LMFDB - Embedded newform 1008.2.cz.h.607.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.4
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.h.367.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29235 - 1.15318i) q^{3} +(-2.47996 + 1.43180i) q^{5} +(-1.38867 + 2.25202i) q^{7} +(0.340334 + 2.98063i) q^{9} +O(q^{10})$	\(q+(-1.29235 - 1.15318i) q^{3} +(-2.47996 + 1.43180i) q^{5} +(-1.38867 + 2.25202i) q^{7} +(0.340334 + 2.98063i) q^{9} +(3.57856 + 2.06608i) q^{11} +(-3.14042 - 1.81312i) q^{13} +(4.85611 + 1.00946i) q^{15} +(-3.36233 + 1.94124i) q^{17} +(3.57038 - 6.18407i) q^{19} +(4.39164 - 1.30900i) q^{21} +(5.18202 - 2.99184i) q^{23} +(1.60013 - 2.77151i) q^{25} +(2.99739 - 4.24449i) q^{27} +(-2.87794 - 4.98473i) q^{29} -10.4745 q^{31} +(-2.24218 - 6.79685i) q^{33} +(0.219406 - 7.57322i) q^{35} +(-2.02541 + 3.50812i) q^{37} +(1.96766 + 5.96467i) q^{39} +(2.64042 + 1.52444i) q^{41} +(-0.533900 + 0.308247i) q^{43} +(-5.11170 - 6.90455i) q^{45} +1.07320 q^{47} +(-3.14317 - 6.25464i) q^{49} +(6.58392 + 1.36862i) q^{51} +(-2.65366 - 4.59628i) q^{53} -11.8329 q^{55} +(-11.7455 + 3.87468i) q^{57} +9.29532 q^{59} -11.9419i q^{61} +(-7.18505 - 3.37269i) q^{63} +10.3842 q^{65} -1.58249i q^{67} +(-10.1471 - 2.10932i) q^{69} -5.90262i q^{71} +(-6.78880 + 3.91952i) q^{73} +(-5.26398 + 1.73651i) q^{75} +(-9.62232 + 5.18987i) q^{77} -4.05971i q^{79} +(-8.76835 + 2.02882i) q^{81} +(-1.69905 - 2.94285i) q^{83} +(5.55897 - 9.62841i) q^{85} +(-2.02901 + 9.76081i) q^{87} +(9.80008 + 5.65808i) q^{89} +(8.44421 - 4.55445i) q^{91} +(13.5367 + 12.0790i) q^{93} +20.4483i q^{95} +(2.52862 - 1.45990i) q^{97} +(-4.94033 + 11.3695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9	$ 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9} + 9 q^{11} - 3 q^{13} + 6 q^{15} - 3 q^{17} + 4 q^{19} + 13 q^{21} + 6 q^{23} + 15 q^{25} - 9 q^{27} + 18 q^{29} - 34 q^{31} - 21 q^{33} + 42 q^{35} - 3 q^{37} - 27 q^{39} + 36 q^{41} - 24 q^{43} + 21 q^{45} + 42 q^{47} + 30 q^{49} + 6 q^{51} - 12 q^{53} + 30 q^{55} - 13 q^{57} + 12 q^{59} + 3 q^{63} + 6 q^{69} + 48 q^{73} - 36 q^{75} - 48 q^{77} - 31 q^{81} + 48 q^{83} - 21 q^{85} - 15 q^{87} + 39 q^{89} - 9 q^{91} + 10 q^{93} + 3 q^{97} - 30 q^{99}+O(q^{100}) $ 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9 + 9 * q^11 - 3 * q^13 + 6 * q^15 - 3 * q^17 + 4 * q^19 + 13 * q^21 + 6 * q^23 + 15 * q^25 - 9 * q^27 + 18 * q^29 - 34 * q^31 - 21 * q^33 + 42 * q^35 - 3 * q^37 - 27 * q^39 + 36 * q^41 - 24 * q^43 + 21 * q^45 + 42 * q^47 + 30 * q^49 + 6 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 + 12 * q^59 + 3 * q^63 + 6 * q^69 + 48 * q^73 - 36 * q^75 - 48 * q^77 - 31 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 + 10 * q^93 + 3 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.29235	−	1.15318i	−0.746138	−	0.665791i
$3$	−1.29235	−	1.15318i	−0.746138	−	0.665791i
$4$		0			0
$5$	−2.47996	+	1.43180i	−1.10907	+	0.640323i	−0.938589	−	0.345038i	$-0.887866\pi$
$5$	−2.47996	+	1.43180i	−1.10907	+	0.640323i	−0.170483	+	0.985361i	$0.554533\pi$
$6$		0			0
$7$	−1.38867	+	2.25202i	−0.524870	+	0.851183i
$7$	−1.38867	+	2.25202i	−0.524870	+	0.851183i
$8$		0			0
$9$	0.340334	+	2.98063i	0.113445	+	0.993544i
$10$		0			0
$11$	3.57856	+	2.06608i	1.07898	+	0.622948i	0.930620	−	0.365986i	$-0.119268\pi$
$11$	3.57856	+	2.06608i	1.07898	+	0.622948i	0.148357	+	0.988934i	$0.452601\pi$
$12$		0			0
$13$	−3.14042	−	1.81312i	−0.870996	−	0.502870i	−0.00331710	−	0.999994i	$-0.501056\pi$
$13$	−3.14042	−	1.81312i	−0.870996	−	0.502870i	−0.867679	+	0.497125i	$0.834389\pi$
$14$		0			0
$15$	4.85611	+	1.00946i	1.25384	+	0.260640i
$16$		0			0
$17$	−3.36233	+	1.94124i	−0.815486	+	0.470821i	−0.848857	−	0.528622i	$-0.822709\pi$
$17$	−3.36233	+	1.94124i	−0.815486	+	0.470821i	0.0333714	+	0.999443i	$0.489376\pi$
$18$		0			0
$19$	3.57038	−	6.18407i	0.819101	−	1.41872i	−0.0872450	−	0.996187i	$-0.527806\pi$
$19$	3.57038	−	6.18407i	0.819101	−	1.41872i	0.906346	−	0.422537i	$-0.138860\pi$
$20$		0			0
$21$	4.39164	−	1.30900i	0.958335	−	0.285646i
$22$		0			0
$23$	5.18202	−	2.99184i	1.08052	−	0.623841i	0.149487	−	0.988764i	$-0.452238\pi$
$23$	5.18202	−	2.99184i	1.08052	−	0.623841i	0.931038	+	0.364922i	$0.118904\pi$
$24$		0			0
$25$	1.60013	−	2.77151i	0.320026	−	0.554301i
$26$		0			0
$27$	2.99739	−	4.24449i	0.576847	−	0.816852i
$28$		0			0
$29$	−2.87794	−	4.98473i	−0.534420	−	0.925642i	−0.999191	−	0.0402113i	$-0.987197\pi$
$29$	−2.87794	−	4.98473i	−0.534420	−	0.925642i	0.464772	−	0.885431i	$-0.346136\pi$
$30$		0			0
$31$	−10.4745			−1.88127			−0.940637	−	0.339413i	$-0.889772\pi$
$31$	−10.4745			−1.88127			−0.940637	+	0.339413i	$0.889772\pi$
$32$		0			0
$33$	−2.24218	−	6.79685i	−0.390313	−	1.18318i
$34$		0			0
$35$	0.219406	−	7.57322i	0.0370864	−	1.28011i
$36$		0			0
$37$	−2.02541	+	3.50812i	−0.332976	+	0.576731i	−0.983094	−	0.183102i	$-0.941386\pi$
$37$	−2.02541	+	3.50812i	−0.332976	+	0.576731i	0.650118	+	0.759833i	$0.274719\pi$
$38$		0			0
$39$	1.96766	+	5.96467i	0.315077	+	0.955112i
$40$		0			0
$41$	2.64042	+	1.52444i	0.412364	+	0.238078i	0.691805	−	0.722085i	$-0.256816\pi$
$41$	2.64042	+	1.52444i	0.412364	+	0.238078i	−0.279441	+	0.960163i	$0.590149\pi$
$42$		0			0
$43$	−0.533900	+	0.308247i	−0.0814190	+	0.0470073i	−0.540157	−	0.841564i	$-0.681635\pi$
$43$	−0.533900	+	0.308247i	−0.0814190	+	0.0470073i	0.458738	+	0.888572i	$0.348302\pi$
$44$		0			0
$45$	−5.11170	−	6.90455i	−0.762007	−	1.02927i
$46$		0			0
$47$	1.07320			0.156543			0.0782714	−	0.996932i	$-0.475060\pi$
$47$	1.07320			0.156543			0.0782714	+	0.996932i	$0.475060\pi$
$48$		0			0
$49$	−3.14317	−	6.25464i	−0.449024	−	0.893520i
$50$		0			0
$51$	6.58392	+	1.36862i	0.921934	+	0.191646i
$52$		0			0
$53$	−2.65366	−	4.59628i	−0.364509	−	0.631347i	0.624189	−	0.781274i	$-0.285430\pi$
$53$	−2.65366	−	4.59628i	−0.364509	−	0.631347i	−0.988697	+	0.149926i	$0.952096\pi$
$54$		0			0
$55$	−11.8329			−1.59555
$56$		0			0
$57$	−11.7455	+	3.87468i	−1.55574	+	0.513214i
$58$		0			0
$59$	9.29532			1.21015			0.605074	−	0.796169i	$-0.293144\pi$
$59$	9.29532			1.21015			0.605074	+	0.796169i	$0.293144\pi$
$60$		0			0
$61$		−	11.9419i		−	1.52900i	−0.644625	−	0.764499i	$-0.722986\pi$
$61$		−	11.9419i		−	1.52900i	0.644625	−	0.764499i	$-0.277014\pi$
$62$		0			0
$63$	−7.18505	−	3.37269i	−0.905231	−	0.424919i
$64$		0			0
$65$	10.3842			1.28800
$66$		0			0
$67$		−	1.58249i		−	0.193331i	−0.995317	−	0.0966657i	$-0.969182\pi$
$67$		−	1.58249i		−	0.193331i	0.995317	−	0.0966657i	$-0.0308178\pi$
$68$		0			0
$69$	−10.1471	−	2.10932i	−1.22157	−	0.253932i
$70$		0			0
$71$		−	5.90262i		−	0.700512i	−0.936654	−	0.350256i	$-0.886095\pi$
$71$		−	5.90262i		−	0.700512i	0.936654	−	0.350256i	$-0.113905\pi$
$72$		0			0
$73$	−6.78880	+	3.91952i	−0.794569	+	0.458745i	−0.841569	−	0.540150i	$-0.818367\pi$
$73$	−6.78880	+	3.91952i	−0.794569	+	0.458745i	0.0469993	+	0.998895i	$0.485034\pi$
$74$		0			0
$75$	−5.26398	+	1.73651i	−0.607832	+	0.200515i
$76$		0			0
$77$	−9.62232	+	5.18987i	−1.09657	+	0.591440i
$78$		0			0
$79$		−	4.05971i		−	0.456753i	−0.973573	−	0.228377i	$-0.926658\pi$
$79$		−	4.05971i		−	0.456753i	0.973573	−	0.228377i	$-0.0733418\pi$
$80$		0			0
$81$	−8.76835	+	2.02882i	−0.974261	+	0.225425i
$82$		0			0
$83$	−1.69905	−	2.94285i	−0.186495	−	0.323019i	0.757584	−	0.652738i	$-0.226380\pi$
$83$	−1.69905	−	2.94285i	−0.186495	−	0.323019i	−0.944079	+	0.329718i	$0.893046\pi$
$84$		0			0
$85$	5.55897	−	9.62841i	0.602955	−	1.04435i
$86$		0			0
$87$	−2.02901	+	9.76081i	−0.217533	+	1.04647i
$88$		0			0
$89$	9.80008	+	5.65808i	1.03881	+	0.599755i	0.919495	−	0.393102i	$-0.128598\pi$
$89$	9.80008	+	5.65808i	1.03881	+	0.599755i	0.119311	+	0.992857i	$0.461931\pi$
$90$		0			0
$91$	8.44421	−	4.55445i	0.885194	−	0.477436i
$92$		0			0
$93$	13.5367	+	12.0790i	1.40369	+	1.25254i
$94$		0			0
$95$			20.4483i			2.09795i
$96$		0			0
$97$	2.52862	−	1.45990i	0.256742	−	0.148230i	−0.366105	−	0.930573i	$-0.619309\pi$
$97$	2.52862	−	1.45990i	0.256742	−	0.148230i	0.622848	+	0.782343i	$0.285976\pi$
$98$		0			0
$99$	−4.94033	+	11.3695i	−0.496522	+	1.14268i
$100$		0			0
$101$	15.2827	+	8.82348i	1.52069	+	0.877969i	0.999702	+	0.0244038i	$0.00776875\pi$
$101$	15.2827	+	8.82348i	1.52069	+	0.877969i	0.520985	+	0.853566i	$0.325565\pi$
$102$		0			0
$103$	−4.58267	−	7.93742i	−0.451544	−	0.782097i	0.546938	−	0.837173i	$-0.315793\pi$
$103$	−4.58267	−	7.93742i	−0.451544	−	0.782097i	−0.998482	+	0.0550757i	$0.982460\pi$
$104$		0			0
$105$	−9.01687	+	9.53423i	−0.879956	+	0.930446i
$106$		0			0
$107$	−6.05068	−	3.49336i	−0.584941	−	0.337716i	0.178153	−	0.984003i	$-0.442988\pi$
$107$	−6.05068	−	3.49336i	−0.584941	−	0.337716i	−0.763095	+	0.646287i	$0.776321\pi$
$108$		0			0
$109$	−5.18274	−	8.97677i	−0.496416	−	0.859818i	0.503575	−	0.863951i	$-0.332018\pi$
$109$	−5.18274	−	8.97677i	−0.496416	−	0.859818i	−0.999991	+	0.00413307i	$0.998684\pi$
$110$		0			0
$111$	6.66304	−	2.19804i	0.632428	−	0.208629i
$112$		0			0
$113$	8.03699	−	13.9205i	0.756056	−	1.30953i	−0.188791	−	0.982017i	$-0.560457\pi$
$113$	8.03699	−	13.9205i	0.756056	−	1.30953i	0.944848	−	0.327510i	$-0.106210\pi$
$114$		0			0
$115$	−8.56746	+	14.8393i	−0.798919	+	1.38377i
$116$		0			0
$117$	4.33546	−	9.97751i	0.400814	−	0.922421i
$118$		0			0
$119$	0.297472	−	10.2678i	0.0272692	−	0.941247i
$120$		0			0
$121$	3.03741	+	5.26096i	0.276129	+	0.478269i
$122$		0			0
$123$	−1.65438	−	5.01500i	−0.149170	−	0.452187i
$124$		0			0
$125$		−	5.15375i		−	0.460966i
$126$		0			0
$127$		−	1.05321i		−	0.0934571i	−0.998908	−	0.0467285i	$-0.985120\pi$
$127$		−	1.05321i		−	0.0934571i	0.998908	−	0.0467285i	$-0.0148796\pi$
$128$		0			0
$129$	1.04545	+	0.217322i	0.0920468	+	0.0191341i
$130$		0			0
$131$	−5.77810	−	10.0080i	−0.504835	−	0.874400i	−0.999984	−	0.00559217i	$-0.998220\pi$
$131$	−5.77810	−	10.0080i	−0.504835	−	0.874400i	0.495149	−	0.868808i	$-0.335113\pi$
$132$		0			0
$133$	8.96855	+	16.6282i	0.777672	+	1.44185i
$134$		0			0
$135$	−1.35612	+	14.8178i	−0.116716	+	1.27532i
$136$		0			0
$137$	−9.78415	+	16.9466i	−0.835916	+	1.44785i	0.0573662	+	0.998353i	$0.481730\pi$
$137$	−9.78415	+	16.9466i	−0.835916	+	1.44785i	−0.893282	+	0.449496i	$0.851604\pi$
$138$		0			0
$139$	9.22828	−	15.9838i	0.782732	−	1.35573i	−0.147612	−	0.989045i	$-0.547159\pi$
$139$	9.22828	−	15.9838i	0.782732	−	1.35573i	0.930345	−	0.366687i	$-0.119508\pi$
$140$		0			0
$141$	−1.38695	−	1.23760i	−0.116803	−	0.104225i
$142$		0			0
$143$	−7.49213	−	12.9768i	−0.626524	−	1.08517i
$144$		0			0
$145$	14.2743	+	8.24129i	1.18542	+	0.684402i
$146$		0			0
$147$	−3.15068	+	11.7078i	−0.259864	+	0.965645i
$148$		0			0
$149$	−4.04967	−	7.01423i	−0.331762	−	0.574628i	0.651096	−	0.758996i	$-0.274310\pi$
$149$	−4.04967	−	7.01423i	−0.331762	−	0.574628i	−0.982857	+	0.184367i	$0.940976\pi$
$150$		0			0
$151$	15.4892	+	8.94271i	1.26050	+	0.727747i	0.973170	−	0.230086i	$-0.0739008\pi$
$151$	15.4892	+	8.94271i	1.26050	+	0.727747i	0.287325	+	0.957833i	$0.407234\pi$
$152$		0			0
$153$	−6.93046	−	9.36121i	−0.560294	−	0.756809i
$154$		0			0
$155$	25.9763	−	14.9974i	2.08647	−	1.20462i
$156$		0			0
$157$		−	14.2826i		−	1.13988i	−0.821687	−	0.569939i	$-0.806967\pi$
$157$		−	14.2826i		−	1.13988i	0.821687	−	0.569939i	$-0.193033\pi$
$158$		0			0
$159$	−1.87089	+	9.00016i	−0.148372	+	0.713759i
$160$		0			0
$161$	−0.458462	+	15.8247i	−0.0361319	+	1.24716i
$162$		0			0
$163$	−11.4769	−	6.62618i	−0.898938	−	0.519002i	−0.0220828	−	0.999756i	$-0.507030\pi$
$163$	−11.4769	−	6.62618i	−0.898938	−	0.519002i	−0.876856	+	0.480754i	$0.840363\pi$
$164$		0			0
$165$	15.2923	+	13.6455i	1.19050	+	1.06230i
$166$		0			0
$167$	3.15413	−	5.46312i	0.244074	−	0.422749i	−0.717797	−	0.696253i	$-0.754849\pi$
$167$	3.15413	−	5.46312i	0.244074	−	0.422749i	0.961871	+	0.273504i	$0.0881826\pi$
$168$		0			0
$169$	0.0748327	+	0.129614i	0.00575636	+	0.00997031i
$170$		0			0
$171$	19.6476	+	8.53733i	1.50249	+	0.652866i
$172$		0			0
$173$			18.3327i			1.39381i	0.717165	+	0.696904i	$0.245440\pi$
$173$			18.3327i			1.39381i	−0.717165	+	0.696904i	$0.754560\pi$
$174$		0			0
$175$	4.01942	+	7.45224i	0.303840	+	0.563336i
$176$		0			0
$177$	−12.0128	−	10.7192i	−0.902937	−	0.805705i
$178$		0			0
$179$	3.27672	−	1.89182i	0.244914	−	0.141401i	−0.372519	−	0.928024i	$-0.621506\pi$
$179$	3.27672	−	1.89182i	0.244914	−	0.141401i	0.617433	+	0.786623i	$0.288173\pi$
$180$		0			0
$181$			18.1976i			1.35262i	0.736619	+	0.676308i	$0.236421\pi$
$181$			18.1976i			1.35262i	−0.736619	+	0.676308i	$0.763579\pi$
$182$		0			0
$183$	−13.7712	+	15.4331i	−1.01799	+	1.14084i
$184$		0			0
$185$		−	11.6000i		−	0.852847i
$186$		0			0
$187$	−16.0431			−1.17319
$188$		0			0
$189$	5.39627	+	12.6444i	0.392521	+	0.919743i
$190$		0			0
$191$			2.08552i			0.150903i	0.997149	+	0.0754514i	$0.0240398\pi$
$191$			2.08552i			0.150903i	−0.997149	+	0.0754514i	$0.975960\pi$
$192$		0			0
$193$	4.20277			0.302522			0.151261	−	0.988494i	$-0.451667\pi$
$193$	4.20277			0.302522			0.151261	+	0.988494i	$0.451667\pi$
$194$		0			0
$195$	−13.4200	−	11.9748i	−0.961023	−	0.857536i
$196$		0			0
$197$	−12.5667			−0.895343			−0.447671	−	0.894198i	$-0.647747\pi$
$197$	−12.5667			−0.895343			−0.447671	+	0.894198i	$0.647747\pi$
$198$		0			0
$199$	0.547222	+	0.947816i	0.0387915	+	0.0671889i	0.884769	−	0.466029i	$-0.154316\pi$
$199$	0.547222	+	0.947816i	0.0387915	+	0.0671889i	−0.845978	+	0.533218i	$0.820983\pi$
$200$		0			0
$201$	−1.82490	+	2.04512i	−0.128718	+	0.144252i
$202$		0			0
$203$	15.2222	+	0.441008i	1.06839	+	0.0309527i
$204$		0			0
$205$	−8.73083			−0.609788
$206$		0			0
$207$	10.6812	+	14.4275i	0.742394	+	1.00278i
$208$		0			0
$209$	25.5536	−	14.7534i	1.76758	−	1.02051i
$210$		0			0
$211$	−4.83624	−	2.79221i	−0.332941	−	0.192223i	0.324205	−	0.945987i	$-0.394903\pi$
$211$	−4.83624	−	2.79221i	−0.332941	−	0.192223i	−0.657146	+	0.753763i	$0.728236\pi$
$212$		0			0
$213$	−6.80681	+	7.62825i	−0.466395	+	0.522679i
$214$		0			0
$215$	0.882700	−	1.52888i	0.0601996	−	0.104269i
$216$		0			0
$217$	14.5457	−	23.5887i	0.987424	−	1.60131i
$218$		0			0
$219$	13.2934	+	2.76335i	0.898287	+	0.186730i
$220$		0			0
$221$	14.0789			0.947047
$222$		0			0
$223$	−1.68072	−	2.91110i	−0.112550	−	0.194942i	0.804248	−	0.594294i	$-0.202568\pi$
$223$	−1.68072	−	2.91110i	−0.112550	−	0.194942i	−0.916798	+	0.399352i	$0.869235\pi$
$224$		0			0
$225$	8.80542	+	3.82616i	0.587028	+	0.255077i
$226$		0			0
$227$	−14.3990	+	24.9398i	−0.955696	+	1.65531i	−0.222928	+	0.974835i	$0.571561\pi$
$227$	−14.3990	+	24.9398i	−0.955696	+	1.65531i	−0.732768	+	0.680479i	$0.761772\pi$
$228$		0			0
$229$	−8.75254	+	5.05328i	−0.578384	+	0.333930i	−0.760491	−	0.649348i	$-0.775042\pi$
$229$	−8.75254	+	5.05328i	−0.578384	+	0.333930i	0.182107	+	0.983279i	$0.441708\pi$
$230$		0			0
$231$	18.4203	+	4.38918i	1.21197	+	0.288787i
$232$		0			0
$233$	3.45155	−	5.97826i	0.226118	−	0.391649i	−0.730536	−	0.682874i	$-0.760730\pi$
$233$	3.45155	−	5.97826i	0.226118	−	0.391649i	0.956654	+	0.291226i	$0.0940630\pi$
$234$		0			0
$235$	−2.66150	+	1.53662i	−0.173617	+	0.100238i
$236$		0			0
$237$	−4.68159	+	5.24657i	−0.304102	+	0.340801i
$238$		0			0
$239$	8.59102	+	4.96003i	0.555707	+	0.320838i	0.751421	−	0.659824i	$-0.229369\pi$
$239$	8.59102	+	4.96003i	0.555707	+	0.320838i	−0.195714	+	0.980661i	$0.562702\pi$
$240$		0			0
$241$	−10.1446	−	5.85701i	−0.653474	−	0.377283i	0.136312	−	0.990666i	$-0.456475\pi$
$241$	−10.1446	−	5.85701i	−0.653474	−	0.377283i	−0.789786	+	0.613383i	$0.789808\pi$
$242$		0			0
$243$	13.6714	+	7.48956i	0.877019	+	0.480456i
$244$		0			0
$245$	16.7503	+	11.0108i	1.07014	+	0.703457i
$246$		0			0
$247$	−22.4250	+	12.9471i	−1.42687	+	0.823802i
$248$		0			0
$249$	−1.19787	+	5.76251i	−0.0759121	+	0.365184i
$250$		0			0
$251$	−5.72769			−0.361529			−0.180764	−	0.983526i	$-0.557857\pi$
$251$	−5.72769			−0.361529			−0.180764	+	0.983526i	$0.557857\pi$
$252$		0			0
$253$	24.7256			1.55448
$254$		0			0
$255$	−18.2875	+	6.03276i	−1.14521	+	0.377786i
$256$		0			0
$257$	−14.5255	+	8.38631i	−0.906077	+	0.523124i	−0.879167	−	0.476514i	$-0.841900\pi$
$257$	−14.5255	+	8.38631i	−0.906077	+	0.523124i	−0.0269103	+	0.999638i	$0.508567\pi$
$258$		0			0
$259$	−5.08770	−	9.43290i	−0.316134	−	0.586132i
$260$		0			0
$261$	13.8782	−	10.2746i	0.859039	−	0.635979i
$262$		0			0
$263$	11.6664	+	6.73558i	0.719379	+	0.415334i	0.814524	−	0.580130i	$-0.196998\pi$
$263$	11.6664	+	6.73558i	0.719379	+	0.415334i	−0.0951451	+	0.995463i	$0.530332\pi$
$264$		0			0
$265$	13.1619	+	7.59905i	0.808532	+	0.466806i
$266$		0			0
$267$	−6.14032	−	18.6135i	−0.375782	−	1.13913i
$268$		0			0
$269$	−5.77595	+	3.33474i	−0.352166	+	0.203323i	−0.665639	−	0.746274i	$-0.731841\pi$
$269$	−5.77595	+	3.33474i	−0.352166	+	0.203323i	0.313473	+	0.949597i	$0.398507\pi$
$270$		0			0
$271$	−10.4482	+	18.0968i	−0.634684	+	1.09930i	0.351898	+	0.936038i	$0.385536\pi$
$271$	−10.4482	+	18.0968i	−0.634684	+	1.09930i	−0.986582	+	0.163266i	$0.947797\pi$
$272$		0			0
$273$	−16.1650	−	3.85179i	−0.978349	−	0.233121i
$274$		0			0
$275$	11.4523	−	6.61201i	0.690602	−	0.398719i
$276$		0			0
$277$	−13.1915	+	22.8483i	−0.792600	+	1.37282i	0.131753	+	0.991283i	$0.457940\pi$
$277$	−13.1915	+	22.8483i	−0.792600	+	1.37282i	−0.924352	+	0.381540i	$0.875394\pi$
$278$		0			0
$279$	−3.56483	−	31.2206i	−0.213421	−	1.86913i
$280$		0			0
$281$	7.27047	+	12.5928i	0.433720	+	0.751225i	0.997190	−	0.0749113i	$-0.0238674\pi$
$281$	7.27047	+	12.5928i	0.433720	+	0.751225i	−0.563470	+	0.826136i	$0.690534\pi$
$282$		0			0
$283$	−28.6048			−1.70038			−0.850190	−	0.526476i	$-0.823513\pi$
$283$	−28.6048			−1.70038			−0.850190	+	0.526476i	$0.823513\pi$
$284$		0			0
$285$	23.5807	−	26.4264i	1.39680	−	1.56536i
$286$		0			0
$287$	−7.09976	+	3.82931i	−0.419085	+	0.226037i
$288$		0			0
$289$	−0.963138	+	1.66820i	−0.0566552	+	0.0981296i
$290$		0			0
$291$	−4.95139	−	1.02926i	−0.290256	−	0.0603364i
$292$		0			0
$293$	−2.24488	−	1.29608i	−0.131148	−	0.0757181i	0.432991	−	0.901398i	$-0.357458\pi$
$293$	−2.24488	−	1.29608i	−0.131148	−	0.0757181i	−0.564138	+	0.825680i	$0.690792\pi$
$294$		0			0
$295$	−23.0520	+	13.3091i	−1.34214	+	0.774885i
$296$		0			0
$297$	19.4958	−	8.99631i	1.13126	−	0.522019i
$298$		0			0
$299$	−21.6983			−1.25484
$300$		0			0
$301$	0.0472351	−	1.63041i	0.00272258	−	0.0939751i
$302$		0			0
$303$	−9.57552	−	29.0268i	−0.550099	−	1.66755i
$304$		0			0
$305$	17.0984	+	29.6153i	0.979052	+	1.69577i
$306$		0			0
$307$	5.70286			0.325480			0.162740	−	0.986669i	$-0.447967\pi$
$307$	5.70286			0.325480			0.162740	+	0.986669i	$0.447967\pi$
$308$		0			0
$309$	−3.23089	+	15.5426i	−0.183799	+	0.884187i
$310$		0			0
$311$	−8.43180			−0.478123			−0.239062	−	0.971004i	$-0.576840\pi$
$311$	−8.43180			−0.478123			−0.239062	+	0.971004i	$0.576840\pi$
$312$		0			0
$313$		−	7.43614i		−	0.420315i	−0.977668	−	0.210158i	$-0.932602\pi$
$313$		−	7.43614i		−	0.420315i	0.977668	−	0.210158i	$-0.0673977\pi$
$314$		0			0
$315$	22.6477	−	1.92346i	1.27605	−	0.108375i
$316$		0			0
$317$	−11.1735			−0.627565			−0.313782	−	0.949495i	$-0.601596\pi$
$317$	−11.1735			−0.627565			−0.313782	+	0.949495i	$0.601596\pi$
$318$		0			0
$319$		−	23.7843i		−	1.33166i
$320$		0			0
$321$	3.79111	+	11.4922i	0.211599	+	0.641432i
$322$		0			0
$323$			27.7239i			1.54260i
$324$		0			0
$325$	−10.0502	+	5.80247i	−0.557483	+	0.321863i
$326$		0			0
$327$	−3.65395	+	17.5778i	−0.202064	+	0.972053i
$328$		0			0
$329$	−1.49033	+	2.41687i	−0.0821646	+	0.133247i
$330$		0			0
$331$		−	4.68380i		−	0.257445i	−0.991681	−	0.128723i	$-0.958912\pi$
$331$		−	4.68380i		−	0.257445i	0.991681	−	0.128723i	$-0.0410877\pi$
$332$		0			0
$333$	−11.1457	−	4.84308i	−0.610782	−	0.265399i
$334$		0			0
$335$	2.26581	+	3.92450i	0.123794	+	0.214418i
$336$		0			0
$337$	1.27951	−	2.21618i	0.0696994	−	0.120723i	−0.829070	−	0.559145i	$-0.811129\pi$
$337$	1.27951	−	2.21618i	0.0696994	−	0.120723i	0.898769	+	0.438423i	$0.144463\pi$
$338$		0			0
$339$	−26.4395	+	8.72199i	−1.43599	+	0.473713i
$340$		0			0
$341$	−37.4837	−	21.6412i	−2.02985	−	1.17194i
$342$		0			0
$343$	18.4504	+	1.60720i	0.996227	+	0.0867804i
$344$		0			0
$345$	28.1846	−	9.29767i	1.51741	−	0.500570i
$346$		0			0
$347$		−	17.6967i		−	0.950009i	−0.879983	−	0.475005i	$-0.842446\pi$
$347$		−	17.6967i		−	0.950009i	0.879983	−	0.475005i	$-0.157554\pi$
$348$		0			0
$349$	−5.85513	+	3.38046i	−0.313418	+	0.180952i	−0.648455	−	0.761253i	$-0.724585\pi$
$349$	−5.85513	+	3.38046i	−0.313418	+	0.180952i	0.335037	+	0.942205i	$0.391251\pi$
$350$		0			0
$351$	−17.1088	+	7.89485i	−0.913202	+	0.421396i
$352$		0			0
$353$	−10.9011	−	6.29373i	−0.580205	−	0.334981i	0.181010	−	0.983481i	$-0.442063\pi$
$353$	−10.9011	−	6.29373i	−0.580205	−	0.334981i	−0.761215	+	0.648500i	$0.775397\pi$
$354$		0			0
$355$	8.45140	+	14.6383i	0.448554	+	0.776918i
$356$		0			0
$357$	−12.2251	+	12.9265i	−0.647020	+	0.684145i
$358$		0			0
$359$	−2.42351	−	1.39921i	−0.127908	−	0.0738476i	0.434681	−	0.900585i	$-0.356861\pi$
$359$	−2.42351	−	1.39921i	−0.127908	−	0.0738476i	−0.562589	+	0.826737i	$0.690195\pi$
$360$		0			0
$361$	−15.9952	−	27.7045i	−0.841852	−	1.45813i
$362$		0			0
$363$	2.14145	−	10.3017i	0.112397	−	0.540698i
$364$		0			0
$365$	11.2240	−	19.4405i	0.587489	−	1.01756i
$366$		0			0
$367$	17.4330	−	30.1948i	0.909995	−	1.57616i	0.0959272	−	0.995388i	$-0.469418\pi$
$367$	17.4330	−	30.1948i	0.909995	−	1.57616i	0.814068	−	0.580770i	$-0.197248\pi$
$368$		0			0
$369$	−3.64519	+	8.38893i	−0.189761	+	0.436710i
$370$		0			0
$371$	14.0360	+	0.406641i	0.728712	+	0.0211117i
$372$		0			0
$373$	14.3961	+	24.9349i	0.745404	+	1.29108i	0.950006	+	0.312233i	$0.101077\pi$
$373$	14.3961	+	24.9349i	0.745404	+	1.29108i	−0.204602	+	0.978845i	$0.565590\pi$
$374$		0			0
$375$	−5.94323	+	6.66045i	−0.306907	+	0.343944i
$376$		0			0
$377$			20.8722i			1.07497i
$378$		0			0
$379$		−	19.6591i		−	1.00982i	−0.863172	−	0.504909i	$-0.831526\pi$
$379$		−	19.6591i		−	1.00982i	0.863172	−	0.504909i	$-0.168474\pi$
$380$		0			0
$381$	−1.21454	+	1.36111i	−0.0622229	+	0.0697319i
$382$		0			0
$383$	2.85043	+	4.93709i	0.145650	+	0.252273i	0.929615	−	0.368531i	$-0.120139\pi$
$383$	2.85043	+	4.93709i	0.145650	+	0.252273i	−0.783965	+	0.620805i	$0.786806\pi$
$384$		0			0
$385$	16.4321	−	26.6479i	0.837456	−	1.35811i
$386$		0			0
$387$	−1.10048	−	1.48645i	−0.0559404	−	0.0755606i
$388$		0			0
$389$	11.9132	−	20.6343i	0.604024	−	1.04620i	−0.388181	−	0.921583i	$-0.626896\pi$
$389$	11.9132	−	20.6343i	0.604024	−	1.04620i	0.992205	−	0.124617i	$-0.0397703\pi$
$390$		0			0
$391$	−11.6158	+	20.1191i	−0.587435	+	1.01747i
$392$		0			0
$393$	−4.07370	+	19.5970i	−0.205491	+	0.988538i
$394$		0			0
$395$	5.81272	+	10.0679i	0.292469	+	0.506572i
$396$		0			0
$397$	8.12109	+	4.68871i	0.407586	+	0.235320i	0.689752	−	0.724046i	$-0.257720\pi$
$397$	8.12109	+	4.68871i	0.407586	+	0.235320i	−0.282166	+	0.959366i	$0.591053\pi$
$398$		0			0
$399$	7.58489	−	31.8319i	0.379719	−	1.59359i
$400$		0			0
$401$	−14.3594	−	24.8713i	−0.717076	−	1.24201i	−0.962153	−	0.272509i	$-0.912147\pi$
$401$	−14.3594	−	24.8713i	−0.717076	−	1.24201i	0.245077	−	0.969504i	$-0.421187\pi$
$402$		0			0
$403$	32.8943	+	18.9916i	1.63858	+	0.946037i
$404$		0			0
$405$	18.8403	−	17.5860i	0.936180	−	0.873853i
$406$		0			0
$407$	−14.4961	+	8.36935i	−0.718547	+	0.414853i
$408$		0			0
$409$		−	12.4753i		−	0.616863i	−0.951246	−	0.308432i	$-0.900196\pi$
$409$		−	12.4753i		−	0.616863i	0.951246	−	0.308432i	$-0.0998041\pi$
$410$		0			0
$411$	32.1871	−	10.6181i	1.58767	−	0.523750i
$412$		0			0
$413$	−12.9082	+	20.9332i	−0.635170	+	1.03006i
$414$		0			0
$415$	8.42716	+	4.86542i	0.413673	+	0.238834i
$416$		0			0
$417$	−30.3585	+	10.0148i	−1.48666	+	0.490427i
$418$		0			0
$419$	−0.329987	+	0.571554i	−0.0161209	+	0.0279222i	−0.873973	−	0.485974i	$-0.838465\pi$
$419$	−0.329987	+	0.571554i	−0.0161209	+	0.0279222i	0.857852	+	0.513896i	$0.171798\pi$
$420$		0			0
$421$	−7.27295	−	12.5971i	−0.354462	−	0.613946i	0.632564	−	0.774508i	$-0.282003\pi$
$421$	−7.27295	−	12.5971i	−0.354462	−	0.613946i	−0.987026	+	0.160562i	$0.948669\pi$
$422$		0			0
$423$	0.365248	+	3.19883i	0.0177590	+	0.155532i
$424$		0			0
$425$			12.4250i			0.602700i
$426$		0			0
$427$	26.8933	+	16.5834i	1.30146	+	0.802525i
$428$		0			0
$429$	−5.28213	+	25.4103i	−0.255024	+	1.22682i
$430$		0			0
$431$	−1.70770	+	0.985942i	−0.0822571	+	0.0474911i	−0.540564	−	0.841303i	$-0.681789\pi$
$431$	−1.70770	+	0.985942i	−0.0822571	+	0.0474911i	0.458307	+	0.888794i	$0.348456\pi$
$432$		0			0
$433$		−	21.7042i		−	1.04304i	−0.853239	−	0.521519i	$-0.825365\pi$
$433$		−	21.7042i		−	1.04304i	0.853239	−	0.521519i	$-0.174635\pi$
$434$		0			0
$435$	−8.94370	−	27.1116i	−0.428818	−	1.29990i
$436$		0			0
$437$		−	42.7280i		−	2.04396i
$438$		0			0
$439$	3.67053			0.175185			0.0875925	−	0.996156i	$-0.472083\pi$
$439$	3.67053			0.175185			0.0875925	+	0.996156i	$0.472083\pi$
$440$		0			0
$441$	17.5731	−	11.4973i	0.836812	−	0.547490i
$442$		0			0
$443$		−	22.3807i		−	1.06334i	−0.846952	−	0.531670i	$-0.821565\pi$
$443$		−	22.3807i		−	1.06334i	0.846952	−	0.531670i	$-0.178435\pi$
$444$		0			0
$445$	−32.4051			−1.53615
$446$		0			0
$447$	−2.85511	+	13.7349i	−0.135042	+	0.649636i
$448$		0			0
$449$	−15.4434			−0.728818			−0.364409	−	0.931239i	$-0.618729\pi$
$449$	−15.4434			−0.728818			−0.364409	+	0.931239i	$0.618729\pi$
$450$		0			0
$451$	6.29927	+	10.9106i	0.296621	+	0.513762i
$452$		0			0
$453$	−9.70490	−	29.4190i	−0.455976	−	1.38223i
$454$		0			0
$455$	−14.4202	+	23.3853i	−0.676030	+	1.09632i
$456$		0			0
$457$	−28.1770			−1.31807			−0.659033	−	0.752114i	$-0.729034\pi$
$457$	−28.1770			−1.31807			−0.659033	+	0.752114i	$0.729034\pi$
$458$		0			0
$459$	−1.83863	+	20.0900i	−0.0858198	+	0.937723i
$460$		0			0
$461$	26.1406	−	15.0923i	1.21749	−	0.702917i	0.253108	−	0.967438i	$-0.418547\pi$
$461$	26.1406	−	15.0923i	1.21749	−	0.702917i	0.964380	+	0.264521i	$0.0852139\pi$
$462$		0			0
$463$	14.2515	+	8.22812i	0.662325	+	0.382393i	0.793162	−	0.609011i	$-0.208433\pi$
$463$	14.2515	+	8.22812i	0.662325	+	0.382393i	−0.130838	+	0.991404i	$0.541767\pi$
$464$		0			0
$465$	−50.8653	−	10.5735i	−2.35882	−	0.490336i
$466$		0			0
$467$	10.5534	−	18.2790i	0.488353	−	0.845853i	−0.511557	−	0.859249i	$-0.670931\pi$
$467$	10.5534	−	18.2790i	0.488353	−	0.845853i	0.999910	+	0.0133965i	$0.00426435\pi$
$468$		0			0
$469$	3.56379	+	2.19756i	0.164560	+	0.101474i
$470$		0			0
$471$	−16.4705	+	18.4582i	−0.758921	+	0.850507i
$472$		0			0
$473$	−2.54746			−0.117132
$474$		0			0
$475$	−11.4261	−	19.7906i	−0.524267	−	0.908057i
$476$		0			0
$477$	12.7967	−	9.47387i	0.585920	−	0.433779i
$478$		0			0
$479$	−10.9194	+	18.9129i	−0.498920	+	0.864154i	−0.999999	−	0.00124688i	$-0.999603\pi$
$479$	−10.9194	+	18.9129i	−0.498920	+	0.864154i	0.501079	+	0.865401i	$0.332936\pi$
$480$		0			0
$481$	12.7213	−	7.34464i	0.580041	−	0.334887i
$482$		0			0
$483$	18.8413	−	19.9223i	0.857307	−	0.906497i
$484$		0			0
$485$	−4.18058	+	7.24098i	−0.189830	+	0.328796i
$486$		0			0
$487$	21.3355	−	12.3180i	0.966802	−	0.558183i	0.0685422	−	0.997648i	$-0.478165\pi$
$487$	21.3355	−	12.3180i	0.966802	−	0.558183i	0.898260	+	0.439465i	$0.144832\pi$
$488$		0			0
$489$	7.19094	+	21.7983i	0.325185	+	0.985753i
$490$		0			0
$491$	−26.8084	−	15.4778i	−1.20985	−	0.698505i	−0.247120	−	0.968985i	$-0.579484\pi$
$491$	−26.8084	−	15.4778i	−1.20985	−	0.698505i	−0.962726	+	0.270480i	$0.912818\pi$
$492$		0			0
$493$	19.3532	+	11.1736i	0.871623	+	0.503232i
$494$		0			0
$495$	−4.02715	−	35.2696i	−0.181007	−	1.58525i
$496$		0			0
$497$	13.2928	+	8.19682i	0.596264	+	0.367678i
$498$		0			0
$499$	24.4167	−	14.0970i	1.09304	−	0.631068i	0.158657	−	0.987334i	$-0.449284\pi$
$499$	24.4167	−	14.0970i	1.09304	−	0.631068i	0.934385	+	0.356266i	$0.115950\pi$
$500$		0			0
$501$	−10.3762	+	3.42296i	−0.463575	+	0.152927i
$502$		0			0
$503$	−3.67393			−0.163813			−0.0819063	−	0.996640i	$-0.526101\pi$
$503$	−3.67393			−0.163813			−0.0819063	+	0.996640i	$0.526101\pi$
$504$		0			0
$505$	−50.5340			−2.24873
$506$		0			0
$507$	0.0527588	−	0.253802i	0.00234310	−	0.0112718i
$508$		0			0
$509$	−25.8048	+	14.8984i	−1.14378	+	0.660361i	−0.947364	−	0.320159i	$-0.896264\pi$
$509$	−25.8048	+	14.8984i	−1.14378	+	0.660361i	−0.196416	+	0.980521i	$0.562930\pi$
$510$		0			0
$511$	0.600617	−	20.7314i	0.0265697	−	0.917105i
$512$		0			0
$513$	−15.5464	−	33.6905i	−0.686391	−	1.48747i
$514$		0			0
$515$	22.7297	+	13.1230i	1.00159	+	0.578268i
$516$		0			0
$517$	3.84053	+	2.21733i	0.168906	+	0.0975181i
$518$		0			0
$519$	21.1409	−	23.6922i	0.927984	−	1.03997i
$520$		0			0
$521$	−2.43292	+	1.40465i	−0.106588	+	0.0615388i	−0.552346	−	0.833615i	$-0.686267\pi$
$521$	−2.43292	+	1.40465i	−0.106588	+	0.0615388i	0.445758	+	0.895153i	$0.352934\pi$
$522$		0			0
$523$	−1.80981	+	3.13468i	−0.0791374	+	0.137070i	−0.902878	−	0.429897i	$-0.858550\pi$
$523$	−1.80981	+	3.13468i	−0.0791374	+	0.137070i	0.823741	+	0.566967i	$0.191883\pi$
$524$		0			0
$525$	3.39931	−	14.2660i	0.148358	−	0.622621i
$526$		0			0
$527$	35.2188	−	20.3336i	1.53415	−	0.885744i
$528$		0			0
$529$	6.40219	−	11.0889i	0.278356	−	0.482127i
$530$		0			0
$531$	3.16352	+	27.7059i	0.137285	+	1.20234i
$532$		0			0
$533$	−5.52801	−	9.57480i	−0.239445	−	0.414731i
$534$		0			0
$535$	20.0072			0.864989
$536$		0			0
$537$	−6.41628	−	1.33377i	−0.276883	−	0.0575566i
$538$		0			0
$539$	1.67460	−	28.8767i	0.0721300	−	1.24381i
$540$		0			0
$541$	−1.92075	+	3.32683i	−0.0825793	+	0.143032i	−0.904357	−	0.426776i	$-0.859649\pi$
$541$	−1.92075	+	3.32683i	−0.0825793	+	0.143032i	0.821778	+	0.569808i	$0.192982\pi$
$542$		0			0
$543$	20.9852	−	23.5177i	0.900560	−	1.00924i
$544$		0			0
$545$	25.7060	+	14.8413i	1.10112	+	0.635733i
$546$		0			0
$547$	2.24341	−	1.29523i	0.0959214	−	0.0553802i	−0.451272	−	0.892386i	$-0.649030\pi$
$547$	2.24341	−	1.29523i	0.0959214	−	0.0553802i	0.547193	+	0.837006i	$0.315696\pi$
$548$		0			0
$549$	35.5943	−	4.06422i	1.51913	−	0.173457i
$550$		0			0
$551$	−41.1013			−1.75097
$552$		0			0
$553$	9.14254	+	5.63762i	0.388780	+	0.239736i
$554$		0			0
$555$	−13.3769	+	14.9912i	−0.567818	+	0.636342i
$556$		0			0
$557$	−9.88825	−	17.1270i	−0.418979	−	0.725692i	0.576858	−	0.816844i	$-0.304278\pi$
$557$	−9.88825	−	17.1270i	−0.418979	−	0.725692i	−0.995837	+	0.0911519i	$0.970945\pi$
$558$		0			0
$559$	2.23556			0.0945542
$560$		0			0
$561$	20.7333	+	18.5006i	0.875361	+	0.781098i
$562$		0			0
$563$	−13.2532			−0.558555			−0.279278	−	0.960210i	$-0.590095\pi$
$563$	−13.2532			−0.558555			−0.279278	+	0.960210i	$0.590095\pi$
$564$		0			0
$565$			46.0296i			1.93648i
$566$		0			0
$567$	7.60743	−	22.5638i	0.319482	−	0.947592i
$568$		0			0
$569$	−10.7869			−0.452211			−0.226105	−	0.974103i	$-0.572599\pi$
$569$	−10.7869			−0.452211			−0.226105	+	0.974103i	$0.572599\pi$
$570$		0			0
$571$			33.1898i			1.38895i	0.719517	+	0.694475i	$0.244363\pi$
$571$			33.1898i			1.38895i	−0.719517	+	0.694475i	$0.755637\pi$
$572$		0			0
$573$	2.40499	−	2.69522i	0.100470	−	0.112594i
$574$		0			0
$575$		−	19.1493i		−	0.798582i
$576$		0			0
$577$	−39.6973	+	22.9192i	−1.65262	+	0.954141i	−0.676631	+	0.736322i	$0.736561\pi$
$577$	−39.6973	+	22.9192i	−1.65262	+	0.954141i	−0.975989	+	0.217818i	$0.930106\pi$
$578$		0			0
$579$	−5.43145	−	4.84657i	−0.225723	−	0.201416i
$580$		0			0
$581$	8.98677	+	0.260359i	0.372834	+	0.0108015i
$582$		0			0
$583$		−	21.9308i		−	0.908280i
$584$		0			0
$585$	3.53408	+	30.9514i	0.146116	+	1.27968i
$586$		0			0
$587$	11.5052	+	19.9277i	0.474872	+	0.822503i	0.999586	−	0.0287760i	$-0.00916095\pi$
$587$	11.5052	+	19.9277i	0.474872	+	0.822503i	−0.524714	+	0.851279i	$0.675828\pi$
$588$		0			0
$589$	−37.3979	+	64.7751i	−1.54095	+	2.66901i
$590$		0			0
$591$	16.2406	+	14.4918i	0.668050	+	0.596111i
$592$		0			0
$593$	−0.552106	−	0.318759i	−0.0226723	−	0.0130898i	0.488621	−	0.872496i	$-0.337500\pi$
$593$	−0.552106	−	0.318759i	−0.0226723	−	0.0130898i	−0.511293	+	0.859406i	$0.670833\pi$
$594$		0			0
$595$	13.9638	+	25.8896i	0.572458	+	1.06137i
$596$		0			0
$597$	0.385804	−	1.85596i	0.0157899	−	0.0759593i
$598$		0			0
$599$			26.9454i			1.10096i	0.834849	+	0.550479i	$0.185555\pi$
$599$			26.9454i			1.10096i	−0.834849	+	0.550479i	$0.814445\pi$
$600$		0			0
$601$	38.0460	−	21.9658i	1.55193	−	0.896005i	0.553942	−	0.832555i	$-0.313123\pi$
$601$	38.0460	−	21.9658i	1.55193	−	0.896005i	0.997985	−	0.0634499i	$-0.0202103\pi$
$602$		0			0
$603$	4.71681	−	0.538574i	0.192083	−	0.0219324i
$604$		0			0
$605$	−15.0653	−	8.69797i	−0.612492	−	0.353623i
$606$		0			0
$607$	−2.37625	−	4.11578i	−0.0964489	−	0.167054i	0.813763	−	0.581196i	$-0.197415\pi$
$607$	−2.37625	−	4.11578i	−0.0964489	−	0.167054i	−0.910212	+	0.414142i	$0.864082\pi$
$608$		0			0
$609$	−19.1639	−	18.1240i	−0.776559	−	0.734420i
$610$		0			0
$611$	−3.37031	−	1.94585i	−0.136348	−	0.0787207i
$612$		0			0
$613$	10.1971	+	17.6619i	0.411857	+	0.713357i	0.995093	−	0.0989460i	$-0.0315471\pi$
$613$	10.1971	+	17.6619i	0.411857	+	0.713357i	−0.583236	+	0.812303i	$0.698214\pi$
$614$		0			0
$615$	11.2833	+	10.0683i	0.454986	+	0.405991i
$616$		0			0
$617$	4.93084	−	8.54047i	0.198508	−	0.343827i	−0.749537	−	0.661963i	$-0.769724\pi$
$617$	4.93084	−	8.54047i	0.198508	−	0.343827i	0.948045	+	0.318136i	$0.103057\pi$
$618$		0			0
$619$	1.89212	−	3.27725i	0.0760508	−	0.131724i	−0.825492	−	0.564414i	$-0.809102\pi$
$619$	1.89212	−	3.27725i	0.0760508	−	0.131724i	0.901543	+	0.432690i	$0.142436\pi$
$620$		0			0
$621$	2.83369	−	30.9627i	0.113712	−	1.24249i
$622$		0			0
$623$	−26.3512	+	14.2127i	−1.05574	+	0.569421i
$624$		0			0
$625$	15.3798	+	26.6386i	0.615193	+	1.06555i
$626$		0			0
$627$	−50.0376	−	10.4015i	−1.99831	−	0.415396i
$628$		0			0
$629$		−	15.7273i		−	0.627088i
$630$		0			0
$631$		−	6.29213i		−	0.250486i	−0.992126	−	0.125243i	$-0.960029\pi$
$631$		−	6.29213i		−	0.250486i	0.992126	−	0.125243i	$-0.0399710\pi$
$632$		0			0
$633$	3.03019	+	9.18558i	0.120439	+	0.365094i
$634$		0			0
$635$	1.50799	+	2.61191i	0.0598427	+	0.103651i
$636$		0			0
$637$	−1.46957	+	25.3412i	−0.0582264	+	1.00405i
$638$		0			0
$639$	17.5935	−	2.00886i	0.695990	−	0.0794695i
$640$		0			0
$641$	19.2732	−	33.3821i	0.761244	−	1.31851i	−0.180965	−	0.983489i	$-0.557922\pi$
$641$	19.2732	−	33.3821i	0.761244	−	1.31851i	0.942210	−	0.335024i	$-0.108745\pi$
$642$		0			0
$643$	16.4997	−	28.5783i	0.650685	−	1.12702i	−0.332272	−	0.943184i	$-0.607815\pi$
$643$	16.4997	−	28.5783i	0.650685	−	1.12702i	0.982957	−	0.183836i	$-0.0588514\pi$
$644$		0			0
$645$	−2.90384	+	0.957933i	−0.114338	+	0.0377186i
$646$		0			0
$647$	−11.0733	−	19.1796i	−0.435337	−	0.754026i	0.561986	−	0.827147i	$-0.310038\pi$
$647$	−11.0733	−	19.1796i	−0.435337	−	0.754026i	−0.997323	+	0.0731206i	$0.976704\pi$
$648$		0			0
$649$	33.2639	+	19.2049i	1.30572	+	0.753859i
$650$		0			0
$651$	−46.0002	+	13.7111i	−1.80289	+	0.537380i
$652$		0			0
$653$	−16.7556	−	29.0215i	−0.655696	−	1.13570i	−0.981719	−	0.190337i	$-0.939042\pi$
$653$	−16.7556	−	29.0215i	−0.655696	−	1.13570i	0.326023	−	0.945362i	$-0.394291\pi$
$654$		0			0
$655$	28.6589	+	16.5462i	1.11980	+	0.646515i
$656$		0			0
$657$	−13.9931	−	18.9010i	−0.545923	−	0.737398i
$658$		0			0
$659$	−32.6980	+	18.8782i	−1.27373	+	0.735391i	−0.975689	−	0.219160i	$-0.929668\pi$
$659$	−32.6980	+	18.8782i	−1.27373	+	0.735391i	−0.298046	+	0.954551i	$0.596335\pi$
$660$		0			0
$661$			12.6766i			0.493064i	0.969135	+	0.246532i	$0.0792910\pi$
$661$			12.6766i			0.493064i	−0.969135	+	0.246532i	$0.920709\pi$
$662$		0			0
$663$	−18.1948	−	16.2355i	−0.706628	−	0.630535i
$664$		0			0
$665$	−46.0500	−	28.3961i	−1.78574	−	1.10115i
$666$		0			0
$667$	−29.8270	−	17.2206i	−1.15491	−	0.666786i
$668$		0			0
$669$	−1.18495	+	5.70034i	−0.0458128	+	0.220388i
$670$		0			0
$671$	24.6729	−	42.7347i	0.952486	−	1.64975i
$672$		0			0
$673$	−7.17772	−	12.4322i	−0.276681	−	0.479225i	0.693877	−	0.720094i	$-0.255901\pi$
$673$	−7.17772	−	12.4322i	−0.276681	−	0.479225i	−0.970558	+	0.240868i	$0.922568\pi$
$674$		0			0
$675$	−6.96741	−	15.0990i	−0.268176	−	0.581161i
$676$		0			0
$677$		−	27.7939i		−	1.06821i	−0.845420	−	0.534103i	$-0.820650\pi$
$677$		−	27.7939i		−	1.06821i	0.845420	−	0.534103i	$-0.179350\pi$
$678$		0			0
$679$	−0.223711	+	7.72182i	−0.00858525	+	0.296336i
$680$		0			0
$681$	47.3687	−	15.6263i	1.81517	−	0.598799i
$682$		0			0
$683$	−30.3691	+	17.5336i	−1.16204	+	0.670905i	−0.951793	−	0.306743i	$-0.900761\pi$
$683$	−30.3691	+	17.5336i	−1.16204	+	0.670905i	−0.210249	+	0.977648i	$0.567428\pi$
$684$		0			0
$685$		−	56.0360i		−	2.14102i
$686$		0			0
$687$	17.1387	+	3.56268i	0.653882	+	0.135925i
$688$		0			0
$689$			19.2457i			0.733202i
$690$		0			0
$691$	−19.8858			−0.756491			−0.378246	−	0.925705i	$-0.623473\pi$
$691$	−19.8858			−0.756491			−0.378246	+	0.925705i	$0.623473\pi$
$692$		0			0
$693$	−18.7439	−	26.9143i	−0.712022	−	1.02239i
$694$		0			0
$695$			52.8524i			2.00480i
$696$		0			0
$697$	−11.8373			−0.448369
$698$		0			0
$699$	−11.3546	+	3.74573i	−0.429472	+	0.141676i
$700$		0			0
$701$	−5.54811			−0.209549			−0.104775	−	0.994496i	$-0.533412\pi$
$701$	−5.54811			−0.209549			−0.104775	+	0.994496i	$0.533412\pi$
$702$		0			0
$703$	14.4630	+	25.0506i	0.545481	+	0.944801i
$704$		0			0
$705$	5.21159	+	1.08335i	0.196280	+	0.0408014i
$706$		0			0
$707$	−41.0934	+	22.1640i	−1.54548	+	0.833563i
$708$		0			0
$709$	−41.3134			−1.55156			−0.775779	−	0.631005i	$-0.782643\pi$
$709$	−41.3134			−1.55156			−0.775779	+	0.631005i	$0.782643\pi$
$710$		0			0
$711$	12.1005	−	1.38166i	0.453805	−	0.0518163i
$712$		0			0
$713$	−54.2790	+	31.3380i	−2.03276	+	1.17362i
$714$		0			0
$715$	37.1604	+	21.4545i	1.38972	+	0.802355i
$716$		0			0
$717$	−5.38278	−	16.3171i	−0.201024	−	0.609374i
$718$		0			0
$719$	21.1467	−	36.6272i	0.788639	−	1.36596i	−0.138161	−	0.990410i	$-0.544119\pi$
$719$	21.1467	−	36.6272i	0.788639	−	1.36596i	0.926801	−	0.375554i	$-0.122547\pi$
$720$		0			0
$721$	24.2391	+	0.702237i	0.902709	+	0.0261527i
$722$		0			0
$723$	6.35621	+	19.2679i	0.236390	+	0.716582i
$724$		0			0
$725$	−18.4203			−0.684113
$726$		0			0
$727$	9.19628	+	15.9284i	0.341071	+	0.590753i	0.984632	−	0.174642i	$-0.0558769\pi$
$727$	9.19628	+	15.9284i	0.341071	+	0.590753i	−0.643561	+	0.765395i	$0.722544\pi$
$728$		0			0
$729$	−9.03135	−	25.4447i	−0.334494	−	0.942398i
$730$		0			0
$731$	1.19677	−	2.07286i	0.0442640	−	0.0766675i
$732$		0			0
$733$	25.6444	−	14.8058i	0.947198	−	0.546865i	0.0549884	−	0.998487i	$-0.482488\pi$
$733$	25.6444	−	14.8058i	0.947198	−	0.546865i	0.892209	+	0.451622i	$0.149154\pi$
$734$		0			0
$735$	−8.94977	−	33.5461i	−0.330117	−	1.23737i
$736$		0			0
$737$	3.26955	−	5.66303i	0.120435	−	0.208600i
$738$		0			0
$739$	−34.2963	+	19.8010i	−1.26161	+	0.728392i	−0.973386	−	0.229171i	$-0.926398\pi$
$739$	−34.2963	+	19.8010i	−1.26161	+	0.728392i	−0.288225	+	0.957563i	$0.593065\pi$
$740$		0			0
$741$	43.9113	+	9.12799i	1.61312	+	0.335325i
$742$		0			0
$743$	12.9802	+	7.49414i	0.476199	+	0.274933i	0.718831	−	0.695185i	$-0.244677\pi$
$743$	12.9802	+	7.49414i	0.476199	+	0.274933i	−0.242632	+	0.970118i	$0.578011\pi$
$744$		0			0
$745$	20.0860	+	11.5967i	0.735895	+	0.424869i
$746$		0			0
$747$	8.19330	−	6.06581i	0.299777	−	0.221936i
$748$		0			0
$749$	16.2695	−	8.77510i	0.594476	−	0.320635i
$750$		0			0
$751$	38.2057	−	22.0581i	1.39415	−	0.804911i	0.400375	−	0.916351i	$-0.368880\pi$
$751$	38.2057	−	22.0581i	1.39415	−	0.804911i	0.993771	+	0.111441i	$0.0355465\pi$
$752$		0			0
$753$	7.40218	+	6.60508i	0.269750	+	0.240703i
$754$		0			0
$755$	−51.2168			−1.86397
$756$		0			0
$757$	−18.5707			−0.674964			−0.337482	−	0.941332i	$-0.609575\pi$
$757$	−18.5707			−0.674964			−0.337482	+	0.941332i	$0.609575\pi$
$758$		0			0
$759$	−31.9541	−	28.5131i	−1.15986	−	1.03496i
$760$		0			0
$761$	23.7761	−	13.7272i	0.861884	−	0.497609i	−0.00275857	−	0.999996i	$-0.500878\pi$
$761$	23.7761	−	13.7272i	0.861884	−	0.497609i	0.864643	+	0.502387i	$0.167545\pi$
$762$		0			0
$763$	27.4130	+	0.794190i	0.992416	+	0.0287516i
$764$		0			0
$765$	30.5907	+	13.2924i	1.10601	+	0.480586i
$766$		0			0
$767$	−29.1912	−	16.8536i	−1.05403	−	0.608547i
$768$		0			0
$769$	−18.6472	−	10.7660i	−0.672434	−	0.388230i	0.124564	−	0.992212i	$-0.460247\pi$
$769$	−18.6472	−	10.7660i	−0.672434	−	0.388230i	−0.796998	+	0.603981i	$0.793580\pi$
$770$		0			0
$771$	28.4430	+	5.91255i	1.02435	+	0.212935i
$772$		0			0
$773$	0.368251	−	0.212610i	0.0132451	−	0.00764705i	−0.493363	−	0.869824i	$-0.664233\pi$
$773$	0.368251	−	0.212610i	0.0132451	−	0.00764705i	0.506608	+	0.862177i	$0.330899\pi$
$774$		0			0
$775$	−16.7606	+	29.0301i	−0.602057	+	1.04279i
$776$		0			0
$777$	−4.30277	+	18.0577i	−0.154361	+	0.647815i
$778$		0			0
$779$	18.8546	−	10.8857i	0.675535	−	0.390020i
$780$		0			0
$781$	12.1953	−	21.1229i	0.436383	−	0.755837i
$782$		0			0
$783$	−29.7839	−	2.72581i	−1.06439	−	0.0974123i
$784$		0			0
$785$	20.4499	+	35.4203i	0.729890	+	1.26421i
$786$		0			0
$787$	−14.9796			−0.533966			−0.266983	−	0.963701i	$-0.586027\pi$
$787$	−14.9796			−0.533966			−0.266983	+	0.963701i	$0.586027\pi$
$788$		0			0
$789$	−7.30966	−	22.1582i	−0.260231	−	0.788852i
$790$		0			0
$791$	20.1884	+	37.4304i	0.717816	+	1.33087i
$792$		0			0
$793$	−21.6521	+	37.5025i	−0.768887	+	1.33175i
$794$		0			0
$795$	−8.24673	−	24.9988i	−0.292481	−	0.886615i
$796$		0			0
$797$	10.3494	+	5.97520i	0.366593	+	0.211653i	0.671969	−	0.740579i	$-0.265449\pi$
$797$	10.3494	+	5.97520i	0.366593	+	0.211653i	−0.305376	+	0.952232i	$0.598782\pi$
$798$		0			0
$799$	−3.60847	+	2.08335i	−0.127659	+	0.0737037i
$800$		0			0
$801$	−13.5294	+	31.1361i	−0.478036	+	1.10014i
$802$		0			0
$803$	−32.3922			−1.14310
$804$		0			0
$805$	−21.5209	−	39.9010i	−0.758512	−	1.40632i
$806$		0			0
$807$	11.3101	+	2.35107i	0.398135	+	0.0827617i
$808$		0			0
$809$	24.6125	+	42.6301i	0.865329	+	1.49879i	0.866720	+	0.498795i	$0.166224\pi$
$809$	24.6125	+	42.6301i	0.865329	+	1.49879i	−0.00139091	+	0.999999i	$0.500443\pi$
$810$		0			0
$811$	17.0819			0.599828			0.299914	−	0.953966i	$-0.403042\pi$
$811$	17.0819			0.599828			0.299914	+	0.953966i	$0.403042\pi$
$812$		0			0
$813$	34.3717	−	11.3387i	1.20547	−	0.397667i
$814$		0			0
$815$	37.9496			1.32932
$816$		0			0
$817$			4.40224i			0.154015i
$818$		0			0
$819$	16.4490	+	23.6191i	0.574774	+	0.825317i
$820$		0			0
$821$	−22.7287			−0.793236			−0.396618	−	0.917984i	$-0.629816\pi$
$821$	−22.7287			−0.793236			−0.396618	+	0.917984i	$0.629816\pi$
$822$		0			0
$823$		−	51.6244i		−	1.79951i	−0.436391	−	0.899757i	$-0.643744\pi$
$823$		−	51.6244i		−	1.79951i	0.436391	−	0.899757i	$-0.356256\pi$
$824$		0			0
$825$	−22.4253	−	4.66162i	−0.780748	−	0.162297i
$826$		0			0
$827$			48.6190i			1.69065i	0.534254	+	0.845324i	$0.320593\pi$
$827$			48.6190i			1.69065i	−0.534254	+	0.845324i	$0.679407\pi$
$828$		0			0
$829$	30.5374	−	17.6308i	1.06061	−	0.612342i	0.135007	−	0.990845i	$-0.456894\pi$
$829$	30.5374	−	17.6308i	1.06061	−	0.612342i	0.925600	+	0.378503i	$0.123561\pi$
$830$		0			0
$831$	43.3963	−	14.3158i	1.50540	−	0.496610i
$832$		0			0
$833$	22.7102	+	14.9285i	0.786860	+	0.517243i
$834$		0			0
$835$			18.0644i			0.625145i
$836$		0			0
$837$	−31.3961	+	44.4589i	−1.08521	+	1.53672i
$838$		0			0
$839$	−1.78515	−	3.09198i	−0.0616304	−	0.106747i	0.833564	−	0.552423i	$-0.186297\pi$
$839$	−1.78515	−	3.09198i	−0.0616304	−	0.106747i	−0.895194	+	0.445676i	$0.852963\pi$
$840$		0			0
$841$	−2.06505	+	3.57677i	−0.0712086	+	0.123337i
$842$		0			0
$843$	5.12585	−	24.6585i	0.176544	−	0.849285i
$844$		0			0
$845$	−0.371164	−	0.214292i	−0.0127684	−	0.00737186i
$846$		0			0
$847$	−16.0657	−	0.465446i	−0.552025	−	0.0159929i
$848$		0			0
$849$	36.9674	+	32.9866i	1.26872	+	1.13210i
$850$		0			0
$851$			24.2388i			0.830896i
$852$		0			0
$853$	−8.56199	+	4.94327i	−0.293157	+	0.169254i	−0.639365	−	0.768904i	$-0.720803\pi$
$853$	−8.56199	+	4.94327i	−0.293157	+	0.169254i	0.346208	+	0.938158i	$0.387469\pi$
$854$		0			0
$855$	−60.9490	+	6.95927i	−2.08441	+	0.238002i
$856$		0			0
$857$	−27.6174	−	15.9449i	−0.943392	−	0.544668i	−0.0523701	−	0.998628i	$-0.516678\pi$
$857$	−27.6174	−	15.9449i	−0.943392	−	0.544668i	−0.891022	+	0.453960i	$0.850011\pi$
$858$		0			0
$859$	13.6928	+	23.7166i	0.467192	+	0.809200i	0.999297	−	0.0374781i	$-0.0119325\pi$
$859$	13.6928	+	23.7166i	0.467192	+	0.809200i	−0.532106	+	0.846678i	$0.678599\pi$
$860$		0			0
$861$	13.5913	+	3.23852i	0.463189	+	0.110369i
$862$		0			0
$863$	26.1355	+	15.0893i	0.889663	+	0.513647i	0.873832	−	0.486228i	$-0.161627\pi$
$863$	26.1355	+	15.0893i	0.889663	+	0.513647i	0.0158307	+	0.999875i	$0.494961\pi$
$864$		0			0
$865$	−26.2488	−	45.4643i	−0.892486	−	1.54583i
$866$		0			0
$867$	3.16846	−	1.04523i	0.107606	−	0.0354978i
$868$		0			0
$869$	8.38771	−	14.5279i	0.284534	−	0.492827i
$870$		0			0
$871$	−2.86924	+	4.96967i	−0.0972206	+	0.168391i
$872$		0			0
$873$	5.21200	+	7.04003i	0.176399	+	0.238269i
$874$		0			0
$875$	11.6063	+	7.15689i	0.392366	+	0.241947i
$876$		0			0
$877$	−9.49886	−	16.4525i	−0.320754	−	0.555562i	0.659890	−	0.751362i	$-0.270603\pi$
$877$	−9.49886	−	16.4525i	−0.320754	−	0.555562i	−0.980644	+	0.195801i	$0.937269\pi$
$878$		0			0
$879$	1.40655	+	4.26376i	0.0474418	+	0.143813i
$880$		0			0
$881$			48.0372i			1.61841i	0.587523	+	0.809207i	$0.300103\pi$
$881$			48.0372i			1.61841i	−0.587523	+	0.809207i	$0.699897\pi$
$882$		0			0
$883$		−	10.4536i		−	0.351792i	−0.984409	−	0.175896i	$-0.943718\pi$
$883$		−	10.4536i		−	0.351792i	0.984409	−	0.175896i	$-0.0562822\pi$
$884$		0			0
$885$	45.1391	+	9.38321i	1.51733	+	0.315413i
$886$		0			0
$887$	−15.9253	−	27.5834i	−0.534719	−	0.926161i	−0.999177	−	0.0405653i	$-0.987084\pi$
$887$	−15.9253	−	27.5834i	−0.534719	−	0.926161i	0.464458	−	0.885595i	$-0.346249\pi$
$888$		0			0
$889$	2.37184	+	1.46256i	0.0795490	+	0.0490528i
$890$		0			0
$891$	−35.5698	−	10.8559i	−1.19163	−	0.363685i
$892$		0			0
$893$	3.83174	−	6.63677i	0.128224	−	0.222091i
$894$		0			0
$895$	−5.41742	+	9.38325i	−0.181084	+	0.313647i
$896$		0			0
$897$	28.0418	+	25.0221i	0.936287	+	0.835464i
$898$		0			0
$899$	30.1449	+	52.2126i	1.00539	+	1.74139i
$900$		0			0
$901$	17.8450	+	10.3028i	0.594503	+	0.343237i
$902$		0			0
$903$	−1.94120	+	2.05259i	−0.0645992	+	0.0683058i
$904$		0			0
$905$	−26.0554	−	45.1293i	−0.866111	−	1.50015i
$906$		0			0
$907$	−16.9760	−	9.80107i	−0.563677	−	0.325439i	0.190943	−	0.981601i	$-0.438845\pi$
$907$	−16.9760	−	9.80107i	−0.563677	−	0.325439i	−0.754620	+	0.656162i	$0.772179\pi$
$908$		0			0
$909$	−21.0983	+	48.5551i	−0.699787	+	1.61047i
$910$		0			0
$911$	5.50917	−	3.18072i	0.182527	−	0.105382i	−0.405952	−	0.913894i	$-0.633060\pi$
$911$	5.50917	−	3.18072i	0.182527	−	0.105382i	0.588479	+	0.808512i	$0.299727\pi$
$912$		0			0
$913$		−	14.0416i		−	0.464708i
$914$		0			0
$915$	12.0548	−	57.9909i	0.398519	−	1.91712i
$916$		0			0
$917$	30.5620	+	0.885422i	1.00925	+	0.0292392i
$918$		0			0
$919$	−34.9688	−	20.1892i	−1.15351	−	0.665981i	−0.203772	−	0.979018i	$-0.565320\pi$
$919$	−34.9688	−	20.1892i	−1.15351	−	0.665981i	−0.949741	+	0.313037i	$0.898653\pi$
$920$		0			0
$921$	−7.37009	−	6.57645i	−0.242853	−	0.216701i
$922$		0			0
$923$	−10.7022	+	18.5367i	−0.352267	+	0.610144i
$924$		0			0
$925$	6.48184	+	11.2269i	0.213122	+	0.369138i
$926$		0			0
$927$	22.0989	−	16.3606i	0.725823	−	0.537354i
$928$		0			0
$929$			20.2026i			0.662826i	0.943486	+	0.331413i	$0.107525\pi$
$929$			20.2026i			0.662826i	−0.943486	+	0.331413i	$0.892475\pi$
$930$		0			0
$931$	−49.9014	−	2.89385i	−1.63545	−	0.0948421i
$932$		0			0
$933$	10.8968	+	9.72341i	0.356746	+	0.318330i
$934$		0			0
$935$	39.7862	−	22.9706i	1.30115	−	0.751219i
$936$		0			0
$937$			26.4532i			0.864188i	0.901829	+	0.432094i	$0.142225\pi$
$937$			26.4532i			0.864188i	−0.901829	+	0.432094i	$0.857775\pi$
$938$		0			0
$939$	−8.57523	+	9.61009i	−0.279842	+	0.313613i
$940$		0			0
$941$			16.8076i			0.547913i	0.961742	+	0.273957i	$0.0883324\pi$
$941$			16.8076i			0.547913i	−0.961742	+	0.273957i	$0.911668\pi$
$942$		0			0
$943$	18.2436			0.594092
$944$		0			0
$945$	−31.4868	−	23.6311i	−1.02427	−	0.768721i
$946$		0			0
$947$		−	12.3509i		−	0.401351i	−0.979658	−	0.200675i	$-0.935686\pi$
$947$		−	12.3509i		−	0.401351i	0.979658	−	0.200675i	$-0.0643137\pi$
$948$		0			0
$949$	28.4263			0.922756
$950$		0			0
$951$	14.4400	+	12.8851i	0.468250	+	0.417827i
$952$		0			0
$953$	2.87383			0.0930926			0.0465463	−	0.998916i	$-0.485179\pi$
$953$	2.87383			0.0930926			0.0465463	+	0.998916i	$0.485179\pi$
$954$		0			0
$955$	−2.98606	−	5.17200i	−0.0966265	−	0.167362i
$956$		0			0
$957$	−27.4276	+	30.7376i	−0.886609	+	0.993605i
$958$		0			0
$959$	−24.5771	−	45.5674i	−0.793637	−	1.47145i
$960$		0			0
$961$	78.7151			2.53920
$962$		0			0
$963$	8.35318	−	19.2238i	0.269177	−	0.619477i
$964$		0			0
$965$	−10.4227	+	6.01755i	−0.335519	+	0.193712i
$966$		0			0
$967$	−11.4107	−	6.58797i	−0.366943	−	0.211855i	0.305179	−	0.952295i	$-0.401284\pi$
$967$	−11.4107	−	6.58797i	−0.366943	−	0.211855i	−0.672122	+	0.740440i	$0.734617\pi$
$968$		0			0
$969$	31.9708	−	35.8290i	1.02705	−	1.15099i
$970$		0			0
$971$	−14.7421	+	25.5341i	−0.473097	+	0.819428i	−0.999526	−	0.0307910i	$-0.990197\pi$
$971$	−14.7421	+	25.5341i	−0.473097	+	0.819428i	0.526429	+	0.850219i	$0.323531\pi$
$972$		0			0
$973$	23.1808	+	42.9786i	0.743143	+	1.37783i
$974$		0			0
$975$	19.6796	+	4.09087i	0.630253	+	0.131013i
$976$		0			0
$977$	49.4890			1.58329			0.791647	−	0.610978i	$-0.209224\pi$
$977$	49.4890			1.58329			0.791647	+	0.610978i	$0.209224\pi$
$978$		0			0
$979$	23.3801	+	40.4956i	0.747233	+	1.29424i
$980$		0			0
$981$	24.9926	−	18.5029i	0.797952	−	0.590754i
$982$		0			0
$983$	1.11801	−	1.93645i	0.0356590	−	0.0617633i	−0.847645	−	0.530564i	$-0.821980\pi$
$983$	1.11801	−	1.93645i	0.0356590	−	0.0617633i	0.883304	+	0.468800i	$0.155314\pi$
$984$		0			0
$985$	31.1650	−	17.9931i	0.992999	−	0.573308i
$986$		0			0
$987$	4.71313	−	1.40482i	0.150021	−	0.0447159i
$988$		0			0
$989$	−1.84445	+	3.19468i	−0.0586502	+	0.101585i
$990$		0			0
$991$	−23.8064	+	13.7447i	−0.756237	+	0.436614i	−0.827943	−	0.560812i	$-0.810489\pi$
$991$	−23.8064	+	13.7447i	−0.756237	+	0.436614i	0.0717062	+	0.997426i	$0.477156\pi$
$992$		0			0
$993$	−5.40129	+	6.05311i	−0.171405	+	0.192090i
$994$		0			0
$995$	−2.71418	−	1.56703i	−0.0860451	−	0.0496782i
$996$		0			0
$997$	−5.82004	−	3.36020i	−0.184322	−	0.106419i	0.404999	−	0.914317i	$-0.367272\pi$
$997$	−5.82004	−	3.36020i	−0.184322	−	0.106419i	−0.589322	+	0.807898i	$0.700605\pi$
$998$		0			0
$999$	8.81921	+	19.1120i	0.279028	+	0.604678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.h.607.4	yes	24
3.2	odd	2		3024.2.cz.g.1279.11		24
4.3	odd	2		1008.2.cz.g.607.9	yes	24
7.3	odd	6		1008.2.bf.h.31.7	yes	24
9.2	odd	6		3024.2.bf.h.2287.11		24
9.7	even	3		1008.2.bf.g.943.6	yes	24
12.11	even	2		3024.2.cz.h.1279.11		24
21.17	even	6		3024.2.bf.g.1711.2		24
28.3	even	6		1008.2.bf.g.31.6	✓	24
36.7	odd	6		1008.2.bf.h.943.7	yes	24
36.11	even	6		3024.2.bf.g.2287.11		24
63.38	even	6		3024.2.cz.h.2719.11		24
63.52	odd	6		1008.2.cz.g.367.9	yes	24
84.59	odd	6		3024.2.bf.h.1711.2		24
252.115	even	6	inner	1008.2.cz.h.367.4	yes	24
252.227	odd	6		3024.2.cz.g.2719.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.6	✓	24	28.3	even	6
1008.2.bf.g.943.6	yes	24	9.7	even	3
1008.2.bf.h.31.7	yes	24	7.3	odd	6
1008.2.bf.h.943.7	yes	24	36.7	odd	6
1008.2.cz.g.367.9	yes	24	63.52	odd	6
1008.2.cz.g.607.9	yes	24	4.3	odd	2
1008.2.cz.h.367.4	yes	24	252.115	even	6	inner
1008.2.cz.h.607.4	yes	24	1.1	even	1	trivial
3024.2.bf.g.1711.2		24	21.17	even	6
3024.2.bf.g.2287.11		24	36.11	even	6
3024.2.bf.h.1711.2		24	84.59	odd	6
3024.2.bf.h.2287.11		24	9.2	odd	6
3024.2.cz.g.1279.11		24	3.2	odd	2
3024.2.cz.g.2719.11		24	252.227	odd	6
3024.2.cz.h.1279.11		24	12.11	even	2
3024.2.cz.h.2719.11		24	63.38	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.29235 - 1.15318i) q^{3} +(-2.47996 + 1.43180i) q^{5} +(-1.38867 + 2.25202i) q^{7} +(0.340334 + 2.98063i) q^{9} +O(q^{10})\)	\(q+(-1.29235 - 1.15318i) q^{3} +(-2.47996 + 1.43180i) q^{5} +(-1.38867 + 2.25202i) q^{7} +(0.340334 + 2.98063i) q^{9} +(3.57856 + 2.06608i) q^{11} +(-3.14042 - 1.81312i) q^{13} +(4.85611 + 1.00946i) q^{15} +(-3.36233 + 1.94124i) q^{17} +(3.57038 - 6.18407i) q^{19} +(4.39164 - 1.30900i) q^{21} +(5.18202 - 2.99184i) q^{23} +(1.60013 - 2.77151i) q^{25} +(2.99739 - 4.24449i) q^{27} +(-2.87794 - 4.98473i) q^{29} -10.4745 q^{31} +(-2.24218 - 6.79685i) q^{33} +(0.219406 - 7.57322i) q^{35} +(-2.02541 + 3.50812i) q^{37} +(1.96766 + 5.96467i) q^{39} +(2.64042 + 1.52444i) q^{41} +(-0.533900 + 0.308247i) q^{43} +(-5.11170 - 6.90455i) q^{45} +1.07320 q^{47} +(-3.14317 - 6.25464i) q^{49} +(6.58392 + 1.36862i) q^{51} +(-2.65366 - 4.59628i) q^{53} -11.8329 q^{55} +(-11.7455 + 3.87468i) q^{57} +9.29532 q^{59} -11.9419i q^{61} +(-7.18505 - 3.37269i) q^{63} +10.3842 q^{65} -1.58249i q^{67} +(-10.1471 - 2.10932i) q^{69} -5.90262i q^{71} +(-6.78880 + 3.91952i) q^{73} +(-5.26398 + 1.73651i) q^{75} +(-9.62232 + 5.18987i) q^{77} -4.05971i q^{79} +(-8.76835 + 2.02882i) q^{81} +(-1.69905 - 2.94285i) q^{83} +(5.55897 - 9.62841i) q^{85} +(-2.02901 + 9.76081i) q^{87} +(9.80008 + 5.65808i) q^{89} +(8.44421 - 4.55445i) q^{91} +(13.5367 + 12.0790i) q^{93} +20.4483i q^{95} +(2.52862 - 1.45990i) q^{97} +(-4.94033 + 11.3695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9	\( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9} + 9 q^{11} - 3 q^{13} + 6 q^{15} - 3 q^{17} + 4 q^{19} + 13 q^{21} + 6 q^{23} + 15 q^{25} - 9 q^{27} + 18 q^{29} - 34 q^{31} - 21 q^{33} + 42 q^{35} - 3 q^{37} - 27 q^{39} + 36 q^{41} - 24 q^{43} + 21 q^{45} + 42 q^{47} + 30 q^{49} + 6 q^{51} - 12 q^{53} + 30 q^{55} - 13 q^{57} + 12 q^{59} + 3 q^{63} + 6 q^{69} + 48 q^{73} - 36 q^{75} - 48 q^{77} - 31 q^{81} + 48 q^{83} - 21 q^{85} - 15 q^{87} + 39 q^{89} - 9 q^{91} + 10 q^{93} + 3 q^{97} - 30 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9 + 9 * q^11 - 3 * q^13 + 6 * q^15 - 3 * q^17 + 4 * q^19 + 13 * q^21 + 6 * q^23 + 15 * q^25 - 9 * q^27 + 18 * q^29 - 34 * q^31 - 21 * q^33 + 42 * q^35 - 3 * q^37 - 27 * q^39 + 36 * q^41 - 24 * q^43 + 21 * q^45 + 42 * q^47 + 30 * q^49 + 6 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 + 12 * q^59 + 3 * q^63 + 6 * q^69 + 48 * q^73 - 36 * q^75 - 48 * q^77 - 31 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 + 10 * q^93 + 3 * q^97 - 30 * q^99

Introduction

L-functions

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