LMFDB - Embedded newform 252.2.bm.a.185.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(173,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bm (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:	$2.01223013094$
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} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.3
Root			$1.08696 + 1.34852i$ of defining polynomial
Character	$\chi$	$=$	252.185
Dual form			252.2.bm.a.173.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31579 - 1.12637i) q^{3} +0.0764245 q^{5} +(-2.39886 - 1.11601i) q^{7} +(0.462593 + 2.96412i) q^{9} +O(q^{10})$	\(q+(-1.31579 - 1.12637i) q^{3} +0.0764245 q^{5} +(-2.39886 - 1.11601i) q^{7} +(0.462593 + 2.96412i) q^{9} -5.38437i q^{11} +(-4.60313 - 2.65762i) q^{13} +(-0.100558 - 0.0860820i) q^{15} +(-1.89092 + 3.27516i) q^{17} +(-4.33939 + 2.50535i) q^{19} +(1.89935 + 4.17043i) q^{21} -2.33784i q^{23} -4.99416 q^{25} +(2.73001 - 4.42120i) q^{27} +(8.84430 - 5.10626i) q^{29} +(4.97636 - 2.87310i) q^{31} +(-6.06478 + 7.08469i) q^{33} +(-0.183331 - 0.0852905i) q^{35} +(0.354486 + 0.613988i) q^{37} +(3.06328 + 8.68167i) q^{39} +(3.29910 - 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +(0.0353534 + 0.226531i) q^{45} +(-1.46192 + 2.53213i) q^{47} +(4.50904 + 5.35430i) q^{49} +(6.17708 - 2.17955i) q^{51} +(10.4835 + 6.05264i) q^{53} -0.411498i q^{55} +(8.53166 + 1.59124i) q^{57} +(-0.289951 - 0.502210i) q^{59} +(-2.40641 - 1.38934i) q^{61} +(2.19830 - 7.62676i) q^{63} +(-0.351792 - 0.203107i) q^{65} +(-2.63593 - 4.56556i) q^{67} +(-2.63327 + 3.07610i) q^{69} +3.32103i q^{71} +(-6.17326 - 3.56413i) q^{73} +(6.57125 + 5.62526i) q^{75} +(-6.00902 + 12.9163i) q^{77} +(-0.469123 + 0.812544i) q^{79} +(-8.57202 + 2.74236i) q^{81} +(-6.49790 - 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +(-17.3887 - 3.24318i) q^{87} +(-1.51794 - 2.62915i) q^{89} +(8.07632 + 11.5124i) q^{91} +(-9.78400 - 1.82482i) q^{93} +(-0.331636 + 0.191470i) q^{95} +(6.18183 - 3.56908i) q^{97} +(15.9599 - 2.49077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 16 q^{25} - 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} + 15 q^{35} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 13 q^{49} + 15 q^{51} + 15 q^{57} - 15 q^{59} + 3 q^{61} - 9 q^{63} - 39 q^{65} - 7 q^{67} - 21 q^{69} - 15 q^{75} - 45 q^{77} - q^{79} + 6 q^{85} - 3 q^{87} - 21 q^{89} + 9 q^{91} - 69 q^{93} + 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - q^7 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 16 * q^25 - 9 * q^27 + 6 * q^29 + 6 * q^31 - 27 * q^33 + 15 * q^35 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 13 * q^49 + 15 * q^51 + 15 * q^57 - 15 * q^59 + 3 * q^61 - 9 * q^63 - 39 * q^65 - 7 * q^67 - 21 * q^69 - 15 * q^75 - 45 * q^77 - q^79 + 6 * q^85 - 3 * q^87 - 21 * q^89 + 9 * q^91 - 69 * q^93 + 6 * q^95 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−1.31579	−	1.12637i	−0.759670	−	0.650309i
$3$	−1.31579	−	1.12637i	−0.759670	−	0.650309i
$4$		0			0
$5$	0.0764245			0.0341781			0.0170890	−	0.999854i	$-0.494560\pi$
$5$	0.0764245			0.0341781			0.0170890	+	0.999854i	$0.494560\pi$
$6$		0			0
$7$	−2.39886	−	1.11601i	−0.906683	−	0.421812i
$7$	−2.39886	−	1.11601i	−0.906683	−	0.421812i
$8$		0			0
$9$	0.462593	+	2.96412i	0.154198	+	0.988040i
$10$		0			0
$11$		−	5.38437i		−	1.62345i	−0.584040	−	0.811725i	$-0.698529\pi$
$11$		−	5.38437i		−	1.62345i	0.584040	−	0.811725i	$-0.301471\pi$
$12$		0			0
$13$	−4.60313	−	2.65762i	−1.27668	−	0.737091i	−0.300442	−	0.953800i	$-0.597134\pi$
$13$	−4.60313	−	2.65762i	−1.27668	−	0.737091i	−0.976236	+	0.216709i	$0.930468\pi$
$14$		0			0
$15$	−0.100558	−	0.0860820i	−0.0259641	−	0.0222263i
$16$		0			0
$17$	−1.89092	+	3.27516i	−0.458615	+	0.794344i	−0.998888	−	0.0471458i	$-0.984987\pi$
$17$	−1.89092	+	3.27516i	−0.458615	+	0.794344i	0.540273	+	0.841490i	$0.318321\pi$
$18$		0			0
$19$	−4.33939	+	2.50535i	−0.995525	+	0.574767i	−0.906921	−	0.421300i	$-0.861574\pi$
$19$	−4.33939	+	2.50535i	−0.995525	+	0.574767i	−0.0886040	+	0.996067i	$0.528241\pi$
$20$		0			0
$21$	1.89935	+	4.17043i	0.414472	+	0.910062i
$22$		0			0
$23$		−	2.33784i		−	0.487473i	−0.969841	−	0.243737i	$-0.921627\pi$
$23$		−	2.33784i		−	0.487473i	0.969841	−	0.243737i	$-0.0783732\pi$
$24$		0			0
$25$	−4.99416			−0.998832
$26$		0			0
$27$	2.73001	−	4.42120i	0.525392	−	0.850861i
$28$		0			0
$29$	8.84430	−	5.10626i	1.64235	−	0.948209i	0.662349	−	0.749196i	$-0.269560\pi$
$29$	8.84430	−	5.10626i	1.64235	−	0.948209i	0.979997	−	0.199013i	$-0.0637736\pi$
$30$		0			0
$31$	4.97636	−	2.87310i	0.893780	−	0.516024i	0.0186031	−	0.999827i	$-0.494078\pi$
$31$	4.97636	−	2.87310i	0.893780	−	0.516024i	0.875177	+	0.483803i	$0.160745\pi$
$32$		0			0
$33$	−6.06478	+	7.08469i	−1.05574	+	1.23329i
$34$		0			0
$35$	−0.183331	−	0.0852905i	−0.0309887	−	0.0144167i
$36$		0			0
$37$	0.354486	+	0.613988i	0.0582771	+	0.100939i	0.893692	−	0.448681i	$-0.148106\pi$
$37$	0.354486	+	0.613988i	0.0582771	+	0.100939i	−0.835415	+	0.549620i	$0.814773\pi$
$38$		0			0
$39$	3.06328	+	8.68167i	0.490518	+	1.39018i
$40$		0			0
$41$	3.29910	−	5.71422i	0.515234	−	0.892411i	−0.484610	−	0.874730i	$-0.661039\pi$
$41$	3.29910	−	5.71422i	0.515234	−	0.892411i	0.999844	−	0.0176805i	$-0.00562816\pi$
$42$		0			0
$43$	0.716520	+	1.24105i	0.109268	+	0.189258i	0.915474	−	0.402377i	$-0.131816\pi$
$43$	0.716520	+	1.24105i	0.109268	+	0.189258i	−0.806206	+	0.591635i	$0.798483\pi$
$44$		0			0
$45$	0.0353534	+	0.226531i	0.00527017	+	0.0337693i
$46$		0			0
$47$	−1.46192	+	2.53213i	−0.213244	+	0.369349i	−0.952728	−	0.303825i	$-0.901736\pi$
$47$	−1.46192	+	2.53213i	−0.213244	+	0.369349i	0.739484	+	0.673174i	$0.235069\pi$
$48$		0			0
$49$	4.50904	+	5.35430i	0.644148	+	0.764900i
$50$		0			0
$51$	6.17708	−	2.17955i	0.864964	−	0.305198i
$52$		0			0
$53$	10.4835	+	6.05264i	1.44002	+	0.831394i	0.997850	−	0.0655390i	$-0.0208767\pi$
$53$	10.4835	+	6.05264i	1.44002	+	0.831394i	0.442167	+	0.896933i	$0.354210\pi$
$54$		0			0
$55$		−	0.411498i		−	0.0554863i
$56$		0			0
$57$	8.53166	+	1.59124i	1.13005	+	0.210765i
$58$		0			0
$59$	−0.289951	−	0.502210i	−0.0377484	−	0.0653822i	0.846534	−	0.532335i	$-0.178685\pi$
$59$	−0.289951	−	0.502210i	−0.0377484	−	0.0653822i	−0.884282	+	0.466953i	$0.845352\pi$
$60$		0			0
$61$	−2.40641	−	1.38934i	−0.308109	−	0.177887i	0.337971	−	0.941156i	$-0.390259\pi$
$61$	−2.40641	−	1.38934i	−0.308109	−	0.177887i	−0.646080	+	0.763270i	$0.723593\pi$
$62$		0			0
$63$	2.19830	−	7.62676i	0.276959	−	0.960882i
$64$		0			0
$65$	−0.351792	−	0.203107i	−0.0436344	−	0.0251923i
$66$		0			0
$67$	−2.63593	−	4.56556i	−0.322030	−	0.557771i	0.658877	−	0.752251i	$-0.271032\pi$
$67$	−2.63593	−	4.56556i	−0.322030	−	0.557771i	−0.980907	+	0.194479i	$0.937698\pi$
$68$		0			0
$69$	−2.63327	+	3.07610i	−0.317008	+	0.370319i
$70$		0			0
$71$			3.32103i			0.394134i	0.980390	+	0.197067i	$0.0631416\pi$
$71$			3.32103i			0.394134i	−0.980390	+	0.197067i	$0.936858\pi$
$72$		0			0
$73$	−6.17326	−	3.56413i	−0.722525	−	0.417150i	0.0931564	−	0.995651i	$-0.470304\pi$
$73$	−6.17326	−	3.56413i	−0.722525	−	0.417150i	−0.815681	+	0.578502i	$0.803638\pi$
$74$		0			0
$75$	6.57125	+	5.62526i	0.758783	+	0.649549i
$76$		0			0
$77$	−6.00902	+	12.9163i	−0.684791	+	1.47195i
$78$		0			0
$79$	−0.469123	+	0.812544i	−0.0527804	+	0.0914184i	−0.891208	−	0.453594i	$-0.850142\pi$
$79$	−0.469123	+	0.812544i	−0.0527804	+	0.0914184i	0.838428	+	0.545012i	$0.183475\pi$
$80$		0			0
$81$	−8.57202	+	2.74236i	−0.952446	+	0.304707i
$82$		0			0
$83$	−6.49790	−	11.2547i	−0.713238	−	1.23536i	−0.963635	−	0.267221i	$-0.913895\pi$
$83$	−6.49790	−	11.2547i	−0.713238	−	1.23536i	0.250398	−	0.968143i	$-0.419439\pi$
$84$		0			0
$85$	−0.144512	+	0.250303i	−0.0156746	+	0.0271491i
$86$		0			0
$87$	−17.3887	−	3.24318i	−1.86427	−	0.347706i
$88$		0			0
$89$	−1.51794	−	2.62915i	−0.160901	−	0.278689i	0.774291	−	0.632830i	$-0.218107\pi$
$89$	−1.51794	−	2.62915i	−0.160901	−	0.278689i	−0.935192	+	0.354141i	$0.884773\pi$
$90$		0			0
$91$	8.07632	+	11.5124i	0.846629	+	1.20683i
$92$		0			0
$93$	−9.78400	−	1.82482i	−1.01455	−	0.189225i
$94$		0			0
$95$	−0.331636	+	0.191470i	−0.0340251	+	0.0196444i
$96$		0			0
$97$	6.18183	−	3.56908i	0.627670	−	0.362385i	−0.152179	−	0.988353i	$-0.548629\pi$
$97$	6.18183	−	3.56908i	0.627670	−	0.362385i	0.779849	+	0.625967i	$0.215296\pi$
$98$		0			0
$99$	15.9599	−	2.49077i	1.60403	−	0.250332i
$100$		0			0
$101$	8.17257			0.813201			0.406600	−	0.913606i	$-0.366714\pi$
$101$	8.17257			0.813201			0.406600	+	0.913606i	$0.366714\pi$
$102$		0			0
$103$			7.46628i			0.735675i	0.929890	+	0.367837i	$0.119902\pi$
$103$			7.46628i			0.735675i	−0.929890	+	0.367837i	$0.880098\pi$
$104$		0			0
$105$	0.145157	+	0.318723i	0.0141658	+	0.0311042i
$106$		0			0
$107$	3.99991	−	2.30935i	0.386686	−	0.223253i	−0.294037	−	0.955794i	$-0.594999\pi$
$107$	3.99991	−	2.30935i	0.386686	−	0.223253i	0.680723	+	0.732541i	$0.261666\pi$
$108$		0			0
$109$	5.22792	−	9.05503i	0.500744	−	0.867314i	−0.499256	−	0.866455i	$-0.666393\pi$
$109$	5.22792	−	9.05503i	0.500744	−	0.867314i	1.00000		0.000859385i	$-0.000273551\pi$
$110$		0			0
$111$	0.225148	−	1.20716i	0.0213701	−	0.114578i
$112$		0			0
$113$	−16.6379	−	9.60591i	−1.56516	−	0.903648i	−0.996720	−	0.0809270i	$-0.974212\pi$
$113$	−16.6379	−	9.60591i	−1.56516	−	0.903648i	−0.568445	−	0.822721i	$-0.692455\pi$
$114$		0			0
$115$		−	0.178668i		−	0.0166609i
$116$		0			0
$117$	5.74812	−	14.8736i	0.531414	−	1.37507i
$118$		0			0
$119$	8.19116	−	5.74637i	0.750882	−	0.526769i
$120$		0			0
$121$	−17.9915			−1.63559
$122$		0			0
$123$	−10.7772	+	3.80269i	−0.971750	+	0.342877i
$124$		0			0
$125$	−0.763798			−0.0683162
$126$		0			0
$127$	1.26488			0.112240			0.0561198	−	0.998424i	$-0.482127\pi$
$127$	1.26488			0.112240			0.0561198	+	0.998424i	$0.482127\pi$
$128$		0			0
$129$	0.455089	−	2.44002i	0.0400684	−	0.214832i
$130$		0			0
$131$	−14.4879			−1.26581			−0.632906	−	0.774229i	$-0.718138\pi$
$131$	−14.4879			−1.26581			−0.632906	+	0.774229i	$0.718138\pi$
$132$		0			0
$133$	13.2056	−	1.16717i	1.14507	−	0.101206i
$134$		0			0
$135$	0.208640	−	0.337888i	0.0179569	−	0.0290808i
$136$		0			0
$137$			15.4053i			1.31616i	0.752947	+	0.658081i	$0.228632\pi$
$137$			15.4053i			1.31616i	−0.752947	+	0.658081i	$0.771368\pi$
$138$		0			0
$139$	−0.374701	−	0.216333i	−0.0317817	−	0.0183492i	0.484025	−	0.875054i	$-0.339174\pi$
$139$	−0.374701	−	0.216333i	−0.0317817	−	0.0183492i	−0.515807	+	0.856705i	$0.672508\pi$
$140$		0			0
$141$	4.77569	−	1.68508i	0.402185	−	0.141909i
$142$		0			0
$143$	−14.3096	+	24.7850i	−1.19663	+	2.07262i
$144$		0			0
$145$	0.675921	−	0.390243i	0.0561322	−	0.0324079i
$146$		0			0
$147$	0.0979760	−	12.1240i	0.00808092	−	0.999967i
$148$		0			0
$149$		−	4.67117i		−	0.382677i	−0.981524	−	0.191338i	$-0.938717\pi$
$149$		−	4.67117i		−	0.382677i	0.981524	−	0.191338i	$-0.0612828\pi$
$150$		0			0
$151$	−8.24552			−0.671011			−0.335506	−	0.942038i	$-0.608907\pi$
$151$	−8.24552			−0.671011			−0.335506	+	0.942038i	$0.608907\pi$
$152$		0			0
$153$	−10.5827	−	4.08984i	−0.855561	−	0.330644i
$154$		0			0
$155$	0.380316	−	0.219575i	0.0305477	−	0.0176367i
$156$		0			0
$157$	15.2334	−	8.79500i	1.21576	−	0.701917i	0.251749	−	0.967793i	$-0.418994\pi$
$157$	15.2334	−	8.79500i	1.21576	−	0.701917i	0.964007	+	0.265875i	$0.0856609\pi$
$158$		0			0
$159$	−6.97653	−	19.7722i	−0.553275	−	1.56804i
$160$		0			0
$161$	−2.60905	+	5.60814i	−0.205622	+	0.441984i
$162$		0			0
$163$	−5.27097	−	9.12959i	−0.412854	−	0.715085i	0.582346	−	0.812941i	$-0.302135\pi$
$163$	−5.27097	−	9.12959i	−0.412854	−	0.715085i	−0.995201	+	0.0978563i	$0.968801\pi$
$164$		0			0
$165$	−0.463498	+	0.541444i	−0.0360832	+	0.0421513i
$166$		0			0
$167$	−4.59146	+	7.95265i	−0.355298	+	0.615395i	−0.987169	−	0.159679i	$-0.948954\pi$
$167$	−4.59146	+	7.95265i	−0.355298	+	0.615395i	0.631871	+	0.775074i	$0.282287\pi$
$168$		0			0
$169$	7.62587	+	13.2084i	0.586605	+	1.01603i
$170$		0			0
$171$	−9.43353	−	11.7035i	−0.721400	−	0.894991i
$172$		0			0
$173$	−1.22358	+	2.11931i	−0.0930274	+	0.161128i	−0.908784	−	0.417268i	$-0.862988\pi$
$173$	−1.22358	+	2.11931i	−0.0930274	+	0.161128i	0.815756	+	0.578396i	$0.196321\pi$
$174$		0			0
$175$	11.9803	+	5.57354i	0.905624	+	0.421320i
$176$		0			0
$177$	−0.184159	+	0.987394i	−0.0138423	+	0.0742171i
$178$		0			0
$179$	5.05509	+	2.91856i	0.377835	+	0.218143i	0.676876	−	0.736097i	$-0.263333\pi$
$179$	5.05509	+	2.91856i	0.377835	+	0.218143i	−0.299041	+	0.954240i	$0.596667\pi$
$180$		0			0
$181$		−	16.0704i		−	1.19451i	−0.802053	−	0.597253i	$-0.796259\pi$
$181$		−	16.0704i		−	1.19451i	0.802053	−	0.597253i	$-0.203741\pi$
$182$		0			0
$183$	1.60141	+	4.53857i	0.118380	+	0.335501i
$184$		0			0
$185$	0.0270914	+	0.0469237i	0.00199180	+	0.00344990i
$186$		0			0
$187$	17.6347	+	10.1814i	1.28958	+	0.744537i
$188$		0			0
$189$	−11.4830	+	7.55911i	−0.835267	+	0.549844i
$190$		0			0
$191$	−6.90415	−	3.98611i	−0.499567	−	0.288425i	0.228968	−	0.973434i	$-0.426465\pi$
$191$	−6.90415	−	3.98611i	−0.499567	−	0.288425i	−0.728535	+	0.685009i	$0.759798\pi$
$192$		0			0
$193$	−0.359027	−	0.621853i	−0.0258433	−	0.0447620i	0.852814	−	0.522214i	$-0.174894\pi$
$193$	−0.359027	−	0.621853i	−0.0258433	−	0.0447620i	−0.878658	+	0.477452i	$0.841560\pi$
$194$		0			0
$195$	0.234110	+	0.663492i	0.0167650	+	0.0475137i
$196$		0			0
$197$		−	13.5035i		−	0.962083i	−0.876698	−	0.481042i	$-0.840259\pi$
$197$		−	13.5035i		−	0.962083i	0.876698	−	0.481042i	$-0.159741\pi$
$198$		0			0
$199$	21.2568	+	12.2726i	1.50685	+	0.869983i	0.999968	+	0.00796947i	$0.00253679\pi$
$199$	21.2568	+	12.2726i	1.50685	+	0.869983i	0.506886	+	0.862013i	$0.330797\pi$
$200$		0			0
$201$	−1.67418	+	8.97632i	−0.118087	+	0.633141i
$202$		0			0
$203$	−26.9149	+	2.37886i	−1.88905	+	0.166963i
$204$		0			0
$205$	0.252132	−	0.436706i	0.0176097	−	0.0305009i
$206$		0			0
$207$	6.92963	−	1.08147i	0.481643	−	0.0751671i
$208$		0			0
$209$	13.4897	+	23.3649i	0.933105	+	1.61618i
$210$		0			0
$211$	−11.7838	+	20.4101i	−0.811227	+	1.40509i	0.100778	+	0.994909i	$0.467867\pi$
$211$	−11.7838	+	20.4101i	−0.811227	+	1.40509i	−0.912005	+	0.410178i	$0.865467\pi$
$212$		0			0
$213$	3.74070	−	4.36977i	0.256309	−	0.299412i
$214$		0			0
$215$	0.0547597	+	0.0948465i	0.00373458	+	0.00646848i
$216$		0			0
$217$	−15.1440	+	1.33849i	−1.02804	+	0.0908628i
$218$		0			0
$219$	4.10817	+	11.6430i	0.277604	+	0.786760i
$220$		0			0
$221$	17.4083	−	10.0507i	1.17101	−	0.676081i
$222$		0			0
$223$	−6.47489	+	3.73828i	−0.433590	+	0.250334i	−0.700875	−	0.713284i	$-0.747207\pi$
$223$	−6.47489	+	3.73828i	−0.433590	+	0.250334i	0.267285	+	0.963618i	$0.413874\pi$
$224$		0			0
$225$	−2.31026	−	14.8033i	−0.154017	−	0.986886i
$226$		0			0
$227$	0.637402			0.0423058			0.0211529	−	0.999776i	$-0.493266\pi$
$227$	0.637402			0.0423058			0.0211529	+	0.999776i	$0.493266\pi$
$228$		0			0
$229$			1.82848i			0.120829i	0.998173	+	0.0604146i	$0.0192423\pi$
$229$			1.82848i			0.120829i	−0.998173	+	0.0604146i	$0.980758\pi$
$230$		0			0
$231$	22.4551	−	10.2268i	1.47744	−	0.672874i
$232$		0			0
$233$	17.4232	−	10.0593i	1.14143	−	0.659007i	0.194649	−	0.980873i	$-0.437643\pi$
$233$	17.4232	−	10.0593i	1.14143	−	0.659007i	0.946785	+	0.321866i	$0.104310\pi$
$234$		0			0
$235$	−0.111727	+	0.193516i	−0.00728825	+	0.0126236i
$236$		0			0
$237$	1.53249	−	0.540731i	0.0995458	−	0.0351242i
$238$		0			0
$239$	−2.41455	−	1.39404i	−0.156184	−	0.0901730i	0.419871	−	0.907584i	$-0.362075\pi$
$239$	−2.41455	−	1.39404i	−0.156184	−	0.0901730i	−0.576055	+	0.817411i	$0.695409\pi$
$240$		0			0
$241$		−	23.1291i		−	1.48988i	−0.667134	−	0.744938i	$-0.732479\pi$
$241$		−	23.1291i		−	1.48988i	0.667134	−	0.744938i	$-0.267521\pi$
$242$		0			0
$243$	14.3679	+	6.04688i	0.921698	+	0.387907i
$244$		0			0
$245$	0.344601	+	0.409200i	0.0220157	+	0.0261428i
$246$		0			0
$247$	26.6331			1.69462
$248$		0			0
$249$	−4.12707	+	22.1278i	−0.261542	+	1.40229i
$250$		0			0
$251$	18.6541			1.17743			0.588717	−	0.808339i	$-0.299633\pi$
$251$	18.6541			1.17743			0.588717	+	0.808339i	$0.299633\pi$
$252$		0			0
$253$	−12.5878			−0.791388
$254$		0			0
$255$	0.472080	−	0.166571i	0.0295628	−	0.0104311i
$256$		0			0
$257$	10.8737			0.678286			0.339143	−	0.940735i	$-0.389863\pi$
$257$	10.8737			0.678286			0.339143	+	0.940735i	$0.389863\pi$
$258$		0			0
$259$	−0.165144	−	1.86848i	−0.0102616	−	0.116102i
$260$		0			0
$261$	19.2269	+	23.8535i	1.19011	+	1.47649i
$262$		0			0
$263$		−	18.9970i		−	1.17141i	−0.810525	−	0.585704i	$-0.800818\pi$
$263$		−	18.9970i		−	1.17141i	0.810525	−	0.585704i	$-0.199182\pi$
$264$		0			0
$265$	0.801194	+	0.462570i	0.0492170	+	0.0284154i
$266$		0			0
$267$	−0.964101	+	5.16915i	−0.0590020	+	0.316347i
$268$		0			0
$269$	−4.29788	+	7.44415i	−0.262046	+	0.453878i	−0.966786	−	0.255589i	$-0.917731\pi$
$269$	−4.29788	+	7.44415i	−0.262046	+	0.453878i	0.704739	+	0.709467i	$0.251064\pi$
$270$		0			0
$271$	1.58706	−	0.916292i	0.0964073	−	0.0556608i	−0.451021	−	0.892513i	$-0.648940\pi$
$271$	1.58706	−	0.916292i	0.0964073	−	0.0556608i	0.547429	+	0.836852i	$0.315607\pi$
$272$		0			0
$273$	2.34046	−	24.2448i	0.141651	−	1.46736i
$274$		0			0
$275$			26.8904i			1.62155i
$276$		0			0
$277$	15.8186			0.950449			0.475224	−	0.879865i	$-0.342367\pi$
$277$	15.8186			0.950449			0.475224	+	0.879865i	$0.342367\pi$
$278$		0			0
$279$	10.8182	+	13.4214i	0.647671	+	0.803521i
$280$		0			0
$281$	−9.95916	+	5.74992i	−0.594114	+	0.343012i	−0.766722	−	0.641979i	$-0.778114\pi$
$281$	−9.95916	+	5.74992i	−0.594114	+	0.343012i	0.172609	+	0.984990i	$0.444780\pi$
$282$		0			0
$283$	−8.59806	+	4.96409i	−0.511101	+	0.295085i	−0.733286	−	0.679920i	$-0.762014\pi$
$283$	−8.59806	+	4.96409i	−0.511101	+	0.295085i	0.222185	+	0.975005i	$0.428681\pi$
$284$		0			0
$285$	0.652028	+	0.121610i	0.0386228	+	0.00720355i
$286$		0			0
$287$	−14.2912	+	10.0258i	−0.843584	+	0.591802i
$288$		0			0
$289$	1.34887	+	2.33631i	0.0793454	+	0.137430i
$290$		0			0
$291$	−12.1541	−	2.26686i	−0.712484	−	0.132886i
$292$		0			0
$293$	8.63598	−	14.9580i	0.504520	−	0.873854i	−0.495467	−	0.868627i	$-0.665003\pi$
$293$	8.63598	−	14.9580i	0.504520	−	0.873854i	0.999986	−	0.00522664i	$-0.00166370\pi$
$294$		0			0
$295$	−0.0221594	−	0.0383812i	−0.00129017	−	0.00223464i
$296$		0			0
$297$	−23.8054	−	14.6994i	−1.38133	−	0.852947i
$298$		0			0
$299$	−6.21308	+	10.7614i	−0.359312	+	0.622346i
$300$		0			0
$301$	−0.333806	−	3.77675i	−0.0192402	−	0.217688i
$302$		0			0
$303$	−10.7534	−	9.20531i	−0.617764	−	0.528831i
$304$		0			0
$305$	−0.183908	−	0.106180i	−0.0105306	−	0.00607982i
$306$		0			0
$307$			21.6425i			1.23520i	0.786490	+	0.617602i	$0.211896\pi$
$307$			21.6425i			1.23520i	−0.786490	+	0.617602i	$0.788104\pi$
$308$		0			0
$309$	8.40978	−	9.82404i	0.478416	−	0.558870i
$310$		0			0
$311$	10.1016	+	17.4964i	0.572808	+	0.992133i	0.996276	+	0.0862215i	$0.0274793\pi$
$311$	10.1016	+	17.4964i	0.572808	+	0.992133i	−0.423468	+	0.905911i	$0.639187\pi$
$312$		0			0
$313$	−18.9146	−	10.9203i	−1.06911	−	0.617254i	−0.141175	−	0.989985i	$-0.545088\pi$
$313$	−18.9146	−	10.9203i	−1.06911	−	0.617254i	−0.927939	+	0.372731i	$0.878421\pi$
$314$		0			0
$315$	0.168004	−	0.582871i	0.00946593	−	0.0328411i
$316$		0			0
$317$	−21.5288	−	12.4297i	−1.20918	−	0.698120i	−0.246599	−	0.969117i	$-0.579313\pi$
$317$	−21.5288	−	12.4297i	−1.20918	−	0.698120i	−0.962580	+	0.270997i	$0.912647\pi$
$318$		0			0
$319$	−27.4940	−	47.6210i	−1.53937	−	2.66626i
$320$		0			0
$321$	−7.86421	−	1.46676i	−0.438938	−	0.0818664i
$322$		0			0
$323$		−	18.9496i		−	1.05439i
$324$		0			0
$325$	22.9888	+	13.2726i	1.27519	+	0.736230i
$326$		0			0
$327$	−17.0781	+	6.02593i	−0.944422	+	0.333235i
$328$		0			0
$329$	6.33283	−	4.44269i	0.349140	−	0.244933i
$330$		0			0
$331$	−8.07219	+	13.9814i	−0.443688	+	0.768490i	−0.997960	−	0.0638459i	$-0.979663\pi$
$331$	−8.07219	+	13.9814i	−0.443688	+	0.768490i	0.554272	+	0.832336i	$0.312997\pi$
$332$		0			0
$333$	−1.65595	+	1.33476i	−0.0907455	+	0.0731447i
$334$		0			0
$335$	−0.201449	−	0.348920i	−0.0110063	−	0.0190635i
$336$		0			0
$337$	−7.81522	+	13.5364i	−0.425722	+	0.737372i	−0.996488	−	0.0837408i	$-0.973313\pi$
$337$	−7.81522	+	13.5364i	−0.425722	+	0.737372i	0.570765	+	0.821113i	$0.306647\pi$
$338$		0			0
$339$	11.0722	+	31.3798i	0.601359	+	1.70431i
$340$		0			0
$341$	−15.4698	−	26.7946i	−0.837739	−	1.45101i
$342$		0			0
$343$	−4.84108	−	17.8764i	−0.261394	−	0.965232i
$344$		0			0
$345$	−0.201246	+	0.235089i	−0.0108347	+	0.0126568i
$346$		0			0
$347$	28.0445	−	16.1915i	1.50551	−	0.869206i	0.505529	−	0.862810i	$-0.331297\pi$
$347$	28.0445	−	16.1915i	1.50551	−	0.869206i	0.999980	−	0.00639573i	$-0.00203584\pi$
$348$		0			0
$349$	−26.0421	+	15.0354i	−1.39400	+	0.804827i	−0.993755	−	0.111581i	$-0.964409\pi$
$349$	−26.0421	+	15.0354i	−1.39400	+	0.804827i	−0.400246	+	0.916408i	$0.631075\pi$
$350$		0			0
$351$	−24.3165	+	13.0960i	−1.29792	+	0.699014i
$352$		0			0
$353$	17.0121			0.905465			0.452733	−	0.891646i	$-0.350449\pi$
$353$	17.0121			0.905465			0.452733	+	0.891646i	$0.350449\pi$
$354$		0			0
$355$			0.253808i			0.0134707i
$356$		0			0
$357$	−17.2503	−	1.66525i	−0.912985	−	0.0881346i
$358$		0			0
$359$	25.2692	−	14.5892i	1.33366	−	0.769987i	0.347798	−	0.937570i	$-0.386930\pi$
$359$	25.2692	−	14.5892i	1.33366	−	0.769987i	0.985858	+	0.167583i	$0.0535962\pi$
$360$		0			0
$361$	3.05356	−	5.28892i	0.160714	−	0.278364i
$362$		0			0
$363$	23.6729	+	20.2650i	1.24251	+	1.06364i
$364$		0			0
$365$	−0.471788	−	0.272387i	−0.0246945	−	0.0142574i
$366$		0			0
$367$		−	18.1266i		−	0.946200i	−0.881009	−	0.473100i	$-0.843135\pi$
$367$		−	18.1266i		−	0.946200i	0.881009	−	0.473100i	$-0.156865\pi$
$368$		0			0
$369$	18.4638	+	7.13559i	0.961185	+	0.371464i
$370$		0			0
$371$	−18.3936	−	26.2191i	−0.954946	−	1.36123i
$372$		0			0
$373$	−20.3646			−1.05444			−0.527219	−	0.849730i	$-0.676765\pi$
$373$	−20.3646			−1.05444			−0.527219	+	0.849730i	$0.676765\pi$
$374$		0			0
$375$	1.00500	+	0.860318i	0.0518978	+	0.0444266i
$376$		0			0
$377$	−54.2820			−2.79566
$378$		0			0
$379$	−21.9961			−1.12986			−0.564931	−	0.825138i	$-0.691097\pi$
$379$	−21.9961			−1.12986			−0.564931	+	0.825138i	$0.691097\pi$
$380$		0			0
$381$	−1.66431	−	1.42472i	−0.0852651	−	0.0729904i
$382$		0			0
$383$	32.6253			1.66708			0.833538	−	0.552462i	$-0.186312\pi$
$383$	32.6253			1.66708			0.833538	+	0.552462i	$0.186312\pi$
$384$		0			0
$385$	−0.459236	+	0.987125i	−0.0234048	+	0.0503085i
$386$		0			0
$387$	−3.34716	+	2.69795i	−0.170146	+	0.137145i
$388$		0			0
$389$			15.7501i			0.798560i	0.916829	+	0.399280i	$0.130740\pi$
$389$			15.7501i			0.798560i	−0.916829	+	0.399280i	$0.869260\pi$
$390$		0			0
$391$	7.65680	+	4.42066i	0.387221	+	0.223562i
$392$		0			0
$393$	19.0630	+	16.3187i	0.961600	+	0.823168i
$394$		0			0
$395$	−0.0358524	+	0.0620983i	−0.00180393	+	0.00312450i
$396$		0			0
$397$	−2.95864	+	1.70817i	−0.148490	+	0.0857308i	−0.572404	−	0.819972i	$-0.693989\pi$
$397$	−2.95864	+	1.70817i	−0.148490	+	0.0857308i	0.423914	+	0.905702i	$0.360656\pi$
$398$		0			0
$399$	−18.6904	−	13.3386i	−0.935691	−	0.667765i
$400$		0			0
$401$		−	0.983052i		−	0.0490913i	−0.999699	−	0.0245456i	$-0.992186\pi$
$401$		−	0.983052i		−	0.0490913i	0.999699	−	0.0245456i	$-0.00781390\pi$
$402$		0			0
$403$	−30.5424			−1.52143
$404$		0			0
$405$	−0.655112	+	0.209583i	−0.0325528	+	0.0104143i
$406$		0			0
$407$	3.30594	−	1.90868i	0.163869	−	0.0946099i
$408$		0			0
$409$	25.0195	−	14.4450i	1.23714	−	0.714260i	0.268627	−	0.963244i	$-0.413430\pi$
$409$	25.0195	−	14.4450i	1.23714	−	0.714260i	0.968508	+	0.248984i	$0.0800966\pi$
$410$		0			0
$411$	17.3520	−	20.2701i	0.855912	−	0.999849i
$412$		0			0
$413$	0.135080	+	1.52832i	0.00664684	+	0.0752037i
$414$		0			0
$415$	−0.496599	−	0.860135i	−0.0243771	−	0.0422223i
$416$		0			0
$417$	0.249355	+	0.706699i	0.0122110	+	0.0346072i
$418$		0			0
$419$	6.28926	−	10.8933i	0.307251	−	0.532174i	−0.670509	−	0.741901i	$-0.733924\pi$
$419$	6.28926	−	10.8933i	0.307251	−	0.532174i	0.977760	+	0.209727i	$0.0672577\pi$
$420$		0			0
$421$	−13.0232	−	22.5568i	−0.634710	−	1.09935i	−0.986576	−	0.163300i	$-0.947786\pi$
$421$	−13.0232	−	22.5568i	−0.634710	−	1.09935i	0.351866	−	0.936050i	$-0.385547\pi$
$422$		0			0
$423$	−8.18180	−	3.16197i	−0.397813	−	0.153740i
$424$		0			0
$425$	9.44354	−	16.3567i	0.458079	−	0.793416i
$426$		0			0
$427$	4.22211	+	6.01840i	0.204322	+	0.291251i
$428$		0			0
$429$	46.7454	−	16.4939i	2.25689	−	0.796331i
$430$		0			0
$431$	6.28454	+	3.62838i	0.302716	+	0.174773i	0.643662	−	0.765310i	$-0.277414\pi$
$431$	6.28454	+	3.62838i	0.302716	+	0.174773i	−0.340947	+	0.940083i	$0.610748\pi$
$432$		0			0
$433$			8.29113i			0.398446i	0.979954	+	0.199223i	$0.0638419\pi$
$433$			8.29113i			0.398446i	−0.979954	+	0.199223i	$0.936158\pi$
$434$		0			0
$435$	−1.32893	−	0.247858i	−0.0637171	−	0.0118839i
$436$		0			0
$437$	5.85710	+	10.1448i	0.280183	+	0.485292i
$438$		0			0
$439$	−2.83357	−	1.63596i	−0.135239	−	0.0780802i	0.430854	−	0.902422i	$-0.358212\pi$
$439$	−2.83357	−	1.63596i	−0.135239	−	0.0780802i	−0.566093	+	0.824341i	$0.691546\pi$
$440$		0			0
$441$	−13.7849	+	15.8422i	−0.656426	+	0.754390i
$442$		0			0
$443$	2.46737	+	1.42454i	0.117228	+	0.0676817i	0.557468	−	0.830199i	$-0.311773\pi$
$443$	2.46737	+	1.42454i	0.117228	+	0.0676817i	−0.440239	+	0.897880i	$0.645106\pi$
$444$		0			0
$445$	−0.116008	−	0.200931i	−0.00549929	−	0.00952505i
$446$		0			0
$447$	−5.26145	+	6.14626i	−0.248858	+	0.290708i
$448$		0			0
$449$			19.9802i			0.942925i	0.881886	+	0.471463i	$0.156274\pi$
$449$			19.9802i			0.942925i	−0.881886	+	0.471463i	$0.843726\pi$
$450$		0			0
$451$	−30.7675	−	17.7636i	−1.44878	−	0.836455i
$452$		0			0
$453$	10.8494	+	9.28749i	0.509747	+	0.436364i
$454$		0			0
$455$	0.617229	+	0.879828i	0.0289361	+	0.0412470i
$456$		0			0
$457$	−9.15008	+	15.8484i	−0.428023	+	0.741357i	−0.996697	−	0.0812053i	$-0.974123\pi$
$457$	−9.15008	+	15.8484i	−0.428023	+	0.741357i	0.568675	+	0.822563i	$0.307456\pi$
$458$		0			0
$459$	9.31792	+	17.3014i	0.434923	+	0.807559i
$460$		0			0
$461$	4.52954	+	7.84539i	0.210962	+	0.365396i	0.952016	−	0.306049i	$-0.0990071\pi$
$461$	4.52954	+	7.84539i	0.210962	+	0.365396i	−0.741054	+	0.671445i	$0.765674\pi$
$462$		0			0
$463$	10.8227	−	18.7455i	0.502974	−	0.871176i	−0.497021	−	0.867739i	$-0.665573\pi$
$463$	10.8227	−	18.7455i	0.502974	−	0.871176i	0.999994	−	0.00343694i	$-0.00109401\pi$
$464$		0			0
$465$	−0.747737	−	0.139461i	−0.0346755	−	0.00646733i
$466$		0			0
$467$	−13.7761	−	23.8610i	−0.637484	−	1.10415i	−0.985983	−	0.166845i	$-0.946642\pi$
$467$	−13.7761	−	23.8610i	−0.637484	−	1.10415i	0.348500	−	0.937309i	$-0.386691\pi$
$468$		0			0
$469$	1.22800	+	13.8938i	0.0567038	+	0.641558i
$470$		0			0
$471$	−29.9503	−	5.58604i	−1.38004	−	0.257391i
$472$		0			0
$473$	6.68227	−	3.85801i	0.307251	−	0.177392i
$474$		0			0
$475$	21.6716	−	12.5121i	0.994362	−	0.574095i
$476$		0			0
$477$	−13.0912	+	33.8742i	−0.599403	+	1.55099i
$478$		0			0
$479$	4.94651			0.226012			0.113006	−	0.993594i	$-0.463952\pi$
$479$	4.94651			0.226012			0.113006	+	0.993594i	$0.463952\pi$
$480$		0			0
$481$		−	3.76835i		−	0.171822i
$482$		0			0
$483$	9.74979	−	4.44037i	0.443631	−	0.202044i
$484$		0			0
$485$	0.472443	−	0.272765i	0.0214525	−	0.0123856i
$486$		0			0
$487$	−4.78573	+	8.28913i	−0.216862	+	0.375616i	−0.953847	−	0.300293i	$-0.902916\pi$
$487$	−4.78573	+	8.28913i	−0.216862	+	0.375616i	0.736985	+	0.675909i	$0.236249\pi$
$488$		0			0
$489$	−3.34780	+	17.9496i	−0.151393	+	0.811711i
$490$		0			0
$491$	−33.0010	−	19.0531i	−1.48931	−	0.859855i	−0.489387	−	0.872067i	$-0.662779\pi$
$491$	−33.0010	−	19.0531i	−1.48931	−	0.859855i	−0.999925	+	0.0122119i	$0.996113\pi$
$492$		0			0
$493$			38.6220i			1.73945i
$494$		0			0
$495$	1.21973	−	0.190356i	0.0548227	−	0.00855586i
$496$		0			0
$497$	3.70631	−	7.96668i	0.166251	−	0.357355i
$498$		0			0
$499$	−24.8384			−1.11192			−0.555960	−	0.831209i	$-0.687649\pi$
$499$	−24.8384			−1.11192			−0.555960	+	0.831209i	$0.687649\pi$
$500$		0			0
$501$	14.9990	−	5.29232i	0.670106	−	0.236443i
$502$		0			0
$503$	27.2820			1.21645			0.608223	−	0.793766i	$-0.291883\pi$
$503$	27.2820			1.21645			0.608223	+	0.793766i	$0.291883\pi$
$504$		0			0
$505$	0.624584			0.0277936
$506$		0			0
$507$	4.84348	−	25.9690i	0.215106	−	1.15332i
$508$		0			0
$509$	41.7721			1.85152			0.925758	−	0.378117i	$-0.123428\pi$
$509$	41.7721			1.85152			0.925758	+	0.378117i	$0.123428\pi$
$510$		0			0
$511$	10.8312	+	15.4393i	0.479142	+	0.682993i
$512$		0			0
$513$	−0.769953	+	26.0250i	−0.0339942	+	1.14903i
$514$		0			0
$515$			0.570607i			0.0251439i
$516$		0			0
$517$	13.6339	+	7.87154i	0.599619	+	0.346190i
$518$		0			0
$519$	3.99710	−	1.41036i	0.175453	−	0.0619078i
$520$		0			0
$521$	−2.02629	+	3.50963i	−0.0887732	+	0.153760i	−0.906993	−	0.421146i	$-0.861628\pi$
$521$	−2.02629	+	3.50963i	−0.0887732	+	0.153760i	0.818220	+	0.574906i	$0.194961\pi$
$522$		0			0
$523$	26.2429	−	15.1514i	1.14752	−	0.662523i	0.199241	−	0.979951i	$-0.436152\pi$
$523$	26.2429	−	15.1514i	1.14752	−	0.662523i	0.948282	+	0.317428i	$0.102819\pi$
$524$		0			0
$525$	−9.48565	−	20.8278i	−0.413988	−	0.908999i
$526$		0			0
$527$			21.7312i			0.946625i
$528$		0			0
$529$	17.5345			0.762370
$530$		0			0
$531$	1.35448	−	1.09177i	0.0587795	−	0.0473788i
$532$		0			0
$533$	−30.3724	+	17.5355i	−1.31558	+	0.759548i
$534$		0			0
$535$	0.305691	−	0.176491i	0.0132162	−	0.00763037i
$536$		0			0
$537$	−3.36406	−	9.53410i	−0.145170	−	0.411427i
$538$		0			0
$539$	28.8296	−	24.2783i	1.24178	−	1.04574i
$540$		0			0
$541$	8.82681	+	15.2885i	0.379494	+	0.657303i	0.990989	−	0.133946i	$-0.0427647\pi$
$541$	8.82681	+	15.2885i	0.379494	+	0.657303i	−0.611495	+	0.791249i	$0.709431\pi$
$542$		0			0
$543$	−18.1012	+	21.1453i	−0.776798	+	0.907431i
$544$		0			0
$545$	0.399541	−	0.692026i	0.0171145	−	0.0296431i
$546$		0			0
$547$	−2.18319	−	3.78140i	−0.0933466	−	0.161681i	0.815571	−	0.578657i	$-0.196423\pi$
$547$	−2.18319	−	3.78140i	−0.0933466	−	0.161681i	−0.908917	+	0.416976i	$0.863090\pi$
$548$		0			0
$549$	3.00498	−	7.77558i	0.128250	−	0.331853i
$550$		0			0
$551$	−25.5859	+	44.3161i	−1.09000	+	1.88793i
$552$		0			0
$553$	2.03217	−	1.42563i	0.0864165	−	0.0606240i
$554$		0			0
$555$	0.0172068	−	0.0922564i	0.000730387	−	0.00391607i
$556$		0			0
$557$	−14.7527	−	8.51750i	−0.625094	−	0.360898i	0.153756	−	0.988109i	$-0.450863\pi$
$557$	−14.7527	−	8.51750i	−0.625094	−	0.360898i	−0.778849	+	0.627211i	$0.784196\pi$
$558$		0			0
$559$		−	7.61695i		−	0.322163i
$560$		0			0
$561$	−11.7355	−	33.2597i	−0.495474	−	1.40423i
$562$		0			0
$563$	−6.45992	−	11.1889i	−0.272253	−	0.471556i	0.697185	−	0.716891i	$-0.254436\pi$
$563$	−6.45992	−	11.1889i	−0.272253	−	0.471556i	−0.969438	+	0.245335i	$0.921102\pi$
$564$		0			0
$565$	−1.27155	−	0.734127i	−0.0534943	−	0.0308850i
$566$		0			0
$567$	23.6236	+	2.98793i	0.992096	+	0.125481i
$568$		0			0
$569$	−18.8280	−	10.8704i	−0.789313	−	0.455710i	0.0504079	−	0.998729i	$-0.483948\pi$
$569$	−18.8280	−	10.8704i	−0.789313	−	0.455710i	−0.839720	+	0.543019i	$0.817281\pi$
$570$		0			0
$571$	16.8254	+	29.1425i	0.704122	+	1.21958i	0.967007	+	0.254748i	$0.0819925\pi$
$571$	16.8254	+	29.1425i	0.704122	+	1.21958i	−0.262885	+	0.964827i	$0.584674\pi$
$572$		0			0
$573$	4.59457	+	13.0215i	0.191941	+	0.543980i
$574$		0			0
$575$			11.6755i			0.486904i
$576$		0			0
$577$	12.5598	+	7.25141i	0.522871	+	0.301880i	0.738109	−	0.674682i	$-0.235719\pi$
$577$	12.5598	+	7.25141i	0.522871	+	0.301880i	−0.215237	+	0.976562i	$0.569052\pi$
$578$		0			0
$579$	−0.228032	+	1.22262i	−0.00947668	+	0.0508105i
$580$		0			0
$581$	3.02718	+	34.2502i	0.125589	+	1.42094i
$582$		0			0
$583$	32.5897	−	56.4469i	1.34973	−	2.33779i
$584$		0			0
$585$	0.439297	−	1.13671i	0.0181627	−	0.0469971i
$586$		0			0
$587$	15.8417	+	27.4386i	0.653857	+	1.13251i	0.982179	+	0.187948i	$0.0601837\pi$
$587$	15.8417	+	27.4386i	0.653857	+	1.13251i	−0.328322	+	0.944566i	$0.606483\pi$
$588$		0			0
$589$	−14.3963	+	24.9350i	−0.593187	+	1.02743i
$590$		0			0
$591$	−15.2099	+	17.7677i	−0.625651	+	0.730866i
$592$		0			0
$593$	−3.54101	−	6.13320i	−0.145412	−	0.251860i	0.784115	−	0.620616i	$-0.213117\pi$
$593$	−3.54101	−	6.13320i	−0.145412	−	0.251860i	−0.929526	+	0.368755i	$0.879784\pi$
$594$		0			0
$595$	0.626005	−	0.439163i	0.0256637	−	0.0180039i
$596$		0			0
$597$	−14.1459	−	40.0911i	−0.578955	−	1.64082i
$598$		0			0
$599$	−5.20178	+	3.00325i	−0.212539	+	0.122709i	−0.602491	−	0.798126i	$-0.705825\pi$
$599$	−5.20178	+	3.00325i	−0.212539	+	0.122709i	0.389952	+	0.920835i	$0.372492\pi$
$600$		0			0
$601$	−0.530083	+	0.306043i	−0.0216225	+	0.0124838i	−0.510772	−	0.859716i	$-0.670640\pi$
$601$	−0.530083	+	0.306043i	−0.0216225	+	0.0124838i	0.489150	+	0.872200i	$0.337307\pi$
$602$		0			0
$603$	12.3135	−	9.92519i	0.501444	−	0.404185i
$604$		0			0
$605$	−1.37499			−0.0559012
$606$		0			0
$607$		−	2.04959i		−	0.0831904i	−0.999135	−	0.0415952i	$-0.986756\pi$
$607$		−	2.04959i		−	0.0831904i	0.999135	−	0.0415952i	$-0.0132440\pi$
$608$		0			0
$609$	38.0937	+	27.1860i	1.54363	+	1.10163i
$610$		0			0
$611$	13.4588	−	7.77047i	0.544487	−	0.314360i
$612$		0			0
$613$	−4.93166	+	8.54189i	−0.199188	+	0.345003i	−0.948265	−	0.317479i	$-0.897164\pi$
$613$	−4.93166	+	8.54189i	−0.199188	+	0.345003i	0.749077	+	0.662482i	$0.230497\pi$
$614$		0			0
$615$	−0.823644	+	0.290619i	−0.0332125	+	0.0117189i
$616$		0			0
$617$	23.2143	+	13.4028i	0.934571	+	0.539575i	0.888254	−	0.459352i	$-0.151918\pi$
$617$	23.2143	+	13.4028i	0.934571	+	0.539575i	0.0463170	+	0.998927i	$0.485252\pi$
$618$		0			0
$619$			0.0696297i			0.00279865i	0.999999	+	0.00139933i	$0.000445420\pi$
$619$			0.0696297i			0.00279865i	−0.999999	+	0.00139933i	$0.999555\pi$
$620$		0			0
$621$	−10.3361	−	6.38233i	−0.414772	−	0.256114i
$622$		0			0
$623$	0.707163	+	8.00098i	0.0283319	+	0.320553i
$624$		0			0
$625$	24.9124			0.996497
$626$		0			0
$627$	8.56785	−	45.9377i	0.342167	−	1.83457i
$628$		0			0
$629$	−2.68121			−0.106907
$630$		0			0
$631$	11.8214			0.470603			0.235301	−	0.971922i	$-0.424392\pi$
$631$	11.8214			0.470603			0.235301	+	0.971922i	$0.424392\pi$
$632$		0			0
$633$	38.4942	−	13.5825i	1.53001	−	0.539855i
$634$		0			0
$635$	0.0966675			0.00383613
$636$		0			0
$637$	−6.52600	−	36.6299i	−0.258569	−	1.45133i
$638$		0			0
$639$	−9.84394	+	1.53628i	−0.389420	+	0.0607745i
$640$		0			0
$641$			20.5159i			0.810330i	0.914244	+	0.405165i	$0.132786\pi$
$641$			20.5159i			0.810330i	−0.914244	+	0.405165i	$0.867214\pi$
$642$		0			0
$643$	−15.6081	−	9.01132i	−0.615522	−	0.355372i	0.159602	−	0.987182i	$-0.448979\pi$
$643$	−15.6081	−	9.01132i	−0.615522	−	0.355372i	−0.775123	+	0.631810i	$0.782312\pi$
$644$		0			0
$645$	0.0347800	−	0.186477i	0.00136946	−	0.00734254i
$646$		0			0
$647$	−9.11827	+	15.7933i	−0.358476	+	0.620899i	−0.987706	−	0.156320i	$-0.950037\pi$
$647$	−9.11827	+	15.7933i	−0.358476	+	0.620899i	0.629230	+	0.777219i	$0.283370\pi$
$648$		0			0
$649$	−2.70409	+	1.56121i	−0.106145	+	0.0612827i
$650$		0			0
$651$	21.4339	+	15.2965i	0.840061	+	0.599518i
$652$		0			0
$653$		−	9.00158i		−	0.352259i	−0.984367	−	0.176129i	$-0.943642\pi$
$653$		−	9.00158i		−	0.352259i	0.984367	−	0.176129i	$-0.0563577\pi$
$654$		0			0
$655$	−1.10723			−0.0432630
$656$		0			0
$657$	7.70881	−	19.9470i	0.300749	−	0.778207i
$658$		0			0
$659$	30.4806	−	17.5980i	1.18735	−	0.685519i	0.229650	−	0.973273i	$-0.426242\pi$
$659$	30.4806	−	17.5980i	1.18735	−	0.685519i	0.957704	+	0.287754i	$0.0929086\pi$
$660$		0			0
$661$	−10.8797	+	6.28141i	−0.423172	+	0.244318i	−0.696433	−	0.717621i	$-0.745231\pi$
$661$	−10.8797	+	6.28141i	−0.423172	+	0.244318i	0.273262	+	0.961940i	$0.411898\pi$
$662$		0			0
$663$	−34.2263	−	6.38356i	−1.32924	−	0.247917i
$664$		0			0
$665$	1.00923	−	0.0892002i	0.0391363	−	0.00345904i
$666$		0			0
$667$	−11.9376	−	20.6765i	−0.462226	−	0.800599i
$668$		0			0
$669$	12.7302	+	2.37432i	0.492180	+	0.0917966i
$670$		0			0
$671$	−7.48072	+	12.9570i	−0.288790	+	0.500199i
$672$		0			0
$673$	23.8913	+	41.3810i	0.920942	+	1.59512i	0.797960	+	0.602710i	$0.205913\pi$
$673$	23.8913	+	41.3810i	0.920942	+	1.59512i	0.122982	+	0.992409i	$0.460754\pi$
$674$		0			0
$675$	−13.6341	+	22.0802i	−0.524778	+	0.849867i
$676$		0			0
$677$	−18.5235	+	32.0837i	−0.711918	+	1.23308i	0.252219	+	0.967670i	$0.418840\pi$
$677$	−18.5235	+	32.0837i	−0.711918	+	1.23308i	−0.964136	+	0.265407i	$0.914494\pi$
$678$		0			0
$679$	−18.8125	+	1.66273i	−0.721956	+	0.0638097i
$680$		0			0
$681$	−0.838685	−	0.717949i	−0.0321385	−	0.0275118i
$682$		0			0
$683$	−21.6844	−	12.5195i	−0.829732	−	0.479046i	0.0240289	−	0.999711i	$-0.492351\pi$
$683$	−21.6844	−	12.5195i	−0.829732	−	0.479046i	−0.853761	+	0.520665i	$0.825684\pi$
$684$		0			0
$685$			1.17734i			0.0449839i
$686$		0			0
$687$	2.05954	−	2.40589i	0.0785763	−	0.0917904i
$688$		0			0
$689$	−32.1712	−	55.7222i	−1.22563	−	2.12285i
$690$		0			0
$691$	40.2655	+	23.2473i	1.53177	+	0.884370i	0.999280	+	0.0379352i	$0.0120781\pi$
$691$	40.2655	+	23.2473i	1.53177	+	0.884370i	0.532493	+	0.846434i	$0.321255\pi$
$692$		0			0
$693$	−41.0653	−	11.8364i	−1.55994	−	0.449629i
$694$		0			0
$695$	−0.0286363	−	0.0165332i	−0.00108624	−	0.000627139i
$696$		0			0
$697$	12.4767	+	21.6102i	0.472587	+	0.818545i
$698$		0			0
$699$	−34.2558	−	6.38905i	−1.29567	−	0.241656i
$700$		0			0
$701$		−	36.0041i		−	1.35986i	−0.733279	−	0.679928i	$-0.762011\pi$
$701$		−	36.0041i		−	1.35986i	0.733279	−	0.679928i	$-0.237989\pi$
$702$		0			0
$703$	−3.07651	−	1.77622i	−0.116033	−	0.0669915i
$704$		0			0
$705$	0.364979	−	0.128781i	0.0137459	−	0.00485018i
$706$		0			0
$707$	−19.6048	−	9.12067i	−0.737315	−	0.343018i
$708$		0			0
$709$	−15.9158	+	27.5670i	−0.597731	+	1.03530i	0.395424	+	0.918499i	$0.370598\pi$
$709$	−15.9158	+	27.5670i	−0.597731	+	1.03530i	−0.993155	+	0.116802i	$0.962736\pi$
$710$		0			0
$711$	−2.62549	−	1.01466i	−0.0984636	−	0.0380527i
$712$		0			0
$713$	−6.71685	−	11.6339i	−0.251548	−	0.435694i
$714$		0			0
$715$	−1.09360	+	1.89418i	−0.0408985	+	0.0708382i
$716$		0			0
$717$	1.60683	+	4.55393i	0.0600082	+	0.170070i
$718$		0			0
$719$	−20.0271	−	34.6879i	−0.746883	−	1.29364i	−0.949310	−	0.314342i	$-0.898216\pi$
$719$	−20.0271	−	34.6879i	−0.746883	−	1.29364i	0.202427	−	0.979297i	$-0.435117\pi$
$720$		0			0
$721$	8.33245	−	17.9106i	0.310317	−	0.667024i
$722$		0			0
$723$	−26.0518	+	30.4330i	−0.968878	+	1.13181i
$724$		0			0
$725$	−44.1699	+	25.5015i	−1.64043	+	0.947101i
$726$		0			0
$727$	−3.39242	+	1.95862i	−0.125818	+	0.0726411i	−0.561588	−	0.827417i	$-0.689809\pi$
$727$	−3.39242	+	1.95862i	−0.125818	+	0.0726411i	0.435770	+	0.900058i	$0.356476\pi$
$728$		0			0
$729$	−12.0940	−	24.1399i	−0.447927	−	0.894070i
$730$		0			0
$731$	−5.41952			−0.200448
$732$		0			0
$733$		−	23.5835i		−	0.871078i	−0.900170	−	0.435539i	$-0.856558\pi$
$733$		−	23.5835i		−	0.871078i	0.900170	−	0.435539i	$-0.143442\pi$
$734$		0			0
$735$	0.00748776	−	0.926567i	0.000276190	−	0.0341769i
$736$		0			0
$737$	−24.5827	+	14.1928i	−0.905514	+	0.522798i
$738$		0			0
$739$	16.8641	−	29.2094i	0.620355	−	1.07449i	−0.369065	−	0.929404i	$-0.620322\pi$
$739$	16.8641	−	29.2094i	0.620355	−	1.07449i	0.989420	−	0.145083i	$-0.0463448\pi$
$740$		0			0
$741$	−35.0434	−	29.9986i	−1.28735	−	1.10203i
$742$		0			0
$743$	29.4003	+	16.9743i	1.07859	+	0.622725i	0.930516	−	0.366251i	$-0.119359\pi$
$743$	29.4003	+	16.9743i	1.07859	+	0.622725i	0.148076	+	0.988976i	$0.452692\pi$
$744$		0			0
$745$		−	0.356991i		−	0.0130792i
$746$		0			0
$747$	30.3544	−	24.4669i	1.11061	−	0.895197i
$748$		0			0
$749$	−12.1725	+	1.07586i	−0.444773	+	0.0393110i
$750$		0			0
$751$	3.39663			0.123945			0.0619724	−	0.998078i	$-0.480261\pi$
$751$	3.39663			0.123945			0.0619724	+	0.998078i	$0.480261\pi$
$752$		0			0
$753$	−24.5448	−	21.0113i	−0.894461	−	0.765695i
$754$		0			0
$755$	−0.630160			−0.0229339
$756$		0			0
$757$	29.1344			1.05891			0.529454	−	0.848339i	$-0.322397\pi$
$757$	29.1344			1.05891			0.529454	+	0.848339i	$0.322397\pi$
$758$		0			0
$759$	16.5629	+	14.1785i	0.601194	+	0.514646i
$760$		0			0
$761$	16.7258			0.606309			0.303154	−	0.952941i	$-0.401960\pi$
$761$	16.7258			0.606309			0.303154	+	0.952941i	$0.401960\pi$
$762$		0			0
$763$	−22.6465	+	15.8873i	−0.819860	+	0.575159i
$764$		0			0
$765$	−0.808777	−	0.312564i	−0.0292414	−	0.0113008i
$766$		0			0
$767$			3.08232i			0.111296i
$768$		0			0
$769$	−24.0816	−	13.9035i	−0.868404	−	0.501373i	−0.00158643	−	0.999999i	$-0.500505\pi$
$769$	−24.0816	−	13.9035i	−0.868404	−	0.501373i	−0.866818	+	0.498625i	$0.833838\pi$
$770$		0			0
$771$	−14.3075	−	12.2478i	−0.515273	−	0.441095i
$772$		0			0
$773$	−6.42238	+	11.1239i	−0.230997	+	0.400098i	−0.958102	−	0.286428i	$-0.907532\pi$
$773$	−6.42238	+	11.1239i	−0.230997	+	0.400098i	0.727105	+	0.686526i	$0.240865\pi$
$774$		0			0
$775$	−24.8527	+	14.3487i	−0.892736	+	0.515421i
$776$		0			0
$777$	−1.88730	+	2.64453i	−0.0677065	+	0.0948721i
$778$		0			0
$779$			33.0617i			1.18456i
$780$		0			0
$781$	17.8817			0.639856
$782$		0			0
$783$	1.56927	−	53.0426i	0.0560812	−	1.89559i
$784$		0			0
$785$	1.16420	−	0.672153i	0.0415522	−	0.0239902i
$786$		0			0
$787$	6.55243	−	3.78305i	0.233569	−	0.134851i	−0.378648	−	0.925541i	$-0.623611\pi$
$787$	6.55243	−	3.78305i	0.233569	−	0.134851i	0.612217	+	0.790689i	$0.290278\pi$
$788$		0			0
$789$	−21.3977	+	24.9961i	−0.761777	+	0.889884i
$790$		0			0
$791$	29.1917	+	41.6113i	1.03794	+	1.47953i
$792$		0			0
$793$	7.38467	+	12.7906i	0.262237	+	0.454208i
$794$		0			0
$795$	−0.533178	−	1.51108i	−0.0189099	−	0.0535926i
$796$		0			0
$797$	−4.03362	+	6.98643i	−0.142878	+	0.247472i	−0.928579	−	0.371134i	$-0.878969\pi$
$797$	−4.03362	+	6.98643i	−0.142878	+	0.247472i	0.785701	+	0.618606i	$0.212302\pi$
$798$		0			0
$799$	−5.52875	−	9.57608i	−0.195593	−	0.338777i
$800$		0			0
$801$	7.09092	−	5.71557i	0.250545	−	0.201950i
$802$		0			0
$803$	−19.1906	+	33.2391i	−0.677222	+	1.17298i
$804$		0			0
$805$	−0.199396	+	0.428599i	−0.00702777	+	0.0151061i
$806$		0			0
$807$	14.0399	−	4.95392i	0.494229	−	0.174386i
$808$		0			0
$809$	−0.0849492	−	0.0490454i	−0.00298665	−	0.00172435i	0.498506	−	0.866886i	$-0.333882\pi$
$809$	−0.0849492	−	0.0490454i	−0.00298665	−	0.00172435i	−0.501493	+	0.865162i	$0.667216\pi$
$810$		0			0
$811$		−	30.3085i		−	1.06428i	−0.846658	−	0.532138i	$-0.821389\pi$
$811$		−	30.3085i		−	1.06428i	0.846658	−	0.532138i	$-0.178611\pi$
$812$		0			0
$813$	−3.12032	−	0.581972i	−0.109434	−	0.0204107i
$814$		0			0
$815$	−0.402831	−	0.697724i	−0.0141106	−	0.0244402i
$816$		0			0
$817$	−6.21853	−	3.59027i	−0.217559	−	0.125608i
$818$		0			0
$819$	−30.3881	+	29.2647i	−1.06184	+	1.02259i
$820$		0			0
$821$	−19.5499	−	11.2871i	−0.682295	−	0.393923i	0.118424	−	0.992963i	$-0.462216\pi$
$821$	−19.5499	−	11.2871i	−0.682295	−	0.393923i	−0.800719	+	0.599040i	$0.795549\pi$
$822$		0			0
$823$	12.2655	+	21.2445i	0.427549	+	0.740536i	0.996655	−	0.0817282i	$-0.0260439\pi$
$823$	12.2655	+	21.2445i	0.427549	+	0.740536i	−0.569106	+	0.822264i	$0.692711\pi$
$824$		0			0
$825$	30.2885	−	35.3821i	1.05451	−	1.23185i
$826$		0			0
$827$			40.3057i			1.40157i	0.713375	+	0.700783i	$0.247166\pi$
$827$			40.3057i			1.40157i	−0.713375	+	0.700783i	$0.752834\pi$
$828$		0			0
$829$	−46.8081	−	27.0247i	−1.62571	−	0.938605i	−0.985353	−	0.170529i	$-0.945452\pi$
$829$	−46.8081	−	27.0247i	−1.62571	−	0.938605i	−0.640359	−	0.768076i	$-0.721214\pi$
$830$		0			0
$831$	−20.8139	−	17.8176i	−0.722027	−	0.618085i
$832$		0			0
$833$	−26.0624	+	4.64330i	−0.903010	+	0.160881i
$834$		0			0
$835$	−0.350900	+	0.607777i	−0.0121434	+	0.0210330i
$836$		0			0
$837$	0.882971	−	29.8451i	0.0305200	−	1.03160i
$838$		0			0
$839$	−11.8650	−	20.5507i	−0.409624	−	0.709489i	0.585224	−	0.810872i	$-0.301007\pi$
$839$	−11.8650	−	20.5507i	−0.409624	−	0.709489i	−0.994847	+	0.101383i	$0.967673\pi$
$840$		0			0
$841$	37.6478	−	65.2079i	1.29820	−	2.24855i
$842$		0			0
$843$	19.5807	+	3.65200i	0.674394	+	0.125781i
$844$		0			0
$845$	0.582803	+	1.00944i	0.0200490	+	0.0347259i
$846$		0			0
$847$	43.1589	+	20.0787i	1.48296	+	0.689911i
$848$		0			0
$849$	16.9046	+	3.15288i	0.580165	+	0.108207i
$850$		0			0
$851$	1.43540	−	0.828731i	0.0492050	−	0.0284085i
$852$		0			0
$853$	48.0748	−	27.7560i	1.64605	−	0.950347i	0.667429	−	0.744673i	$-0.267395\pi$
$853$	48.0748	−	27.7560i	1.64605	−	0.950347i	0.978621	−	0.205674i	$-0.0659387\pi$
$854$		0			0
$855$	−0.720953	−	0.894436i	−0.0246561	−	0.0305891i
$856$		0			0
$857$	30.6097			1.04561			0.522803	−	0.852453i	$-0.324886\pi$
$857$	30.6097			1.04561			0.522803	+	0.852453i	$0.324886\pi$
$858$		0			0
$859$			42.1401i			1.43780i	0.695113	+	0.718900i	$0.255354\pi$
$859$			42.1401i			1.43780i	−0.695113	+	0.718900i	$0.744646\pi$
$860$		0			0
$861$	30.0969	+	2.90539i	1.02570	+	0.0990154i
$862$		0			0
$863$	22.7782	−	13.1510i	0.775379	−	0.447665i	−0.0594112	−	0.998234i	$-0.518922\pi$
$863$	22.7782	−	13.1510i	0.775379	−	0.447665i	0.834790	+	0.550568i	$0.185589\pi$
$864$		0			0
$865$	−0.0935118	+	0.161967i	−0.00317950	+	0.00550705i
$866$		0			0
$867$	0.856720	−	4.59342i	0.0290957	−	0.156001i
$868$		0			0
$869$	4.37504	+	2.52593i	0.148413	+	0.0856863i
$870$		0			0
$871$			28.0211i			0.949460i
$872$		0			0
$873$	13.4389	+	16.6727i	0.454836	+	0.564284i
$874$		0			0
$875$	1.83224	+	0.852407i	0.0619411	+	0.0288166i
$876$		0			0
$877$	35.7066			1.20573			0.602863	−	0.797845i	$-0.294027\pi$
$877$	35.7066			1.20573			0.602863	+	0.797845i	$0.294027\pi$
$878$		0			0
$879$	−28.2113	+	9.95421i	−0.951543	+	0.335747i
$880$		0			0
$881$	−12.4482			−0.419392			−0.209696	−	0.977767i	$-0.567247\pi$
$881$	−12.4482			−0.419392			−0.209696	+	0.977767i	$0.567247\pi$
$882$		0			0
$883$	2.35637			0.0792982			0.0396491	−	0.999214i	$-0.487376\pi$
$883$	2.35637			0.0792982			0.0396491	+	0.999214i	$0.487376\pi$
$884$		0			0
$885$	−0.0140743	+	0.0754610i	−0.000473101	+	0.00253660i
$886$		0			0
$887$	−33.4597			−1.12347			−0.561734	−	0.827318i	$-0.689866\pi$
$887$	−33.4597			−1.12347			−0.561734	+	0.827318i	$0.689866\pi$
$888$		0			0
$889$	−3.03426	−	1.41162i	−0.101766	−	0.0473441i
$890$		0			0
$891$	14.7659	+	46.1549i	0.494676	+	1.54625i
$892$		0			0
$893$		−	14.6505i		−	0.490261i
$894$		0			0
$895$	0.386333	+	0.223049i	0.0129137	+	0.00745572i
$896$		0			0
$897$	20.2964	−	7.16147i	0.677676	−	0.239114i
$898$		0			0
$899$	29.3416	−	50.8212i	0.978597	−	1.69498i
$900$		0			0
$901$	−39.6468	+	22.8901i	−1.32083	+	0.762579i
$902$		0			0
$903$	−3.81479	+	5.34538i	−0.126948	+	0.177883i
$904$		0			0
$905$		−	1.22817i		−	0.0408259i
$906$		0			0
$907$	−0.935925			−0.0310769			−0.0155384	−	0.999879i	$-0.504946\pi$
$907$	−0.935925			−0.0310769			−0.0155384	+	0.999879i	$0.504946\pi$
$908$		0			0
$909$	3.78057	+	24.2245i	0.125394	+	0.803475i
$910$		0			0
$911$	28.8739	−	16.6703i	0.956634	−	0.552313i	0.0614988	−	0.998107i	$-0.480412\pi$
$911$	28.8739	−	16.6703i	0.956634	−	0.552313i	0.895136	+	0.445794i	$0.147079\pi$
$912$		0			0
$913$	−60.5995	+	34.9871i	−2.00555	+	1.15791i
$914$		0			0
$915$	0.122387	+	0.346858i	0.00404599	+	0.0114668i
$916$		0			0
$917$	34.7544	+	16.1686i	1.14769	+	0.533935i
$918$		0			0
$919$	−1.73484	−	3.00483i	−0.0572270	−	0.0991200i	0.835993	−	0.548741i	$-0.184893\pi$
$919$	−1.73484	−	3.00483i	−0.0572270	−	0.0991200i	−0.893220	+	0.449621i	$0.851559\pi$
$920$		0			0
$921$	24.3774	−	28.4770i	0.803264	−	0.938348i
$922$		0			0
$923$	8.82603	−	15.2871i	0.290512	−	0.503182i
$924$		0			0
$925$	−1.77036	−	3.06635i	−0.0582090	−	0.100821i
$926$		0			0
$927$	−22.1310	+	3.45385i	−0.726876	+	0.113439i
$928$		0			0
$929$	7.57680	−	13.1234i	0.248587	−	0.430565i	−0.714547	−	0.699587i	$-0.753367\pi$
$929$	7.57680	−	13.1234i	0.248587	−	0.430565i	0.963134	+	0.269022i	$0.0867005\pi$
$930$		0			0
$931$	−32.9809	−	11.9377i	−1.08091	−	0.391243i
$932$		0			0
$933$	6.41590	−	34.3997i	0.210047	−	1.12620i
$934$		0			0
$935$	1.34772	+	0.778108i	0.0440752	+	0.0254468i
$936$		0			0
$937$			33.6651i			1.09979i	0.835233	+	0.549896i	$0.185333\pi$
$937$			33.6651i			1.09979i	−0.835233	+	0.549896i	$0.814667\pi$
$938$		0			0
$939$	12.5872	+	35.6736i	0.410769	+	1.16416i
$940$		0			0
$941$	−18.8980	−	32.7323i	−0.616058	−	1.06704i	−0.990198	−	0.139671i	$-0.955395\pi$
$941$	−18.8980	−	32.7323i	−0.616058	−	1.06704i	0.374140	−	0.927372i	$-0.377938\pi$
$942$		0			0
$943$	−13.3589	−	7.71277i	−0.435026	−	0.251162i
$944$		0			0
$945$	−0.877584	+	0.577701i	−0.0285478	+	0.0187926i
$946$		0			0
$947$	9.47426	+	5.46997i	0.307872	+	0.177750i	0.645974	−	0.763360i	$-0.276452\pi$
$947$	9.47426	+	5.46997i	0.307872	+	0.177750i	−0.338102	+	0.941110i	$0.609785\pi$
$948$		0			0
$949$	18.9442	+	32.8123i	0.614955	+	1.06513i
$950$		0			0
$951$	14.3270	+	40.6042i	0.464584	+	1.31668i
$952$		0			0
$953$			11.0914i			0.359284i	0.983732	+	0.179642i	$0.0574939\pi$
$953$			11.0914i			0.359284i	−0.983732	+	0.179642i	$0.942506\pi$
$954$		0			0
$955$	−0.527646	−	0.304637i	−0.0170742	−	0.00985781i
$956$		0			0
$957$	−17.4625	+	93.6275i	−0.564482	+	3.02655i
$958$		0			0
$959$	17.1925	−	36.9551i	0.555174	−	1.19334i
$960$		0			0
$961$	1.00942	−	1.74838i	0.0325621	−	0.0563992i
$962$		0			0
$963$	8.69552	+	10.7879i	0.280209	+	0.347636i
$964$		0			0
$965$	−0.0274384	−	0.0475248i	−0.000883275	−	0.00152988i
$966$		0			0
$967$	20.1446	−	34.8915i	0.647807	−	1.12203i	−0.335839	−	0.941920i	$-0.609020\pi$
$967$	20.1446	−	34.8915i	0.647807	−	1.12203i	0.983646	−	0.180115i	$-0.0576470\pi$
$968$		0			0
$969$	−21.3442	+	24.9337i	−0.685676	+	0.800985i
$970$		0			0
$971$	23.8458	+	41.3021i	0.765248	+	1.32545i	0.940115	+	0.340856i	$0.110717\pi$
$971$	23.8458	+	41.3021i	0.765248	+	1.32545i	−0.174867	+	0.984592i	$0.555950\pi$
$972$		0			0
$973$	0.657423	+	0.937123i	0.0210760	+	0.0300428i
$974$		0			0
$975$	−15.2985	−	43.3577i	−0.489945	−	1.38856i
$976$		0			0
$977$	−14.4540	+	8.34504i	−0.462426	+	0.266982i	−0.713064	−	0.701099i	$-0.752693\pi$
$977$	−14.4540	+	8.34504i	−0.462426	+	0.266982i	0.250638	+	0.968081i	$0.419360\pi$
$978$		0			0
$979$	−14.1563	+	8.17314i	−0.452437	+	0.261215i
$980$		0			0
$981$	29.2586	+	11.3074i	0.934155	+	0.361017i
$982$		0			0
$983$	33.8509			1.07968			0.539838	−	0.841769i	$-0.318485\pi$
$983$	33.8509			1.07968			0.539838	+	0.841769i	$0.318485\pi$
$984$		0			0
$985$		−	1.03200i		−	0.0328821i
$986$		0			0
$987$	−13.3368	−	1.28746i	−0.424514	−	0.0409802i
$988$		0			0
$989$	2.90137	−	1.67511i	0.0922583	−	0.0532653i
$990$		0			0
$991$	−4.09775	+	7.09751i	−0.130169	+	0.225460i	−0.923742	−	0.383016i	$-0.874885\pi$
$991$	−4.09775	+	7.09751i	−0.130169	+	0.225460i	0.793572	+	0.608476i	$0.208219\pi$
$992$		0			0
$993$	26.3695	−	9.30435i	0.836812	−	0.295265i
$994$		0			0
$995$	1.62454	+	0.937928i	0.0515014	+	0.0297343i
$996$		0			0
$997$		−	21.6380i		−	0.685282i	−0.939466	−	0.342641i	$-0.888679\pi$
$997$		−	21.6380i		−	0.685282i	0.939466	−	0.342641i	$-0.111321\pi$
$998$		0			0
$999$	3.68231	+	0.108942i	0.116503	+	0.00344677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bm.a.185.3	yes	16
3.2	odd	2		756.2.bm.a.17.5		16
4.3	odd	2		1008.2.df.d.689.6		16
7.2	even	3		1764.2.w.b.509.8		16
7.3	odd	6		1764.2.x.a.293.5		16
7.4	even	3		1764.2.x.b.293.4		16
7.5	odd	6		252.2.w.a.5.1	✓	16
7.6	odd	2		1764.2.bm.a.1697.6		16
9.2	odd	6		252.2.w.a.101.1	yes	16
9.4	even	3		2268.2.t.a.1781.5		16
9.5	odd	6		2268.2.t.b.1781.4		16
9.7	even	3		756.2.w.a.521.5		16
12.11	even	2		3024.2.df.d.17.5		16
21.2	odd	6		5292.2.w.b.1097.4		16
21.5	even	6		756.2.w.a.341.5		16
21.11	odd	6		5292.2.x.b.881.4		16
21.17	even	6		5292.2.x.a.881.5		16
21.20	even	2		5292.2.bm.a.2285.4		16
28.19	even	6		1008.2.ca.d.257.8		16
36.7	odd	6		3024.2.ca.d.2033.5		16
36.11	even	6		1008.2.ca.d.353.8		16
63.2	odd	6		1764.2.bm.a.1685.6		16
63.5	even	6		2268.2.t.a.2105.5		16
63.11	odd	6		1764.2.x.a.1469.5		16
63.16	even	3		5292.2.bm.a.4625.4		16
63.20	even	6		1764.2.w.b.1109.8		16
63.25	even	3		5292.2.x.a.4409.5		16
63.34	odd	6		5292.2.w.b.521.4		16
63.38	even	6		1764.2.x.b.1469.4		16
63.40	odd	6		2268.2.t.b.2105.4		16
63.47	even	6	inner	252.2.bm.a.173.3	yes	16
63.52	odd	6		5292.2.x.b.4409.4		16
63.61	odd	6		756.2.bm.a.89.5		16
84.47	odd	6		3024.2.ca.d.2609.5		16
252.47	odd	6		1008.2.df.d.929.6		16
252.187	even	6		3024.2.df.d.1601.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.1	✓	16	7.5	odd	6
252.2.w.a.101.1	yes	16	9.2	odd	6
252.2.bm.a.173.3	yes	16	63.47	even	6	inner
252.2.bm.a.185.3	yes	16	1.1	even	1	trivial
756.2.w.a.341.5		16	21.5	even	6
756.2.w.a.521.5		16	9.7	even	3
756.2.bm.a.17.5		16	3.2	odd	2
756.2.bm.a.89.5		16	63.61	odd	6
1008.2.ca.d.257.8		16	28.19	even	6
1008.2.ca.d.353.8		16	36.11	even	6
1008.2.df.d.689.6		16	4.3	odd	2
1008.2.df.d.929.6		16	252.47	odd	6
1764.2.w.b.509.8		16	7.2	even	3
1764.2.w.b.1109.8		16	63.20	even	6
1764.2.x.a.293.5		16	7.3	odd	6
1764.2.x.a.1469.5		16	63.11	odd	6
1764.2.x.b.293.4		16	7.4	even	3
1764.2.x.b.1469.4		16	63.38	even	6
1764.2.bm.a.1685.6		16	63.2	odd	6
1764.2.bm.a.1697.6		16	7.6	odd	2
2268.2.t.a.1781.5		16	9.4	even	3
2268.2.t.a.2105.5		16	63.5	even	6
2268.2.t.b.1781.4		16	9.5	odd	6
2268.2.t.b.2105.4		16	63.40	odd	6
3024.2.ca.d.2033.5		16	36.7	odd	6
3024.2.ca.d.2609.5		16	84.47	odd	6
3024.2.df.d.17.5		16	12.11	even	2
3024.2.df.d.1601.5		16	252.187	even	6
5292.2.w.b.521.4		16	63.34	odd	6
5292.2.w.b.1097.4		16	21.2	odd	6
5292.2.x.a.881.5		16	21.17	even	6
5292.2.x.a.4409.5		16	63.25	even	3
5292.2.x.b.881.4		16	21.11	odd	6
5292.2.x.b.4409.4		16	63.52	odd	6
5292.2.bm.a.2285.4		16	21.20	even	2
5292.2.bm.a.4625.4		16	63.16	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31579 - 1.12637i) q^{3} +0.0764245 q^{5} +(-2.39886 - 1.11601i) q^{7} +(0.462593 + 2.96412i) q^{9} +O(q^{10})\)	\(q+(-1.31579 - 1.12637i) q^{3} +0.0764245 q^{5} +(-2.39886 - 1.11601i) q^{7} +(0.462593 + 2.96412i) q^{9} -5.38437i q^{11} +(-4.60313 - 2.65762i) q^{13} +(-0.100558 - 0.0860820i) q^{15} +(-1.89092 + 3.27516i) q^{17} +(-4.33939 + 2.50535i) q^{19} +(1.89935 + 4.17043i) q^{21} -2.33784i q^{23} -4.99416 q^{25} +(2.73001 - 4.42120i) q^{27} +(8.84430 - 5.10626i) q^{29} +(4.97636 - 2.87310i) q^{31} +(-6.06478 + 7.08469i) q^{33} +(-0.183331 - 0.0852905i) q^{35} +(0.354486 + 0.613988i) q^{37} +(3.06328 + 8.68167i) q^{39} +(3.29910 - 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +(0.0353534 + 0.226531i) q^{45} +(-1.46192 + 2.53213i) q^{47} +(4.50904 + 5.35430i) q^{49} +(6.17708 - 2.17955i) q^{51} +(10.4835 + 6.05264i) q^{53} -0.411498i q^{55} +(8.53166 + 1.59124i) q^{57} +(-0.289951 - 0.502210i) q^{59} +(-2.40641 - 1.38934i) q^{61} +(2.19830 - 7.62676i) q^{63} +(-0.351792 - 0.203107i) q^{65} +(-2.63593 - 4.56556i) q^{67} +(-2.63327 + 3.07610i) q^{69} +3.32103i q^{71} +(-6.17326 - 3.56413i) q^{73} +(6.57125 + 5.62526i) q^{75} +(-6.00902 + 12.9163i) q^{77} +(-0.469123 + 0.812544i) q^{79} +(-8.57202 + 2.74236i) q^{81} +(-6.49790 - 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +(-17.3887 - 3.24318i) q^{87} +(-1.51794 - 2.62915i) q^{89} +(8.07632 + 11.5124i) q^{91} +(-9.78400 - 1.82482i) q^{93} +(-0.331636 + 0.191470i) q^{95} +(6.18183 - 3.56908i) q^{97} +(15.9599 - 2.49077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 16 q^{25} - 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} + 15 q^{35} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 13 q^{49} + 15 q^{51} + 15 q^{57} - 15 q^{59} + 3 q^{61} - 9 q^{63} - 39 q^{65} - 7 q^{67} - 21 q^{69} - 15 q^{75} - 45 q^{77} - q^{79} + 6 q^{85} - 3 q^{87} - 21 q^{89} + 9 q^{91} - 69 q^{93} + 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - q^7 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 16 * q^25 - 9 * q^27 + 6 * q^29 + 6 * q^31 - 27 * q^33 + 15 * q^35 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 13 * q^49 + 15 * q^51 + 15 * q^57 - 15 * q^59 + 3 * q^61 - 9 * q^63 - 39 * q^65 - 7 * q^67 - 21 * q^69 - 15 * q^75 - 45 * q^77 - q^79 + 6 * q^85 - 3 * q^87 - 21 * q^89 + 9 * q^91 - 69 * q^93 + 6 * q^95 + 3 * q^97 - 9 * q^99

Introduction

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