−1.23890	+	0.715280i	−0.968870	−	0.247571i	$-0.920368\pi$
$991$	−39.0008	+	22.5171i	−1.23890	+	0.715280i	−0.270032	+	0.962851i	$0.587034\pi$
$992$		0			0
$993$	47.9578	−	28.7992i	1.52189	−	0.913914i
$994$		0			0
$995$	−3.73687	−	2.15748i	−0.118467	−	0.0683967i
$996$		0			0
$997$	−6.92908	−	4.00051i	−0.219446	−	0.126697i	0.386248	−	0.922395i	$-0.373771\pi$
$997$	−6.92908	−	4.00051i	−0.219446	−	0.126697i	−0.605694	+	0.795698i	$0.707104\pi$
$998$		0			0
$999$	−6.67740	+	13.0802i	−0.211264	+	0.413839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.i.607.6	yes	32
3.2	odd	2		3024.2.cz.i.1279.4		32
4.3	odd	2	inner	1008.2.cz.i.607.11	yes	32
7.3	odd	6		1008.2.bf.i.31.11	yes	32
9.2	odd	6		3024.2.bf.i.2287.4		32
9.7	even	3		1008.2.bf.i.943.6	yes	32
12.11	even	2		3024.2.cz.i.1279.3		32
21.17	even	6		3024.2.bf.i.1711.14		32
28.3	even	6		1008.2.bf.i.31.6	✓	32
36.7	odd	6		1008.2.bf.i.943.11	yes	32
36.11	even	6		3024.2.bf.i.2287.3		32
63.38	even	6		3024.2.cz.i.2719.3		32
63.52	odd	6	inner	1008.2.cz.i.367.11	yes	32
84.59	odd	6		3024.2.bf.i.1711.13		32
252.115	even	6	inner	1008.2.cz.i.367.6	yes	32
252.227	odd	6		3024.2.cz.i.2719.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.6	✓	32	28.3	even	6
1008.2.bf.i.31.11	yes	32	7.3	odd	6
1008.2.bf.i.943.6	yes	32	9.7	even	3
1008.2.bf.i.943.11	yes	32	36.7	odd	6
1008.2.cz.i.367.6	yes	32	252.115	even	6	inner
1008.2.cz.i.367.11	yes	32	63.52	odd	6	inner
1008.2.cz.i.607.6	yes	32	1.1	even	1	trivial
1008.2.cz.i.607.11	yes	32	4.3	odd	2	inner
3024.2.bf.i.1711.13		32	84.59	odd	6
3024.2.bf.i.1711.14		32	21.17	even	6
3024.2.bf.i.2287.3		32	36.11	even	6
3024.2.bf.i.2287.4		32	9.2	odd	6
3024.2.cz.i.1279.3		32	12.11	even	2
3024.2.cz.i.1279.4		32	3.2	odd	2
3024.2.cz.i.2719.3		32	63.38	even	6
3024.2.cz.i.2719.4		32	252.227	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891691 - 1.48489i) q^{3} +(2.03373 - 1.17418i) q^{5} +(1.63327 - 2.08145i) q^{7} +(-1.40978 + 2.64812i) q^{9} +(0.383599 + 0.221471i) q^{11} +(1.96099 + 1.13218i) q^{13} +(-3.55698 - 1.97286i) q^{15} +(4.01950 - 2.32066i) q^{17} +(3.30879 - 5.73100i) q^{19} +(-4.54709 - 0.569213i) q^{21} +(0.984190 - 0.568223i) q^{23} +(0.257380 - 0.445795i) q^{25} +(5.18924 - 0.267947i) q^{27} +(4.37712 + 7.58140i) q^{29} -4.64068 q^{31} +(-0.0131924 - 0.767085i) q^{33} +(0.877649 - 6.15086i) q^{35} +(-1.41316 + 2.44767i) q^{37} +(-0.0674408 - 3.92140i) q^{39} +(-4.55283 - 2.62858i) q^{41} +(-3.81500 + 2.20259i) q^{43} +(0.242252 + 7.04089i) q^{45} -5.34726 q^{47} +(-1.66485 - 6.79914i) q^{49} +(-7.03007 - 3.89919i) q^{51} +(-1.54428 - 2.67478i) q^{53} +1.04018 q^{55} +(-11.4603 + 0.197096i) q^{57} -1.37914 q^{59} -10.2608i q^{61} +(3.20938 + 7.25947i) q^{63} +5.31751 q^{65} +2.43388i q^{67} +(-1.72134 - 0.954732i) q^{69} -7.20644i q^{71} +(3.17824 - 1.83496i) q^{73} +(-0.891458 + 0.0153314i) q^{75} +(1.08750 - 0.436720i) q^{77} -8.38938i q^{79} +(-5.02507 - 7.46650i) q^{81} +(7.87941 + 13.6475i) q^{83} +(5.44973 - 9.43920i) q^{85} +(7.35448 - 13.2598i) q^{87} +(5.32537 + 3.07461i) q^{89} +(5.55940 - 2.23255i) q^{91} +(4.13805 + 6.89088i) q^{93} -15.5404i q^{95} +(-14.9489 + 8.63074i) q^{97} +(-1.12727 + 0.703592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85}+ \cdots + 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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