LMFDB - Embedded newform 1008.2.cc.b.209.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(209,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1008.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.2
Root			$-1.62181 + 0.608059i$ of defining polynomial
Character	$\chi$	$=$	1008.209
Dual form			1008.2.cc.b.545.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62181 - 0.608059i) q^{3} +(-1.94556 - 3.36980i) q^{5} +(-2.09985 + 1.60954i) q^{7} +(2.26053 + 1.97231i) q^{9} +O(q^{10})$	\(q+(-1.62181 - 0.608059i) q^{3} +(-1.94556 - 3.36980i) q^{5} +(-2.09985 + 1.60954i) q^{7} +(2.26053 + 1.97231i) q^{9} +(-3.41614 - 1.97231i) q^{11} +(-2.46687 + 1.42425i) q^{13} +(1.10628 + 6.64819i) q^{15} -0.742117 q^{17} +1.78474i q^{19} +(4.38425 - 1.33354i) q^{21} +(5.41535 - 3.12656i) q^{23} +(-5.07039 + 8.78217i) q^{25} +(-2.46687 - 4.57324i) q^{27} +(-2.50079 - 1.44383i) q^{29} +(3.04125 - 1.75587i) q^{31} +(4.34105 + 5.27592i) q^{33} +(9.50923 + 3.94462i) q^{35} +3.00158 q^{37} +(4.86681 - 0.809856i) q^{39} +(5.24705 + 9.08816i) q^{41} +(-0.471521 + 0.816699i) q^{43} +(2.24831 - 11.4548i) q^{45} +(1.09263 - 1.89248i) q^{47} +(1.81873 - 6.75960i) q^{49} +(1.20357 + 0.451251i) q^{51} +15.3490i q^{55} +(1.08523 - 2.89450i) q^{57} +(0.0105673 + 0.0183031i) q^{59} +(2.13832 + 1.23456i) q^{61} +(-7.92129 - 0.503130i) q^{63} +(9.59886 + 5.54191i) q^{65} +(6.72463 + 11.6474i) q^{67} +(-10.6838 + 1.77782i) q^{69} -1.94304i q^{71} +4.85486i q^{73} +(13.5633 - 11.1599i) q^{75} +(10.3479 - 1.35688i) q^{77} +(1.81806 - 3.14898i) q^{79} +(1.21999 + 8.91693i) q^{81} +(-4.02998 + 6.98012i) q^{83} +(1.44383 + 2.50079i) q^{85} +(3.17787 + 3.86224i) q^{87} +9.26646 q^{89} +(2.88766 - 6.96124i) q^{91} +(-6.00000 + 0.998423i) q^{93} +(6.01422 - 3.47231i) q^{95} +(-16.2983 - 9.40980i) q^{97} +(-3.83228 - 11.1962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 16 * q - 2 * q^7 + 12 * q^9	$ 16 q - 2 q^{7} + 12 q^{9} + 12 q^{11} + 18 q^{21} + 48 q^{23} - 8 q^{25} - 12 q^{29} - 8 q^{37} + 36 q^{39} - 4 q^{43} - 8 q^{49} - 12 q^{51} + 48 q^{57} - 24 q^{63} + 84 q^{65} + 28 q^{67} + 78 q^{77} + 4 q^{79} + 36 q^{81} - 12 q^{85} - 24 q^{91} - 96 q^{93} - 12 q^{95} + 72 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 + 12 * q^9 + 12 * q^11 + 18 * q^21 + 48 * q^23 - 8 * q^25 - 12 * q^29 - 8 * q^37 + 36 * q^39 - 4 * q^43 - 8 * q^49 - 12 * q^51 + 48 * q^57 - 24 * q^63 + 84 * q^65 + 28 * q^67 + 78 * q^77 + 4 * q^79 + 36 * q^81 - 12 * q^85 - 24 * q^91 - 96 * q^93 - 12 * q^95 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.62181	−	0.608059i	−0.936352	−	0.351063i
$3$	−1.62181	−	0.608059i	−0.936352	−	0.351063i
$4$		0			0
$5$	−1.94556	−	3.36980i	−0.870080	−	1.50702i	−0.861913	−	0.507056i	$-0.830734\pi$
$5$	−1.94556	−	3.36980i	−0.870080	−	1.50702i	−0.00816625	−	0.999967i	$-0.502599\pi$
$6$		0			0
$7$	−2.09985	+	1.60954i	−0.793668	+	0.608351i
$7$	−2.09985	+	1.60954i	−0.793668	+	0.608351i
$8$		0			0
$9$	2.26053	+	1.97231i	0.753510	+	0.657437i
$10$		0			0
$11$	−3.41614	−	1.97231i	−1.03001	−	0.594674i	−0.113019	−	0.993593i	$-0.536052\pi$
$11$	−3.41614	−	1.97231i	−1.03001	−	0.594674i	−0.916986	+	0.398919i	$0.869385\pi$
$12$		0			0
$13$	−2.46687	+	1.42425i	−0.684186	+	0.395015i	−0.801430	−	0.598088i	$-0.795927\pi$
$13$	−2.46687	+	1.42425i	−0.684186	+	0.395015i	0.117244	+	0.993103i	$0.462594\pi$
$14$		0			0
$15$	1.10628	+	6.64819i	0.285641	+	1.71656i
$16$		0			0
$17$	−0.742117			−0.179990			−0.0899949	−	0.995942i	$-0.528685\pi$
$17$	−0.742117			−0.179990			−0.0899949	+	0.995942i	$0.528685\pi$
$18$		0			0
$19$			1.78474i			0.409447i	0.978820	+	0.204723i	$0.0656295\pi$
$19$			1.78474i			0.409447i	−0.978820	+	0.204723i	$0.934370\pi$
$20$		0			0
$21$	4.38425	−	1.33354i	0.956722	−	0.291003i
$22$		0			0
$23$	5.41535	−	3.12656i	1.12918	−	0.651932i	0.185451	−	0.982654i	$-0.440626\pi$
$23$	5.41535	−	3.12656i	1.12918	−	0.651932i	0.943728	+	0.330722i	$0.107292\pi$
$24$		0			0
$25$	−5.07039	+	8.78217i	−1.01408	+	1.75643i
$26$		0			0
$27$	−2.46687	−	4.57324i	−0.474749	−	0.880121i
$28$		0			0
$29$	−2.50079	−	1.44383i	−0.464385	−	0.268113i	0.249501	−	0.968374i	$-0.419733\pi$
$29$	−2.50079	−	1.44383i	−0.464385	−	0.268113i	−0.713886	+	0.700262i	$0.753067\pi$
$30$		0			0
$31$	3.04125	−	1.75587i	0.546225	−	0.315363i	−0.201373	−	0.979515i	$-0.564540\pi$
$31$	3.04125	−	1.75587i	0.546225	−	0.315363i	0.747598	+	0.664152i	$0.231207\pi$
$32$		0			0
$33$	4.34105	+	5.27592i	0.755680	+	0.918420i
$34$		0			0
$35$	9.50923	+	3.94462i	1.60735	+	0.666762i
$36$		0			0
$37$	3.00158			0.493456			0.246728	−	0.969085i	$-0.420645\pi$
$37$	3.00158			0.493456			0.246728	+	0.969085i	$0.420645\pi$
$38$		0			0
$39$	4.86681	−	0.809856i	0.779314	−	0.129681i
$40$		0			0
$41$	5.24705	+	9.08816i	0.819452	+	1.41933i	0.906087	+	0.423092i	$0.139055\pi$
$41$	5.24705	+	9.08816i	0.819452	+	1.41933i	−0.0866345	+	0.996240i	$0.527611\pi$
$42$		0			0
$43$	−0.471521	+	0.816699i	−0.0719063	+	0.124545i	−0.899737	−	0.436433i	$-0.856242\pi$
$43$	−0.471521	+	0.816699i	−0.0719063	+	0.124545i	0.827830	+	0.560978i	$0.189575\pi$
$44$		0			0
$45$	2.24831	−	11.4548i	0.335158	−	1.70758i
$46$		0			0
$47$	1.09263	−	1.89248i	0.159376	−	0.276047i	−0.775268	−	0.631633i	$-0.782385\pi$
$47$	1.09263	−	1.89248i	0.159376	−	0.276047i	0.934644	+	0.355585i	$0.115718\pi$
$48$		0			0
$49$	1.81873	−	6.75960i	0.259819	−	0.965657i
$50$		0			0
$51$	1.20357	+	0.451251i	0.168534	+	0.0631877i
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$			15.3490i			2.06965i
$56$		0			0
$57$	1.08523	−	2.89450i	0.143742	−	0.383386i
$58$		0			0
$59$	0.0105673	+	0.0183031i	0.00137575	+	0.00238286i	0.866712	−	0.498808i	$-0.166229\pi$
$59$	0.0105673	+	0.0183031i	0.00137575	+	0.00238286i	−0.865337	+	0.501191i	$0.832895\pi$
$60$		0			0
$61$	2.13832	+	1.23456i	0.273783	+	0.158069i	0.630606	−	0.776103i	$-0.282807\pi$
$61$	2.13832	+	1.23456i	0.273783	+	0.158069i	−0.356822	+	0.934172i	$0.616140\pi$
$62$		0			0
$63$	−7.92129	−	0.503130i	−0.997989	−	0.0633885i
$64$		0			0
$65$	9.59886	+	5.54191i	1.19059	+	0.687389i
$66$		0			0
$67$	6.72463	+	11.6474i	0.821544	+	1.42296i	0.904532	+	0.426406i	$0.140221\pi$
$67$	6.72463	+	11.6474i	0.821544	+	1.42296i	−0.0829874	+	0.996551i	$0.526446\pi$
$68$		0			0
$69$	−10.6838	+	1.77782i	−1.28618	+	0.214025i
$70$		0			0
$71$		−	1.94304i		−	0.230597i	−0.993331	−	0.115298i	$-0.963218\pi$
$71$		−	1.94304i		−	0.230597i	0.993331	−	0.115298i	$-0.0367824\pi$
$72$		0			0
$73$			4.85486i			0.568218i	0.958792	+	0.284109i	$0.0916978\pi$
$73$			4.85486i			0.568218i	−0.958792	+	0.284109i	$0.908302\pi$
$74$		0			0
$75$	13.5633	−	11.1599i	1.56615	−	1.28863i
$76$		0			0
$77$	10.3479	−	1.35688i	1.17925	−	0.154630i
$78$		0			0
$79$	1.81806	−	3.14898i	0.204548	−	0.354288i	−0.745440	−	0.666572i	$-0.767761\pi$
$79$	1.81806	−	3.14898i	0.204548	−	0.354288i	0.949989	+	0.312284i	$0.101094\pi$
$80$		0			0
$81$	1.21999	+	8.91693i	0.135554	+	0.990770i
$82$		0			0
$83$	−4.02998	+	6.98012i	−0.442347	+	0.766168i	−0.997863	−	0.0653378i	$-0.979188\pi$
$83$	−4.02998	+	6.98012i	−0.442347	+	0.766168i	0.555516	+	0.831506i	$0.312521\pi$
$84$		0			0
$85$	1.44383	+	2.50079i	0.156605	+	0.271249i
$86$		0			0
$87$	3.17787	+	3.86224i	0.340703	+	0.414076i
$88$		0			0
$89$	9.26646			0.982243			0.491122	−	0.871091i	$-0.336587\pi$
$89$	9.26646			0.982243			0.491122	+	0.871091i	$0.336587\pi$
$90$		0			0
$91$	2.88766	−	6.96124i	0.302709	−	0.729736i
$92$		0			0
$93$	−6.00000	+	0.998423i	−0.622171	+	0.103532i
$94$		0			0
$95$	6.01422	−	3.47231i	0.617046	−	0.356251i
$96$		0			0
$97$	−16.2983	−	9.40980i	−1.65484	−	0.955421i	−0.975043	−	0.222018i	$-0.928736\pi$
$97$	−16.2983	−	9.40980i	−1.65484	−	0.955421i	−0.679794	−	0.733403i	$-0.737931\pi$
$98$		0			0
$99$	−3.83228	−	11.1962i	−0.385159	−	1.12526i
$100$		0			0
$101$	−4.14079	+	7.17206i	−0.412024	+	0.713647i	−0.995111	−	0.0987631i	$-0.968511\pi$
$101$	−4.14079	+	7.17206i	−0.412024	+	0.713647i	0.583087	+	0.812410i	$0.301845\pi$
$102$		0			0
$103$	−14.7646	+	8.52435i	−1.45480	+	0.839929i	−0.998748	−	0.0500247i	$-0.984070\pi$
$103$	−14.7646	+	8.52435i	−1.45480	+	0.839929i	−0.456051	+	0.889953i	$0.650737\pi$
$104$		0			0
$105$	−13.0236	−	12.1796i	−1.27097	−	1.18861i
$106$		0			0
$107$			14.3369i			1.38600i	0.720936	+	0.693001i	$0.243712\pi$
$107$			14.3369i			1.38600i	−0.720936	+	0.693001i	$0.756288\pi$
$108$		0			0
$109$	11.2800			1.08042			0.540212	−	0.841529i	$-0.318344\pi$
$109$	11.2800			1.08042			0.540212	+	0.841529i	$0.318344\pi$
$110$		0			0
$111$	−4.86799	−	1.82513i	−0.462049	−	0.173234i
$112$		0			0
$113$	−8.51501	+	4.91614i	−0.801024	+	0.462472i	−0.843829	−	0.536612i	$-0.819704\pi$
$113$	−8.51501	+	4.91614i	−0.801024	+	0.462472i	0.0428049	+	0.999083i	$0.486371\pi$
$114$		0			0
$115$	−21.0718	−	12.1658i	−1.96495	−	1.13447i
$116$		0			0
$117$	−8.38548	−	1.64588i	−0.775238	−	0.152161i
$118$		0			0
$119$	1.55833	−	1.19447i	0.142852	−	0.109497i
$120$		0			0
$121$	2.28001	+	3.94910i	0.207274	+	0.359009i
$122$		0			0
$123$	−2.98358	−	17.9298i	−0.269021	−	1.61667i
$124$		0			0
$125$	20.0033			1.78915
$126$		0			0
$127$	−2.94462			−0.261293			−0.130646	−	0.991429i	$-0.541705\pi$
$127$	−2.94462			−0.261293			−0.130646	+	0.991429i	$0.541705\pi$
$128$		0			0
$129$	1.26132	−	1.03782i	0.111053	−	0.0913747i
$130$		0			0
$131$	7.53255	+	13.0468i	0.658122	+	1.13990i	0.981101	+	0.193495i	$0.0619823\pi$
$131$	7.53255	+	13.0468i	0.658122	+	1.13990i	−0.322979	+	0.946406i	$0.604684\pi$
$132$		0			0
$133$	−2.87261	−	3.74768i	−0.249087	−	0.324965i
$134$		0			0
$135$	−10.6115	+	17.2104i	−0.913293	+	1.48123i
$136$		0			0
$137$	−13.6139	−	7.85997i	−1.16311	−	0.671523i	−0.211064	−	0.977472i	$-0.567693\pi$
$137$	−13.6139	−	7.85997i	−1.16311	−	0.671523i	−0.952048	+	0.305950i	$0.901026\pi$
$138$		0			0
$139$	2.86373	−	1.65337i	0.242898	−	0.140237i	−0.373610	−	0.927586i	$-0.621880\pi$
$139$	2.86373	−	1.65337i	0.242898	−	0.140237i	0.616508	+	0.787349i	$0.288547\pi$
$140$		0			0
$141$	−2.92277	+	2.40487i	−0.246142	+	0.202526i
$142$		0			0
$143$	11.2362			0.939620
$144$		0			0
$145$			11.2362i			0.933118i
$146$		0			0
$147$	−7.05987	+	9.85689i	−0.582288	+	0.812982i
$148$		0			0
$149$	9.52765	−	5.50079i	0.780535	−	0.450642i	−0.0560848	−	0.998426i	$-0.517862\pi$
$149$	9.52765	−	5.50079i	0.780535	−	0.450642i	0.836620	+	0.547784i	$0.184528\pi$
$150$		0			0
$151$	−0.719988	+	1.24706i	−0.0585918	+	0.101484i	−0.893834	−	0.448399i	$-0.851994\pi$
$151$	−0.719988	+	1.24706i	−0.0585918	+	0.101484i	0.835242	+	0.549883i	$0.185328\pi$
$152$		0			0
$153$	−1.67758	−	1.46368i	−0.135624	−	0.118332i
$154$		0			0
$155$	−11.8339	−	6.83228i	−0.950518	−	0.548782i
$156$		0			0
$157$	−14.3822	+	8.30354i	−1.14782	+	0.662695i	−0.948355	−	0.317210i	$-0.897254\pi$
$157$	−14.3822	+	8.30354i	−1.14782	+	0.662695i	−0.199465	+	0.979905i	$0.563921\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.33909	+	15.2815i	−0.499591	+	1.20435i
$162$		0			0
$163$	12.3955			0.970887			0.485444	−	0.874268i	$-0.338658\pi$
$163$	12.3955			0.970887			0.485444	+	0.874268i	$0.338658\pi$
$164$		0			0
$165$	9.33307	−	24.8931i	0.726579	−	1.93792i
$166$		0			0
$167$	−5.86087	−	10.1513i	−0.453528	−	0.785534i	0.545074	−	0.838388i	$-0.316502\pi$
$167$	−5.86087	−	10.1513i	−0.453528	−	0.785534i	−0.998602	+	0.0528541i	$0.983168\pi$
$168$		0			0
$169$	−2.44304	+	4.23147i	−0.187926	+	0.325498i
$170$		0			0
$171$	−3.52006	+	4.03445i	−0.269185	+	0.308522i
$172$		0			0
$173$	8.38548	−	14.5241i	0.637536	−	1.10425i	−0.348435	−	0.937333i	$-0.613287\pi$
$173$	8.38548	−	14.5241i	0.637536	−	1.10425i	0.985972	−	0.166913i	$-0.0533798\pi$
$174$		0			0
$175$	−3.48824	−	26.6022i	−0.263686	−	2.01094i
$176$		0			0
$177$	−0.00600879	−	0.0361097i	−0.000451648	−	0.00271417i
$178$		0			0
$179$		−	5.77532i		−	0.431668i	−0.976430	−	0.215834i	$-0.930753\pi$
$179$		−	5.77532i		−	0.431668i	0.976430	−	0.215834i	$-0.0692470\pi$
$180$		0			0
$181$			5.53310i			0.411272i	0.978629	+	0.205636i	$0.0659263\pi$
$181$			5.53310i			0.411272i	−0.978629	+	0.205636i	$0.934074\pi$
$182$		0			0
$183$	−2.71726	−	3.30244i	−0.200865	−	0.244123i
$184$		0			0
$185$	−5.83974	−	10.1147i	−0.429346	−	0.743649i
$186$		0			0
$187$	2.53518	+	1.46368i	0.185390	+	0.107035i
$188$		0			0
$189$	12.5409	+	5.63259i	0.912216	+	0.409711i
$190$		0			0
$191$	5.38124	+	3.10686i	0.389373	+	0.224805i	0.681888	−	0.731456i	$-0.261159\pi$
$191$	5.38124	+	3.10686i	0.389373	+	0.224805i	−0.292515	+	0.956261i	$0.594492\pi$
$192$		0			0
$193$	3.90271	+	6.75970i	0.280923	+	0.486574i	0.971612	−	0.236578i	$-0.0760260\pi$
$193$	3.90271	+	6.75970i	0.280923	+	0.486574i	−0.690689	+	0.723152i	$0.742693\pi$
$194$		0			0
$195$	−12.1977	−	14.8246i	−0.873497	−	1.06161i
$196$		0			0
$197$		−	12.7737i		−	0.910092i	−0.890468	−	0.455046i	$-0.849623\pi$
$197$		−	12.7737i		−	0.910092i	0.890468	−	0.455046i	$-0.150377\pi$
$198$		0			0
$199$		−	1.81201i		−	0.128450i	−0.997935	−	0.0642250i	$-0.979542\pi$
$199$		−	1.81201i		−	0.128450i	0.997935	−	0.0642250i	$-0.0204575\pi$
$200$		0			0
$201$	−3.82377	−	22.9788i	−0.269708	−	1.62080i
$202$		0			0
$203$	7.57519	−	0.993303i	0.531674	−	0.0697162i
$204$		0			0
$205$	20.4169	−	35.3631i	1.42598	−	2.46986i
$206$		0			0
$207$	18.4081	+	3.61308i	1.27945	+	0.251127i
$208$		0			0
$209$	3.52006	−	6.09692i	0.243487	−	0.421732i
$210$		0			0
$211$	1.88766	+	3.26953i	0.129952	+	0.225083i	0.923658	−	0.383218i	$-0.125184\pi$
$211$	1.88766	+	3.26953i	0.129952	+	0.225083i	−0.793706	+	0.608302i	$0.791851\pi$
$212$		0			0
$213$	−1.18148	+	3.15124i	−0.0809539	+	0.215920i
$214$		0			0
$215$	3.66949			0.250257
$216$		0			0
$217$	−3.56002	+	8.58209i	−0.241670	+	0.582590i
$218$		0			0
$219$	2.95204	−	7.87366i	0.199480	−	0.532052i
$220$		0			0
$221$	1.83070	−	1.05696i	0.123146	−	0.0710987i
$222$		0			0
$223$	11.0662	+	6.38910i	0.741051	+	0.427846i	0.822451	−	0.568836i	$-0.192606\pi$
$223$	11.0662	+	6.38910i	0.741051	+	0.427846i	−0.0814006	+	0.996681i	$0.525939\pi$
$224$		0			0
$225$	−28.7829	+	9.85197i	−1.91886	+	0.656798i
$226$		0			0
$227$	−9.99110	+	17.3051i	−0.663133	+	1.14858i	0.316655	+	0.948541i	$0.397440\pi$
$227$	−9.99110	+	17.3051i	−0.663133	+	1.14858i	−0.979788	+	0.200039i	$0.935893\pi$
$228$		0			0
$229$	−8.77402	+	5.06568i	−0.579804	+	0.334750i	−0.761055	−	0.648687i	$-0.775318\pi$
$229$	−8.77402	+	5.06568i	−0.579804	+	0.334750i	0.181252	+	0.983437i	$0.441985\pi$
$230$		0			0
$231$	−17.6074	−	4.09153i	−1.15848	−	0.269203i
$232$		0			0
$233$		−	7.31007i		−	0.478898i	−0.970909	−	0.239449i	$-0.923033\pi$
$233$		−	7.31007i		−	0.478898i	0.970909	−	0.239449i	$-0.0769669\pi$
$234$		0			0
$235$	−8.50307			−0.554679
$236$		0			0
$237$	−4.86332	+	4.00156i	−0.315906	+	0.259929i
$238$		0			0
$239$	−7.28317	+	4.20494i	−0.471109	+	0.271995i	−0.716704	−	0.697378i	$-0.754350\pi$
$239$	−7.28317	+	4.20494i	−0.471109	+	0.271995i	0.245595	+	0.969373i	$0.421017\pi$
$240$		0			0
$241$	7.75277	+	4.47607i	0.499400	+	0.288329i	0.728466	−	0.685082i	$-0.240234\pi$
$241$	7.75277	+	4.47607i	0.499400	+	0.288329i	−0.229066	+	0.973411i	$0.573567\pi$
$242$		0			0
$243$	3.44343	−	15.2034i	0.220896	−	0.975297i
$244$		0			0
$245$	−26.3170	+	7.02242i	−1.68133	+	0.448646i
$246$		0			0
$247$	−2.54191	−	4.40271i	−0.161738	−	0.280138i
$248$		0			0
$249$	10.7802	−	8.86997i	0.683166	−	0.562111i
$250$		0			0
$251$	12.6432			0.798033			0.399017	−	0.916944i	$-0.369352\pi$
$251$	12.6432			0.798033			0.399017	+	0.916944i	$0.369352\pi$
$252$		0			0
$253$	−24.6661			−1.55075
$254$		0			0
$255$	−0.820992	−	4.93374i	−0.0514125	−	0.308962i
$256$		0			0
$257$	8.15329	+	14.1219i	0.508588	+	0.880900i	0.999951	+	0.00994523i	$0.00316572\pi$
$257$	8.15329	+	14.1219i	0.508588	+	0.880900i	−0.491362	+	0.870955i	$0.663501\pi$
$258$		0			0
$259$	−6.30286	+	4.83117i	−0.391641	+	0.300194i
$260$		0			0
$261$	−2.80542	−	8.19615i	−0.173651	−	0.507329i
$262$		0			0
$263$	−20.5434	−	11.8608i	−1.26676	−	0.731366i	−0.292389	−	0.956300i	$-0.594450\pi$
$263$	−20.5434	−	11.8608i	−1.26676	−	0.731366i	−0.974374	+	0.224934i	$0.927783\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−15.0284	−	5.63455i	−0.919725	−	0.344829i
$268$		0			0
$269$	−7.28288			−0.444045			−0.222022	−	0.975042i	$-0.571266\pi$
$269$	−7.28288			−0.444045			−0.222022	+	0.975042i	$0.571266\pi$
$270$		0			0
$271$		−	22.6879i		−	1.37819i	−0.724669	−	0.689097i	$-0.758007\pi$
$271$		−	22.6879i		−	1.37819i	0.724669	−	0.689097i	$-0.241993\pi$
$272$		0			0
$273$	−8.91608	+	9.53393i	−0.539625	+	0.577020i
$274$		0			0
$275$	34.6423	−	20.0007i	2.08901	−	1.20609i
$276$		0			0
$277$	−12.0838	+	20.9298i	−0.726046	+	1.25755i	0.232496	+	0.972597i	$0.425311\pi$
$277$	−12.0838	+	20.9298i	−0.726046	+	1.25755i	−0.958542	+	0.284951i	$0.908023\pi$
$278$		0			0
$279$	10.3380	+	2.02910i	0.618917	+	0.121479i
$280$		0			0
$281$	−4.11229	−	2.37423i	−0.245319	−	0.141635i	0.372300	−	0.928112i	$-0.378569\pi$
$281$	−4.11229	−	2.37423i	−0.245319	−	0.141635i	−0.617619	+	0.786478i	$0.711903\pi$
$282$		0			0
$283$	−25.4484	+	14.6926i	−1.51275	+	0.873387i	−0.512861	+	0.858471i	$0.671415\pi$
$283$	−25.4484	+	14.6926i	−1.51275	+	0.873387i	−0.999889	+	0.0149153i	$0.995252\pi$
$284$		0			0
$285$	−11.8653	+	1.97443i	−0.702838	+	0.116955i
$286$		0			0
$287$	−25.6458	−	10.6384i	−1.51382	−	0.627965i
$288$		0			0
$289$	−16.4493			−0.967604
$290$		0			0
$291$	20.7109	+	25.1712i	1.21410	+	1.47556i
$292$		0			0
$293$	−3.31206	−	5.73666i	−0.193493	−	0.335139i	0.752913	−	0.658121i	$-0.228648\pi$
$293$	−3.31206	−	5.73666i	−0.193493	−	0.335139i	−0.946405	+	0.322981i	$0.895315\pi$
$294$		0			0
$295$	0.0411186	−	0.0712195i	0.00239402	−	0.00414656i
$296$		0			0
$297$	−0.592687	+	20.4883i	−0.0343912	+	1.18885i
$298$		0			0
$299$	−8.90597	+	15.4256i	−0.515046	+	0.892085i
$300$		0			0
$301$	−0.324389	−	2.47388i	−0.0186975	−	0.142592i
$302$		0			0
$303$	11.0766	−	9.11387i	0.636334	−	0.523578i
$304$		0			0
$305$		−	9.60761i		−	0.550130i
$306$		0			0
$307$			21.7242i			1.23987i	0.784655	+	0.619933i	$0.212840\pi$
$307$			21.7242i			1.23987i	−0.784655	+	0.619933i	$0.787160\pi$
$308$		0			0
$309$	29.1287	−	4.84712i	1.65707	−	0.275743i
$310$		0			0
$311$	3.14900	+	5.45422i	0.178563	+	0.309281i	0.941389	−	0.337324i	$-0.109522\pi$
$311$	3.14900	+	5.45422i	0.178563	+	0.309281i	−0.762825	+	0.646605i	$0.776188\pi$
$312$		0			0
$313$	19.2423	+	11.1095i	1.08764	+	0.627948i	0.932946	−	0.360015i	$-0.117229\pi$
$313$	19.2423	+	11.1095i	1.08764	+	0.627948i	0.154691	+	0.987963i	$0.450562\pi$
$314$		0			0
$315$	13.7159	+	27.6721i	0.772802	+	1.55914i
$316$		0			0
$317$	13.5632	+	7.83070i	0.761784	+	0.439816i	0.829936	−	0.557859i	$-0.188377\pi$
$317$	13.5632	+	7.83070i	0.761784	+	0.439816i	−0.0681519	+	0.997675i	$0.521710\pi$
$318$		0			0
$319$	5.69536	+	9.86466i	0.318879	+	0.552315i
$320$		0			0
$321$	8.71769	−	23.2518i	0.486574	−	1.29779i
$322$		0			0
$323$		−	1.32448i		−	0.0736963i
$324$		0			0
$325$		−	28.8859i		−	1.60230i
$326$		0			0
$327$	−18.2940	−	6.85888i	−1.01166	−	0.379297i
$328$		0			0
$329$	0.751687	+	5.73256i	0.0414418	+	0.316046i
$330$		0			0
$331$	0.636129	−	1.10181i	0.0349648	−	0.0605608i	−0.848013	−	0.529975i	$-0.822201\pi$
$331$	0.636129	−	1.10181i	0.0349648	−	0.0605608i	0.882978	+	0.469414i	$0.155535\pi$
$332$		0			0
$333$	6.78515	+	5.92004i	0.371824	+	0.324416i
$334$		0			0
$335$	26.1663	−	45.3214i	1.42962	−	2.47617i
$336$		0			0
$337$	−3.78001	−	6.54717i	−0.205910	−	0.356647i	0.744512	−	0.667609i	$-0.232682\pi$
$337$	−3.78001	−	6.54717i	−0.205910	−	0.356647i	−0.950422	+	0.310962i	$0.899349\pi$
$338$		0			0
$339$	16.7990	−	2.79542i	0.912397	−	0.151826i
$340$		0			0
$341$	−13.8525			−0.750153
$342$		0			0
$343$	7.06081	+	17.1215i	0.381248	+	0.924473i
$344$		0			0
$345$	26.7769	+	32.5434i	1.44162	+	1.75208i
$346$		0			0
$347$	−19.1470	+	11.0545i	−1.02787	+	0.593439i	−0.916373	−	0.400326i	$-0.868897\pi$
$347$	−19.1470	+	11.0545i	−1.02787	+	0.593439i	−0.111494	+	0.993765i	$0.535564\pi$
$348$		0			0
$349$	12.7682	+	7.37173i	0.683467	+	0.394600i	0.801160	−	0.598450i	$-0.204217\pi$
$349$	12.7682	+	7.37173i	0.683467	+	0.394600i	−0.117693	+	0.993050i	$0.537550\pi$
$350$		0			0
$351$	12.5989	+	7.76816i	0.672478	+	0.414634i
$352$		0			0
$353$	−8.63881	+	14.9629i	−0.459798	+	0.796393i	−0.998950	−	0.0458154i	$-0.985411\pi$
$353$	−8.63881	+	14.9629i	−0.459798	+	0.796393i	0.539152	+	0.842208i	$0.318745\pi$
$354$		0			0
$355$	−6.54767	+	3.78030i	−0.347514	+	0.200638i
$356$		0			0
$357$	−3.25363	+	0.989644i	−0.172200	+	0.0523775i
$358$		0			0
$359$			10.9129i			0.575963i	0.957636	+	0.287982i	$0.0929842\pi$
$359$			10.9129i			0.575963i	−0.957636	+	0.287982i	$0.907016\pi$
$360$		0			0
$361$	15.8147			0.832353
$362$		0			0
$363$	−1.29646	−	7.79106i	−0.0680466	−	0.408925i
$364$		0			0
$365$	16.3599	−	9.44541i	0.856318	−	0.494395i
$366$		0			0
$367$	30.9407	+	17.8636i	1.61509	+	0.932472i	0.988166	+	0.153391i	$0.0490194\pi$
$367$	30.9407	+	17.8636i	1.61509	+	0.932472i	0.626923	+	0.779081i	$0.284314\pi$
$368$		0			0
$369$	−6.06355	+	30.8929i	−0.315656	+	1.60822i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	16.0300	+	27.7648i	0.830003	+	1.43761i	0.898035	+	0.439923i	$0.144994\pi$
$373$	16.0300	+	27.7648i	0.830003	+	1.43761i	−0.0680328	+	0.997683i	$0.521672\pi$
$374$		0			0
$375$	−32.4416	−	12.1632i	−1.67528	−	0.628105i
$376$		0			0
$377$	8.22549			0.423634
$378$		0			0
$379$	−34.8891			−1.79214			−0.896068	−	0.443918i	$-0.853588\pi$
$379$	−34.8891			−1.79214			−0.896068	+	0.443918i	$0.853588\pi$
$380$		0			0
$381$	4.77561	+	1.79050i	0.244662	+	0.0917301i
$382$		0			0
$383$	−8.76711	−	15.1851i	−0.447978	−	0.775921i	0.550276	−	0.834983i	$-0.314523\pi$
$383$	−8.76711	−	15.1851i	−0.447978	−	0.775921i	−0.998254	+	0.0590616i	$0.981189\pi$
$384$		0			0
$385$	−24.7048	−	32.2305i	−1.25908	−	1.64262i
$386$		0			0
$387$	−2.67667	+	0.916186i	−0.136063	+	0.0465723i
$388$		0			0
$389$	−6.60060	−	3.81086i	−0.334664	−	0.193218i	0.323246	−	0.946315i	$-0.395226\pi$
$389$	−6.60060	−	3.81086i	−0.334664	−	0.193218i	−0.657910	+	0.753097i	$0.728559\pi$
$390$		0			0
$391$	−4.01882	+	2.32027i	−0.203241	+	0.117341i
$392$		0			0
$393$	−4.28317	−	25.7396i	−0.216057	−	1.29839i
$394$		0			0
$395$	−14.1486			−0.711893
$396$		0			0
$397$		−	37.6469i		−	1.88944i	−0.327873	−	0.944722i	$-0.606332\pi$
$397$		−	37.6469i		−	1.88944i	0.327873	−	0.944722i	$-0.393668\pi$
$398$		0			0
$399$	2.38002	+	7.82474i	0.119150	+	0.391727i
$400$		0			0
$401$	18.5689	−	10.7207i	0.927284	−	0.535368i	0.0413326	−	0.999145i	$-0.486840\pi$
$401$	18.5689	−	10.7207i	0.927284	−	0.535368i	0.885952	+	0.463778i	$0.153506\pi$
$402$		0			0
$403$	−5.00158	+	8.66299i	−0.249146	+	0.431534i
$404$		0			0
$405$	27.6747	−	21.4595i	1.37517	−	1.06633i
$406$		0			0
$407$	−10.2538	−	5.92004i	−0.508262	−	0.293445i
$408$		0			0
$409$	25.6086	−	14.7851i	1.26627	−	0.731079i	0.291986	−	0.956423i	$-0.405684\pi$
$409$	25.6086	−	14.7851i	1.26627	−	0.731079i	0.974279	+	0.225344i	$0.0723506\pi$
$410$		0			0
$411$	17.2998	+	21.0254i	0.853335	+	1.03711i
$412$		0			0
$413$	−0.0516494	−	0.0214252i	−0.00254150	−	0.00105427i
$414$		0			0
$415$	31.3622			1.53951
$416$		0			0
$417$	−5.64977	+	0.940143i	−0.276670	+	0.0460390i
$418$		0			0
$419$	3.56481	+	6.17443i	0.174152	+	0.301641i	0.939868	−	0.341539i	$-0.110948\pi$
$419$	3.56481	+	6.17443i	0.174152	+	0.301641i	−0.765715	+	0.643180i	$0.777615\pi$
$420$		0			0
$421$	−2.31007	+	4.00115i	−0.112586	+	0.195004i	−0.916812	−	0.399319i	$-0.869247\pi$
$421$	−2.31007	+	4.00115i	−0.112586	+	0.195004i	0.804226	+	0.594323i	$0.202580\pi$
$422$		0			0
$423$	6.20248	−	2.12302i	0.301575	−	0.103225i
$424$		0			0
$425$	3.76282	−	6.51739i	0.182524	−	0.316140i
$426$		0			0
$427$	−6.47721	+	0.849330i	−0.313454	+	0.0411020i
$428$		0			0
$429$	−18.2230	−	6.83228i	−0.879815	−	0.329866i
$430$		0			0
$431$		−	4.00771i		−	0.193045i	−0.995331	−	0.0965223i	$-0.969228\pi$
$431$		−	4.00771i		−	0.193045i	0.995331	−	0.0965223i	$-0.0307719\pi$
$432$		0			0
$433$			29.4125i			1.41348i	0.707475	+	0.706738i	$0.249834\pi$
$433$			29.4125i			1.41348i	−0.707475	+	0.706738i	$0.750166\pi$
$434$		0			0
$435$	6.83228	−	18.2230i	0.327583	−	0.873726i
$436$		0			0
$437$	5.58008	+	9.66498i	0.266931	+	0.462339i
$438$		0			0
$439$	18.5130	+	10.6885i	0.883575	+	0.510133i	0.871836	−	0.489799i	$-0.162930\pi$
$439$	18.5130	+	10.6885i	0.883575	+	0.510133i	0.0117398	+	0.999931i	$0.496263\pi$
$440$		0			0
$441$	17.4433	−	11.6932i	0.830635	−	0.556818i
$442$		0			0
$443$	−5.05227	−	2.91693i	−0.240041	−	0.138587i	0.375155	−	0.926962i	$-0.377590\pi$
$443$	−5.05227	−	2.91693i	−0.240041	−	0.138587i	−0.615195	+	0.788375i	$0.710923\pi$
$444$		0			0
$445$	−18.0284	−	31.2262i	−0.854630	−	1.48026i
$446$		0			0
$447$	−18.7968	+	3.12786i	−0.889059	+	0.147943i
$448$		0			0
$449$			22.5823i			1.06573i	0.846202	+	0.532863i	$0.178884\pi$
$449$			22.5823i			1.06573i	−0.846202	+	0.532863i	$0.821116\pi$
$450$		0			0
$451$		−	41.3953i		−	1.94923i
$452$		0			0
$453$	1.92597	−	1.58469i	0.0904898	−	0.0744553i
$454$		0			0
$455$	−29.0761	+	3.81263i	−1.36311	+	0.178739i
$456$		0			0
$457$	−19.9311	+	34.5218i	−0.932340	+	1.61486i	−0.153029	+	0.988222i	$0.548903\pi$
$457$	−19.9311	+	34.5218i	−0.932340	+	1.61486i	−0.779310	+	0.626638i	$0.784430\pi$
$458$		0			0
$459$	1.83070	+	3.39388i	0.0854500	+	0.158413i
$460$		0			0
$461$	−3.68254	+	6.37834i	−0.171513	+	0.297069i	−0.938949	−	0.344056i	$-0.888199\pi$
$461$	−3.68254	+	6.37834i	−0.171513	+	0.297069i	0.767436	+	0.641125i	$0.221532\pi$
$462$		0			0
$463$	14.3457	+	24.8475i	0.666702	+	1.15476i	0.978821	+	0.204718i	$0.0656278\pi$
$463$	14.3457	+	24.8475i	0.666702	+	1.15476i	−0.312119	+	0.950043i	$0.601039\pi$
$464$		0			0
$465$	15.0378	+	18.2763i	0.697363	+	0.847545i
$466$		0			0
$467$	13.6704			0.632590			0.316295	−	0.948661i	$-0.397561\pi$
$467$	13.6704			0.632590			0.316295	+	0.948661i	$0.397561\pi$
$468$		0			0
$469$	−32.8677	−	13.6342i	−1.51769	−	0.629569i
$470$		0			0
$471$	28.3741	−	4.72157i	1.30741	−	0.217558i
$472$		0			0
$473$	3.22157	−	1.85997i	0.148128	−	0.0855216i
$474$		0			0
$475$	−15.6739	−	9.04931i	−0.719166	−	0.415211i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.20537	+	9.01596i	−0.237839	+	0.411950i	−0.960094	−	0.279677i	$-0.909773\pi$
$479$	−5.20537	+	9.01596i	−0.237839	+	0.411950i	0.722255	+	0.691627i	$0.243106\pi$
$480$		0			0
$481$	−7.40449	+	4.27499i	−0.337616	+	0.194923i
$482$		0			0
$483$	19.5729	−	20.9292i	0.890597	−	0.952312i
$484$		0			0
$485$			73.2292i			3.32517i
$486$		0			0
$487$	−2.33850			−0.105968			−0.0529838	−	0.998595i	$-0.516873\pi$
$487$	−2.33850			−0.105968			−0.0529838	+	0.998595i	$0.516873\pi$
$488$		0			0
$489$	−20.1031	−	7.53716i	−0.909092	−	0.340842i
$490$		0			0
$491$	29.3448	−	16.9422i	1.32431	−	0.764591i	0.339898	−	0.940462i	$-0.389608\pi$
$491$	29.3448	−	16.9422i	1.32431	−	0.764591i	0.984413	+	0.175871i	$0.0562742\pi$
$492$		0			0
$493$	1.85588	+	1.07149i	0.0835845	+	0.0482575i
$494$		0			0
$495$	−30.2729	+	34.6968i	−1.36067	+	1.55950i
$496$		0			0
$497$	3.12741	+	4.08010i	0.140284	+	0.183017i
$498$		0			0
$499$	−8.30223	−	14.3799i	−0.371659	−	0.643732i	0.618162	−	0.786051i	$-0.287877\pi$
$499$	−8.30223	−	14.3799i	−0.371659	−	0.643732i	−0.989821	+	0.142319i	$0.954544\pi$
$500$		0			0
$501$	3.33262	+	20.0273i	0.148890	+	0.894753i
$502$		0			0
$503$	35.3661			1.57690			0.788449	−	0.615100i	$-0.210885\pi$
$503$	35.3661			1.57690			0.788449	+	0.615100i	$0.210885\pi$
$504$		0			0
$505$	32.2246			1.43398
$506$		0			0
$507$	6.53513	−	5.37713i	0.290235	−	0.238807i
$508$		0			0
$509$	−18.5291	−	32.0933i	−0.821287	−	1.42251i	−0.904724	−	0.425998i	$-0.859923\pi$
$509$	−18.5291	−	32.0933i	−0.821287	−	1.42251i	0.0834371	−	0.996513i	$-0.473410\pi$
$510$		0			0
$511$	−7.81411	−	10.1945i	−0.345676	−	0.450977i
$512$		0			0
$513$	8.16204	−	4.40271i	0.360363	−	0.194384i
$514$		0			0
$515$	57.4507	+	33.1692i	2.53158	+	1.46161i
$516$		0			0
$517$	−7.46513	+	4.30999i	−0.328316	+	0.189553i
$518$		0			0
$519$	−22.4311	+	18.4564i	−0.984618	+	0.810147i
$520$		0			0
$521$	1.78309			0.0781187			0.0390594	−	0.999237i	$-0.487564\pi$
$521$	1.78309			0.0781187			0.0390594	+	0.999237i	$0.487564\pi$
$522$		0			0
$523$		−	24.0538i		−	1.05180i	−0.850546	−	0.525901i	$-0.823728\pi$
$523$		−	24.0538i		−	1.05180i	0.850546	−	0.525901i	$-0.176272\pi$
$524$		0			0
$525$	−10.5185	+	45.2648i	−0.459063	+	1.97552i
$526$		0			0
$527$	−2.25696	+	1.30306i	−0.0983149	+	0.0567621i
$528$		0			0
$529$	8.05069	−	13.9442i	0.350030	−	0.606270i
$530$		0			0
$531$	−0.0122117	+	0.0622167i	−0.000529942	+	0.00269998i
$532$		0			0
$533$	−25.8876	−	14.9462i	−1.12132	−	0.647392i
$534$		0			0
$535$	48.3126	−	27.8933i	2.08874	−	1.20593i
$536$		0			0
$537$	−3.51174	+	9.36647i	−0.151543	+	0.404193i
$538$		0			0
$539$	−19.5451	+	19.5046i	−0.841866	+	0.840124i
$540$		0			0
$541$	30.0032			1.28994			0.644968	−	0.764209i	$-0.276871\pi$
$541$	30.0032			1.28994			0.644968	+	0.764209i	$0.276871\pi$
$542$		0			0
$543$	3.36445	−	8.97363i	0.144382	−	0.385095i
$544$		0			0
$545$	−21.9458	−	38.0113i	−0.940056	−	1.62822i
$546$		0			0
$547$	10.7816	−	18.6743i	0.460987	−	0.798454i	−0.538023	−	0.842930i	$-0.680829\pi$
$547$	10.7816	−	18.6743i	0.460987	−	0.798454i	0.999010	+	0.0444765i	$0.0141620\pi$
$548$		0			0
$549$	2.39880	+	7.00817i	0.102378	+	0.299102i
$550$		0			0
$551$	2.57686	−	4.46325i	0.109778	−	0.190141i
$552$		0			0
$553$	1.25076	+	9.53864i	0.0531878	+	0.405624i
$554$		0			0
$555$	3.32060	+	19.9551i	0.140952	+	0.847045i
$556$		0			0
$557$			36.9477i			1.56552i	0.622321	+	0.782762i	$0.286190\pi$
$557$			36.9477i			1.56552i	−0.622321	+	0.782762i	$0.713810\pi$
$558$		0			0
$559$		−	2.68625i		−	0.113616i
$560$		0			0
$561$	−3.22157	−	3.91535i	−0.136015	−	0.165306i
$562$		0			0
$563$	−7.58422	−	13.1363i	−0.319637	−	0.553627i	0.660776	−	0.750584i	$-0.270228\pi$
$563$	−7.58422	−	13.1363i	−0.319637	−	0.553627i	−0.980412	+	0.196957i	$0.936894\pi$
$564$		0			0
$565$	33.1329	+	19.1293i	1.39391	+	0.804774i
$566$		0			0
$567$	−16.9140	−	16.7606i	−0.710321	−	0.703878i
$568$		0			0
$569$	−31.8084	−	18.3646i	−1.33348	−	0.769885i	−0.347648	−	0.937625i	$-0.613020\pi$
$569$	−31.8084	−	18.3646i	−1.33348	−	0.769885i	−0.985831	+	0.167740i	$0.946353\pi$
$570$		0			0
$571$	5.61387	+	9.72351i	0.234933	+	0.406916i	0.959253	−	0.282548i	$-0.0911795\pi$
$571$	5.61387	+	9.72351i	0.234933	+	0.406916i	−0.724320	+	0.689464i	$0.757846\pi$
$572$		0			0
$573$	−6.83819	−	8.31085i	−0.285670	−	0.347191i
$574$		0			0
$575$			63.4114i			2.64444i
$576$		0			0
$577$		−	36.5515i		−	1.52166i	−0.648952	−	0.760829i	$-0.724792\pi$
$577$		−	36.5515i		−	1.52166i	0.648952	−	0.760829i	$-0.275208\pi$
$578$		0			0
$579$	−2.21916	−	13.3360i	−0.0922253	−	0.554226i
$580$		0			0
$581$	−2.77248	−	21.1436i	−0.115022	−	0.877186i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	10.7682	+	31.4596i	0.445209	+	1.30069i
$586$		0			0
$587$	−4.99738	+	8.65571i	−0.206264	+	0.357259i	−0.950535	−	0.310619i	$-0.899464\pi$
$587$	−4.99738	+	8.65571i	−0.206264	+	0.357259i	0.744271	+	0.667878i	$0.232797\pi$
$588$		0			0
$589$	3.13376	+	5.42784i	0.129124	+	0.223650i
$590$		0			0
$591$	−7.76719	+	20.7166i	−0.319499	+	0.852166i
$592$		0			0
$593$	7.78223			0.319578			0.159789	−	0.987151i	$-0.448919\pi$
$593$	7.78223			0.319578			0.159789	+	0.987151i	$0.448919\pi$
$594$		0			0
$595$	−7.05696	−	2.92737i	−0.289307	−	0.120010i
$596$		0			0
$597$	−1.10181	+	2.93873i	−0.0450940	+	0.120274i
$598$		0			0
$599$	−21.6614	+	12.5062i	−0.885061	+	0.510990i	−0.872324	−	0.488929i	$-0.837388\pi$
$599$	−21.6614	+	12.5062i	−0.885061	+	0.510990i	−0.0127373	+	0.999919i	$0.504055\pi$
$600$		0			0
$601$	25.9925	+	15.0068i	1.06026	+	0.612139i	0.925503	−	0.378740i	$-0.123643\pi$
$601$	25.9925	+	15.0068i	1.06026	+	0.612139i	0.134753	+	0.990879i	$0.456976\pi$
$602$		0			0
$603$	−7.77106	+	39.5924i	−0.316462	+	1.61233i
$604$		0			0
$605$	8.87179	−	15.3664i	0.360689	−	0.624732i
$606$		0			0
$607$	−3.96882	+	2.29140i	−0.161089	+	0.0930050i	−0.578378	−	0.815769i	$-0.696314\pi$
$607$	−3.96882	+	2.29140i	−0.161089	+	0.0930050i	0.417288	+	0.908774i	$0.362981\pi$
$608$		0			0
$609$	−12.8895	−	2.99521i	−0.522309	−	0.121372i
$610$		0			0
$611$			6.22468i			0.251823i
$612$		0			0
$613$	30.5522			1.23399			0.616996	−	0.786966i	$-0.288349\pi$
$613$	30.5522			1.23399			0.616996	+	0.786966i	$0.288349\pi$
$614$		0			0
$615$	−54.6151	+	44.9375i	−2.20229	+	1.81206i
$616$		0			0
$617$	−28.2484	+	16.3092i	−1.13724	+	0.656585i	−0.945745	−	0.324909i	$-0.894666\pi$
$617$	−28.2484	+	16.3092i	−1.13724	+	0.656585i	−0.191493	+	0.981494i	$0.561333\pi$
$618$		0			0
$619$	17.3244	+	10.0023i	0.696327	+	0.402024i	0.805978	−	0.591946i	$-0.201640\pi$
$619$	17.3244	+	10.0023i	0.696327	+	0.402024i	−0.109651	+	0.993970i	$0.534973\pi$
$620$		0			0
$621$	−27.6575	−	17.0529i	−1.10986	−	0.684311i
$622$		0			0
$623$	−19.4582	+	14.9148i	−0.779575	+	0.597548i
$624$		0			0
$625$	−13.5657	−	23.4965i	−0.542628	−	0.939859i
$626$		0			0
$627$	−9.41614	+	7.74763i	−0.376044	+	0.309411i
$628$		0			0
$629$	−2.22752			−0.0888171
$630$		0			0
$631$	−6.09634			−0.242692			−0.121346	−	0.992610i	$-0.538721\pi$
$631$	−6.09634			−0.242692			−0.121346	+	0.992610i	$0.538721\pi$
$632$		0			0
$633$	−1.07336	−	6.45036i	−0.0426624	−	0.256379i
$634$		0			0
$635$	5.72893	+	9.92279i	0.227345	+	0.393774i
$636$		0			0
$637$	5.14076	+	19.2654i	0.203685	+	0.763322i
$638$		0			0
$639$	3.83228	−	4.39230i	0.151603	−	0.173757i
$640$		0			0
$641$	28.9612	+	16.7207i	1.14390	+	0.660429i	0.947393	−	0.320074i	$-0.103708\pi$
$641$	28.9612	+	16.7207i	1.14390	+	0.660429i	0.196504	+	0.980503i	$0.437041\pi$
$642$		0			0
$643$	16.6022	−	9.58527i	0.654726	−	0.378006i	−0.135539	−	0.990772i	$-0.543276\pi$
$643$	16.6022	−	9.58527i	0.654726	−	0.378006i	0.790264	+	0.612766i	$0.209943\pi$
$644$		0			0
$645$	−5.95121	−	2.23126i	−0.234328	−	0.0878559i
$646$		0			0
$647$	−44.6049			−1.75360			−0.876800	−	0.480854i	$-0.840327\pi$
$647$	−44.6049			−1.75360			−0.876800	+	0.480854i	$0.840327\pi$
$648$		0			0
$649$		−	0.0833680i		−	0.00327248i
$650$		0			0
$651$	10.9921	−	11.7538i	0.430814	−	0.460668i
$652$		0			0
$653$	−0.564755	+	0.326061i	−0.0221006	+	0.0127598i	−0.511010	−	0.859575i	$-0.670728\pi$
$653$	−0.564755	+	0.326061i	−0.0221006	+	0.0127598i	0.488909	+	0.872335i	$0.337395\pi$
$654$		0			0
$655$	29.3100	−	50.7664i	1.14524	−	1.98361i
$656$		0			0
$657$	−9.57529	+	10.9746i	−0.373568	+	0.428158i
$658$		0			0
$659$	−26.2738	−	15.1692i	−1.02348	−	0.590908i	−0.108372	−	0.994110i	$-0.534564\pi$
$659$	−26.2738	−	15.1692i	−1.02348	−	0.590908i	−0.915111	+	0.403202i	$0.867897\pi$
$660$		0			0
$661$	11.1004	−	6.40881i	0.431755	−	0.249274i	−0.268339	−	0.963325i	$-0.586475\pi$
$661$	11.1004	−	6.40881i	0.431755	−	0.249274i	0.700094	+	0.714051i	$0.253141\pi$
$662$		0			0
$663$	−3.61175	+	0.601008i	−0.140269	+	0.0233412i
$664$		0			0
$665$	−7.04011	+	16.9715i	−0.273004	+	0.658126i
$666$		0			0
$667$	−18.0569			−0.699165
$668$		0			0
$669$	−14.0624	−	17.0908i	−0.543683	−	0.660769i
$670$		0			0
$671$	−4.86986	−	8.43484i	−0.187999	−	0.325623i
$672$		0			0
$673$	11.2246	−	19.4416i	0.432678	−	0.749420i	−0.564425	−	0.825484i	$-0.690902\pi$
$673$	11.2246	−	19.4416i	0.432678	−	0.749420i	0.997103	+	0.0760644i	$0.0242355\pi$
$674$		0			0
$675$	52.6710	+	1.52367i	2.02731	+	0.0586461i
$676$		0			0
$677$	−25.5903	+	44.3237i	−0.983516	+	1.70350i	−0.335163	+	0.942160i	$0.608791\pi$
$677$	−25.5903	+	44.3237i	−0.983516	+	1.70350i	−0.648353	+	0.761340i	$0.724542\pi$
$678$		0			0
$679$	49.3694	−	6.47360i	1.89462	−	0.248434i
$680$		0			0
$681$	26.7262	−	21.9904i	1.02415	−	0.842673i
$682$		0			0
$683$		−	14.5616i		−	0.557184i	−0.960410	−	0.278592i	$-0.910132\pi$
$683$		−	14.5616i		−	0.557184i	0.960410	−	0.278592i	$-0.0898677\pi$
$684$		0			0
$685$			61.1681i			2.33711i
$686$		0			0
$687$	17.3100	−	2.88045i	0.660419	−	0.109896i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−21.1757	−	12.2258i	−0.805560	−	0.465090i	0.0398517	−	0.999206i	$-0.487311\pi$
$691$	−21.1757	−	12.2258i	−0.805560	−	0.465090i	−0.845412	+	0.534115i	$0.820645\pi$
$692$		0			0
$693$	26.0679	+	17.3420i	0.990238	+	0.658768i
$694$		0			0
$695$	−11.1431	−	6.43347i	−0.422682	−	0.244035i
$696$		0			0
$697$	−3.89393	−	6.74448i	−0.147493	−	0.255465i
$698$		0			0
$699$	−4.44495	+	11.8555i	−0.168123	+	0.448417i
$700$		0			0
$701$			2.21697i			0.0837337i	0.999123	+	0.0418669i	$0.0133305\pi$
$701$			2.21697i			0.0837337i	−0.999123	+	0.0418669i	$0.986669\pi$
$702$		0			0
$703$			5.35703i			0.202044i
$704$		0			0
$705$	13.7903	+	5.17036i	0.519375	+	0.194727i
$706$		0			0
$707$	−2.84871	−	21.7250i	−0.107137	−	0.817054i
$708$		0			0
$709$	12.1962	−	21.1244i	0.458036	−	0.793342i	−0.540821	−	0.841138i	$-0.681886\pi$
$709$	12.1962	−	21.1244i	0.458036	−	0.793342i	0.998857	+	0.0477959i	$0.0152197\pi$
$710$		0			0
$711$	10.3206	−	3.53258i	0.387051	−	0.132482i
$712$		0			0
$713$	10.9796	−	19.0173i	0.411190	−	0.712203i
$714$		0			0
$715$	−21.8607	−	37.8639i	−0.817544	−	1.41603i
$716$		0			0
$717$	14.3688	−	2.39102i	0.536611	−	0.0892941i
$718$		0			0
$719$	−2.22752			−0.0830725			−0.0415363	−	0.999137i	$-0.513225\pi$
$719$	−2.22752			−0.0830725			−0.0415363	+	0.999137i	$0.513225\pi$
$720$		0			0
$721$	17.2831	−	41.6641i	0.643657	−	1.55165i
$722$		0			0
$723$	−9.85181	−	11.9735i	−0.366393	−	0.445298i
$724$		0			0
$725$	25.3599	−	14.6416i	0.941844	−	0.543774i
$726$		0			0
$727$	10.4880	+	6.05523i	0.388977	+	0.224576i	0.681717	−	0.731616i	$-0.261234\pi$
$727$	10.4880	+	6.05523i	0.388977	+	0.224576i	−0.292740	+	0.956192i	$0.594567\pi$
$728$		0			0
$729$	−14.8291	+	22.5632i	−0.549227	+	0.835673i
$730$		0			0
$731$	0.349924	−	0.606086i	0.0129424	−	0.0224169i
$732$		0			0
$733$	−13.5673	+	7.83306i	−0.501118	+	0.289321i	−0.729175	−	0.684327i	$-0.760096\pi$
$733$	−13.5673	+	7.83306i	−0.501118	+	0.289321i	0.228057	+	0.973648i	$0.426763\pi$
$734$		0			0
$735$	46.9512	+	4.61325i	1.73182	+	0.170162i
$736$		0			0
$737$		−	53.0522i		−	1.95420i
$738$		0			0
$739$	8.10454			0.298130			0.149065	−	0.988827i	$-0.452374\pi$
$739$	8.10454			0.298130			0.149065	+	0.988827i	$0.452374\pi$
$740$		0			0
$741$	1.44538	+	8.68599i	0.0530974	+	0.319088i
$742$		0			0
$743$	10.5429	−	6.08697i	0.386783	−	0.223309i	−0.293982	−	0.955811i	$-0.594981\pi$
$743$	10.5429	−	6.08697i	0.386783	−	0.223309i	0.680765	+	0.732502i	$0.261647\pi$
$744$		0			0
$745$	−37.0732	−	21.4042i	−1.35826	−	0.784189i
$746$		0			0
$747$	−22.8769	+	7.83042i	−0.837020	+	0.286500i
$748$		0			0
$749$	−23.0759	−	30.1054i	−0.843176	−	1.10003i
$750$		0			0
$751$	17.3062	+	29.9752i	0.631511	+	1.09381i	0.987243	+	0.159221i	$0.0508983\pi$
$751$	17.3062	+	29.9752i	0.631511	+	1.09381i	−0.355732	+	0.934588i	$0.615768\pi$
$752$		0			0
$753$	−20.5049	−	7.68782i	−0.747240	−	0.280160i
$754$		0			0
$755$	5.60311			0.203918
$756$		0			0
$757$	−39.0553			−1.41949			−0.709744	−	0.704459i	$-0.751190\pi$
$757$	−39.0553			−1.41949			−0.709744	+	0.704459i	$0.751190\pi$
$758$		0			0
$759$	40.0038	+	14.9985i	1.45204	+	0.544410i
$760$		0			0
$761$	−5.11262	−	8.85532i	−0.185332	−	0.321005i	0.758356	−	0.651840i	$-0.226003\pi$
$761$	−5.11262	−	8.85532i	−0.185332	−	0.321005i	−0.943688	+	0.330835i	$0.892670\pi$
$762$		0			0
$763$	−23.6862	+	18.1556i	−0.857499	+	0.657277i
$764$		0			0
$765$	−1.66851	+	8.50079i	−0.0603250	+	0.307347i
$766$		0			0
$767$	−0.0521363	−	0.0301009i	−0.00188253	−	0.00108688i
$768$		0			0
$769$	26.6746	−	15.4006i	0.961910	−	0.555359i	0.0651494	−	0.997876i	$-0.479248\pi$
$769$	26.6746	−	15.4006i	0.961910	−	0.555359i	0.896760	+	0.442517i	$0.145914\pi$
$770$		0			0
$771$	−4.63613	−	27.8607i	−0.166966	−	1.00338i
$772$		0			0
$773$	35.7833			1.28704			0.643518	−	0.765431i	$-0.277474\pi$
$773$	35.7833			1.28704			0.643518	+	0.765431i	$0.277474\pi$
$774$		0			0
$775$			35.6117i			1.27921i
$776$		0			0
$777$	13.1597	−	4.00273i	0.472101	−	0.143597i
$778$		0			0
$779$	−16.2200	+	9.36461i	−0.581141	+	0.335522i
$780$		0			0
$781$	−3.83228	+	6.63771i	−0.137130	+	0.237516i
$782$		0			0
$783$	−0.433877	+	14.9985i	−0.0155055	+	0.536001i
$784$		0			0
$785$	55.9626	+	32.3100i	1.99739	+	1.15319i
$786$		0			0
$787$	13.2859	−	7.67064i	0.473592	−	0.273429i	−0.244150	−	0.969737i	$-0.578509\pi$
$787$	13.2859	−	7.67064i	0.473592	−	0.273429i	0.717742	+	0.696309i	$0.245176\pi$
$788$		0			0
$789$	26.1055	+	31.7275i	0.929380	+	1.12953i
$790$		0			0
$791$	9.96748	−	24.0284i	0.354403	−	0.854353i
$792$		0			0
$793$	−7.03326			−0.249758
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.5200	+	30.3455i	0.620590	+	1.07489i	0.989376	+	0.145379i	$0.0464402\pi$
$797$	17.5200	+	30.3455i	0.620590	+	1.07489i	−0.368786	+	0.929514i	$0.620226\pi$
$798$		0			0
$799$	−0.810856	+	1.40444i	−0.0286860	+	0.0496857i
$800$		0			0
$801$	20.9471	+	18.2763i	0.740130	+	0.645763i
$802$		0			0
$803$	9.57529	−	16.5849i	0.337905	−	0.585268i
$804$		0			0
$805$	63.8289	−	8.36961i	2.24967	−	0.294990i
$806$		0			0
$807$	11.8114	+	4.42841i	0.415782	+	0.155888i
$808$		0			0
$809$		−	27.2925i		−	0.959553i	−0.877391	−	0.479777i	$-0.840718\pi$
$809$		−	27.2925i		−	0.959553i	0.877391	−	0.479777i	$-0.159282\pi$
$810$		0			0
$811$			27.7628i			0.974883i	0.873156	+	0.487442i	$0.162070\pi$
$811$			27.7628i			0.974883i	−0.873156	+	0.487442i	$0.837930\pi$
$812$		0			0
$813$	−13.7956	+	36.7955i	−0.483833	+	1.29047i
$814$		0			0
$815$	−24.1161	−	41.7703i	−0.844749	−	1.46315i
$816$		0			0
$817$	−1.45759	−	0.841542i	−0.0509947	−	0.0294418i
$818$		0			0
$819$	20.2574	−	10.0407i	0.707849	−	0.350851i
$820$		0			0
$821$	−38.4968	−	22.2262i	−1.34355	−	0.775698i	−0.356223	−	0.934401i	$-0.615936\pi$
$821$	−38.4968	−	22.2262i	−1.34355	−	0.775698i	−0.987326	+	0.158703i	$0.949269\pi$
$822$		0			0
$823$	−25.5577	−	44.2672i	−0.890884	−	1.54306i	−0.838818	−	0.544413i	$-0.816753\pi$
$823$	−25.5577	−	44.2672i	−0.890884	−	1.54306i	−0.0520663	−	0.998644i	$-0.516581\pi$
$824$		0			0
$825$	−68.3448	+	11.3728i	−2.37946	+	0.395951i
$826$		0			0
$827$		−	14.5414i		−	0.505653i	−0.967512	−	0.252826i	$-0.918640\pi$
$827$		−	14.5414i		−	0.505653i	0.967512	−	0.252826i	$-0.0813601\pi$
$828$		0			0
$829$			27.9681i			0.971373i	0.874133	+	0.485686i	$0.161430\pi$
$829$			27.9681i			0.971373i	−0.874133	+	0.485686i	$0.838570\pi$
$830$		0			0
$831$	32.3242	−	26.5964i	1.12131	−	0.922620i
$832$		0			0
$833$	−1.34971	+	5.01641i	−0.0467648	+	0.173808i
$834$		0			0
$835$	−22.8053	+	39.5000i	−0.789211	+	1.36695i
$836$		0			0
$837$	−15.5324	−	9.57689i	−0.536877	−	0.331026i
$838$		0			0
$839$	−0.499354	+	0.864906i	−0.0172396	+	0.0298599i	−0.874517	−	0.484996i	$-0.838821\pi$
$839$	−0.499354	+	0.864906i	−0.0172396	+	0.0298599i	0.857277	+	0.514856i	$0.172154\pi$
$840$		0			0
$841$	−10.3307	−	17.8933i	−0.356231	−	0.617011i
$842$		0			0
$843$	5.22568	+	6.35107i	0.179982	+	0.218742i
$844$		0			0
$845$	19.0123			0.654044
$846$		0			0
$847$	−11.1439	−	4.62273i	−0.382910	−	0.158839i
$848$		0			0
$849$	50.2064	−	8.35454i	1.72308	−	0.286727i
$850$		0			0
$851$	16.2546	−	9.38460i	0.557200	−	0.321700i
$852$		0			0
$853$	−8.48739	−	4.90020i	−0.290603	−	0.167780i	0.347611	−	0.937639i	$-0.386993\pi$
$853$	−8.48739	−	4.90020i	−0.290603	−	0.167780i	−0.638214	+	0.769859i	$0.720326\pi$
$854$		0			0
$855$	20.4438	+	4.01264i	0.699163	+	0.137229i
$856$		0			0
$857$	−3.85002	+	6.66842i	−0.131514	+	0.227789i	−0.924260	−	0.381763i	$-0.875317\pi$
$857$	−3.85002	+	6.66842i	−0.131514	+	0.227789i	0.792746	+	0.609552i	$0.208651\pi$
$858$		0			0
$859$	−16.4022	+	9.46979i	−0.559634	+	0.323105i	−0.752999	−	0.658022i	$-0.771393\pi$
$859$	−16.4022	+	9.46979i	−0.559634	+	0.323105i	0.193364	+	0.981127i	$0.438060\pi$
$860$		0			0
$861$	35.1239	+	32.8476i	1.19702	+	1.11944i
$862$		0			0
$863$			17.4540i			0.594141i	0.954856	+	0.297070i	$0.0960096\pi$
$863$			17.4540i			0.594141i	−0.954856	+	0.297070i	$0.903990\pi$
$864$		0			0
$865$	−65.2578			−2.21883
$866$		0			0
$867$	26.6776	+	10.0021i	0.906018	+	0.339690i
$868$		0			0
$869$	−12.4215	+	7.17157i	−0.421371	+	0.243279i
$870$		0			0
$871$	−33.1776	−	19.1551i	−1.12418	−	0.649045i
$872$		0			0
$873$	−18.2836	−	53.4163i	−0.618808	−	1.80787i
$874$		0			0
$875$	−42.0040	+	32.1963i	−1.41999	+	1.08843i
$876$		0			0
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	0.862695	−	0.505725i	$-0.168775\pi$
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	−0.869318	+	0.494253i	$0.835442\pi$
$878$		0			0
$879$	1.88331	+	11.3177i	0.0635224	+	0.381736i
$880$		0			0
$881$	−37.0259			−1.24744			−0.623718	−	0.781650i	$-0.714378\pi$
$881$	−37.0259			−1.24744			−0.623718	+	0.781650i	$0.714378\pi$
$882$		0			0
$883$	29.9586			1.00819			0.504094	−	0.863649i	$-0.331826\pi$
$883$	29.9586			1.00819			0.504094	+	0.863649i	$0.331826\pi$
$884$		0			0
$885$	−0.109992	+	0.0905019i	−0.00369734	+	0.00304219i
$886$		0			0
$887$	−14.4930	−	25.1026i	−0.486626	−	0.842861i	0.513256	−	0.858236i	$-0.328439\pi$
$887$	−14.4930	−	25.1026i	−0.486626	−	0.842861i	−0.999882	+	0.0153745i	$0.995106\pi$
$888$		0			0
$889$	6.18326	−	4.73950i	0.207380	−	0.158958i
$890$		0			0
$891$	13.4193	−	32.8677i	0.449563	−	1.10111i
$892$		0			0
$893$	3.37759	+	1.95005i	0.113027	+	0.0652560i
$894$		0			0
$895$	−19.4617	+	11.2362i	−0.650533	+	0.375586i
$896$		0			0
$897$	23.8235	−	19.6020i	0.795442	−	0.654492i
$898$		0			0
$899$	−10.1407			−0.338211
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−0.978165	+	4.20941i	−0.0325513	+	0.140080i
$904$		0			0
$905$	18.6455	−	10.7650i	0.619796	−	0.357839i
$906$		0			0
$907$	−1.94773	+	3.37357i	−0.0646733	+	0.112017i	−0.896549	−	0.442945i	$-0.853934\pi$
$907$	−1.94773	+	3.37357i	−0.0646733	+	0.112017i	0.831876	+	0.554962i	$0.187267\pi$
$908$		0			0
$909$	−23.5059	+	8.04573i	−0.779642	+	0.266860i
$910$		0			0
$911$	−1.32768	−	0.766538i	−0.0439881	−	0.0253966i	0.477845	−	0.878444i	$-0.341418\pi$
$911$	−1.32768	−	0.766538i	−0.0439881	−	0.0253966i	−0.521833	+	0.853048i	$0.674752\pi$
$912$		0			0
$913$	27.5339	−	15.8967i	0.911240	−	0.526105i
$914$		0			0
$915$	−5.84199	+	15.5817i	−0.193130	+	0.515115i
$916$		0			0
$917$	−36.8166	−	15.2723i	−1.21579	−	0.504334i
$918$		0			0
$919$	−28.2531			−0.931984			−0.465992	−	0.884789i	$-0.654302\pi$
$919$	−28.2531			−0.931984			−0.465992	+	0.884789i	$0.654302\pi$
$920$		0			0
$921$	13.2096	−	35.2325i	0.435270	−	1.16095i
$922$		0			0
$923$	2.76737	+	4.79323i	0.0910892	+	0.157771i
$924$		0			0
$925$	−15.2192	+	26.3603i	−0.500403	+	0.866723i
$926$		0			0
$927$	−50.1885	−	9.85083i	−1.64841	−	0.323544i
$928$		0			0
$929$	−1.64363	+	2.84685i	−0.0539257	+	0.0934021i	−0.891728	−	0.452571i	$-0.850507\pi$
$929$	−1.64363	+	2.84685i	−0.0539257	+	0.0934021i	0.837802	+	0.545974i	$0.183840\pi$
$930$		0			0
$931$	12.0641	+	3.24596i	0.395385	+	0.106382i
$932$		0			0
$933$	−1.79059	−	10.7605i	−0.0586211	−	0.352282i
$934$		0			0
$935$		−	11.3907i		−	0.372517i
$936$		0			0
$937$			35.5084i			1.16001i	0.814613	+	0.580005i	$0.196949\pi$
$937$			35.5084i			1.16001i	−0.814613	+	0.580005i	$0.803051\pi$
$938$		0			0
$939$	−24.4520	−	29.7180i	−0.797962	−	0.969809i
$940$		0			0
$941$	−6.24941	−	10.8243i	−0.203725	−	0.352862i	0.746001	−	0.665945i	$-0.231972\pi$
$941$	−6.24941	−	10.8243i	−0.203725	−	0.352862i	−0.949726	+	0.313083i	$0.898638\pi$
$942$		0			0
$943$	56.8293	+	32.8104i	1.85062	+	1.06845i
$944$		0			0
$945$	−5.41829	−	53.2189i	−0.176257	−	1.73121i
$946$		0			0
$947$	−31.2769	−	18.0577i	−1.01636	−	0.586796i	−0.103313	−	0.994649i	$-0.532944\pi$
$947$	−31.2769	−	18.0577i	−1.01636	−	0.586796i	−0.913048	+	0.407852i	$0.866278\pi$
$948$		0			0
$949$	−6.91452	−	11.9763i	−0.224455	−	0.388767i
$950$		0			0
$951$	−17.2354	−	20.9471i	−0.558895	−	0.679257i
$952$		0			0
$953$		−	45.2925i		−	1.46717i	−0.679599	−	0.733584i	$-0.737846\pi$
$953$		−	45.2925i		−	1.46717i	0.679599	−	0.733584i	$-0.262154\pi$
$954$		0			0
$955$		−	24.1783i		−	0.782392i
$956$		0			0
$957$	−3.23850	−	19.4617i	−0.104686	−	0.629108i
$958$		0			0
$959$	41.2380	−	5.40737i	1.33165	−	0.174613i
$960$		0			0
$961$	−9.33386	+	16.1667i	−0.301092	+	0.521507i
$962$		0			0
$963$	−28.2769	+	32.4090i	−0.911209	+	1.04437i
$964$		0			0
$965$	15.1859	−	26.3028i	0.488851	−	0.846716i
$966$		0			0
$967$	−12.0000	−	20.7845i	−0.385893	−	0.668385i	0.606000	−	0.795465i	$-0.292773\pi$
$967$	−12.0000	−	20.7845i	−0.385893	−	0.668385i	−0.991893	+	0.127079i	$0.959440\pi$
$968$		0			0
$969$	−0.805364	+	2.14806i	−0.0258720	+	0.0690056i
$970$		0			0
$971$	−33.3626			−1.07066			−0.535328	−	0.844644i	$-0.679812\pi$
$971$	−33.3626			−1.07066			−0.535328	+	0.844644i	$0.679812\pi$
$972$		0			0
$973$	−3.35222	+	8.08113i	−0.107467	+	0.259069i
$974$		0			0
$975$	−17.5643	+	46.8475i	−0.562509	+	1.50032i
$976$		0			0
$977$	−29.8846	+	17.2539i	−0.956091	+	0.552000i	−0.894968	−	0.446131i	$-0.852802\pi$
$977$	−29.8846	+	17.2539i	−0.956091	+	0.552000i	−0.0611236	+	0.998130i	$0.519468\pi$
$978$		0			0
$979$	−31.6555	−	18.2763i	−1.01172	−	0.584114i
$980$		0			0
$981$	25.4987	+	22.2476i	0.814111	+	0.710311i
$982$		0			0
$983$	−1.20651	+	2.08973i	−0.0384817	+	0.0666522i	−0.884625	−	0.466304i	$-0.845585\pi$
$983$	−1.20651	+	2.08973i	−0.0384817	+	0.0666522i	0.846143	+	0.532956i	$0.178919\pi$
$984$		0			0
$985$	−43.0450	+	24.8521i	−1.37153	+	0.791852i
$986$		0			0
$987$	2.26664	−	9.75419i	0.0721479	−	0.310479i
$988$		0			0
$989$			5.89695i			0.187512i
$990$		0			0
$991$	−48.5982			−1.54377			−0.771887	−	0.635760i	$-0.780687\pi$
$991$	−48.5982			−1.54377			−0.771887	+	0.635760i	$0.780687\pi$
$992$		0			0
$993$	−1.70164	+	1.40012i	−0.0540000	+	0.0444314i
$994$		0			0
$995$	−6.10612	+	3.52537i	−0.193577	+	0.111762i
$996$		0			0
$997$	−38.8449	−	22.4271i	−1.23023	−	0.710274i	−0.263152	−	0.964754i	$-0.584762\pi$
$997$	−38.8449	−	22.4271i	−1.23023	−	0.710274i	−0.967078	+	0.254481i	$0.918095\pi$
$998$		0			0
$999$	−7.40449	−	13.7269i	−0.234268	−	0.434301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cc.b.209.2		16
3.2	odd	2		3024.2.cc.b.2897.8		16
4.3	odd	2		126.2.m.a.83.4	yes	16
7.6	odd	2	inner	1008.2.cc.b.209.7		16
9.4	even	3		3024.2.cc.b.881.1		16
9.5	odd	6	inner	1008.2.cc.b.545.7		16
12.11	even	2		378.2.m.a.251.8		16
21.20	even	2		3024.2.cc.b.2897.1		16
28.3	even	6		882.2.t.b.803.7		16
28.11	odd	6		882.2.t.b.803.6		16
28.19	even	6		882.2.l.a.227.8		16
28.23	odd	6		882.2.l.a.227.5		16
28.27	even	2		126.2.m.a.83.1	yes	16
36.7	odd	6		1134.2.d.a.1133.16		16
36.11	even	6		1134.2.d.a.1133.1		16
36.23	even	6		126.2.m.a.41.1	✓	16
36.31	odd	6		378.2.m.a.125.5		16
63.13	odd	6		3024.2.cc.b.881.8		16
63.41	even	6	inner	1008.2.cc.b.545.2		16
84.11	even	6		2646.2.t.a.1979.1		16
84.23	even	6		2646.2.l.b.521.4		16
84.47	odd	6		2646.2.l.b.521.1		16
84.59	odd	6		2646.2.t.a.1979.4		16
84.83	odd	2		378.2.m.a.251.5		16
252.23	even	6		882.2.t.b.815.7		16
252.31	even	6		2646.2.l.b.1097.8		16
252.59	odd	6		882.2.l.a.509.1		16
252.67	odd	6		2646.2.l.b.1097.5		16
252.83	odd	6		1134.2.d.a.1133.8		16
252.95	even	6		882.2.l.a.509.4		16
252.103	even	6		2646.2.t.a.2285.1		16
252.131	odd	6		882.2.t.b.815.6		16
252.139	even	6		378.2.m.a.125.8		16
252.167	odd	6		126.2.m.a.41.4	yes	16
252.223	even	6		1134.2.d.a.1133.9		16
252.247	odd	6		2646.2.t.a.2285.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.1	✓	16	36.23	even	6
126.2.m.a.41.4	yes	16	252.167	odd	6
126.2.m.a.83.1	yes	16	28.27	even	2
126.2.m.a.83.4	yes	16	4.3	odd	2
378.2.m.a.125.5		16	36.31	odd	6
378.2.m.a.125.8		16	252.139	even	6
378.2.m.a.251.5		16	84.83	odd	2
378.2.m.a.251.8		16	12.11	even	2
882.2.l.a.227.5		16	28.23	odd	6
882.2.l.a.227.8		16	28.19	even	6
882.2.l.a.509.1		16	252.59	odd	6
882.2.l.a.509.4		16	252.95	even	6
882.2.t.b.803.6		16	28.11	odd	6
882.2.t.b.803.7		16	28.3	even	6
882.2.t.b.815.6		16	252.131	odd	6
882.2.t.b.815.7		16	252.23	even	6
1008.2.cc.b.209.2		16	1.1	even	1	trivial
1008.2.cc.b.209.7		16	7.6	odd	2	inner
1008.2.cc.b.545.2		16	63.41	even	6	inner
1008.2.cc.b.545.7		16	9.5	odd	6	inner
1134.2.d.a.1133.1		16	36.11	even	6
1134.2.d.a.1133.8		16	252.83	odd	6
1134.2.d.a.1133.9		16	252.223	even	6
1134.2.d.a.1133.16		16	36.7	odd	6
2646.2.l.b.521.1		16	84.47	odd	6
2646.2.l.b.521.4		16	84.23	even	6
2646.2.l.b.1097.5		16	252.67	odd	6
2646.2.l.b.1097.8		16	252.31	even	6
2646.2.t.a.1979.1		16	84.11	even	6
2646.2.t.a.1979.4		16	84.59	odd	6
2646.2.t.a.2285.1		16	252.103	even	6
2646.2.t.a.2285.4		16	252.247	odd	6
3024.2.cc.b.881.1		16	9.4	even	3
3024.2.cc.b.881.8		16	63.13	odd	6
3024.2.cc.b.2897.1		16	21.20	even	2
3024.2.cc.b.2897.8		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.62181 - 0.608059i) q^{3} +(-1.94556 - 3.36980i) q^{5} +(-2.09985 + 1.60954i) q^{7} +(2.26053 + 1.97231i) q^{9} +O(q^{10})\)	\(q+(-1.62181 - 0.608059i) q^{3} +(-1.94556 - 3.36980i) q^{5} +(-2.09985 + 1.60954i) q^{7} +(2.26053 + 1.97231i) q^{9} +(-3.41614 - 1.97231i) q^{11} +(-2.46687 + 1.42425i) q^{13} +(1.10628 + 6.64819i) q^{15} -0.742117 q^{17} +1.78474i q^{19} +(4.38425 - 1.33354i) q^{21} +(5.41535 - 3.12656i) q^{23} +(-5.07039 + 8.78217i) q^{25} +(-2.46687 - 4.57324i) q^{27} +(-2.50079 - 1.44383i) q^{29} +(3.04125 - 1.75587i) q^{31} +(4.34105 + 5.27592i) q^{33} +(9.50923 + 3.94462i) q^{35} +3.00158 q^{37} +(4.86681 - 0.809856i) q^{39} +(5.24705 + 9.08816i) q^{41} +(-0.471521 + 0.816699i) q^{43} +(2.24831 - 11.4548i) q^{45} +(1.09263 - 1.89248i) q^{47} +(1.81873 - 6.75960i) q^{49} +(1.20357 + 0.451251i) q^{51} +15.3490i q^{55} +(1.08523 - 2.89450i) q^{57} +(0.0105673 + 0.0183031i) q^{59} +(2.13832 + 1.23456i) q^{61} +(-7.92129 - 0.503130i) q^{63} +(9.59886 + 5.54191i) q^{65} +(6.72463 + 11.6474i) q^{67} +(-10.6838 + 1.77782i) q^{69} -1.94304i q^{71} +4.85486i q^{73} +(13.5633 - 11.1599i) q^{75} +(10.3479 - 1.35688i) q^{77} +(1.81806 - 3.14898i) q^{79} +(1.21999 + 8.91693i) q^{81} +(-4.02998 + 6.98012i) q^{83} +(1.44383 + 2.50079i) q^{85} +(3.17787 + 3.86224i) q^{87} +9.26646 q^{89} +(2.88766 - 6.96124i) q^{91} +(-6.00000 + 0.998423i) q^{93} +(6.01422 - 3.47231i) q^{95} +(-16.2983 - 9.40980i) q^{97} +(-3.83228 - 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 16 * q - 2 * q^7 + 12 * q^9	\( 16 q - 2 q^{7} + 12 q^{9} + 12 q^{11} + 18 q^{21} + 48 q^{23} - 8 q^{25} - 12 q^{29} - 8 q^{37} + 36 q^{39} - 4 q^{43} - 8 q^{49} - 12 q^{51} + 48 q^{57} - 24 q^{63} + 84 q^{65} + 28 q^{67} + 78 q^{77} + 4 q^{79} + 36 q^{81} - 12 q^{85} - 24 q^{91} - 96 q^{93} - 12 q^{95} + 72 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 + 12 * q^9 + 12 * q^11 + 18 * q^21 + 48 * q^23 - 8 * q^25 - 12 * q^29 - 8 * q^37 + 36 * q^39 - 4 * q^43 - 8 * q^49 - 12 * q^51 + 48 * q^57 - 24 * q^63 + 84 * q^65 + 28 * q^67 + 78 * q^77 + 4 * q^79 + 36 * q^81 - 12 * q^85 - 24 * q^91 - 96 * q^93 - 12 * q^95 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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