LMFDB - Embedded newform 1134.2.t.f.1025.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(593,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1134.593");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.t (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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1025.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1134.1025
Dual form			1134.2.t.f.593.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.44949 q^{5} +(-1.62132 + 2.09077i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.44949 q^{5} +(-1.62132 + 2.09077i) q^{7} +1.00000i q^{8} +(-2.12132 - 1.22474i) q^{10} -4.24264i q^{11} +(-3.62132 - 2.09077i) q^{13} +(-2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.22474 - 2.12132i) q^{17} +(4.24264 - 2.44949i) q^{19} +(-1.22474 - 2.12132i) q^{20} +(2.12132 - 3.67423i) q^{22} -6.00000i q^{23} +1.00000 q^{25} +(-2.09077 - 3.62132i) q^{26} +(-2.62132 - 0.358719i) q^{28} +(8.87039 - 5.12132i) q^{29} +(-4.86396 + 2.80821i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.12132 - 1.22474i) q^{34} +(3.97141 - 5.12132i) q^{35} +(1.62132 + 2.80821i) q^{37} +4.89898 q^{38} -2.44949i q^{40} +(-1.22474 + 2.12132i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(3.67423 - 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-3.97141 + 6.87868i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(0.866025 + 0.500000i) q^{50} -4.18154i q^{52} +(-2.15232 - 1.24264i) q^{53} +10.3923i q^{55} +(-2.09077 - 1.62132i) q^{56} +10.2426 q^{58} +(-1.22474 - 2.12132i) q^{59} +(0.621320 + 0.358719i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(8.87039 + 5.12132i) q^{65} +(1.74264 + 3.01834i) q^{67} +2.44949 q^{68} +(6.00000 - 2.44949i) q^{70} -12.7279i q^{71} +(-13.2426 - 7.64564i) q^{73} +3.24264i q^{74} +(4.24264 + 2.44949i) q^{76} +(8.87039 + 6.87868i) q^{77} +(-4.62132 + 8.00436i) q^{79} +(1.22474 - 2.12132i) q^{80} +(-2.12132 + 1.22474i) q^{82} +(-2.74666 - 4.75736i) q^{83} +(-3.00000 + 5.19615i) q^{85} -7.00000i q^{86} +4.24264 q^{88} +(-8.87039 - 15.3640i) q^{89} +(10.2426 - 4.18154i) q^{91} +(5.19615 - 3.00000i) q^{92} +(-6.87868 + 3.97141i) q^{94} +(-10.3923 + 6.00000i) q^{95} +(-5.74264 + 3.31552i) q^{97} +(1.88064 - 6.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^7	$ 8 q + 4 q^{4} + 4 q^{7} - 12 q^{13} - 4 q^{16} + 8 q^{25} - 4 q^{28} + 12 q^{31} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} + 48 q^{58} - 12 q^{61} - 8 q^{64} - 20 q^{67} + 48 q^{70} - 72 q^{73} - 20 q^{79} - 24 q^{85} + 48 q^{91} - 72 q^{94} - 12 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^7 - 12 * q^13 - 4 * q^16 + 8 * q^25 - 4 * q^28 + 12 * q^31 - 4 * q^37 - 28 * q^43 + 24 * q^46 + 20 * q^49 + 48 * q^58 - 12 * q^61 - 8 * q^64 - 20 * q^67 + 48 * q^70 - 72 * q^73 - 20 * q^79 - 24 * q^85 + 48 * q^91 - 72 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.44949			−1.09545			−0.547723	−	0.836660i	$-0.684505\pi$
$5$	−2.44949			−1.09545			−0.547723	+	0.836660i	$0.684505\pi$
$6$		0			0
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.12132	−	1.22474i	−0.670820	−	0.387298i
$11$		−	4.24264i		−	1.27920i	−0.768706	−	0.639602i	$-0.779099\pi$
$11$		−	4.24264i		−	1.27920i	0.768706	−	0.639602i	$-0.220901\pi$
$12$		0			0
$13$	−3.62132	−	2.09077i	−1.00437	−	0.579875i	−0.0948342	−	0.995493i	$-0.530232\pi$
$13$	−3.62132	−	2.09077i	−1.00437	−	0.579875i	−0.909539	+	0.415618i	$0.863565\pi$
$14$	−2.44949	+	1.00000i	−0.654654	+	0.267261i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.22474	−	2.12132i	0.297044	−	0.514496i	−0.678414	−	0.734680i	$-0.737332\pi$
$17$	1.22474	−	2.12132i	0.297044	−	0.514496i	0.975458	+	0.220184i	$0.0706658\pi$
$18$		0			0
$19$	4.24264	−	2.44949i	0.973329	−	0.561951i	0.0730792	−	0.997326i	$-0.476717\pi$
$19$	4.24264	−	2.44949i	0.973329	−	0.561951i	0.900249	+	0.435375i	$0.143384\pi$
$20$	−1.22474	−	2.12132i	−0.273861	−	0.474342i
$21$		0			0
$22$	2.12132	−	3.67423i	0.452267	−	0.783349i
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−2.09077	−	3.62132i	−0.410034	−	0.710199i
$27$		0			0
$28$	−2.62132	−	0.358719i	−0.495383	−	0.0677916i
$29$	8.87039	−	5.12132i	1.64719	−	0.951005i	0.669007	−	0.743256i	$-0.266719\pi$
$29$	8.87039	−	5.12132i	1.64719	−	0.951005i	0.978182	−	0.207750i	$-0.0666139\pi$
$30$		0			0
$31$	−4.86396	+	2.80821i	−0.873593	+	0.504369i	−0.868541	−	0.495618i	$-0.834942\pi$
$31$	−4.86396	+	2.80821i	−0.873593	+	0.504369i	−0.00505256	+	0.999987i	$0.501608\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	2.12132	−	1.22474i	0.363803	−	0.210042i
$35$	3.97141	−	5.12132i	0.671290	−	0.865661i
$36$		0			0
$37$	1.62132	+	2.80821i	0.266543	+	0.461667i	0.967967	−	0.251078i	$-0.0807851\pi$
$37$	1.62132	+	2.80821i	0.266543	+	0.461667i	−0.701423	+	0.712745i	$0.747452\pi$
$38$	4.89898			0.794719
$39$		0			0
$40$		−	2.44949i		−	0.387298i
$41$	−1.22474	+	2.12132i	−0.191273	+	0.331295i	−0.945672	−	0.325121i	$-0.894595\pi$
$41$	−1.22474	+	2.12132i	−0.191273	+	0.331295i	0.754399	+	0.656416i	$0.227928\pi$
$42$		0			0
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	−0.999223	−	0.0394140i	$-0.987451\pi$
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	0.465478	−	0.885059i	$-0.345882\pi$
$44$	3.67423	−	2.12132i	0.553912	−	0.319801i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−3.97141	+	6.87868i	−0.579289	+	1.00336i	0.416272	+	0.909240i	$0.363337\pi$
$47$	−3.97141	+	6.87868i	−0.579289	+	1.00336i	−0.995561	+	0.0941183i	$0.969997\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$		−	4.18154i		−	0.579875i
$53$	−2.15232	−	1.24264i	−0.295643	−	0.170690i	0.344841	−	0.938661i	$-0.387933\pi$
$53$	−2.15232	−	1.24264i	−0.295643	−	0.170690i	−0.640484	+	0.767971i	$0.721266\pi$
$54$		0			0
$55$			10.3923i			1.40130i
$56$	−2.09077	−	1.62132i	−0.279391	−	0.216658i
$57$		0			0
$58$	10.2426			1.34492
$59$	−1.22474	−	2.12132i	−0.159448	−	0.276172i	0.775222	−	0.631689i	$-0.217638\pi$
$59$	−1.22474	−	2.12132i	−0.159448	−	0.276172i	−0.934670	+	0.355517i	$0.884305\pi$
$60$		0			0
$61$	0.621320	+	0.358719i	0.0795519	+	0.0459293i	0.539248	−	0.842147i	$-0.318708\pi$
$61$	0.621320	+	0.358719i	0.0795519	+	0.0459293i	−0.459696	+	0.888076i	$0.652042\pi$
$62$	−5.61642			−0.713286
$63$		0			0
$64$	−1.00000			−0.125000
$65$	8.87039	+	5.12132i	1.10024	+	0.635222i
$66$		0			0
$67$	1.74264	+	3.01834i	0.212897	+	0.368749i	0.952620	−	0.304163i	$-0.0983766\pi$
$67$	1.74264	+	3.01834i	0.212897	+	0.368749i	−0.739723	+	0.672912i	$0.765043\pi$
$68$	2.44949			0.297044
$69$		0			0
$70$	6.00000	−	2.44949i	0.717137	−	0.292770i
$71$		−	12.7279i		−	1.51053i	−0.655422	−	0.755263i	$-0.727509\pi$
$71$		−	12.7279i		−	1.51053i	0.655422	−	0.755263i	$-0.272491\pi$
$72$		0			0
$73$	−13.2426	−	7.64564i	−1.54993	−	0.894855i	−0.998146	−	0.0608704i	$-0.980612\pi$
$73$	−13.2426	−	7.64564i	−1.54993	−	0.894855i	−0.551788	−	0.833984i	$-0.686054\pi$
$74$			3.24264i			0.376949i
$75$		0			0
$76$	4.24264	+	2.44949i	0.486664	+	0.280976i
$77$	8.87039	+	6.87868i	1.01087	+	0.783898i
$78$		0			0
$79$	−4.62132	+	8.00436i	−0.519939	+	0.900561i	0.479792	+	0.877382i	$0.340712\pi$
$79$	−4.62132	+	8.00436i	−0.519939	+	0.900561i	−0.999731	+	0.0231789i	$0.992621\pi$
$80$	1.22474	−	2.12132i	0.136931	−	0.237171i
$81$		0			0
$82$	−2.12132	+	1.22474i	−0.234261	+	0.135250i
$83$	−2.74666	−	4.75736i	−0.301485	−	0.522188i	0.674987	−	0.737829i	$-0.264149\pi$
$83$	−2.74666	−	4.75736i	−0.301485	−	0.522188i	−0.976473	+	0.215641i	$0.930816\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$		−	7.00000i		−	0.754829i
$87$		0			0
$88$	4.24264			0.452267
$89$	−8.87039	−	15.3640i	−0.940259	−	1.62858i	−0.764976	−	0.644059i	$-0.777249\pi$
$89$	−8.87039	−	15.3640i	−0.940259	−	1.62858i	−0.175283	−	0.984518i	$-0.556084\pi$
$90$		0			0
$91$	10.2426	−	4.18154i	1.07372	−	0.438345i
$92$	5.19615	−	3.00000i	0.541736	−	0.312772i
$93$		0			0
$94$	−6.87868	+	3.97141i	−0.709482	+	0.409619i
$95$	−10.3923	+	6.00000i	−1.06623	+	0.615587i
$96$		0			0
$97$	−5.74264	+	3.31552i	−0.583077	+	0.336640i	−0.762355	−	0.647159i	$-0.775957\pi$
$97$	−5.74264	+	3.31552i	−0.583077	+	0.336640i	0.179278	+	0.983798i	$0.442624\pi$
$98$	1.88064	−	6.74264i	0.189973	−	0.681110i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−7.34847			−0.731200			−0.365600	−	0.930772i	$-0.619136\pi$
$101$	−7.34847			−0.731200			−0.365600	+	0.930772i	$0.619136\pi$
$102$		0			0
$103$			6.21076i			0.611965i	0.952037	+	0.305982i	$0.0989849\pi$
$103$			6.21076i			0.611965i	−0.952037	+	0.305982i	$0.901015\pi$
$104$	2.09077	−	3.62132i	0.205017	−	0.355100i
$105$		0			0
$106$	−1.24264	−	2.15232i	−0.120696	−	0.209051i
$107$	−12.5446	+	7.24264i	−1.21273	+	0.700173i	−0.963354	−	0.268233i	$-0.913560\pi$
$107$	−12.5446	+	7.24264i	−1.21273	+	0.700173i	−0.249380	+	0.968406i	$0.580227\pi$
$108$		0			0
$109$	−3.86396	+	6.69258i	−0.370100	+	0.641033i	−0.989581	−	0.143980i	$-0.954010\pi$
$109$	−3.86396	+	6.69258i	−0.370100	+	0.641033i	0.619480	+	0.785012i	$0.287343\pi$
$110$	−5.19615	+	9.00000i	−0.495434	+	0.858116i
$111$		0			0
$112$	−1.00000	−	2.44949i	−0.0944911	−	0.231455i
$113$	1.52192	+	0.878680i	0.143170	+	0.0826592i	0.569874	−	0.821732i	$-0.306992\pi$
$113$	1.52192	+	0.878680i	0.143170	+	0.0826592i	−0.426704	+	0.904391i	$0.640325\pi$
$114$		0			0
$115$			14.6969i			1.37050i
$116$	8.87039	+	5.12132i	0.823595	+	0.475503i
$117$		0			0
$118$		−	2.44949i		−	0.225494i
$119$	2.44949	+	6.00000i	0.224544	+	0.550019i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	0.358719	+	0.621320i	0.0324769	+	0.0562517i
$123$		0			0
$124$	−4.86396	−	2.80821i	−0.436797	−	0.252185i
$125$	9.79796			0.876356
$126$		0			0
$127$	17.7279			1.57310			0.786549	−	0.617527i	$-0.211866\pi$
$127$	17.7279			1.57310			0.786549	+	0.617527i	$0.211866\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	5.12132	+	8.87039i	0.449170	+	0.777984i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−1.75736	+	12.8418i	−0.152382	+	1.11352i
$134$			3.48528i			0.301082i
$135$		0			0
$136$	2.12132	+	1.22474i	0.181902	+	0.105021i
$137$		−	6.00000i		−	0.512615i	−0.966595	−	0.256307i	$-0.917494\pi$
$137$		−	6.00000i		−	0.512615i	0.966595	−	0.256307i	$-0.0825059\pi$
$138$		0			0
$139$	9.98528	+	5.76500i	0.846941	+	0.488981i	0.859617	−	0.510938i	$-0.170702\pi$
$139$	9.98528	+	5.76500i	0.846941	+	0.488981i	−0.0126769	+	0.999920i	$0.504035\pi$
$140$	6.42090	+	0.878680i	0.542665	+	0.0742620i
$141$		0			0
$142$	6.36396	−	11.0227i	0.534052	−	0.925005i
$143$	−8.87039	+	15.3640i	−0.741779	+	1.28480i
$144$		0			0
$145$	−21.7279	+	12.5446i	−1.80441	+	1.04177i
$146$	−7.64564	−	13.2426i	−0.632758	−	1.09597i
$147$		0			0
$148$	−1.62132	+	2.80821i	−0.133272	+	0.230833i
$149$		−	7.75736i		−	0.635508i	−0.948173	−	0.317754i	$-0.897071\pi$
$149$		−	7.75736i		−	0.635508i	0.948173	−	0.317754i	$-0.102929\pi$
$150$		0			0
$151$	17.2426			1.40319			0.701593	−	0.712578i	$-0.252472\pi$
$151$	17.2426			1.40319			0.701593	+	0.712578i	$0.252472\pi$
$152$	2.44949	+	4.24264i	0.198680	+	0.344124i
$153$		0			0
$154$	4.24264	+	10.3923i	0.341882	+	0.837436i
$155$	11.9142	−	6.87868i	0.956973	−	0.552509i
$156$		0			0
$157$	9.00000	−	5.19615i	0.718278	−	0.414698i	−0.0958404	−	0.995397i	$-0.530554\pi$
$157$	9.00000	−	5.19615i	0.718278	−	0.414698i	0.814119	+	0.580699i	$0.197221\pi$
$158$	−8.00436	+	4.62132i	−0.636793	+	0.367653i
$159$		0			0
$160$	2.12132	−	1.22474i	0.167705	−	0.0968246i
$161$	12.5446	+	9.72792i	0.988655	+	0.766668i
$162$		0			0
$163$	−3.74264	−	6.48244i	−0.293146	−	0.507744i	0.681406	−	0.731906i	$-0.261369\pi$
$163$	−3.74264	−	6.48244i	−0.293146	−	0.507744i	−0.974552	+	0.224162i	$0.928036\pi$
$164$	−2.44949			−0.191273
$165$		0			0
$166$		−	5.49333i		−	0.426365i
$167$	10.0951	−	17.4853i	0.781185	−	1.35305i	−0.150067	−	0.988676i	$-0.547949\pi$
$167$	10.0951	−	17.4853i	0.781185	−	1.35305i	0.931252	−	0.364376i	$-0.118718\pi$
$168$		0			0
$169$	2.24264	+	3.88437i	0.172511	+	0.298798i
$170$	−5.19615	+	3.00000i	−0.398527	+	0.230089i
$171$		0			0
$172$	3.50000	−	6.06218i	0.266872	−	0.462237i
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	0.135785	+	0.990738i	$0.456644\pi$
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	−0.925897	+	0.377776i	$0.876689\pi$
$174$		0			0
$175$	−1.62132	+	2.09077i	−0.122560	+	0.158047i
$176$	3.67423	+	2.12132i	0.276956	+	0.159901i
$177$		0			0
$178$		−	17.7408i		−	1.32973i
$179$	16.2189	+	9.36396i	1.21225	+	0.699895i	0.963250	−	0.268607i	$-0.0865633\pi$
$179$	16.2189	+	9.36396i	1.21225	+	0.699895i	0.249004	+	0.968502i	$0.419897\pi$
$180$		0			0
$181$			9.79796i			0.728277i	0.931345	+	0.364138i	$0.118636\pi$
$181$			9.79796i			0.728277i	−0.931345	+	0.364138i	$0.881364\pi$
$182$	10.9612	+	1.50000i	0.812495	+	0.111187i
$183$		0			0
$184$	6.00000			0.442326
$185$	−3.97141	−	6.87868i	−0.291984	−	0.505731i
$186$		0			0
$187$	−9.00000	−	5.19615i	−0.658145	−	0.379980i
$188$	−7.94282			−0.579289
$189$		0			0
$190$	−12.0000			−0.870572
$191$	−18.3712	−	10.6066i	−1.32929	−	0.767467i	−0.344101	−	0.938933i	$-0.611816\pi$
$191$	−18.3712	−	10.6066i	−1.32929	−	0.767467i	−0.985190	+	0.171466i	$0.945150\pi$
$192$		0			0
$193$	−7.74264	−	13.4106i	−0.557327	−	0.965319i	−0.997718	−	0.0675134i	$-0.978493\pi$
$193$	−7.74264	−	13.4106i	−0.557327	−	0.965319i	0.440391	−	0.897806i	$-0.354840\pi$
$194$	−6.63103			−0.476080
$195$		0			0
$196$	5.00000	−	4.89898i	0.357143	−	0.349927i
$197$			16.9706i			1.20910i	0.796566	+	0.604551i	$0.206648\pi$
$197$			16.9706i			1.20910i	−0.796566	+	0.604551i	$0.793352\pi$
$198$		0			0
$199$	3.10660	+	1.79360i	0.220221	+	0.127145i	0.606053	−	0.795425i	$-0.292752\pi$
$199$	3.10660	+	1.79360i	0.220221	+	0.127145i	−0.385832	+	0.922569i	$0.626085\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−6.36396	−	3.67423i	−0.447767	−	0.258518i
$203$	−3.67423	+	26.8492i	−0.257881	+	1.88445i
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−3.10538	+	5.37868i	−0.216362	+	0.374750i
$207$		0			0
$208$	3.62132	−	2.09077i	0.251093	−	0.144969i
$209$	−10.3923	−	18.0000i	−0.718851	−	1.24509i
$210$		0			0
$211$	6.74264	−	11.6786i	0.464183	−	0.803988i	−0.534982	−	0.844864i	$-0.679682\pi$
$211$	6.74264	−	11.6786i	0.464183	−	0.803988i	0.999164	+	0.0408759i	$0.0130148\pi$
$212$		−	2.48528i		−	0.170690i
$213$		0			0
$214$	−14.4853			−0.990193
$215$	8.57321	+	14.8492i	0.584688	+	1.01271i
$216$		0			0
$217$	2.01472	−	14.7224i	0.136768	−	0.999424i
$218$	−6.69258	+	3.86396i	−0.453278	+	0.261700i
$219$		0			0
$220$	−9.00000	+	5.19615i	−0.606780	+	0.350325i
$221$	−8.87039	+	5.12132i	−0.596687	+	0.344497i
$222$		0			0
$223$	−9.00000	+	5.19615i	−0.602685	+	0.347960i	−0.770097	−	0.637927i	$-0.779792\pi$
$223$	−9.00000	+	5.19615i	−0.602685	+	0.347960i	0.167412	+	0.985887i	$0.446459\pi$
$224$	0.358719	−	2.62132i	0.0239680	−	0.175144i
$225$		0			0
$226$	0.878680	+	1.52192i	0.0584489	+	0.101236i
$227$	4.30463			0.285709			0.142854	−	0.989744i	$-0.454372\pi$
$227$	4.30463			0.285709			0.142854	+	0.989744i	$0.454372\pi$
$228$		0			0
$229$			9.08052i			0.600058i	0.953930	+	0.300029i	$0.0969963\pi$
$229$			9.08052i			0.600058i	−0.953930	+	0.300029i	$0.903004\pi$
$230$	−7.34847	+	12.7279i	−0.484544	+	0.839254i
$231$		0			0
$232$	5.12132	+	8.87039i	0.336231	+	0.582369i
$233$	−3.04384	+	1.75736i	−0.199408	+	0.115128i	−0.596379	−	0.802703i	$-0.703395\pi$
$233$	−3.04384	+	1.75736i	−0.199408	+	0.115128i	0.396971	+	0.917831i	$0.370061\pi$
$234$		0			0
$235$	9.72792	−	16.8493i	0.634580	−	1.09912i
$236$	1.22474	−	2.12132i	0.0797241	−	0.138086i
$237$		0			0
$238$	−0.878680	+	6.42090i	−0.0569563	+	0.416205i
$239$	6.71807	+	3.87868i	0.434556	+	0.250891i	0.701286	−	0.712880i	$-0.252610\pi$
$239$	6.71807	+	3.87868i	0.434556	+	0.250891i	−0.266730	+	0.963771i	$0.585943\pi$
$240$		0			0
$241$		−	18.4582i		−	1.18900i	−0.804096	−	0.594499i	$-0.797350\pi$
$241$		−	18.4582i		−	1.18900i	0.804096	−	0.594499i	$-0.202650\pi$
$242$	−6.06218	−	3.50000i	−0.389692	−	0.224989i
$243$		0			0
$244$			0.717439i			0.0459293i
$245$	4.26858	+	16.6066i	0.272710	+	1.06096i
$246$		0			0
$247$	−20.4853			−1.30345
$248$	−2.80821	−	4.86396i	−0.178321	−	0.308862i
$249$		0			0
$250$	8.48528	+	4.89898i	0.536656	+	0.309839i
$251$	−5.49333			−0.346736			−0.173368	−	0.984857i	$-0.555465\pi$
$251$	−5.49333			−0.346736			−0.173368	+	0.984857i	$0.555465\pi$
$252$		0			0
$253$	−25.4558			−1.60040
$254$	15.3528	+	8.86396i	0.963322	+	0.556174i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.30463			0.268516			0.134258	−	0.990946i	$-0.457135\pi$
$257$	4.30463			0.268516			0.134258	+	0.990946i	$0.457135\pi$
$258$		0			0
$259$	−8.50000	−	1.16320i	−0.528164	−	0.0722776i
$260$			10.2426i			0.635222i
$261$		0			0
$262$		0			0
$263$			18.7279i			1.15481i	0.816457	+	0.577407i	$0.195935\pi$
$263$			18.7279i			1.15481i	−0.816457	+	0.577407i	$0.804065\pi$
$264$		0			0
$265$	5.27208	+	3.04384i	0.323861	+	0.186981i
$266$	−7.94282	+	10.2426i	−0.487005	+	0.628017i
$267$		0			0
$268$	−1.74264	+	3.01834i	−0.106449	+	0.184375i
$269$	−4.89898	+	8.48528i	−0.298696	+	0.517357i	−0.975838	−	0.218496i	$-0.929885\pi$
$269$	−4.89898	+	8.48528i	−0.298696	+	0.517357i	0.677142	+	0.735853i	$0.263218\pi$
$270$		0			0
$271$	13.3492	−	7.70719i	0.810909	−	0.468178i	−0.0363626	−	0.999339i	$-0.511577\pi$
$271$	13.3492	−	7.70719i	0.810909	−	0.468178i	0.847271	+	0.531160i	$0.178244\pi$
$272$	1.22474	+	2.12132i	0.0742611	+	0.128624i
$273$		0			0
$274$	3.00000	−	5.19615i	0.181237	−	0.313911i
$275$		−	4.24264i		−	0.255841i
$276$		0			0
$277$	−1.72792			−0.103821			−0.0519104	−	0.998652i	$-0.516531\pi$
$277$	−1.72792			−0.103821			−0.0519104	+	0.998652i	$0.516531\pi$
$278$	5.76500	+	9.98528i	0.345762	+	0.598877i
$279$		0			0
$280$	5.12132	+	3.97141i	0.306057	+	0.237337i
$281$	19.2627	−	11.1213i	1.14912	−	0.663442i	0.200444	−	0.979705i	$-0.435761\pi$
$281$	19.2627	−	11.1213i	1.14912	−	0.663442i	0.948672	+	0.316263i	$0.102428\pi$
$282$		0			0
$283$	20.2279	−	11.6786i	1.20243	−	0.694220i	0.241331	−	0.970443i	$-0.422416\pi$
$283$	20.2279	−	11.6786i	1.20243	−	0.694220i	0.961094	+	0.276222i	$0.0890826\pi$
$284$	11.0227	−	6.36396i	0.654077	−	0.377632i
$285$		0			0
$286$	−15.3640	+	8.87039i	−0.908490	+	0.524517i
$287$	−2.44949	−	6.00000i	−0.144589	−	0.354169i
$288$		0			0
$289$	5.50000	+	9.52628i	0.323529	+	0.560369i
$290$	−25.0892			−1.47329
$291$		0			0
$292$		−	15.2913i		−	0.894855i
$293$	3.97141	−	6.87868i	0.232012	−	0.401857i	−0.726388	−	0.687285i	$-0.758802\pi$
$293$	3.97141	−	6.87868i	0.232012	−	0.401857i	0.958400	+	0.285428i	$0.0921358\pi$
$294$		0			0
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$	−2.80821	+	1.62132i	−0.163224	+	0.0942373i
$297$		0			0
$298$	3.87868	−	6.71807i	0.224686	−	0.389167i
$299$	−12.5446	+	21.7279i	−0.725474	+	1.25656i
$300$		0			0
$301$	18.3492	+	2.51104i	1.05763	+	0.144734i
$302$	14.9326	+	8.62132i	0.859273	+	0.496101i
$303$		0			0
$304$			4.89898i			0.280976i
$305$	−1.52192	−	0.878680i	−0.0871448	−	0.0503131i
$306$		0			0
$307$		−	2.57258i		−	0.146825i	−0.997302	−	0.0734125i	$-0.976611\pi$
$307$		−	2.57258i		−	0.146825i	0.997302	−	0.0734125i	$-0.0233890\pi$
$308$	−1.52192	+	11.1213i	−0.0867193	+	0.633696i
$309$		0			0
$310$	13.7574			0.781366
$311$	8.57321	+	14.8492i	0.486142	+	0.842023i	0.999873	−	0.0159282i	$-0.00507031\pi$
$311$	8.57321	+	14.8492i	0.486142	+	0.842023i	−0.513731	+	0.857951i	$0.671737\pi$
$312$		0			0
$313$	0.514719	+	0.297173i	0.0290936	+	0.0167972i	0.514476	−	0.857505i	$-0.327986\pi$
$313$	0.514719	+	0.297173i	0.0290936	+	0.0167972i	−0.485383	+	0.874302i	$0.661320\pi$
$314$	10.3923			0.586472
$315$		0			0
$316$	−9.24264			−0.519939
$317$	−11.9142	−	6.87868i	−0.669169	−	0.386345i	0.126592	−	0.991955i	$-0.459596\pi$
$317$	−11.9142	−	6.87868i	−0.669169	−	0.386345i	−0.795762	+	0.605610i	$0.792929\pi$
$318$		0			0
$319$	−21.7279	−	37.6339i	−1.21653	−	2.10709i
$320$	2.44949			0.136931
$321$		0			0
$322$	6.00000	+	14.6969i	0.334367	+	0.819028i
$323$		−	12.0000i		−	0.667698i
$324$		0			0
$325$	−3.62132	−	2.09077i	−0.200875	−	0.115975i
$326$		−	7.48528i		−	0.414571i
$327$		0			0
$328$	−2.12132	−	1.22474i	−0.117130	−	0.0676252i
$329$	−7.94282	−	19.4558i	−0.437902	−	1.07264i
$330$		0			0
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$	2.74666	−	4.75736i	0.150743	−	0.261094i
$333$		0			0
$334$	17.4853	−	10.0951i	0.956752	−	0.552381i
$335$	−4.26858	−	7.39340i	−0.233217	−	0.403944i
$336$		0			0
$337$	−14.7279	+	25.5095i	−0.802281	+	1.38959i	0.115830	+	0.993269i	$0.463047\pi$
$337$	−14.7279	+	25.5095i	−0.802281	+	1.38959i	−0.918111	+	0.396323i	$0.870286\pi$
$338$			4.48528i			0.243967i
$339$		0			0
$340$	−6.00000			−0.325396
$341$	11.9142	+	20.6360i	0.645191	+	1.11750i
$342$		0			0
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	6.06218	−	3.50000i	0.326851	−	0.188707i
$345$		0			0
$346$	−18.0000	+	10.3923i	−0.967686	+	0.558694i
$347$	25.0892	−	14.4853i	1.34686	−	0.777611i	0.359058	−	0.933315i	$-0.383098\pi$
$347$	25.0892	−	14.4853i	1.34686	−	0.777611i	0.987804	+	0.155705i	$0.0497649\pi$
$348$		0			0
$349$	21.1066	−	12.1859i	1.12981	−	0.652296i	0.185923	−	0.982564i	$-0.440472\pi$
$349$	21.1066	−	12.1859i	1.12981	−	0.652296i	0.943887	+	0.330268i	$0.107139\pi$
$350$	−2.44949	+	1.00000i	−0.130931	+	0.0534522i
$351$		0			0
$352$	2.12132	+	3.67423i	0.113067	+	0.195837i
$353$	−30.5826			−1.62775			−0.813873	−	0.581043i	$-0.802645\pi$
$353$	−30.5826			−1.62775			−0.813873	+	0.581043i	$0.802645\pi$
$354$		0			0
$355$			31.1769i			1.65470i
$356$	8.87039	−	15.3640i	0.470130	−	0.814288i
$357$		0			0
$358$	9.36396	+	16.2189i	0.494901	+	0.857193i
$359$	−2.15232	+	1.24264i	−0.113595	+	0.0655841i	−0.555721	−	0.831369i	$-0.687558\pi$
$359$	−2.15232	+	1.24264i	−0.113595	+	0.0655841i	0.442126	+	0.896953i	$0.354224\pi$
$360$		0			0
$361$	2.50000	−	4.33013i	0.131579	−	0.227901i
$362$	−4.89898	+	8.48528i	−0.257485	+	0.445976i
$363$		0			0
$364$	8.74264	+	6.77962i	0.458239	+	0.355348i
$365$	32.4377	+	18.7279i	1.69787	+	0.980264i
$366$		0			0
$367$		−	9.20361i		−	0.480425i	−0.970720	−	0.240212i	$-0.922783\pi$
$367$		−	9.20361i		−	0.480425i	0.970720	−	0.240212i	$-0.0772171\pi$
$368$	5.19615	+	3.00000i	0.270868	+	0.156386i
$369$		0			0
$370$		−	7.94282i		−	0.412927i
$371$	6.08767	−	2.48528i	0.316056	−	0.129029i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$	−5.19615	−	9.00000i	−0.268687	−	0.465379i
$375$		0			0
$376$	−6.87868	−	3.97141i	−0.354741	−	0.204810i
$377$	−42.8300			−2.20586
$378$		0			0
$379$	9.48528			0.487226			0.243613	−	0.969872i	$-0.421667\pi$
$379$	9.48528			0.487226			0.243613	+	0.969872i	$0.421667\pi$
$380$	−10.3923	−	6.00000i	−0.533114	−	0.307794i
$381$		0			0
$382$	−10.6066	−	18.3712i	−0.542681	−	0.939951i
$383$	−15.2913			−0.781348			−0.390674	−	0.920529i	$-0.627758\pi$
$383$	−15.2913			−0.781348			−0.390674	+	0.920529i	$0.627758\pi$
$384$		0			0
$385$	−21.7279	−	16.8493i	−1.10736	−	0.858718i
$386$		−	15.4853i		−	0.788180i
$387$		0			0
$388$	−5.74264	−	3.31552i	−0.291538	−	0.168320i
$389$			32.4853i			1.64707i	0.567266	+	0.823535i	$0.308001\pi$
$389$			32.4853i			1.64707i	−0.567266	+	0.823535i	$0.691999\pi$
$390$		0			0
$391$	−12.7279	−	7.34847i	−0.643679	−	0.371628i
$392$	6.77962	−	1.74264i	0.342422	−	0.0880166i
$393$		0			0
$394$	−8.48528	+	14.6969i	−0.427482	+	0.740421i
$395$	11.3199	−	19.6066i	0.569565	−	0.986515i
$396$		0			0
$397$	−25.8640	+	14.9326i	−1.29807	+	0.749444i	−0.980071	−	0.198646i	$-0.936346\pi$
$397$	−25.8640	+	14.9326i	−1.29807	+	0.749444i	−0.318004	+	0.948090i	$0.603012\pi$
$398$	1.79360	+	3.10660i	0.0899049	+	0.155720i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			28.2426i			1.41037i	0.709023	+	0.705185i	$0.249136\pi$
$401$			28.2426i			1.41037i	−0.709023	+	0.705185i	$0.750864\pi$
$402$		0			0
$403$	23.4853			1.16989
$404$	−3.67423	−	6.36396i	−0.182800	−	0.316619i
$405$		0			0
$406$	−16.6066	+	21.4150i	−0.824172	+	1.06281i
$407$	11.9142	−	6.87868i	0.590566	−	0.340963i
$408$		0			0
$409$	11.7426	−	6.77962i	0.580636	−	0.335230i	−0.180750	−	0.983529i	$-0.557852\pi$
$409$	11.7426	−	6.77962i	0.580636	−	0.335230i	0.761386	+	0.648299i	$0.224519\pi$
$410$	5.19615	−	3.00000i	0.256620	−	0.148159i
$411$		0			0
$412$	−5.37868	+	3.10538i	−0.264989	+	0.152991i
$413$	6.42090	+	0.878680i	0.315952	+	0.0432370i
$414$		0			0
$415$	6.72792	+	11.6531i	0.330261	+	0.572028i
$416$	4.18154			0.205017
$417$		0			0
$418$		−	20.7846i		−	1.01661i
$419$	6.42090	−	11.1213i	0.313681	−	0.543312i	−0.665475	−	0.746420i	$-0.731771\pi$
$419$	6.42090	−	11.1213i	0.313681	−	0.543312i	0.979156	+	0.203108i	$0.0651043\pi$
$420$		0			0
$421$	−13.7279	−	23.7775i	−0.669058	−	1.15884i	−0.978168	−	0.207816i	$-0.933364\pi$
$421$	−13.7279	−	23.7775i	−0.669058	−	1.15884i	0.309110	−	0.951026i	$-0.399969\pi$
$422$	11.6786	−	6.74264i	0.568505	−	0.328227i
$423$		0			0
$424$	1.24264	−	2.15232i	0.0603480	−	0.104526i
$425$	1.22474	−	2.12132i	0.0594089	−	0.102899i
$426$		0			0
$427$	−1.75736	+	0.717439i	−0.0850446	+	0.0347193i
$428$	−12.5446	−	7.24264i	−0.606367	−	0.350086i
$429$		0			0
$430$			17.1464i			0.826874i
$431$	−8.87039	−	5.12132i	−0.427272	−	0.246685i	0.270912	−	0.962604i	$-0.412675\pi$
$431$	−8.87039	−	5.12132i	−0.427272	−	0.246685i	−0.698184	+	0.715919i	$0.746008\pi$
$432$		0			0
$433$		−	26.8213i		−	1.28895i	−0.764626	−	0.644475i	$-0.777076\pi$
$433$		−	26.8213i		−	1.28895i	0.764626	−	0.644475i	$-0.222924\pi$
$434$	9.10601	−	11.7426i	0.437103	−	0.563665i
$435$		0			0
$436$	−7.72792			−0.370100
$437$	−14.6969	−	25.4558i	−0.703050	−	1.21772i
$438$		0			0
$439$	21.7279	+	12.5446i	1.03702	+	0.598722i	0.918987	−	0.394288i	$-0.129009\pi$
$439$	21.7279	+	12.5446i	1.03702	+	0.598722i	0.118030	+	0.993010i	$0.462342\pi$
$440$	−10.3923			−0.495434
$441$		0			0
$442$	−10.2426			−0.487193
$443$	22.0454	+	12.7279i	1.04741	+	0.604722i	0.921923	−	0.387374i	$-0.126618\pi$
$443$	22.0454	+	12.7279i	1.04741	+	0.604722i	0.125486	+	0.992095i	$0.459951\pi$
$444$		0			0
$445$	21.7279	+	37.6339i	1.03000	+	1.78402i
$446$	−10.3923			−0.492090
$447$		0			0
$448$	1.62132	−	2.09077i	0.0766002	−	0.0987796i
$449$		−	30.7279i		−	1.45014i	−0.688675	−	0.725070i	$-0.741807\pi$
$449$		−	30.7279i		−	1.45014i	0.688675	−	0.725070i	$-0.258193\pi$
$450$		0			0
$451$	9.00000	+	5.19615i	0.423793	+	0.244677i
$452$			1.75736i			0.0826592i
$453$		0			0
$454$	3.72792	+	2.15232i	0.174960	+	0.101013i
$455$	−25.0892	+	10.2426i	−1.17620	+	0.480182i
$456$		0			0
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	−0.461067	−	0.887365i	$-0.652533\pi$
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	0.999014	−	0.0443868i	$-0.0141334\pi$
$458$	−4.54026	+	7.86396i	−0.212152	+	0.367459i
$459$		0			0
$460$	−12.7279	+	7.34847i	−0.593442	+	0.342624i
$461$	−21.1178	−	36.5772i	−0.983556	−	1.70357i	−0.648187	−	0.761482i	$-0.724472\pi$
$461$	−21.1178	−	36.5772i	−0.983556	−	1.70357i	−0.335369	−	0.942087i	$-0.608861\pi$
$462$		0			0
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	−0.488702	−	0.872451i	$-0.662530\pi$
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	0.999916	−	0.0129968i	$-0.00413714\pi$
$464$			10.2426i			0.475503i
$465$		0			0
$466$	−3.51472			−0.162816
$467$	1.52192	+	2.63604i	0.0704260	+	0.121981i	0.899088	−	0.437768i	$-0.144231\pi$
$467$	1.52192	+	2.63604i	0.0704260	+	0.121981i	−0.828662	+	0.559749i	$0.810897\pi$
$468$		0			0
$469$	−9.13604	−	1.25024i	−0.421863	−	0.0577306i
$470$	16.8493	−	9.72792i	0.777198	−	0.448716i
$471$		0			0
$472$	2.12132	−	1.22474i	0.0976417	−	0.0563735i
$473$	−25.7196	+	14.8492i	−1.18259	+	0.682769i
$474$		0			0
$475$	4.24264	−	2.44949i	0.194666	−	0.112390i
$476$	−3.97141	+	5.12132i	−0.182029	+	0.234735i
$477$		0			0
$478$	3.87868	+	6.71807i	0.177407	+	0.307277i
$479$	2.44949			0.111920			0.0559600	−	0.998433i	$-0.482178\pi$
$479$	2.44949			0.111920			0.0559600	+	0.998433i	$0.482178\pi$
$480$		0			0
$481$		−	13.5592i		−	0.618248i
$482$	9.22911	−	15.9853i	0.420374	−	0.728110i
$483$		0			0
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	14.0665	−	8.12132i	0.638729	−	0.368770i
$486$		0			0
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	−0.999998	−	0.00178012i	$-0.999433\pi$
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	0.501541	+	0.865134i	$0.332767\pi$
$488$	−0.358719	+	0.621320i	−0.0162385	+	0.0281259i
$489$		0			0
$490$	−4.60660	+	16.5160i	−0.208105	+	0.746118i
$491$	0.891519	+	0.514719i	0.0402337	+	0.0232289i	0.519982	−	0.854177i	$-0.325939\pi$
$491$	0.891519	+	0.514719i	0.0402337	+	0.0232289i	−0.479748	+	0.877406i	$0.659272\pi$
$492$		0			0
$493$		−	25.0892i		−	1.12996i
$494$	−17.7408	−	10.2426i	−0.798195	−	0.460838i
$495$		0			0
$496$		−	5.61642i		−	0.252185i
$497$	26.6112	+	20.6360i	1.19367	+	0.925653i
$498$		0			0
$499$	26.4558			1.18433			0.592163	−	0.805818i	$-0.298274\pi$
$499$	26.4558			1.18433			0.592163	+	0.805818i	$0.298274\pi$
$500$	4.89898	+	8.48528i	0.219089	+	0.379473i
$501$		0			0
$502$	−4.75736	−	2.74666i	−0.212331	−	0.122590i
$503$	20.1903			0.900239			0.450120	−	0.892968i	$-0.351381\pi$
$503$	20.1903			0.900239			0.450120	+	0.892968i	$0.351381\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	−22.0454	−	12.7279i	−0.980038	−	0.565825i
$507$		0			0
$508$	8.86396	+	15.3528i	0.393275	+	0.681172i
$509$	−29.9882			−1.32920			−0.664602	−	0.747197i	$-0.731399\pi$
$509$	−29.9882			−1.32920			−0.664602	+	0.747197i	$0.731399\pi$
$510$		0			0
$511$	37.4558	−	15.2913i	1.65695	−	0.676447i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	3.72792	+	2.15232i	0.164432	+	0.0949346i
$515$		−	15.2132i		−	0.670374i
$516$		0			0
$517$	29.1838	+	16.8493i	1.28350	+	0.741029i
$518$	−6.77962	−	5.25736i	−0.297879	−	0.230995i
$519$		0			0
$520$	−5.12132	+	8.87039i	−0.224585	+	0.388992i
$521$	4.60181	−	7.97056i	0.201609	−	0.349197i	−0.747438	−	0.664331i	$-0.768716\pi$
$521$	4.60181	−	7.97056i	0.201609	−	0.349197i	0.949047	+	0.315135i	$0.102050\pi$
$522$		0			0
$523$	15.2574	−	8.80884i	0.667158	−	0.385184i	−0.127841	−	0.991795i	$-0.540805\pi$
$523$	15.2574	−	8.80884i	0.667158	−	0.385184i	0.794999	+	0.606611i	$0.207471\pi$
$524$		0			0
$525$		0			0
$526$	−9.36396	+	16.2189i	−0.408288	+	0.707176i
$527$			13.7574i			0.599280i
$528$		0			0
$529$	−13.0000			−0.565217
$530$	3.04384	+	5.27208i	0.132216	+	0.229004i
$531$		0			0
$532$	−12.0000	+	4.89898i	−0.520266	+	0.212398i
$533$	8.87039	−	5.12132i	0.384219	−	0.221829i
$534$		0			0
$535$	30.7279	−	17.7408i	1.32848	−	0.767001i
$536$	−3.01834	+	1.74264i	−0.130373	+	0.0752706i
$537$		0			0
$538$	−8.48528	+	4.89898i	−0.365826	+	0.211210i
$539$	−28.7635	+	7.39340i	−1.23893	+	0.318456i
$540$		0			0
$541$	−22.7279	−	39.3659i	−0.977150	−	1.69247i	−0.672651	−	0.739960i	$-0.734844\pi$
$541$	−22.7279	−	39.3659i	−0.977150	−	1.69247i	−0.304499	−	0.952513i	$-0.598489\pi$
$542$	15.4144			0.662104
$543$		0			0
$544$			2.44949i			0.105021i
$545$	9.46473	−	16.3934i	0.405425	−	0.702216i
$546$		0			0
$547$	−3.01472	−	5.22165i	−0.128900	−	0.223261i	0.794351	−	0.607460i	$-0.207811\pi$
$547$	−3.01472	−	5.22165i	−0.128900	−	0.223261i	−0.923251	+	0.384198i	$0.874478\pi$
$548$	5.19615	−	3.00000i	0.221969	−	0.128154i
$549$		0			0
$550$	2.12132	−	3.67423i	0.0904534	−	0.156670i
$551$	25.0892	−	43.4558i	1.06884	−	1.85128i
$552$		0			0
$553$	−9.24264	−	22.6398i	−0.393037	−	0.962740i
$554$	−1.49642	−	0.863961i	−0.0635770	−	0.0367062i
$555$		0			0
$556$			11.5300i			0.488981i
$557$	−18.3712	−	10.6066i	−0.778412	−	0.449416i	0.0574555	−	0.998348i	$-0.481701\pi$
$557$	−18.3712	−	10.6066i	−0.778412	−	0.449416i	−0.835867	+	0.548932i	$0.815035\pi$
$558$		0			0
$559$			29.2708i			1.23802i
$560$	2.44949	+	6.00000i	0.103510	+	0.253546i
$561$		0			0
$562$	22.2426			0.938249
$563$	−8.23999	−	14.2721i	−0.347274	−	0.601496i	0.638490	−	0.769630i	$-0.279559\pi$
$563$	−8.23999	−	14.2721i	−0.347274	−	0.601496i	−0.985764	+	0.168134i	$0.946226\pi$
$564$		0			0
$565$	−3.72792	−	2.15232i	−0.156835	−	0.0905486i
$566$	23.3572			0.981776
$567$		0			0
$568$	12.7279			0.534052
$569$	−1.52192	−	0.878680i	−0.0638021	−	0.0368362i	0.467760	−	0.883856i	$-0.345061\pi$
$569$	−1.52192	−	0.878680i	−0.0638021	−	0.0368362i	−0.531562	+	0.847020i	$0.678395\pi$
$570$		0			0
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	0.998978	−	0.0452101i	$-0.0143957\pi$
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	−0.538642	+	0.842535i	$0.681062\pi$
$572$	−17.7408			−0.741779
$573$		0			0
$574$	0.878680	−	6.42090i	0.0366754	−	0.268003i
$575$		−	6.00000i		−	0.250217i
$576$		0			0
$577$	15.2574	+	8.80884i	0.635172	+	0.366717i	0.782752	−	0.622333i	$-0.213815\pi$
$577$	15.2574	+	8.80884i	0.635172	+	0.366717i	−0.147580	+	0.989050i	$0.547148\pi$
$578$			11.0000i			0.457540i
$579$		0			0
$580$	−21.7279	−	12.5446i	−0.902203	−	0.520887i
$581$	14.3998	+	1.97056i	0.597403	+	0.0817527i
$582$		0			0
$583$	−5.27208	+	9.13151i	−0.218347	+	0.378188i
$584$	7.64564	−	13.2426i	0.316379	−	0.547984i
$585$		0			0
$586$	6.87868	−	3.97141i	0.284156	−	0.164057i
$587$	−5.82655	−	10.0919i	−0.240488	−	0.416537i	0.720366	−	0.693594i	$-0.243974\pi$
$587$	−5.82655	−	10.0919i	−0.240488	−	0.416537i	−0.960853	+	0.277058i	$0.910641\pi$
$588$		0			0
$589$	−13.7574	+	23.8284i	−0.566862	+	0.981834i
$590$			6.00000i			0.247016i
$591$		0			0
$592$	−3.24264			−0.133272
$593$	11.3199	+	19.6066i	0.464852	+	0.805147i	0.999195	−	0.0401210i	$-0.0127743\pi$
$593$	11.3199	+	19.6066i	0.464852	+	0.805147i	−0.534343	+	0.845268i	$0.679441\pi$
$594$		0			0
$595$	−6.00000	−	14.6969i	−0.245976	−	0.602516i
$596$	6.71807	−	3.87868i	0.275183	−	0.158877i
$597$		0			0
$598$	−21.7279	+	12.5446i	−0.888521	+	0.512988i
$599$	17.7408	−	10.2426i	0.724868	−	0.418503i	−0.0916735	−	0.995789i	$-0.529222\pi$
$599$	17.7408	−	10.2426i	0.724868	−	0.418503i	0.816542	+	0.577286i	$0.195888\pi$
$600$		0			0
$601$	−14.9558	+	8.63476i	−0.610062	+	0.352219i	−0.772990	−	0.634419i	$-0.781240\pi$
$601$	−14.9558	+	8.63476i	−0.610062	+	0.352219i	0.162928	+	0.986638i	$0.447906\pi$
$602$	14.6354	+	11.3492i	0.596494	+	0.462561i
$603$		0			0
$604$	8.62132	+	14.9326i	0.350797	+	0.607597i
$605$	17.1464			0.697101
$606$		0			0
$607$			26.2779i			1.06659i	0.845930	+	0.533294i	$0.179046\pi$
$607$			26.2779i			1.06659i	−0.845930	+	0.533294i	$0.820954\pi$
$608$	−2.44949	+	4.24264i	−0.0993399	+	0.172062i
$609$		0			0
$610$	−0.878680	−	1.52192i	−0.0355767	−	0.0616207i
$611$	28.7635	−	16.6066i	1.16365	−	0.671831i
$612$		0			0
$613$	−7.10660	+	12.3090i	−0.287033	+	0.497156i	−0.973100	−	0.230383i	$-0.926002\pi$
$613$	−7.10660	+	12.3090i	−0.287033	+	0.497156i	0.686067	+	0.727538i	$0.259336\pi$
$614$	1.28629	−	2.22792i	0.0519105	−	0.0899116i
$615$		0			0
$616$	−6.87868	+	8.87039i	−0.277150	+	0.357398i
$617$	−3.67423	−	2.12132i	−0.147919	−	0.0854011i	0.424214	−	0.905562i	$-0.360551\pi$
$617$	−3.67423	−	2.12132i	−0.147919	−	0.0854011i	−0.572133	+	0.820161i	$0.693884\pi$
$618$		0			0
$619$			32.3146i			1.29883i	0.760432	+	0.649417i	$0.224987\pi$
$619$			32.3146i			1.29883i	−0.760432	+	0.649417i	$0.775013\pi$
$620$	11.9142	+	6.87868i	0.478487	+	0.276254i
$621$		0			0
$622$			17.1464i			0.687509i
$623$	46.5043	+	6.36396i	1.86315	+	0.254967i
$624$		0			0
$625$	−29.0000			−1.16000
$626$	0.297173	+	0.514719i	0.0118774	+	0.0205723i
$627$		0			0
$628$	9.00000	+	5.19615i	0.359139	+	0.207349i
$629$	7.94282			0.316701
$630$		0			0
$631$	−23.2426			−0.925275			−0.462637	−	0.886548i	$-0.653097\pi$
$631$	−23.2426			−0.925275			−0.462637	+	0.886548i	$0.653097\pi$
$632$	−8.00436	−	4.62132i	−0.318396	−	0.183826i
$633$		0			0
$634$	−6.87868	−	11.9142i	−0.273187	−	0.473174i
$635$	−43.4244			−1.72324
$636$		0			0
$637$	−7.86396	+	28.1946i	−0.311581	+	1.11711i
$638$		−	43.4558i		−	1.72043i
$639$		0			0
$640$	2.12132	+	1.22474i	0.0838525	+	0.0484123i
$641$		−	9.21320i		−	0.363900i	−0.983308	−	0.181950i	$-0.941759\pi$
$641$		−	9.21320i		−	0.363900i	0.983308	−	0.181950i	$-0.0582408\pi$
$642$		0			0
$643$	1.50000	+	0.866025i	0.0591542	+	0.0341527i	0.529285	−	0.848444i	$-0.322460\pi$
$643$	1.50000	+	0.866025i	0.0591542	+	0.0341527i	−0.470131	+	0.882597i	$0.655793\pi$
$644$	−2.15232	+	15.7279i	−0.0848132	+	0.619767i
$645$		0			0
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	10.3923	−	18.0000i	0.408564	−	0.707653i	−0.586165	−	0.810191i	$-0.699363\pi$
$647$	10.3923	−	18.0000i	0.408564	−	0.707653i	0.994729	+	0.102538i	$0.0326965\pi$
$648$		0			0
$649$	−9.00000	+	5.19615i	−0.353281	+	0.203967i
$650$	−2.09077	−	3.62132i	−0.0820068	−	0.142040i
$651$		0			0
$652$	3.74264	−	6.48244i	0.146573	−	0.253872i
$653$		−	14.4853i		−	0.566853i	−0.958994	−	0.283426i	$-0.908529\pi$
$653$		−	14.4853i		−	0.566853i	0.958994	−	0.283426i	$-0.0914712\pi$
$654$		0			0
$655$		0			0
$656$	−1.22474	−	2.12132i	−0.0478183	−	0.0828236i
$657$		0			0
$658$	2.84924	−	20.8207i	0.111075	−	0.811674i
$659$	−11.9142	+	6.87868i	−0.464112	+	0.267955i	−0.713772	−	0.700378i	$-0.753015\pi$
$659$	−11.9142	+	6.87868i	−0.464112	+	0.267955i	0.249660	+	0.968334i	$0.419681\pi$
$660$		0			0
$661$	−4.24264	+	2.44949i	−0.165020	+	0.0952741i	−0.580235	−	0.814449i	$-0.697039\pi$
$661$	−4.24264	+	2.44949i	−0.165020	+	0.0952741i	0.415216	+	0.909723i	$0.363706\pi$
$662$	−8.66025	+	5.00000i	−0.336590	+	0.194331i
$663$		0			0
$664$	4.75736	−	2.74666i	0.184621	−	0.106591i
$665$	4.30463	−	31.4558i	0.166927	−	1.21981i
$666$		0			0
$667$	−30.7279	−	53.2223i	−1.18979	−	2.06078i
$668$	20.1903			0.781185
$669$		0			0
$670$		−	8.53716i		−	0.329819i
$671$	1.52192	−	2.63604i	0.0587530	−	0.101763i
$672$		0			0
$673$	−2.72792	−	4.72490i	−0.105154	−	0.182131i	0.808647	−	0.588294i	$-0.200200\pi$
$673$	−2.72792	−	4.72490i	−0.105154	−	0.182131i	−0.913801	+	0.406162i	$0.866867\pi$
$674$	−25.5095	+	14.7279i	−0.982590	+	0.567298i
$675$		0			0
$676$	−2.24264	+	3.88437i	−0.0862554	+	0.149399i
$677$	7.34847	−	12.7279i	0.282425	−	0.489174i	−0.689557	−	0.724232i	$-0.742195\pi$
$677$	7.34847	−	12.7279i	0.282425	−	0.489174i	0.971981	+	0.235058i	$0.0755280\pi$
$678$		0			0
$679$	2.37868	−	17.3821i	0.0912853	−	0.667062i
$680$	−5.19615	−	3.00000i	−0.199263	−	0.115045i
$681$		0			0
$682$			23.8284i			0.912438i
$683$	−1.52192	−	0.878680i	−0.0582346	−	0.0336217i	0.470600	−	0.882347i	$-0.344037\pi$
$683$	−1.52192	−	0.878680i	−0.0582346	−	0.0336217i	−0.528835	+	0.848725i	$0.677371\pi$
$684$		0			0
$685$			14.6969i			0.561541i
$686$	11.0482	+	14.8640i	0.421822	+	0.567509i
$687$		0			0
$688$	7.00000			0.266872
$689$	5.19615	+	9.00000i	0.197958	+	0.342873i
$690$		0			0
$691$	23.2279	+	13.4106i	0.883632	+	0.510165i	0.871854	−	0.489766i	$-0.162918\pi$
$691$	23.2279	+	13.4106i	0.883632	+	0.510165i	0.0117776	+	0.999931i	$0.496251\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	28.9706			1.09971
$695$	−24.4588	−	14.1213i	−0.927777	−	0.535652i
$696$		0			0
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$	24.3718			0.922486
$699$		0			0
$700$	−2.62132	−	0.358719i	−0.0990766	−	0.0135583i
$701$		−	3.51472i		−	0.132749i	−0.997795	−	0.0663745i	$-0.978857\pi$
$701$		−	3.51472i		−	0.132749i	0.997795	−	0.0663745i	$-0.0211432\pi$
$702$		0			0
$703$	13.7574	+	7.94282i	0.518869	+	0.299569i
$704$			4.24264i			0.159901i
$705$		0			0
$706$	−26.4853	−	15.2913i	−0.996787	−	0.575495i
$707$	11.9142	−	15.3640i	0.448080	−	0.577821i
$708$		0			0
$709$	13.1066	−	22.7013i	0.492229	−	0.852565i	−0.507731	−	0.861516i	$-0.669516\pi$
$709$	13.1066	−	22.7013i	0.492229	−	0.852565i	0.999960	+	0.00895033i	$0.00284902\pi$
$710$	−15.5885	+	27.0000i	−0.585024	+	1.01329i
$711$		0			0
$712$	15.3640	−	8.87039i	0.575789	−	0.332432i
$713$	16.8493	+	29.1838i	0.631010	+	1.09294i
$714$		0			0
$715$	21.7279	−	37.6339i	0.812578	−	1.40743i
$716$			18.7279i			0.699895i
$717$		0			0
$718$	−2.48528			−0.0927499
$719$	−5.52938	−	9.57716i	−0.206211	−	0.357168i	0.744307	−	0.667838i	$-0.232780\pi$
$719$	−5.52938	−	9.57716i	−0.206211	−	0.357168i	−0.950518	+	0.310670i	$0.899447\pi$
$720$		0			0
$721$	−12.9853	−	10.0696i	−0.483597	−	0.375013i
$722$	4.33013	−	2.50000i	0.161151	−	0.0930404i
$723$		0			0
$724$	−8.48528	+	4.89898i	−0.315353	+	0.182069i
$725$	8.87039	−	5.12132i	0.329438	−	0.190201i
$726$		0			0
$727$	39.3198	−	22.7013i	1.45829	−	0.841945i	0.459363	−	0.888248i	$-0.348078\pi$
$727$	39.3198	−	22.7013i	1.45829	−	0.841945i	0.998927	+	0.0463038i	$0.0147442\pi$
$728$	4.18154	+	10.2426i	0.154978	+	0.379618i
$729$		0			0
$730$	18.7279	+	32.4377i	0.693151	+	1.20057i
$731$	−17.1464			−0.634184
$732$		0			0
$733$			16.0087i			0.591296i	0.955297	+	0.295648i	$0.0955355\pi$
$733$			16.0087i			0.591296i	−0.955297	+	0.295648i	$0.904465\pi$
$734$	4.60181	−	7.97056i	0.169856	−	0.294199i
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	12.8057	−	7.39340i	0.471706	−	0.272339i
$738$		0			0
$739$	−21.2279	+	36.7678i	−0.780882	+	1.35253i	0.150547	+	0.988603i	$0.451897\pi$
$739$	−21.2279	+	36.7678i	−0.780882	+	1.35253i	−0.931429	+	0.363924i	$0.881437\pi$
$740$	3.97141	−	6.87868i	0.145992	−	0.252865i
$741$		0			0
$742$	6.51472	+	0.891519i	0.239163	+	0.0327287i
$743$	−5.82655	−	3.36396i	−0.213755	−	0.123412i	0.389300	−	0.921111i	$-0.372717\pi$
$743$	−5.82655	−	3.36396i	−0.213755	−	0.123412i	−0.603055	+	0.797699i	$0.706050\pi$
$744$		0			0
$745$			19.0016i			0.696164i
$746$	−19.0526	−	11.0000i	−0.697564	−	0.402739i
$747$		0			0
$748$		−	10.3923i		−	0.379980i
$749$	5.19615	−	37.9706i	0.189863	−	1.38741i
$750$		0			0
$751$	2.54416			0.0928376			0.0464188	−	0.998922i	$-0.485219\pi$
$751$	2.54416			0.0928376			0.0464188	+	0.998922i	$0.485219\pi$
$752$	−3.97141	−	6.87868i	−0.144822	−	0.250840i
$753$		0			0
$754$	−37.0919	−	21.4150i	−1.35081	−	0.779889i
$755$	−42.2357			−1.53711
$756$		0			0
$757$	41.2426			1.49899			0.749495	−	0.662010i	$-0.230297\pi$
$757$	41.2426			1.49899			0.749495	+	0.662010i	$0.230297\pi$
$758$	8.21449	+	4.74264i	0.298364	+	0.172260i
$759$		0			0
$760$	−6.00000	−	10.3923i	−0.217643	−	0.376969i
$761$	24.4949			0.887939			0.443970	−	0.896042i	$-0.353570\pi$
$761$	24.4949			0.887939			0.443970	+	0.896042i	$0.353570\pi$
$762$		0			0
$763$	−7.72792	−	18.9295i	−0.279770	−	0.685293i
$764$		−	21.2132i		−	0.767467i
$765$		0			0
$766$	−13.2426	−	7.64564i	−0.478476	−	0.276248i
$767$			10.2426i			0.369840i
$768$		0			0
$769$	1.02944	+	0.594346i	0.0371225	+	0.0214327i	0.518446	−	0.855110i	$-0.326511\pi$
$769$	1.02944	+	0.594346i	0.0371225	+	0.0214327i	−0.481324	+	0.876543i	$0.659844\pi$
$770$	−10.3923	−	25.4558i	−0.374513	−	0.917365i
$771$		0			0
$772$	7.74264	−	13.4106i	0.278664	−	0.482660i
$773$	4.89898	−	8.48528i	0.176204	−	0.305194i	−0.764373	−	0.644774i	$-0.776951\pi$
$773$	4.89898	−	8.48528i	0.176204	−	0.305194i	0.940577	+	0.339580i	$0.110285\pi$
$774$		0			0
$775$	−4.86396	+	2.80821i	−0.174719	+	0.100874i
$776$	−3.31552	−	5.74264i	−0.119020	−	0.206149i
$777$		0			0
$778$	−16.2426	+	28.1331i	−0.582327	+	1.00862i
$779$			12.0000i			0.429945i
$780$		0			0
$781$	−54.0000			−1.93227
$782$	−7.34847	−	12.7279i	−0.262781	−	0.455150i
$783$		0			0
$784$	6.74264	+	1.88064i	0.240809	+	0.0671656i
$785$	−22.0454	+	12.7279i	−0.786834	+	0.454279i
$786$		0			0
$787$	−9.47056	+	5.46783i	−0.337589	+	0.194907i	−0.659205	−	0.751963i	$-0.729107\pi$
$787$	−9.47056	+	5.46783i	−0.337589	+	0.194907i	0.321616	+	0.946870i	$0.395774\pi$
$788$	−14.6969	+	8.48528i	−0.523557	+	0.302276i
$789$		0			0
$790$	19.6066	−	11.3199i	0.697572	−	0.402743i
$791$	−4.30463	+	1.75736i	−0.153055	+	0.0624845i
$792$		0			0
$793$	−1.50000	−	2.59808i	−0.0532666	−	0.0922604i
$794$	−29.8651			−1.05987
$795$		0			0
$796$			3.58719i			0.127145i
$797$	−1.52192	+	2.63604i	−0.0539091	+	0.0933733i	−0.891721	−	0.452586i	$-0.850501\pi$
$797$	−1.52192	+	2.63604i	−0.0539091	+	0.0933733i	0.837812	+	0.545960i	$0.183835\pi$
$798$		0			0
$799$	9.72792	+	16.8493i	0.344149	+	0.596084i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−14.1213	+	24.4588i	−0.498641	+	0.863672i
$803$	−32.4377	+	56.1838i	−1.14470	+	1.98268i
$804$		0			0
$805$	−30.7279	−	23.8284i	−1.08302	−	0.839842i
$806$	20.3389	+	11.7426i	0.716405	+	0.413617i
$807$		0			0
$808$		−	7.34847i		−	0.258518i
$809$	2.15232	+	1.24264i	0.0756714	+	0.0436889i	0.537358	−	0.843354i	$-0.319422\pi$
$809$	2.15232	+	1.24264i	0.0756714	+	0.0436889i	−0.461687	+	0.887043i	$0.652756\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−25.0892	+	10.2426i	−0.880460	+	0.359446i
$813$		0			0
$814$	13.7574			0.482195
$815$	9.16756	+	15.8787i	0.321126	+	0.556206i
$816$		0			0
$817$	−29.6985	−	17.1464i	−1.03902	−	0.599878i
$818$	13.5592			0.474087
$819$		0			0
$820$	6.00000			0.209529
$821$	−9.50079	−	5.48528i	−0.331580	−	0.191438i	0.324963	−	0.945727i	$-0.394648\pi$
$821$	−9.50079	−	5.48528i	−0.331580	−	0.191438i	−0.656542	+	0.754289i	$0.727982\pi$
$822$		0			0
$823$	5.62132	+	9.73641i	0.195947	+	0.339390i	0.947211	−	0.320612i	$-0.103889\pi$
$823$	5.62132	+	9.73641i	0.195947	+	0.339390i	−0.751264	+	0.660002i	$0.770555\pi$
$824$	−6.21076			−0.216362
$825$		0			0
$826$	5.12132	+	3.97141i	0.178194	+	0.138183i
$827$			20.4853i			0.712343i	0.934421	+	0.356172i	$0.115918\pi$
$827$			20.4853i			0.712343i	−0.934421	+	0.356172i	$0.884082\pi$
$828$		0			0
$829$	−8.48528	−	4.89898i	−0.294706	−	0.170149i	0.345356	−	0.938472i	$-0.387758\pi$
$829$	−8.48528	−	4.89898i	−0.294706	−	0.170149i	−0.640062	+	0.768323i	$0.721091\pi$
$830$			13.4558i			0.467059i
$831$		0			0
$832$	3.62132	+	2.09077i	0.125547	+	0.0724844i
$833$	−16.5160	−	4.60660i	−0.572246	−	0.159609i
$834$		0			0
$835$	−24.7279	+	42.8300i	−0.855745	+	1.48219i
$836$	10.3923	−	18.0000i	0.359425	−	0.622543i
$837$		0			0
$838$	11.1213	−	6.42090i	0.384180	−	0.221806i
$839$	2.74666	+	4.75736i	0.0948253	+	0.164242i	0.909536	−	0.415626i	$-0.136437\pi$
$839$	2.74666	+	4.75736i	0.0948253	+	0.164242i	−0.814710	+	0.579868i	$0.803104\pi$
$840$		0			0
$841$	37.9558	−	65.7415i	1.30882	−	2.26695i
$842$		−	27.4558i		−	0.946191i
$843$		0			0
$844$	13.4853			0.464183
$845$	−5.49333	−	9.51472i	−0.188976	−	0.327316i
$846$		0			0
$847$	11.3492	−	14.6354i	0.389965	−	0.502878i
$848$	2.15232	−	1.24264i	0.0739109	−	0.0426725i
$849$		0			0
$850$	2.12132	−	1.22474i	0.0727607	−	0.0420084i
$851$	16.8493	−	9.72792i	0.577585	−	0.333469i
$852$		0			0
$853$	44.4853	−	25.6836i	1.52315	−	0.879389i	0.523522	−	0.852012i	$-0.324618\pi$
$853$	44.4853	−	25.6836i	1.52315	−	0.879389i	0.999625	−	0.0273771i	$-0.00871549\pi$
$854$	−1.88064	−	0.257359i	−0.0643541	−	0.00880665i
$855$		0			0
$856$	−7.24264	−	12.5446i	−0.247548	−	0.428766i
$857$	−6.75412			−0.230716			−0.115358	−	0.993324i	$-0.536802\pi$
$857$	−6.75412			−0.230716			−0.115358	+	0.993324i	$0.536802\pi$
$858$		0			0
$859$		−	10.9357i		−	0.373120i	−0.982444	−	0.186560i	$-0.940266\pi$
$859$		−	10.9357i		−	0.373120i	0.982444	−	0.186560i	$-0.0597339\pi$
$860$	−8.57321	+	14.8492i	−0.292344	+	0.506355i
$861$		0			0
$862$	−5.12132	−	8.87039i	−0.174433	−	0.302127i
$863$	11.6531	−	6.72792i	0.396676	−	0.229021i	−0.288373	−	0.957518i	$-0.593114\pi$
$863$	11.6531	−	6.72792i	0.396676	−	0.229021i	0.685049	+	0.728497i	$0.259781\pi$
$864$		0			0
$865$	25.4558	−	44.0908i	0.865525	−	1.49913i
$866$	13.4106	−	23.2279i	0.455712	−	0.789317i
$867$		0			0
$868$	13.7574	−	5.61642i	0.466955	−	0.190634i
$869$	33.9596	+	19.6066i	1.15200	+	0.665108i
$870$		0			0
$871$		−	14.5738i		−	0.493816i
$872$	−6.69258	−	3.86396i	−0.226639	−	0.130850i
$873$		0			0
$874$		−	29.3939i		−	0.994263i
$875$	−15.8856	+	20.4853i	−0.537032	+	0.692529i
$876$		0			0
$877$	−3.78680			−0.127871			−0.0639355	−	0.997954i	$-0.520365\pi$
$877$	−3.78680			−0.127871			−0.0639355	+	0.997954i	$0.520365\pi$
$878$	12.5446	+	21.7279i	0.423360	+	0.733282i
$879$		0			0
$880$	−9.00000	−	5.19615i	−0.303390	−	0.175162i
$881$	−4.30463			−0.145027			−0.0725134	−	0.997367i	$-0.523102\pi$
$881$	−4.30463			−0.145027			−0.0725134	+	0.997367i	$0.523102\pi$
$882$		0			0
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$	−8.87039	−	5.12132i	−0.298343	−	0.172249i
$885$		0			0
$886$	12.7279	+	22.0454i	0.427603	+	0.740630i
$887$	29.9882			1.00691			0.503453	−	0.864023i	$-0.332063\pi$
$887$	29.9882			1.00691			0.503453	+	0.864023i	$0.332063\pi$
$888$		0			0
$889$	−28.7426	+	37.0650i	−0.963997	+	1.24312i
$890$			43.4558i			1.45664i
$891$		0			0
$892$	−9.00000	−	5.19615i	−0.301342	−	0.173980i
$893$			38.9117i			1.30213i
$894$		0			0
$895$	−39.7279	−	22.9369i	−1.32796	−	0.766697i
$896$	2.44949	−	1.00000i	0.0818317	−	0.0334077i
$897$		0			0
$898$	15.3640	−	26.6112i	0.512702	−	0.888026i
$899$	−28.7635	+	49.8198i	−0.959316	+	1.66158i
$900$		0			0
$901$	−5.27208	+	3.04384i	−0.175638	+	0.101405i
$902$	5.19615	+	9.00000i	0.173013	+	0.299667i
$903$		0			0
$904$	−0.878680	+	1.52192i	−0.0292245	+	0.0506182i
$905$		−	24.0000i		−	0.797787i
$906$		0			0
$907$	3.48528			0.115727			0.0578634	−	0.998325i	$-0.481571\pi$
$907$	3.48528			0.115727			0.0578634	+	0.998325i	$0.481571\pi$
$908$	2.15232	+	3.72792i	0.0714271	+	0.123715i
$909$		0			0
$910$	−26.8492	−	3.67423i	−0.890044	−	0.121800i
$911$	1.52192	−	0.878680i	0.0504234	−	0.0291120i	−0.474576	−	0.880214i	$-0.657399\pi$
$911$	1.52192	−	0.878680i	0.0504234	−	0.0291120i	0.525000	+	0.851102i	$0.324065\pi$
$912$		0			0
$913$	−20.1838	+	11.6531i	−0.667985	+	0.385661i
$914$	19.9186	−	11.5000i	0.658848	−	0.380386i
$915$		0			0
$916$	−7.86396	+	4.54026i	−0.259833	+	0.150014i
$917$		0			0
$918$		0			0
$919$	−0.136039	−	0.235626i	−0.00448751	−	0.00777260i	0.863773	−	0.503881i	$-0.168095\pi$
$919$	−0.136039	−	0.235626i	−0.00448751	−	0.00777260i	−0.868260	+	0.496109i	$0.834762\pi$
$920$	−14.6969			−0.484544
$921$		0			0
$922$		−	42.2357i		−	1.39096i
$923$	−26.6112	+	46.0919i	−0.875917	+	1.51713i
$924$		0			0
$925$	1.62132	+	2.80821i	0.0533087	+	0.0923334i
$926$	19.0526	−	11.0000i	0.626106	−	0.361482i
$927$		0			0
$928$	−5.12132	+	8.87039i	−0.168116	+	0.291185i
$929$	16.8132	−	29.1213i	0.551623	−	0.955440i	−0.446534	−	0.894766i	$-0.647342\pi$
$929$	16.8132	−	29.1213i	0.551623	−	0.955440i	0.998158	−	0.0606731i	$-0.0193247\pi$
$930$		0			0
$931$	−24.0000	−	24.4949i	−0.786568	−	0.802788i
$932$	−3.04384	−	1.75736i	−0.0997042	−	0.0575642i
$933$		0			0
$934$			3.04384i			0.0995973i
$935$	22.0454	+	12.7279i	0.720962	+	0.416248i
$936$		0			0
$937$		−	53.0992i		−	1.73468i	−0.497719	−	0.867338i	$-0.665829\pi$
$937$		−	53.0992i		−	1.73468i	0.497719	−	0.867338i	$-0.334171\pi$
$938$	−7.28692	−	5.65076i	−0.237926	−	0.184504i
$939$		0			0
$940$	19.4558			0.634580
$941$	−10.7255	−	18.5772i	−0.349642	−	0.605598i	0.636544	−	0.771241i	$-0.280364\pi$
$941$	−10.7255	−	18.5772i	−0.349642	−	0.605598i	−0.986186	+	0.165643i	$0.947030\pi$
$942$		0			0
$943$	12.7279	+	7.34847i	0.414478	+	0.239299i
$944$	2.44949			0.0797241
$945$		0			0
$946$	−29.6985			−0.965581
$947$	−6.71807	−	3.87868i	−0.218308	−	0.126040i	0.386859	−	0.922139i	$-0.373560\pi$
$947$	−6.71807	−	3.87868i	−0.218308	−	0.126040i	−0.605167	+	0.796099i	$0.706893\pi$
$948$		0			0
$949$	31.9706	+	55.3746i	1.03781	+	1.79754i
$950$	4.89898			0.158944
$951$		0			0
$952$	−6.00000	+	2.44949i	−0.194461	+	0.0793884i
$953$			34.9706i			1.13281i	0.824128	+	0.566404i	$0.191666\pi$
$953$			34.9706i			1.13281i	−0.824128	+	0.566404i	$0.808334\pi$
$954$		0			0
$955$	45.0000	+	25.9808i	1.45617	+	0.840718i
$956$			7.75736i			0.250891i
$957$		0			0
$958$	2.12132	+	1.22474i	0.0685367	+	0.0395697i
$959$	12.5446	+	9.72792i	0.405087	+	0.314131i
$960$		0			0
$961$	0.272078	−	0.471253i	0.00877671	−	0.0152017i
$962$	6.77962	−	11.7426i	0.218584	−	0.378598i
$963$		0			0
$964$	15.9853	−	9.22911i	0.514851	−	0.297250i
$965$	18.9655	+	32.8492i	0.610522	+	1.05745i
$966$		0			0
$967$	−8.34924	+	14.4613i	−0.268494	+	0.465044i	−0.968473	−	0.249119i	$-0.919859\pi$
$967$	−8.34924	+	14.4613i	−0.268494	+	0.465044i	0.699979	+	0.714163i	$0.253192\pi$
$968$		−	7.00000i		−	0.224989i
$969$		0			0
$970$	16.2426			0.521520
$971$	−0.594346	−	1.02944i	−0.0190735	−	0.0330362i	0.856331	−	0.516427i	$-0.172738\pi$
$971$	−0.594346	−	1.02944i	−0.0190735	−	0.0330362i	−0.875405	+	0.483391i	$0.839405\pi$
$972$		0			0
$973$	−28.2426	+	11.5300i	−0.905417	+	0.369635i
$974$	−19.0526	+	11.0000i	−0.610483	+	0.352463i
$975$		0			0
$976$	−0.621320	+	0.358719i	−0.0198880	+	0.0114823i
$977$	−5.19615	+	3.00000i	−0.166240	+	0.0959785i	−0.580812	−	0.814038i	$-0.697265\pi$
$977$	−5.19615	+	3.00000i	−0.166240	+	0.0959785i	0.414572	+	0.910017i	$0.363931\pi$
$978$		0			0
$979$	−65.1838	+	37.6339i	−2.08328	+	1.20278i
$980$	−12.2474	+	12.0000i	−0.391230	+	0.383326i
$981$		0			0
$982$	0.514719	+	0.891519i	0.0164253	+	0.0284495i
$983$	−18.3351			−0.584800			−0.292400	−	0.956296i	$-0.594454\pi$
$983$	−18.3351			−0.584800			−0.292400	+	0.956296i	$0.594454\pi$
$984$		0			0
$985$		−	41.5692i		−	1.32451i
$986$	12.5446	−	21.7279i	0.399502	−	0.691958i
$987$		0			0
$988$	−10.2426	−	17.7408i	−0.325862	−	0.564409i
$989$	−36.3731	+	21.0000i	−1.15660	+	0.667761i
$990$		0			0
$991$	−11.1066	+	19.2372i	−0.352813	+	0.611090i	−0.986741	−	0.162302i	$-0.948108\pi$
$991$	−11.1066	+	19.2372i	−0.352813	+	0.611090i	0.633928	+	0.773392i	$0.281441\pi$
$992$	2.80821	−	4.86396i	0.0891607	−	0.154431i
$993$		0			0
$994$	12.7279	+	31.1769i	0.403705	+	0.988872i
$995$	−7.60959	−	4.39340i	−0.241240	−	0.139280i
$996$		0			0
$997$		−	4.77589i		−	0.151254i	−0.997136	−	0.0756269i	$-0.975904\pi$
$997$		−	4.77589i		−	0.151254i	0.997136	−	0.0756269i	$-0.0240958\pi$
$998$	22.9114	+	13.2279i	0.725249	+	0.418723i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.t.f.1025.3		8
3.2	odd	2	inner	1134.2.t.f.1025.2		8
7.5	odd	6		1134.2.l.e.215.1		8
9.2	odd	6		1134.2.l.e.269.3		8
9.4	even	3		378.2.k.d.269.2	yes	8
9.5	odd	6		378.2.k.d.269.3	yes	8
9.7	even	3		1134.2.l.e.269.2		8
21.5	even	6		1134.2.l.e.215.4		8
63.4	even	3		2646.2.d.d.2645.1		8
63.5	even	6		378.2.k.d.215.2	✓	8
63.31	odd	6		2646.2.d.d.2645.3		8
63.32	odd	6		2646.2.d.d.2645.8		8
63.40	odd	6		378.2.k.d.215.3	yes	8
63.47	even	6	inner	1134.2.t.f.593.3		8
63.59	even	6		2646.2.d.d.2645.6		8
63.61	odd	6	inner	1134.2.t.f.593.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.d.215.2	✓	8	63.5	even	6
378.2.k.d.215.3	yes	8	63.40	odd	6
378.2.k.d.269.2	yes	8	9.4	even	3
378.2.k.d.269.3	yes	8	9.5	odd	6
1134.2.l.e.215.1		8	7.5	odd	6
1134.2.l.e.215.4		8	21.5	even	6
1134.2.l.e.269.2		8	9.7	even	3
1134.2.l.e.269.3		8	9.2	odd	6
1134.2.t.f.593.2		8	63.61	odd	6	inner
1134.2.t.f.593.3		8	63.47	even	6	inner
1134.2.t.f.1025.2		8	3.2	odd	2	inner
1134.2.t.f.1025.3		8	1.1	even	1	trivial
2646.2.d.d.2645.1		8	63.4	even	3
2646.2.d.d.2645.3		8	63.31	odd	6
2646.2.d.d.2645.6		8	63.59	even	6
2646.2.d.d.2645.8		8	63.32	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.44949 q^{5} +(-1.62132 + 2.09077i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.44949 q^{5} +(-1.62132 + 2.09077i) q^{7} +1.00000i q^{8} +(-2.12132 - 1.22474i) q^{10} -4.24264i q^{11} +(-3.62132 - 2.09077i) q^{13} +(-2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.22474 - 2.12132i) q^{17} +(4.24264 - 2.44949i) q^{19} +(-1.22474 - 2.12132i) q^{20} +(2.12132 - 3.67423i) q^{22} -6.00000i q^{23} +1.00000 q^{25} +(-2.09077 - 3.62132i) q^{26} +(-2.62132 - 0.358719i) q^{28} +(8.87039 - 5.12132i) q^{29} +(-4.86396 + 2.80821i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.12132 - 1.22474i) q^{34} +(3.97141 - 5.12132i) q^{35} +(1.62132 + 2.80821i) q^{37} +4.89898 q^{38} -2.44949i q^{40} +(-1.22474 + 2.12132i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(3.67423 - 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-3.97141 + 6.87868i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(0.866025 + 0.500000i) q^{50} -4.18154i q^{52} +(-2.15232 - 1.24264i) q^{53} +10.3923i q^{55} +(-2.09077 - 1.62132i) q^{56} +10.2426 q^{58} +(-1.22474 - 2.12132i) q^{59} +(0.621320 + 0.358719i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(8.87039 + 5.12132i) q^{65} +(1.74264 + 3.01834i) q^{67} +2.44949 q^{68} +(6.00000 - 2.44949i) q^{70} -12.7279i q^{71} +(-13.2426 - 7.64564i) q^{73} +3.24264i q^{74} +(4.24264 + 2.44949i) q^{76} +(8.87039 + 6.87868i) q^{77} +(-4.62132 + 8.00436i) q^{79} +(1.22474 - 2.12132i) q^{80} +(-2.12132 + 1.22474i) q^{82} +(-2.74666 - 4.75736i) q^{83} +(-3.00000 + 5.19615i) q^{85} -7.00000i q^{86} +4.24264 q^{88} +(-8.87039 - 15.3640i) q^{89} +(10.2426 - 4.18154i) q^{91} +(5.19615 - 3.00000i) q^{92} +(-6.87868 + 3.97141i) q^{94} +(-10.3923 + 6.00000i) q^{95} +(-5.74264 + 3.31552i) q^{97} +(1.88064 - 6.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^7	\( 8 q + 4 q^{4} + 4 q^{7} - 12 q^{13} - 4 q^{16} + 8 q^{25} - 4 q^{28} + 12 q^{31} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} + 48 q^{58} - 12 q^{61} - 8 q^{64} - 20 q^{67} + 48 q^{70} - 72 q^{73} - 20 q^{79} - 24 q^{85} + 48 q^{91} - 72 q^{94} - 12 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^7 - 12 * q^13 - 4 * q^16 + 8 * q^25 - 4 * q^28 + 12 * q^31 - 4 * q^37 - 28 * q^43 + 24 * q^46 + 20 * q^49 + 48 * q^58 - 12 * q^61 - 8 * q^64 - 20 * q^67 + 48 * q^70 - 72 * q^73 - 20 * q^79 - 24 * q^85 + 48 * q^91 - 72 * q^94 - 12 * q^97

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