LMFDB - Embedded newform 1008.2.ca.c.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(257,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1008.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.1
Root			$1.58110 - 0.707199i$ of defining polynomial
Character	$\chi$	$=$	1008.257
Dual form			1008.2.ca.c.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64774 - 0.533822i) q^{3} +(-0.450129 - 0.779646i) q^{5} +(-1.57151 - 2.12847i) q^{7} +(2.43007 + 1.75919i) q^{9} +O(q^{10})$	\(q+(-1.64774 - 0.533822i) q^{3} +(-0.450129 - 0.779646i) q^{5} +(-1.57151 - 2.12847i) q^{7} +(2.43007 + 1.75919i) q^{9} +(2.70900 + 1.56404i) q^{11} +(-1.99033 - 1.14912i) q^{13} +(0.325502 + 1.52494i) q^{15} +(-2.57638 - 4.46242i) q^{17} +(-2.38111 - 1.37474i) q^{19} +(1.45321 + 4.34605i) q^{21} +(1.48584 - 0.857850i) q^{23} +(2.09477 - 3.62824i) q^{25} +(-3.06502 - 4.19591i) q^{27} +(-1.85590 + 1.07151i) q^{29} +10.0032i q^{31} +(-3.62880 - 4.02326i) q^{33} +(-0.952070 + 2.18330i) q^{35} +(-4.73701 + 8.20475i) q^{37} +(2.66612 + 2.95593i) q^{39} +(1.22134 - 2.11542i) q^{41} +(0.273155 + 0.473119i) q^{43} +(0.277705 - 2.68646i) q^{45} -7.86068 q^{47} +(-2.06074 + 6.68980i) q^{49} +(1.86306 + 8.72821i) q^{51} +(-12.0733 + 6.97054i) q^{53} -2.81608i q^{55} +(3.18958 + 3.53629i) q^{57} -7.98443 q^{59} +7.25411i q^{61} +(-0.0744824 - 7.93690i) q^{63} +2.06901i q^{65} -3.67050 q^{67} +(-2.90621 + 0.620337i) q^{69} -14.1484i q^{71} +(-10.9190 + 6.30409i) q^{73} +(-5.38846 + 4.86016i) q^{75} +(-0.928202 - 8.22392i) q^{77} +6.54804 q^{79} +(2.81047 + 8.54993i) q^{81} +(-0.184437 - 0.319454i) q^{83} +(-2.31940 + 4.01733i) q^{85} +(3.63003 - 0.774838i) q^{87} +(6.00244 - 10.3965i) q^{89} +(0.681960 + 6.04220i) q^{91} +(5.33990 - 16.4826i) q^{93} +2.47523i q^{95} +(8.86815 - 5.12003i) q^{97} +(3.83161 + 8.56640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^7	$ 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49} - 6 q^{51} - 36 q^{53} + 6 q^{57} - 60 q^{59} - 36 q^{63} + 28 q^{67} - 42 q^{69} - 60 q^{75} - 42 q^{77} - 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{87} - 24 q^{89} + 12 q^{91} - 42 q^{93} + 6 q^{97} - 18 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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			0
$2$		0			0
$3$	−1.64774	−	0.533822i	−0.951321	−	0.308202i
$3$	−1.64774	−	0.533822i	−0.951321	−	0.308202i
$4$		0			0
$5$	−0.450129	−	0.779646i	−0.201304	−	0.348668i	0.747645	−	0.664099i	$-0.231185\pi$
$5$	−0.450129	−	0.779646i	−0.201304	−	0.348668i	−0.948949	+	0.315430i	$0.897851\pi$
$6$		0			0
$7$	−1.57151	−	2.12847i	−0.593974	−	0.804485i
$7$	−1.57151	−	2.12847i	−0.593974	−	0.804485i
$8$		0			0
$9$	2.43007	+	1.75919i	0.810023	+	0.586398i
$10$		0			0
$11$	2.70900	+	1.56404i	0.816795	+	0.471577i	0.849310	−	0.527894i	$-0.177018\pi$
$11$	2.70900	+	1.56404i	0.816795	+	0.471577i	−0.0325150	+	0.999471i	$0.510352\pi$
$12$		0			0
$13$	−1.99033	−	1.14912i	−0.552019	−	0.318708i	0.197917	−	0.980219i	$-0.436582\pi$
$13$	−1.99033	−	1.14912i	−0.552019	−	0.318708i	−0.749936	+	0.661511i	$0.769916\pi$
$14$		0			0
$15$	0.325502	+	1.52494i	0.0840442	+	0.393738i
$16$		0			0
$17$	−2.57638	−	4.46242i	−0.624863	−	1.08230i	−0.988567	−	0.150780i	$-0.951821\pi$
$17$	−2.57638	−	4.46242i	−0.624863	−	1.08230i	0.363704	−	0.931515i	$-0.381512\pi$
$18$		0			0
$19$	−2.38111	−	1.37474i	−0.546264	−	0.315386i	0.201350	−	0.979519i	$-0.435467\pi$
$19$	−2.38111	−	1.37474i	−0.546264	−	0.315386i	−0.747614	+	0.664134i	$0.768801\pi$
$20$		0			0
$21$	1.45321	+	4.34605i	0.317116	+	0.948387i
$22$		0			0
$23$	1.48584	−	0.857850i	0.309819	−	0.178874i	−0.337027	−	0.941495i	$-0.609421\pi$
$23$	1.48584	−	0.857850i	0.309819	−	0.178874i	0.646845	+	0.762621i	$0.276088\pi$
$24$		0			0
$25$	2.09477	−	3.62824i	0.418954	−	0.725649i
$26$		0			0
$27$	−3.06502	−	4.19591i	−0.589863	−	0.807504i
$28$		0			0
$29$	−1.85590	+	1.07151i	−0.344633	+	0.198974i	−0.662319	−	0.749222i	$-0.730428\pi$
$29$	−1.85590	+	1.07151i	−0.344633	+	0.198974i	0.317686	+	0.948196i	$0.397094\pi$
$30$		0			0
$31$			10.0032i			1.79662i	0.439363	+	0.898309i	$0.355204\pi$
$31$			10.0032i			1.79662i	−0.439363	+	0.898309i	$0.644796\pi$
$32$		0			0
$33$	−3.62880	−	4.02326i	−0.631693	−	0.700359i
$34$		0			0
$35$	−0.952070	+	2.18330i	−0.160929	+	0.369046i
$36$		0			0
$37$	−4.73701	+	8.20475i	−0.778760	+	1.34885i	0.153896	+	0.988087i	$0.450818\pi$
$37$	−4.73701	+	8.20475i	−0.778760	+	1.34885i	−0.932657	+	0.360766i	$0.882515\pi$
$38$		0			0
$39$	2.66612	+	2.95593i	0.426921	+	0.473327i
$40$		0			0
$41$	1.22134	−	2.11542i	0.190741	−	0.330373i	−0.754755	−	0.656007i	$-0.772244\pi$
$41$	1.22134	−	2.11542i	0.190741	−	0.330373i	0.945496	+	0.325634i	$0.105578\pi$
$42$		0			0
$43$	0.273155	+	0.473119i	0.0416558	+	0.0721499i	0.886102	−	0.463491i	$-0.153403\pi$
$43$	0.273155	+	0.473119i	0.0416558	+	0.0721499i	−0.844446	+	0.535641i	$0.820070\pi$
$44$		0			0
$45$	0.277705	−	2.68646i	0.0413979	−	0.400474i
$46$		0			0
$47$	−7.86068			−1.14660			−0.573299	−	0.819346i	$-0.694337\pi$
$47$	−7.86068			−1.14660			−0.573299	+	0.819346i	$0.694337\pi$
$48$		0			0
$49$	−2.06074	+	6.68980i	−0.294391	+	0.955685i
$50$		0			0
$51$	1.86306	+	8.72821i	0.260880	+	1.22219i
$52$		0			0
$53$	−12.0733	+	6.97054i	−1.65840	+	0.957478i	−0.684947	+	0.728593i	$0.740175\pi$
$53$	−12.0733	+	6.97054i	−1.65840	+	0.957478i	−0.973454	+	0.228885i	$0.926492\pi$
$54$		0			0
$55$		−	2.81608i		−	0.379721i
$56$		0			0
$57$	3.18958	+	3.53629i	0.422470	+	0.468393i
$58$		0			0
$59$	−7.98443			−1.03948			−0.519742	−	0.854323i	$-0.673972\pi$
$59$	−7.98443			−1.03948			−0.519742	+	0.854323i	$0.673972\pi$
$60$		0			0
$61$			7.25411i			0.928793i	0.885627	+	0.464397i	$0.153729\pi$
$61$			7.25411i			0.928793i	−0.885627	+	0.464397i	$0.846271\pi$
$62$		0			0
$63$	−0.0744824	−	7.93690i	−0.00938390	−	0.999956i
$64$		0			0
$65$			2.06901i			0.256629i
$66$		0			0
$67$	−3.67050			−0.448423			−0.224212	−	0.974540i	$-0.571981\pi$
$67$	−3.67050			−0.448423			−0.224212	+	0.974540i	$0.571981\pi$
$68$		0			0
$69$	−2.90621	+	0.620337i	−0.349867	+	0.0746798i
$70$		0			0
$71$		−	14.1484i		−	1.67911i	−0.543275	−	0.839555i	$-0.682816\pi$
$71$		−	14.1484i		−	1.67911i	0.543275	−	0.839555i	$-0.317184\pi$
$72$		0			0
$73$	−10.9190	+	6.30409i	−1.27797	+	0.737838i	−0.976475	−	0.215629i	$-0.930820\pi$
$73$	−10.9190	+	6.30409i	−1.27797	+	0.737838i	−0.301498	+	0.953467i	$0.597487\pi$
$74$		0			0
$75$	−5.38846	+	4.86016i	−0.622206	+	0.561203i
$76$		0			0
$77$	−0.928202	−	8.22392i	−0.105778	−	0.937203i
$78$		0			0
$79$	6.54804			0.736712			0.368356	−	0.929685i	$-0.379921\pi$
$79$	6.54804			0.736712			0.368356	+	0.929685i	$0.379921\pi$
$80$		0			0
$81$	2.81047	+	8.54993i	0.312274	+	0.949992i
$82$		0			0
$83$	−0.184437	−	0.319454i	−0.0202446	−	0.0350646i	0.855726	−	0.517430i	$-0.173111\pi$
$83$	−0.184437	−	0.319454i	−0.0202446	−	0.0350646i	−0.875970	+	0.482365i	$0.839778\pi$
$84$		0			0
$85$	−2.31940	+	4.01733i	−0.251575	+	0.435740i
$86$		0			0
$87$	3.63003	−	0.774838i	0.389180	−	0.0830714i
$88$		0			0
$89$	6.00244	−	10.3965i	0.636258	−	1.10203i	−0.349990	−	0.936754i	$-0.613815\pi$
$89$	6.00244	−	10.3965i	0.636258	−	1.10203i	0.986247	−	0.165277i	$-0.0528518\pi$
$90$		0			0
$91$	0.681960	+	6.04220i	0.0714888	+	0.633395i
$92$		0			0
$93$	5.33990	−	16.4826i	0.553722	−	1.70916i
$94$		0			0
$95$			2.47523i			0.253953i
$96$		0			0
$97$	8.86815	−	5.12003i	0.900424	−	0.519860i	0.0230864	−	0.999733i	$-0.492651\pi$
$97$	8.86815	−	5.12003i	0.900424	−	0.519860i	0.877338	+	0.479873i	$0.159317\pi$
$98$		0			0
$99$	3.83161	+	8.56640i	0.385091	+	0.860955i
$100$		0			0
$101$	−1.35969	+	2.35506i	−0.135294	+	0.234337i	−0.925710	−	0.378234i	$-0.876531\pi$
$101$	−1.35969	+	2.35506i	−0.135294	+	0.234337i	0.790415	+	0.612571i	$0.209865\pi$
$102$		0			0
$103$	−1.18861	+	0.686242i	−0.117117	+	0.0676174i	−0.557414	−	0.830235i	$-0.688206\pi$
$103$	−1.18861	+	0.686242i	−0.117117	+	0.0676174i	0.440297	+	0.897852i	$0.354873\pi$
$104$		0			0
$105$	2.73425	−	3.08927i	0.266836	−	0.301482i
$106$		0			0
$107$	−12.3585	−	7.13519i	−1.19474	−	0.689785i	−0.235364	−	0.971907i	$-0.575628\pi$
$107$	−12.3585	−	7.13519i	−1.19474	−	0.689785i	−0.959378	+	0.282122i	$0.908962\pi$
$108$		0			0
$109$	−2.64583	−	4.58271i	−0.253425	−	0.438944i	0.711042	−	0.703150i	$-0.248224\pi$
$109$	−2.64583	−	4.58271i	−0.253425	−	0.438944i	−0.964466	+	0.264206i	$0.914890\pi$
$110$		0			0
$111$	12.1852	−	10.9905i	1.15657	−	1.04318i
$112$		0			0
$113$	−2.30371	−	1.33005i	−0.216715	−	0.125121i	0.387713	−	0.921780i	$-0.373265\pi$
$113$	−2.30371	−	1.33005i	−0.216715	−	0.125121i	−0.604428	+	0.796659i	$0.706598\pi$
$114$		0			0
$115$	−1.33764	−	0.772286i	−0.124735	−	0.0720160i
$116$		0			0
$117$	−2.81512	−	6.29382i	−0.260258	−	0.581864i
$118$		0			0
$119$	−5.44931	+	12.4964i	−0.499537	+	1.14555i
$120$		0			0
$121$	−0.607537	−	1.05229i	−0.0552307	−	0.0956623i
$122$		0			0
$123$	−3.14170	+	2.83368i	−0.283277	+	0.255504i
$124$		0			0
$125$	−8.27295			−0.739955
$126$		0			0
$127$	−6.10587			−0.541808			−0.270904	−	0.962606i	$-0.587323\pi$
$127$	−6.10587			−0.541808			−0.270904	+	0.962606i	$0.587323\pi$
$128$		0			0
$129$	−0.197527	−	0.925391i	−0.0173913	−	0.0814761i
$130$		0			0
$131$	3.97879	+	6.89147i	0.347629	+	0.602111i	0.985828	−	0.167761i	$-0.0536536\pi$
$131$	3.97879	+	6.89147i	0.347629	+	0.602111i	−0.638199	+	0.769871i	$0.720320\pi$
$132$		0			0
$133$	0.815855	+	7.22852i	0.0707436	+	0.626792i
$134$		0			0
$135$	−1.89167	+	4.27833i	−0.162809	+	0.368220i
$136$		0			0
$137$	18.9140	+	10.9200i	1.61593	+	0.932957i	0.987958	+	0.154719i	$0.0494473\pi$
$137$	18.9140	+	10.9200i	1.61593	+	0.932957i	0.627970	+	0.778237i	$0.283886\pi$
$138$		0			0
$139$	11.7109	+	6.76127i	0.993302	+	0.573483i	0.906260	−	0.422721i	$-0.138925\pi$
$139$	11.7109	+	6.76127i	0.993302	+	0.573483i	0.0870425	+	0.996205i	$0.472258\pi$
$140$		0			0
$141$	12.9523	+	4.19620i	1.09078	+	0.353384i
$142$		0			0
$143$	−3.59454	−	6.22593i	−0.300591	−	0.520639i
$144$		0			0
$145$	1.67079	+	0.964632i	0.138752	+	0.0801083i
$146$		0			0
$147$	6.96671	−	9.92295i	0.574604	−	0.818431i
$148$		0			0
$149$	−4.41192	+	2.54722i	−0.361438	+	0.208676i	−0.669711	−	0.742621i	$-0.733582\pi$
$149$	−4.41192	+	2.54722i	−0.361438	+	0.208676i	0.308273	+	0.951298i	$0.400249\pi$
$150$		0			0
$151$	−10.5877	+	18.3385i	−0.861618	+	1.49237i	0.00874783	+	0.999962i	$0.497215\pi$
$151$	−10.5877	+	18.3385i	−0.861618	+	1.49237i	−0.870366	+	0.492405i	$0.836118\pi$
$152$		0			0
$153$	1.58949	−	15.3763i	0.128502	−	1.24310i
$154$		0			0
$155$	7.79892	−	4.50271i	0.626424	−	0.361666i
$156$		0			0
$157$			0.359924i			0.0287250i	0.999897	+	0.0143625i	$0.00457189\pi$
$157$			0.359924i			0.0287250i	−0.999897	+	0.0143625i	$0.995428\pi$
$158$		0			0
$159$	23.6147	−	5.04061i	1.87277	−	0.399746i
$160$		0			0
$161$	−4.16091	−	1.81444i	−0.327926	−	0.142998i
$162$		0			0
$163$	−6.18640	+	10.7152i	−0.484557	+	0.839277i	−0.999843	−	0.0177416i	$-0.994352\pi$
$163$	−6.18640	+	10.7152i	−0.484557	+	0.839277i	0.515286	+	0.857018i	$0.327686\pi$
$164$		0			0
$165$	−1.50329	+	4.64016i	−0.117031	+	0.361236i
$166$		0			0
$167$	7.40866	−	12.8322i	0.573299	−	0.992984i	−0.422925	−	0.906165i	$-0.638997\pi$
$167$	7.40866	−	12.8322i	0.573299	−	0.992984i	0.996224	−	0.0868188i	$-0.0276701\pi$
$168$		0			0
$169$	−3.85905	−	6.68407i	−0.296850	−	0.514159i
$170$		0			0
$171$	−3.36784	−	7.52954i	−0.257545	−	0.575798i
$172$		0			0
$173$	4.63544			0.352426			0.176213	−	0.984352i	$-0.443615\pi$
$173$	4.63544			0.352426			0.176213	+	0.984352i	$0.443615\pi$
$174$		0			0
$175$	−11.0145	+	1.24317i	−0.832621	+	0.0939746i
$176$		0			0
$177$	13.1562	+	4.26226i	0.988883	+	0.320371i
$178$		0			0
$179$	5.25855	−	3.03602i	0.393042	−	0.226923i	−0.290435	−	0.956895i	$-0.593800\pi$
$179$	5.25855	−	3.03602i	0.393042	−	0.226923i	0.683477	+	0.729972i	$0.260467\pi$
$180$		0			0
$181$		−	7.12701i		−	0.529746i	−0.964283	−	0.264873i	$-0.914670\pi$
$181$		−	7.12701i		−	0.529746i	0.964283	−	0.264873i	$-0.0853301\pi$
$182$		0			0
$183$	3.87240	−	11.9529i	0.286256	−	0.883581i
$184$		0			0
$185$	8.52907			0.627070
$186$		0			0
$187$		−	16.1183i		−	1.17868i
$188$		0			0
$189$	−4.11416	+	13.1177i	−0.299261	+	0.954171i
$190$		0			0
$191$		−	14.4006i		−	1.04199i	−0.853558	−	0.520997i	$-0.825560\pi$
$191$		−	14.4006i		−	1.04199i	0.853558	−	0.520997i	$-0.174440\pi$
$192$		0			0
$193$	17.8115			1.28210			0.641048	−	0.767501i	$-0.278500\pi$
$193$	17.8115			1.28210			0.641048	+	0.767501i	$0.278500\pi$
$194$		0			0
$195$	1.10448	−	3.40918i	0.0790935	−	0.244136i
$196$		0			0
$197$		−	19.1025i		−	1.36100i	−0.732750	−	0.680498i	$-0.761764\pi$
$197$		−	19.1025i		−	1.36100i	0.732750	−	0.680498i	$-0.238236\pi$
$198$		0			0
$199$	−11.6008	+	6.69771i	−0.822357	+	0.474788i	−0.851229	−	0.524795i	$-0.824142\pi$
$199$	−11.6008	+	6.69771i	−0.822357	+	0.474788i	0.0288716	+	0.999583i	$0.490809\pi$
$200$		0			0
$201$	6.04802	+	1.95940i	0.426595	+	0.138205i
$202$		0			0
$203$	5.19723	+	2.26635i	0.364774	+	0.159066i
$204$		0			0
$205$	−2.19904			−0.153587
$206$		0			0
$207$	5.11982	+	0.529247i	0.355852	+	0.0367852i
$208$		0			0
$209$	−4.30029	−	7.44832i	−0.297457	−	0.515211i
$210$		0			0
$211$	9.37193	−	16.2327i	0.645190	−	1.11750i	−0.339067	−	0.940762i	$-0.610111\pi$
$211$	9.37193	−	16.2327i	0.645190	−	1.11750i	0.984258	−	0.176740i	$-0.0565552\pi$
$212$		0			0
$213$	−7.55274	+	23.3129i	−0.517505	+	1.59737i
$214$		0			0
$215$	0.245910	−	0.425929i	0.0167709	−	0.0290481i
$216$		0			0
$217$	21.2914	−	15.7200i	1.44535	−	1.06714i
$218$		0			0
$219$	21.3569	−	4.55868i	1.44317	−	0.308047i
$220$		0			0
$221$			11.8423i			0.796597i
$222$		0			0
$223$	−2.21609	+	1.27946i	−0.148400	+	0.0856789i	−0.572362	−	0.820001i	$-0.693973\pi$
$223$	−2.21609	+	1.27946i	−0.148400	+	0.0856789i	0.423961	+	0.905680i	$0.360639\pi$
$224$		0			0
$225$	11.4732	−	5.13178i	0.764881	−	0.342119i
$226$		0			0
$227$	4.36455	−	7.55962i	0.289685	−	0.501749i	−0.684049	−	0.729436i	$-0.739783\pi$
$227$	4.36455	−	7.55962i	0.289685	−	0.501749i	0.973735	+	0.227686i	$0.0731161\pi$
$228$		0			0
$229$	−3.40979	+	1.96865i	−0.225325	+	0.130092i	−0.608414	−	0.793620i	$-0.708194\pi$
$229$	−3.40979	+	1.96865i	−0.225325	+	0.130092i	0.383088	+	0.923712i	$0.374861\pi$
$230$		0			0
$231$	−2.86068	+	14.0464i	−0.188219	+	0.924182i
$232$		0			0
$233$	−3.92147	−	2.26406i	−0.256904	−	0.148324i	0.366018	−	0.930608i	$-0.380721\pi$
$233$	−3.92147	−	2.26406i	−0.256904	−	0.148324i	−0.622921	+	0.782284i	$0.714054\pi$
$234$		0			0
$235$	3.53832	+	6.12855i	0.230815	+	0.399782i
$236$		0			0
$237$	−10.7894	−	3.49548i	−0.700849	−	0.227056i
$238$		0			0
$239$	7.55315	+	4.36081i	0.488573	+	0.282078i	0.723982	−	0.689819i	$-0.242310\pi$
$239$	7.55315	+	4.36081i	0.488573	+	0.282078i	−0.235409	+	0.971896i	$0.575643\pi$
$240$		0			0
$241$	−17.1314	−	9.89079i	−1.10353	−	0.637122i	−0.166382	−	0.986061i	$-0.553209\pi$
$241$	−17.1314	−	9.89079i	−1.10353	−	0.637122i	−0.937145	+	0.348939i	$0.886542\pi$
$242$		0			0
$243$	−0.0667715	−	15.5883i	−0.00428340	−	0.999991i
$244$		0			0
$245$	6.14327	−	1.40463i	0.392479	−	0.0897383i
$246$		0			0
$247$	3.15947	+	5.47236i	0.201032	+	0.348198i
$248$		0			0
$249$	0.133372	+	0.624832i	0.00845209	+	0.0395971i
$250$		0			0
$251$	−3.80791			−0.240353			−0.120176	−	0.992753i	$-0.538346\pi$
$251$	−3.80791			−0.240353			−0.120176	+	0.992753i	$0.538346\pi$
$252$		0			0
$253$	5.36686			0.337411
$254$		0			0
$255$	5.96630	−	5.38134i	0.373624	−	0.336993i
$256$		0			0
$257$	−7.53771	−	13.0557i	−0.470189	−	0.814392i	0.529230	−	0.848479i	$-0.322481\pi$
$257$	−7.53771	−	13.0557i	−0.470189	−	0.814392i	−0.999419	+	0.0340869i	$0.989148\pi$
$258$		0			0
$259$	24.9078	−	2.81124i	1.54769	−	0.174682i
$260$		0			0
$261$	−6.39496	−	0.661062i	−0.395838	−	0.0409187i
$262$		0			0
$263$	6.59852	+	3.80965i	0.406882	+	0.234913i	0.689449	−	0.724334i	$-0.257853\pi$
$263$	6.59852	+	3.80965i	0.406882	+	0.234913i	−0.282567	+	0.959248i	$0.591186\pi$
$264$		0			0
$265$	10.8691	+	6.27529i	0.667684	+	0.385488i
$266$		0			0
$267$	−15.4403	+	13.9265i	−0.944933	+	0.852289i
$268$		0			0
$269$	−4.32720	−	7.49493i	−0.263834	−	0.456974i	0.703424	−	0.710771i	$-0.251654\pi$
$269$	−4.32720	−	7.49493i	−0.263834	−	0.456974i	−0.967257	+	0.253797i	$0.918320\pi$
$270$		0			0
$271$	15.6611	+	9.04193i	0.951343	+	0.549258i	0.893498	−	0.449068i	$-0.148244\pi$
$271$	15.6611	+	9.04193i	0.951343	+	0.549258i	0.0578449	+	0.998326i	$0.481577\pi$
$272$		0			0
$273$	2.10177	−	10.3200i	0.127205	−	0.624595i
$274$		0			0
$275$	11.3495	−	6.55262i	0.684398	−	0.395138i
$276$		0			0
$277$	−4.99073	+	8.64419i	−0.299864	+	0.519379i	−0.976105	−	0.217301i	$-0.930275\pi$
$277$	−4.99073	+	8.64419i	−0.299864	+	0.519379i	0.676241	+	0.736681i	$0.263608\pi$
$278$		0			0
$279$	−17.5975	+	24.3083i	−1.05353	+	1.45530i
$280$		0			0
$281$	−13.0297	+	7.52272i	−0.777289	+	0.448768i	−0.835469	−	0.549538i	$-0.814804\pi$
$281$	−13.0297	+	7.52272i	−0.777289	+	0.448768i	0.0581797	+	0.998306i	$0.481470\pi$
$282$		0			0
$283$		−	4.02933i		−	0.239519i	−0.992803	−	0.119759i	$-0.961788\pi$
$283$		−	4.02933i		−	0.239519i	0.992803	−	0.119759i	$-0.0382123\pi$
$284$		0			0
$285$	1.32133	−	4.07853i	0.0782690	−	0.241591i
$286$		0			0
$287$	−6.42194	+	0.724819i	−0.379075	+	0.0427847i
$288$		0			0
$289$	−4.77544	+	8.27131i	−0.280908	+	0.486548i
$290$		0			0
$291$	−17.3456	+	3.70245i	−1.01681	+	0.217041i
$292$		0			0
$293$	6.59608	−	11.4248i	0.385347	−	0.667441i	−0.606470	−	0.795106i	$-0.707415\pi$
$293$	6.59608	−	11.4248i	0.385347	−	0.667441i	0.991817	+	0.127665i	$0.0407483\pi$
$294$		0			0
$295$	3.59402	+	6.22503i	0.209252	+	0.362435i
$296$		0			0
$297$	−1.74055	−	16.1606i	−0.100997	−	0.937730i
$298$		0			0
$299$	−3.94309			−0.228035
$300$		0			0
$301$	0.577752	−	1.32491i	0.0333011	−	0.0763666i
$302$		0			0
$303$	3.49760	−	3.15468i	0.200932	−	0.181232i
$304$		0			0
$305$	5.65564	−	3.26528i	0.323841	−	0.186970i
$306$		0			0
$307$		−	28.7690i		−	1.64194i	−0.570974	−	0.820968i	$-0.693434\pi$
$307$		−	28.7690i		−	1.64194i	0.570974	−	0.820968i	$-0.306566\pi$
$308$		0			0
$309$	2.32484	−	0.496242i	0.132255	−	0.0282302i
$310$		0			0
$311$	−30.8457			−1.74910			−0.874550	−	0.484936i	$-0.838843\pi$
$311$	−30.8457			−1.74910			−0.874550	+	0.484936i	$0.838843\pi$
$312$		0			0
$313$			18.3661i			1.03811i	0.854740	+	0.519056i	$0.173717\pi$
$313$			18.3661i			1.03811i	−0.854740	+	0.519056i	$0.826283\pi$
$314$		0			0
$315$	−6.15445	+	3.63070i	−0.346764	+	0.204567i
$316$		0			0
$317$		−	17.4560i		−	0.980426i	−0.871603	−	0.490213i	$-0.836919\pi$
$317$		−	17.4560i		−	0.980426i	0.871603	−	0.490213i	$-0.163081\pi$
$318$		0			0
$319$	−6.70353			−0.375326
$320$		0			0
$321$	16.5546	+	18.3542i	0.923990	+	1.02443i
$322$		0			0
$323$			14.1673i			0.788292i
$324$		0			0
$325$	−8.33857	+	4.81428i	−0.462541	+	0.267048i
$326$		0			0
$327$	1.91328	+	8.96350i	0.105805	+	0.495683i
$328$		0			0
$329$	12.3531	+	16.7312i	0.681049	+	0.922420i
$330$		0			0
$331$	−10.4294			−0.573254			−0.286627	−	0.958042i	$-0.592534\pi$
$331$	−10.4294			−0.573254			−0.286627	+	0.958042i	$0.592534\pi$
$332$		0			0
$333$	−25.9450	+	11.6048i	−1.42178	+	0.635938i
$334$		0			0
$335$	1.65220	+	2.86169i	0.0902693	+	0.156351i
$336$		0			0
$337$	−15.8312	+	27.4204i	−0.862380	+	1.49369i	0.00724616	+	0.999974i	$0.497693\pi$
$337$	−15.8312	+	27.4204i	−0.862380	+	1.49369i	−0.869626	+	0.493712i	$0.835640\pi$
$338$		0			0
$339$	3.08590	+	3.42134i	0.167603	+	0.185822i
$340$		0			0
$341$	−15.6454	+	27.0986i	−0.847244	+	1.46747i
$342$		0			0
$343$	17.4775	−	6.12685i	0.943694	−	0.330819i
$344$		0			0
$345$	1.79181	+	1.98658i	0.0964679	+	0.106954i
$346$		0			0
$347$			12.5252i			0.672389i	0.941793	+	0.336195i	$0.109140\pi$
$347$			12.5252i			0.672389i	−0.941793	+	0.336195i	$0.890860\pi$
$348$		0			0
$349$	12.2560	−	7.07599i	0.656047	−	0.378769i	−0.134722	−	0.990883i	$-0.543014\pi$
$349$	12.2560	−	7.07599i	0.656047	−	0.378769i	0.790769	+	0.612115i	$0.209681\pi$
$350$		0			0
$351$	1.27880	+	11.8733i	0.0682572	+	0.633751i
$352$		0			0
$353$	−2.48267	+	4.30012i	−0.132139	+	0.228872i	−0.924501	−	0.381180i	$-0.875518\pi$
$353$	−2.48267	+	4.30012i	−0.132139	+	0.228872i	0.792362	+	0.610052i	$0.208851\pi$
$354$		0			0
$355$	−11.0308	+	6.36862i	−0.585452	+	0.338011i
$356$		0			0
$357$	15.6499	−	17.6819i	0.828280	−	0.935825i
$358$		0			0
$359$	−15.0013	−	8.66098i	−0.791736	−	0.457109i	0.0488375	−	0.998807i	$-0.484448\pi$
$359$	−15.0013	−	8.66098i	−0.791736	−	0.457109i	−0.840573	+	0.541698i	$0.817782\pi$
$360$		0			0
$361$	−5.72021	−	9.90769i	−0.301063	−	0.521457i
$362$		0			0
$363$	0.439328	+	2.05821i	0.0230588	+	0.108028i
$364$		0			0
$365$	9.82992	+	5.67531i	0.514522	+	0.297059i
$366$		0			0
$367$	−1.18799	−	0.685884i	−0.0620124	−	0.0358029i	0.468673	−	0.883372i	$-0.344732\pi$
$367$	−1.18799	−	0.685884i	−0.0620124	−	0.0358029i	−0.530686	+	0.847569i	$0.678066\pi$
$368$		0			0
$369$	6.68937	−	2.99204i	0.348235	−	0.155760i
$370$		0			0
$371$	33.8099	+	14.7434i	1.75532	+	0.765441i
$372$		0			0
$373$	2.40488	+	4.16537i	0.124520	+	0.215675i	0.921545	−	0.388271i	$-0.126928\pi$
$373$	2.40488	+	4.16537i	0.124520	+	0.215675i	−0.797025	+	0.603946i	$0.793594\pi$
$374$		0			0
$375$	13.6316	+	4.41628i	0.703935	+	0.228056i
$376$		0			0
$377$	4.92515			0.253658
$378$		0			0
$379$	−19.5669			−1.00508			−0.502542	−	0.864553i	$-0.667602\pi$
$379$	−19.5669			−1.00508			−0.502542	+	0.864553i	$0.667602\pi$
$380$		0			0
$381$	10.0609	+	3.25944i	0.515433	+	0.166986i
$382$		0			0
$383$	−15.7349	−	27.2536i	−0.804014	−	1.39259i	−0.916955	−	0.398992i	$-0.869360\pi$
$383$	−15.7349	−	27.2536i	−0.804014	−	1.39259i	0.112940	−	0.993602i	$-0.463973\pi$
$384$		0			0
$385$	−5.99394	+	4.42549i	−0.305479	+	0.225544i
$386$		0			0
$387$	−0.168522	+	1.63024i	−0.00856646	+	0.0828700i
$388$		0			0
$389$	3.52130	+	2.03303i	0.178537	+	0.103078i	0.586605	−	0.809873i	$-0.300464\pi$
$389$	3.52130	+	2.03303i	0.178537	+	0.103078i	−0.408068	+	0.912952i	$0.633797\pi$
$390$		0			0
$391$	−7.65617	−	4.42029i	−0.387189	−	0.223544i
$392$		0			0
$393$	−2.87718	−	13.4793i	−0.145135	−	0.679940i
$394$		0			0
$395$	−2.94746	−	5.10515i	−0.148303	−	0.256868i
$396$		0			0
$397$	−3.81692	−	2.20370i	−0.191566	−	0.110601i	0.401150	−	0.916013i	$-0.368611\pi$
$397$	−3.81692	−	2.20370i	−0.191566	−	0.110601i	−0.592715	+	0.805412i	$0.701944\pi$
$398$		0			0
$399$	2.51443	−	12.3462i	0.125879	−	0.618084i
$400$		0			0
$401$	16.0586	−	9.27141i	0.801926	−	0.462992i	−0.0422180	−	0.999108i	$-0.513442\pi$
$401$	16.0586	−	9.27141i	0.801926	−	0.462992i	0.844144	+	0.536116i	$0.180109\pi$
$402$		0			0
$403$	11.4948	−	19.9096i	0.572597	−	0.991768i
$404$		0			0
$405$	5.40085	−	6.03974i	0.268370	−	0.300117i
$406$		0			0
$407$	−25.6652	+	14.8178i	−1.27218	+	0.734491i
$408$		0			0
$409$		−	24.8902i		−	1.23074i	−0.788238	−	0.615370i	$-0.789006\pi$
$409$		−	24.8902i		−	1.23074i	0.788238	−	0.615370i	$-0.210994\pi$
$410$		0			0
$411$	−25.3359	−	28.0899i	−1.24973	−	1.38557i
$412$		0			0
$413$	12.5476	+	16.9946i	0.617426	+	0.836249i
$414$		0			0
$415$	−0.166041	+	0.287591i	−0.00815062	+	0.0141173i
$416$		0			0
$417$	−15.6871	−	17.3923i	−0.768200	−	0.851705i
$418$		0			0
$419$	2.57422	−	4.45869i	0.125759	−	0.217821i	−0.796270	−	0.604941i	$-0.793197\pi$
$419$	2.57422	−	4.45869i	0.125759	−	0.217821i	0.922029	+	0.387120i	$0.126530\pi$
$420$		0			0
$421$	−13.5022	−	23.3864i	−0.658055	−	1.13978i	−0.981119	−	0.193408i	$-0.938046\pi$
$421$	−13.5022	−	23.3864i	−0.658055	−	1.13978i	0.323063	−	0.946377i	$-0.395287\pi$
$422$		0			0
$423$	−19.1020	−	13.8285i	−0.928771	−	0.672363i
$424$		0			0
$425$	−21.5877			−1.04715
$426$		0			0
$427$	15.4401	−	11.3999i	0.747200	−	0.551679i
$428$		0			0
$429$	2.59932	+	12.1775i	0.125496	+	0.587937i
$430$		0			0
$431$	8.10874	−	4.68159i	0.390584	−	0.225504i	−0.291829	−	0.956471i	$-0.594264\pi$
$431$	8.10874	−	4.68159i	0.390584	−	0.225504i	0.682413	+	0.730966i	$0.260930\pi$
$432$		0			0
$433$			21.0373i			1.01099i	0.862830	+	0.505494i	$0.168690\pi$
$433$			21.0373i			1.01099i	−0.862830	+	0.505494i	$0.831310\pi$
$434$		0			0
$435$	−2.23808	−	2.48136i	−0.107308	−	0.118972i
$436$		0			0
$437$	−4.71727			−0.225657
$438$		0			0
$439$			20.4229i			0.974730i	0.873198	+	0.487365i	$0.162042\pi$
$439$			20.4229i			0.974730i	−0.873198	+	0.487365i	$0.837958\pi$
$440$		0			0
$441$	−16.7764	+	12.6314i	−0.798875	+	0.601497i
$442$		0			0
$443$			32.3649i			1.53770i	0.639427	+	0.768852i	$0.279172\pi$
$443$			32.3649i			1.53770i	−0.639427	+	0.768852i	$0.720828\pi$
$444$		0			0
$445$	−10.8075			−0.512324
$446$		0			0
$447$	8.62944	−	1.84197i	0.408158	−	0.0871223i
$448$		0			0
$449$		−	21.5693i		−	1.01792i	−0.860791	−	0.508958i	$-0.830031\pi$
$449$		−	21.5693i		−	1.01792i	0.860791	−	0.508958i	$-0.169969\pi$
$450$		0			0
$451$	6.61721	−	3.82045i	0.311592	−	0.179898i
$452$		0			0
$453$	27.2353	−	24.5651i	1.27963	−	1.15417i
$454$		0			0
$455$	4.40381	−	3.25146i	0.206454	−	0.152431i
$456$		0			0
$457$	21.0700			0.985611			0.492806	−	0.870139i	$-0.335971\pi$
$457$	21.0700			0.985611			0.492806	+	0.870139i	$0.335971\pi$
$458$		0			0
$459$	−10.8273	+	24.4876i	−0.505374	+	1.14298i
$460$		0			0
$461$	15.8412	+	27.4378i	0.737800	+	1.27791i	0.953484	+	0.301444i	$0.0974687\pi$
$461$	15.8412	+	27.4378i	0.737800	+	1.27791i	−0.215684	+	0.976463i	$0.569198\pi$
$462$		0			0
$463$	−4.40058	+	7.62202i	−0.204512	+	0.354225i	−0.949977	−	0.312319i	$-0.898894\pi$
$463$	−4.40058	+	7.62202i	−0.204512	+	0.354225i	0.745465	+	0.666545i	$0.232227\pi$
$464$		0			0
$465$	−15.2542	+	3.25604i	−0.707397	+	0.150995i
$466$		0			0
$467$	−9.49444	+	16.4449i	−0.439350	+	0.760977i	−0.997639	−	0.0686693i	$-0.978125\pi$
$467$	−9.49444	+	16.4449i	−0.439350	+	0.760977i	0.558289	+	0.829646i	$0.311458\pi$
$468$		0			0
$469$	5.76822	+	7.81254i	0.266352	+	0.360750i
$470$		0			0
$471$	0.192135	−	0.593059i	0.00885312	−	0.0273267i
$472$		0			0
$473$			1.70891i			0.0785756i
$474$		0			0
$475$	−9.97575	+	5.75950i	−0.457719	+	0.264264i
$476$		0			0
$477$	−41.6016	−	4.30045i	−1.90481	−	0.196904i
$478$		0			0
$479$	−12.0701	+	20.9060i	−0.551495	+	0.955218i	0.446672	+	0.894698i	$0.352609\pi$
$479$	−12.0701	+	20.9060i	−0.551495	+	0.955218i	−0.998167	+	0.0605197i	$0.980724\pi$
$480$		0			0
$481$	18.8565	−	10.8868i	0.859781	−	0.496395i
$482$		0			0
$483$	5.88749	+	5.21091i	0.267890	+	0.237104i
$484$		0			0
$485$	−7.98362	−	4.60935i	−0.362518	−	0.209300i
$486$		0			0
$487$	−7.05542	−	12.2204i	−0.319712	−	0.553757i	0.660716	−	0.750636i	$-0.270253\pi$
$487$	−7.05542	−	12.2204i	−0.319712	−	0.553757i	−0.980428	+	0.196879i	$0.936919\pi$
$488$		0			0
$489$	15.9136	−	14.3533i	0.719636	−	0.649080i
$490$		0			0
$491$	18.8344	+	10.8740i	0.849982	+	0.490738i	0.860645	−	0.509206i	$-0.170061\pi$
$491$	18.8344	+	10.8740i	0.849982	+	0.490738i	−0.0106626	+	0.999943i	$0.503394\pi$
$492$		0			0
$493$	9.56302	+	5.52121i	0.430697	+	0.248663i
$494$		0			0
$495$	4.95404	−	6.84328i	0.222668	−	0.307582i
$496$		0			0
$497$	−30.1144	+	22.2343i	−1.35082	+	0.997347i
$498$		0			0
$499$	−4.21233	−	7.29596i	−0.188570	−	0.326612i	0.756204	−	0.654336i	$-0.227052\pi$
$499$	−4.21233	−	7.29596i	−0.188570	−	0.326612i	−0.944774	+	0.327724i	$0.893718\pi$
$500$		0			0
$501$	−19.0576	+	17.1891i	−0.851431	+	0.767954i
$502$		0			0
$503$	8.71316			0.388501			0.194250	−	0.980952i	$-0.437773\pi$
$503$	8.71316			0.388501			0.194250	+	0.980952i	$0.437773\pi$
$504$		0			0
$505$	2.44815			0.108941
$506$		0			0
$507$	2.79059	+	13.0736i	0.123935	+	0.580620i
$508$		0			0
$509$	−14.9177	−	25.8382i	−0.661214	−	1.14526i	−0.980297	−	0.197530i	$-0.936708\pi$
$509$	−14.9177	−	25.8382i	−0.661214	−	1.14526i	0.319082	−	0.947727i	$-0.396625\pi$
$510$		0			0
$511$	30.5773	+	13.3338i	1.35266	+	0.589853i
$512$		0			0
$513$	1.52987	+	14.2045i	0.0675456	+	0.627145i
$514$		0			0
$515$	1.07005	+	0.617794i	0.0471521	+	0.0272233i
$516$		0			0
$517$	−21.2946	−	12.2944i	−0.936536	−	0.540709i
$518$		0			0
$519$	−7.63798	−	2.47450i	−0.335270	−	0.108618i
$520$		0			0
$521$	−9.89004	−	17.1301i	−0.433291	−	0.750482i	0.563864	−	0.825868i	$-0.309314\pi$
$521$	−9.89004	−	17.1301i	−0.433291	−	0.750482i	−0.997154	+	0.0753863i	$0.975981\pi$
$522$		0			0
$523$	10.5932	+	6.11597i	0.463207	+	0.267433i	0.713392	−	0.700766i	$-0.247158\pi$
$523$	10.5932	+	6.11597i	0.463207	+	0.267433i	−0.250185	+	0.968198i	$0.580491\pi$
$524$		0			0
$525$	18.8127	+	3.83139i	0.821053	+	0.167215i
$526$		0			0
$527$	44.6382	−	25.7719i	1.94447	−	1.12264i
$528$		0			0
$529$	−10.0282	+	17.3693i	−0.436008	+	0.755188i
$530$		0			0
$531$	−19.4027	−	14.0462i	−0.842006	−	0.609552i
$532$		0			0
$533$	−4.86174	+	2.80693i	−0.210585	+	0.121581i
$534$		0			0
$535$			12.8470i			0.555425i
$536$		0			0
$537$	−10.2854	+	2.19544i	−0.443848	+	0.0947402i
$538$		0			0
$539$	−16.0457	+	14.8996i	−0.691136	+	0.641771i
$540$		0			0
$541$	−0.348944	+	0.604389i	−0.0150023	+	0.0259847i	−0.873429	−	0.486951i	$-0.838109\pi$
$541$	−0.348944	+	0.604389i	−0.0150023	+	0.0259847i	0.858427	+	0.512936i	$0.171442\pi$
$542$		0			0
$543$	−3.80455	+	11.7434i	−0.163269	+	0.503959i
$544$		0			0
$545$	−2.38193	+	4.12562i	−0.102031	+	0.176722i
$546$		0			0
$547$	−21.0049	−	36.3815i	−0.898103	−	1.55556i	−0.829917	−	0.557887i	$-0.811612\pi$
$547$	−21.0049	−	36.3815i	−0.898103	−	1.55556i	−0.0681854	−	0.997673i	$-0.521721\pi$
$548$		0			0
$549$	−12.7614	+	17.6280i	−0.544643	+	0.752344i
$550$		0			0
$551$	5.89215			0.251014
$552$		0			0
$553$	−10.2903	−	13.9373i	−0.437587	−	0.592673i
$554$		0			0
$555$	−14.0537	−	4.55300i	−0.596544	−	0.193264i
$556$		0			0
$557$	4.85612	−	2.80368i	0.205760	−	0.118796i	−0.393579	−	0.919291i	$-0.628763\pi$
$557$	4.85612	−	2.80368i	0.205760	−	0.118796i	0.599340	+	0.800495i	$0.295430\pi$
$558$		0			0
$559$		−	1.25555i		−	0.0531042i
$560$		0			0
$561$	−8.60428	+	26.5586i	−0.363273	+	1.12131i
$562$		0			0
$563$	35.1896			1.48306			0.741532	−	0.670918i	$-0.234100\pi$
$563$	35.1896			1.48306			0.741532	+	0.670918i	$0.234100\pi$
$564$		0			0
$565$			2.39478i			0.100749i
$566$		0			0
$567$	13.7816	−	19.4183i	0.578771	−	0.815490i
$568$		0			0
$569$		−	8.81739i		−	0.369644i	−0.982772	−	0.184822i	$-0.940829\pi$
$569$		−	8.81739i		−	0.369644i	0.982772	−	0.184822i	$-0.0591709\pi$
$570$		0			0
$571$	11.8828			0.497280			0.248640	−	0.968596i	$-0.420016\pi$
$571$	11.8828			0.497280			0.248640	+	0.968596i	$0.420016\pi$
$572$		0			0
$573$	−7.68738	+	23.7285i	−0.321145	+	0.991271i
$574$		0			0
$575$		−	7.18799i		−	0.299760i
$576$		0			0
$577$	15.8314	−	9.14028i	0.659071	−	0.380515i	−0.132852	−	0.991136i	$-0.542413\pi$
$577$	15.8314	−	9.14028i	0.659071	−	0.380515i	0.791923	+	0.610621i	$0.209080\pi$
$578$		0			0
$579$	−29.3486	−	9.50814i	−1.21969	−	0.395145i
$580$		0			0
$581$	−0.390103	+	0.894591i	−0.0161842	+	0.0371139i
$582$		0			0
$583$	−43.6089			−1.80610
$584$		0			0
$585$	−3.63979	+	5.02783i	−0.150487	+	0.207875i
$586$		0			0
$587$	1.75389	+	3.03782i	0.0723907	+	0.125384i	0.899949	−	0.435996i	$-0.143604\pi$
$587$	1.75389	+	3.03782i	0.0723907	+	0.125384i	−0.827558	+	0.561380i	$0.810270\pi$
$588$		0			0
$589$	13.7517	−	23.8186i	0.566628	−	0.981429i
$590$		0			0
$591$	−10.1973	+	31.4759i	−0.419462	+	1.29474i
$592$		0			0
$593$	−24.2336	+	41.9738i	−0.995155	+	1.72366i	−0.412428	+	0.910990i	$0.635319\pi$
$593$	−24.2336	+	41.9738i	−0.995155	+	1.72366i	−0.582727	+	0.812668i	$0.698014\pi$
$594$		0			0
$595$	12.1957	−	1.37648i	0.499975	−	0.0564302i
$596$		0			0
$597$	22.6904	−	4.84331i	0.928656	−	0.198224i
$598$		0			0
$599$		−	25.1463i		−	1.02745i	−0.857955	−	0.513724i	$-0.828266\pi$
$599$		−	25.1463i		−	1.02745i	0.857955	−	0.513724i	$-0.171734\pi$
$600$		0			0
$601$	11.2731	−	6.50854i	0.459840	−	0.265489i	−0.252137	−	0.967692i	$-0.581133\pi$
$601$	11.2731	−	6.50854i	0.459840	−	0.265489i	0.711977	+	0.702203i	$0.247800\pi$
$602$		0			0
$603$	−8.91958	−	6.45713i	−0.363233	−	0.262955i
$604$		0			0
$605$	−0.546940	+	0.947328i	−0.0222363	+	0.0385144i
$606$		0			0
$607$	7.10546	−	4.10234i	0.288402	−	0.166509i	−0.348819	−	0.937190i	$-0.613417\pi$
$607$	7.10546	−	4.10234i	0.288402	−	0.166509i	0.637221	+	0.770681i	$0.280084\pi$
$608$		0			0
$609$	−7.35384	−	6.50874i	−0.297993	−	0.263747i
$610$		0			0
$611$	15.6454	+	9.03286i	0.632944	+	0.365430i
$612$		0			0
$613$	2.35051	+	4.07120i	0.0949361	+	0.164434i	0.909582	−	0.415525i	$-0.136402\pi$
$613$	2.35051	+	4.07120i	0.0949361	+	0.164434i	−0.814646	+	0.579959i	$0.803069\pi$
$614$		0			0
$615$	3.62343	+	1.17389i	0.146111	+	0.0473360i
$616$		0			0
$617$	17.0178	+	9.82521i	0.685109	+	0.395548i	0.801777	−	0.597623i	$-0.203888\pi$
$617$	17.0178	+	9.82521i	0.685109	+	0.395548i	−0.116668	+	0.993171i	$0.537221\pi$
$618$		0			0
$619$	−30.0586	−	17.3544i	−1.20816	−	0.697531i	−0.245802	−	0.969320i	$-0.579051\pi$
$619$	−30.0586	−	17.3544i	−1.20816	−	0.697531i	−0.962357	+	0.271789i	$0.912385\pi$
$620$		0			0
$621$	−8.15358	−	3.60513i	−0.327192	−	0.144669i
$622$		0			0
$623$	−31.5615	+	3.56223i	−1.26449	+	0.142718i
$624$		0			0
$625$	−6.74995	−	11.6912i	−0.269998	−	0.467650i
$626$		0			0
$627$	3.10967	+	14.5685i	0.124188	+	0.581808i
$628$		0			0
$629$	48.8174			1.94648
$630$		0			0
$631$	−22.9139			−0.912188			−0.456094	−	0.889932i	$-0.650752\pi$
$631$	−22.9139			−0.912188			−0.456094	+	0.889932i	$0.650752\pi$
$632$		0			0
$633$	−24.1078	+	21.7442i	−0.958199	+	0.864254i
$634$		0			0
$635$	2.74843	+	4.76041i	0.109068	+	0.188911i
$636$		0			0
$637$	11.7889	−	10.9469i	0.467094	−	0.433732i
$638$		0			0
$639$	24.8898	−	34.3816i	0.984627	−	1.36012i
$640$		0			0
$641$	11.9968	+	6.92634i	0.473844	+	0.273574i	0.717848	−	0.696200i	$-0.245127\pi$
$641$	11.9968	+	6.92634i	0.473844	+	0.273574i	−0.244003	+	0.969774i	$0.578461\pi$
$642$		0			0
$643$	27.9684	+	16.1476i	1.10297	+	0.636797i	0.936998	−	0.349334i	$-0.113592\pi$
$643$	27.9684	+	16.1476i	1.10297	+	0.636797i	0.165967	+	0.986131i	$0.446925\pi$
$644$		0			0
$645$	−0.632565	+	0.570546i	−0.0249072	+	0.0224652i
$646$		0			0
$647$	8.96715	+	15.5316i	0.352535	+	0.610609i	0.986693	−	0.162595i	$-0.0519864\pi$
$647$	8.96715	+	15.5316i	0.352535	+	0.610609i	−0.634158	+	0.773204i	$0.718653\pi$
$648$		0			0
$649$	−21.6298	−	12.4880i	−0.849046	−	0.490197i
$650$		0			0
$651$	−43.4742	+	14.5366i	−1.70389	+	0.569736i
$652$		0			0
$653$	6.49080	−	3.74747i	0.254005	−	0.146650i	−0.367592	−	0.929987i	$-0.619818\pi$
$653$	6.49080	−	3.74747i	0.254005	−	0.146650i	0.621597	+	0.783338i	$0.286484\pi$
$654$		0			0
$655$	3.58194	−	6.20410i	0.139958	−	0.242414i
$656$		0			0
$657$	−37.6241	−	3.88928i	−1.46785	−	0.151735i
$658$		0			0
$659$	9.32497	−	5.38377i	0.363249	−	0.209722i	−0.307256	−	0.951627i	$-0.599411\pi$
$659$	9.32497	−	5.38377i	0.363249	−	0.209722i	0.670505	+	0.741905i	$0.266077\pi$
$660$		0			0
$661$			11.6409i			0.452778i	0.974037	+	0.226389i	$0.0726920\pi$
$661$			11.6409i			0.452778i	−0.974037	+	0.226389i	$0.927308\pi$
$662$		0			0
$663$	6.32166	−	19.5129i	0.245513	−	0.757819i
$664$		0			0
$665$	5.26845	−	3.88984i	0.204302	−	0.150842i
$666$		0			0
$667$	−1.83838	+	3.18417i	−0.0711825	+	0.123292i
$668$		0			0
$669$	4.33453	−	0.925215i	0.167583	−	0.0357709i
$670$		0			0
$671$	−11.3457	+	19.6514i	−0.437997	+	0.758634i
$672$		0			0
$673$	−0.550931	−	0.954241i	−0.0212368	−	0.0367833i	0.855212	−	0.518279i	$-0.173427\pi$
$673$	−0.550931	−	0.954241i	−0.0212368	−	0.0367833i	−0.876449	+	0.481496i	$0.840094\pi$
$674$		0			0
$675$	−21.6443	+	2.33116i	−0.833089	+	0.0897265i
$676$		0			0
$677$	−11.2324			−0.431695			−0.215847	−	0.976427i	$-0.569251\pi$
$677$	−11.2324			−0.431695			−0.215847	+	0.976427i	$0.569251\pi$
$678$		0			0
$679$	−24.8342	−	10.8294i	−0.953048	−	0.415594i
$680$		0			0
$681$	−11.2271	+	10.1264i	−0.430224	+	0.388043i
$682$		0			0
$683$	−37.6792	+	21.7541i	−1.44175	+	0.832396i	−0.997967	−	0.0637365i	$-0.979698\pi$
$683$	−37.6792	+	21.7541i	−1.44175	+	0.832396i	−0.443786	+	0.896133i	$0.646365\pi$
$684$		0			0
$685$		−	19.6616i		−	0.751231i
$686$		0			0
$687$	6.66935	−	1.42359i	0.254451	−	0.0543132i
$688$		0			0
$689$	32.0399			1.22062
$690$		0			0
$691$			32.2260i			1.22593i	0.790108	+	0.612967i	$0.210024\pi$
$691$			32.2260i			1.22593i	−0.790108	+	0.612967i	$0.789976\pi$
$692$		0			0
$693$	12.2119	−	21.6176i	0.463891	−	0.821184i
$694$		0			0
$695$		−	12.1738i		−	0.461777i
$696$		0			0
$697$	−12.5865			−0.476748
$698$		0			0
$699$	5.25294	+	5.82394i	0.198684	+	0.220282i
$700$		0			0
$701$			21.8995i			0.827133i	0.910474	+	0.413566i	$0.135717\pi$
$701$			21.8995i			0.827133i	−0.910474	+	0.413566i	$0.864283\pi$
$702$		0			0
$703$	22.5587	−	13.0243i	0.850818	−	0.491220i
$704$		0			0
$705$	−2.55866	−	11.9871i	−0.0963649	−	0.451459i
$706$		0			0
$707$	7.14942	−	0.806927i	0.268882	−	0.0303476i
$708$		0			0
$709$	−18.0470			−0.677770			−0.338885	−	0.940828i	$-0.610050\pi$
$709$	−18.0470			−0.677770			−0.338885	+	0.940828i	$0.610050\pi$
$710$		0			0
$711$	15.9122	+	11.5193i	0.596753	+	0.432006i
$712$		0			0
$713$	8.58120	+	14.8631i	0.321369	+	0.556627i
$714$		0			0
$715$	−3.23602	+	5.60494i	−0.121020	+	0.209613i
$716$		0			0
$717$	−10.1177	−	11.2175i	−0.377852	−	0.418925i
$718$		0			0
$719$	4.65944	−	8.07039i	0.173768	−	0.300975i	−0.765966	−	0.642881i	$-0.777739\pi$
$719$	4.65944	−	8.07039i	0.173768	−	0.300975i	0.939734	+	0.341906i	$0.111072\pi$
$720$		0			0
$721$	3.32854	+	1.45147i	0.123961	+	0.0540557i
$722$		0			0
$723$	22.9480	+	25.4425i	0.853446	+	0.946217i
$724$		0			0
$725$			8.97823i			0.333443i
$726$		0			0
$727$	6.73516	−	3.88855i	0.249793	−	0.144218i	−0.369876	−	0.929081i	$-0.620600\pi$
$727$	6.73516	−	3.88855i	0.249793	−	0.144218i	0.619670	+	0.784863i	$0.287267\pi$
$728$		0			0
$729$	−8.21136	+	25.7211i	−0.304124	+	0.952632i
$730$		0			0
$731$	1.40750	−	2.43787i	0.0520583	−	0.0901677i
$732$		0			0
$733$	31.2841	−	18.0619i	1.15550	−	0.667131i	0.205282	−	0.978703i	$-0.434189\pi$
$733$	31.2841	−	18.0619i	1.15550	−	0.667131i	0.950222	+	0.311572i	$0.100856\pi$
$734$		0			0
$735$	−10.8723	−	0.964957i	−0.401031	−	0.0355930i
$736$		0			0
$737$	−9.94341	−	5.74083i	−0.366270	−	0.211466i
$738$		0			0
$739$	−12.0693	−	20.9046i	−0.443975	−	0.768987i	0.554005	−	0.832513i	$-0.313099\pi$
$739$	−12.0693	−	20.9046i	−0.443975	−	0.768987i	−0.997980	+	0.0635263i	$0.979765\pi$
$740$		0			0
$741$	−2.28471	−	10.7036i	−0.0839308	−	0.393207i
$742$		0			0
$743$	−10.5762	−	6.10618i	−0.388003	−	0.224014i	0.293291	−	0.956023i	$-0.405249\pi$
$743$	−10.5762	−	6.10618i	−0.388003	−	0.224014i	−0.681295	+	0.732009i	$0.738583\pi$
$744$		0			0
$745$	3.97186	+	2.29316i	0.145518	+	0.0840147i
$746$		0			0
$747$	0.113788	−	1.10076i	0.00416327	−	0.0402745i
$748$		0			0
$749$	4.23447	+	37.5177i	0.154724	+	1.37087i
$750$		0			0
$751$	−11.7190	−	20.2980i	−0.427634	−	0.740684i	0.569028	−	0.822318i	$-0.307320\pi$
$751$	−11.7190	−	20.2980i	−0.427634	−	0.740684i	−0.996662	+	0.0816339i	$0.973986\pi$
$752$		0			0
$753$	6.27443	+	2.03274i	0.228653	+	0.0740773i
$754$		0			0
$755$	19.0634			0.693788
$756$		0			0
$757$	3.52341			0.128060			0.0640302	−	0.997948i	$-0.479605\pi$
$757$	3.52341			0.128060			0.0640302	+	0.997948i	$0.479605\pi$
$758$		0			0
$759$	−8.84316	−	2.86495i	−0.320987	−	0.103991i
$760$		0			0
$761$	10.7021	+	18.5365i	0.387950	+	0.671949i	0.992174	−	0.124866i	$-0.0398500\pi$
$761$	10.7021	+	18.5365i	0.387950	+	0.671949i	−0.604224	+	0.796815i	$0.706517\pi$
$762$		0			0
$763$	−5.59621	+	12.8333i	−0.202596	+	0.464597i
$764$		0			0
$765$	−12.7036	+	5.68209i	−0.459299	+	0.205437i
$766$		0			0
$767$	15.8917	+	9.17506i	0.573815	+	0.331292i
$768$		0			0
$769$	−23.4043	−	13.5125i	−0.843982	−	0.487273i	0.0146339	−	0.999893i	$-0.495342\pi$
$769$	−23.4043	−	13.5125i	−0.843982	−	0.487273i	−0.858616	+	0.512620i	$0.828675\pi$
$770$		0			0
$771$	5.45074	+	25.5361i	0.196304	+	0.919661i
$772$		0			0
$773$	8.10280	+	14.0345i	0.291437	+	0.504784i	0.974150	−	0.225903i	$-0.0725332\pi$
$773$	8.10280	+	14.0345i	0.291437	+	0.504784i	−0.682712	+	0.730687i	$0.739200\pi$
$774$		0			0
$775$	36.2939	+	20.9543i	1.30371	+	0.752700i
$776$		0			0
$777$	−42.5422	−	8.66413i	−1.52619	−	0.310824i
$778$		0			0
$779$	−5.81628	+	3.35803i	−0.208390	+	0.120314i
$780$		0			0
$781$	22.1288	−	38.3281i	0.791829	−	1.37149i
$782$		0			0
$783$	10.1843	+	4.50302i	0.363958	+	0.160925i
$784$		0			0
$785$	0.280613	−	0.162012i	0.0100155	−	0.00578246i
$786$		0			0
$787$		−	38.2571i		−	1.36372i	−0.731483	−	0.681860i	$-0.761171\pi$
$787$		−	38.2571i		−	1.36372i	0.731483	−	0.681860i	$-0.238829\pi$
$788$		0			0
$789$	−8.83894	−	9.79974i	−0.314674	−	0.348880i
$790$		0			0
$791$	0.789335	+	6.99356i	0.0280655	+	0.248662i
$792$		0			0
$793$	8.33583	−	14.4381i	0.296014	−	0.512712i
$794$		0			0
$795$	−14.5595	−	16.1422i	−0.516374	−	0.572504i
$796$		0			0
$797$	4.38709	−	7.59866i	0.155399	−	0.269158i	−0.777805	−	0.628505i	$-0.783667\pi$
$797$	4.38709	−	7.59866i	0.155399	−	0.269158i	0.933204	+	0.359347i	$0.117000\pi$
$798$		0			0
$799$	20.2521	+	35.0776i	0.716467	+	1.24096i
$800$		0			0
$801$	32.8759	−	14.7048i	1.16161	−	0.519570i
$802$		0			0
$803$	−39.4395			−1.39179
$804$		0			0
$805$	0.458323	+	4.06077i	0.0161538	+	0.143123i
$806$		0			0
$807$	3.12913	+	14.6596i	0.110150	+	0.516043i
$808$		0			0
$809$	26.6053	−	15.3606i	0.935394	−	0.540050i	0.0468805	−	0.998901i	$-0.485072\pi$
$809$	26.6053	−	15.3606i	0.935394	−	0.540050i	0.888513	+	0.458851i	$0.151739\pi$
$810$		0			0
$811$		−	8.70634i		−	0.305721i	−0.988248	−	0.152861i	$-0.951151\pi$
$811$		−	8.70634i		−	0.305721i	0.988248	−	0.152861i	$-0.0488485\pi$
$812$		0			0
$813$	−20.9785	−	23.2589i	−0.735750	−	0.815726i
$814$		0			0
$815$	11.1387			0.390172
$816$		0			0
$817$		−	1.50206i		−	0.0525506i
$818$		0			0
$819$	−8.97220	+	15.8827i	−0.313514	+	0.554985i
$820$		0			0
$821$		−	52.4347i		−	1.82998i	−0.403473	−	0.914992i	$-0.632197\pi$
$821$		−	52.4347i		−	1.82998i	0.403473	−	0.914992i	$-0.367803\pi$
$822$		0			0
$823$	−8.36398			−0.291550			−0.145775	−	0.989318i	$-0.546568\pi$
$823$	−8.36398			−0.291550			−0.145775	+	0.989318i	$0.546568\pi$
$824$		0			0
$825$	−22.1988	+	4.73839i	−0.772865	+	0.164970i
$826$		0			0
$827$		−	26.4934i		−	0.921267i	−0.887590	−	0.460634i	$-0.847622\pi$
$827$		−	26.4934i		−	0.921267i	0.887590	−	0.460634i	$-0.152378\pi$
$828$		0			0
$829$	−5.14134	+	2.96835i	−0.178566	+	0.103095i	−0.586619	−	0.809863i	$-0.699541\pi$
$829$	−5.14134	+	2.96835i	−0.178566	+	0.103095i	0.408053	+	0.912958i	$0.366208\pi$
$830$		0			0
$831$	12.8379	−	11.5792i	0.445340	−	0.401678i
$832$		0			0
$833$	35.1619	−	8.03958i	1.21829	−	0.278555i
$834$		0			0
$835$	−13.3394			−0.461629
$836$		0			0
$837$	41.9723	−	30.6598i	1.45078	−	1.05976i
$838$		0			0
$839$	3.80537	+	6.59110i	0.131376	+	0.227550i	0.924207	−	0.381891i	$-0.124727\pi$
$839$	3.80537	+	6.59110i	0.131376	+	0.227550i	−0.792831	+	0.609441i	$0.791394\pi$
$840$		0			0
$841$	−12.2037	+	21.1375i	−0.420819	+	0.728880i
$842$		0			0
$843$	25.4854	−	5.43990i	0.877763	−	0.187360i
$844$		0			0
$845$	−3.47414	+	6.01739i	−0.119514	+	0.207004i
$846$		0			0
$847$	−1.28500	+	2.94680i	−0.0441533	+	0.101253i
$848$		0			0
$849$	−2.15094	+	6.63927i	−0.0738202	+	0.227859i
$850$		0			0
$851$			16.2546i			0.557200i
$852$		0			0
$853$	−24.8764	+	14.3624i	−0.851751	+	0.491759i	−0.861241	−	0.508196i	$-0.830312\pi$
$853$	−24.8764	+	14.3624i	−0.851751	+	0.491759i	0.00949029	+	0.999955i	$0.496979\pi$
$854$		0			0
$855$	−4.35442	+	6.01498i	−0.148918	+	0.205708i
$856$		0			0
$857$	−20.1198	+	34.8486i	−0.687280	+	1.19040i	0.285434	+	0.958398i	$0.407862\pi$
$857$	−20.1198	+	34.8486i	−0.687280	+	1.19040i	−0.972714	+	0.232006i	$0.925471\pi$
$858$		0			0
$859$	13.3256	−	7.69355i	0.454664	−	0.262501i	−0.255134	−	0.966906i	$-0.582119\pi$
$859$	13.3256	−	7.69355i	0.454664	−	0.262501i	0.709798	+	0.704405i	$0.248786\pi$
$860$		0			0
$861$	10.9686	+	2.23386i	0.373808	+	0.0761297i
$862$		0			0
$863$	−16.6494	−	9.61252i	−0.566751	−	0.327214i	0.189099	−	0.981958i	$-0.439443\pi$
$863$	−16.6494	−	9.61252i	−0.566751	−	0.327214i	−0.755851	+	0.654744i	$0.772776\pi$
$864$		0			0
$865$	−2.08655	−	3.61400i	−0.0709447	−	0.122880i
$866$		0			0
$867$	12.2841	−	11.0797i	0.417189	−	0.376286i
$868$		0			0
$869$	17.7386	+	10.2414i	0.601742	+	0.347416i
$870$		0			0
$871$	7.30552	+	4.21785i	0.247538	+	0.142916i
$872$		0			0
$873$	30.5573	+	3.15878i	1.03421	+	0.106909i
$874$		0			0
$875$	13.0010	+	17.6087i	0.439514	+	0.595283i
$876$		0			0
$877$	5.39035	+	9.33636i	0.182019	+	0.315267i	0.942568	−	0.334014i	$-0.108403\pi$
$877$	5.39035	+	9.33636i	0.182019	+	0.315267i	−0.760549	+	0.649281i	$0.775070\pi$
$878$		0			0
$879$	−16.9674	+	15.3038i	−0.572296	+	0.516186i
$880$		0			0
$881$	−44.2875			−1.49208			−0.746041	−	0.665900i	$-0.768048\pi$
$881$	−44.2875			−1.49208			−0.746041	+	0.665900i	$0.768048\pi$
$882$		0			0
$883$	47.6098			1.60220			0.801098	−	0.598533i	$-0.204249\pi$
$883$	47.6098			1.60220			0.801098	+	0.598533i	$0.204249\pi$
$884$		0			0
$885$	−2.59895	−	12.1758i	−0.0873626	−	0.409284i
$886$		0			0
$887$	−0.989965	−	1.71467i	−0.0332398	−	0.0575730i	0.848927	−	0.528510i	$-0.177249\pi$
$887$	−0.989965	−	1.71467i	−0.0332398	−	0.0575730i	−0.882167	+	0.470937i	$0.843916\pi$
$888$		0			0
$889$	9.59541	+	12.9961i	0.321820	+	0.435876i
$890$		0			0
$891$	−5.75889	+	27.5575i	−0.192930	+	0.923210i
$892$		0			0
$893$	18.7172	+	10.8064i	0.626346	+	0.361621i
$894$		0			0
$895$	−4.73405	−	2.73320i	−0.158242	−	0.0913609i
$896$		0			0
$897$	6.49717	+	2.10491i	0.216934	+	0.0702807i
$898$		0			0
$899$	−10.7184	−	18.5649i	−0.357480	−	0.619173i
$900$		0			0
$901$	62.2109	+	35.9175i	2.07255	+	1.19659i
$902$		0			0
$903$	−1.65925	+	1.87469i	−0.0552164	+	0.0623857i
$904$		0			0
$905$	−5.55654	+	3.20807i	−0.184706	+	0.106640i
$906$		0			0
$907$	17.0252	−	29.4886i	0.565314	−	0.979152i	−0.431707	−	0.902014i	$-0.642088\pi$
$907$	17.0252	−	29.4886i	0.565314	−	0.979152i	0.997020	−	0.0771381i	$-0.0245782\pi$
$908$		0			0
$909$	−7.44715	+	3.33099i	−0.247006	+	0.110482i
$910$		0			0
$911$	6.58371	−	3.80111i	0.218128	−	0.125936i	−0.386955	−	0.922099i	$-0.626473\pi$
$911$	6.58371	−	3.80111i	0.218128	−	0.125936i	0.605083	+	0.796162i	$0.293140\pi$
$912$		0			0
$913$		−	1.15387i		−	0.0381875i
$914$		0			0
$915$	−11.0621	+	2.36122i	−0.365701	+	0.0780597i
$916$		0			0
$917$	8.41556	−	19.2987i	0.277906	−	0.637300i
$918$		0			0
$919$	4.11136	−	7.12109i	0.135621	−	0.234903i	−0.790213	−	0.612832i	$-0.790030\pi$
$919$	4.11136	−	7.12109i	0.135621	−	0.234903i	0.925835	+	0.377929i	$0.123364\pi$
$920$		0			0
$921$	−15.3575	+	47.4038i	−0.506048	+	1.56201i
$922$		0			0
$923$	−16.2582	+	28.1601i	−0.535146	+	0.926900i
$924$		0			0
$925$	19.8459	+	34.3741i	0.652529	+	1.13021i
$926$		0			0
$927$	−4.09563	−	0.423374i	−0.134518	−	0.0139054i
$928$		0			0
$929$	5.07963			0.166657			0.0833287	−	0.996522i	$-0.473445\pi$
$929$	5.07963			0.166657			0.0833287	+	0.996522i	$0.473445\pi$
$930$		0			0
$931$	14.1035	−	13.0962i	0.462225	−	0.429210i
$932$		0			0
$933$	50.8256	+	16.4661i	1.66395	+	0.539076i
$934$		0			0
$935$	−12.5665	+	7.25530i	−0.410970	+	0.237274i
$936$		0			0
$937$		−	10.8127i		−	0.353236i	−0.984280	−	0.176618i	$-0.943484\pi$
$937$		−	10.8127i		−	0.353236i	0.984280	−	0.176618i	$-0.0565157\pi$
$938$		0			0
$939$	9.80422	−	30.2625i	0.319949	−	0.987578i
$940$		0			0
$941$	−19.1639			−0.624724			−0.312362	−	0.949963i	$-0.601120\pi$
$941$	−19.1639			−0.624724			−0.312362	+	0.949963i	$0.601120\pi$
$942$		0			0
$943$		−	4.19090i		−	0.136474i
$944$		0			0
$945$	12.0791	−	2.69706i	0.392932	−	0.0877352i
$946$		0			0
$947$		−	25.3953i		−	0.825237i	−0.910904	−	0.412618i	$-0.864614\pi$
$947$		−	25.3953i		−	0.825237i	0.910904	−	0.412618i	$-0.135386\pi$
$948$		0			0
$949$	28.9766			0.940620
$950$		0			0
$951$	−9.31839	+	28.7629i	−0.302170	+	0.932700i
$952$		0			0
$953$		−	18.4818i		−	0.598686i	−0.954146	−	0.299343i	$-0.903233\pi$
$953$		−	18.4818i		−	0.598686i	0.954146	−	0.299343i	$-0.0967674\pi$
$954$		0			0
$955$	−11.2274	+	6.48215i	−0.363310	+	0.209757i
$956$		0			0
$957$	11.0456	+	3.57849i	0.357055	+	0.115676i
$958$		0			0
$959$	−6.48060	−	57.4185i	−0.209270	−	1.85414i
$960$		0			0
$961$	−69.0630			−2.22784
$962$		0			0
$963$	−17.4798	−	39.0800i	−0.563280	−	1.25934i
$964$		0			0
$965$	−8.01745	−	13.8866i	−0.258091	−	0.447026i
$966$		0			0
$967$	9.64551	−	16.7065i	0.310179	−	0.537245i	−0.668222	−	0.743962i	$-0.732944\pi$
$967$	9.64551	−	16.7065i	0.310179	−	0.537245i	0.978401	+	0.206717i	$0.0662778\pi$
$968$		0			0
$969$	7.56284	−	23.3441i	0.242953	−	0.749919i
$970$		0			0
$971$	0.975444	−	1.68952i	0.0313035	−	0.0542192i	−0.849949	−	0.526865i	$-0.823367\pi$
$971$	0.975444	−	1.68952i	0.0313035	−	0.0542192i	0.881253	+	0.472645i	$0.156701\pi$
$972$		0			0
$973$	−4.01256	−	35.5515i	−0.128637	−	1.13973i
$974$		0			0
$975$	16.3097	−	3.48135i	0.522329	−	0.111492i
$976$		0			0
$977$		−	16.7265i		−	0.535129i	−0.963540	−	0.267564i	$-0.913781\pi$
$977$		−	16.7265i		−	0.535129i	0.963540	−	0.267564i	$-0.0862188\pi$
$978$		0			0
$979$	32.5213	−	18.7762i	1.03938	−	0.600089i
$980$		0			0
$981$	1.63233	−	15.7908i	0.0521164	−	0.504162i
$982$		0			0
$983$	16.1458	−	27.9653i	0.514970	−	0.891955i	−0.484879	−	0.874581i	$-0.661136\pi$
$983$	16.1458	−	27.9653i	0.514970	−	0.891955i	0.999849	−	0.0173733i	$-0.00553037\pi$
$984$		0			0
$985$	−14.8932	+	8.59858i	−0.474536	+	0.273974i
$986$		0			0
$987$	−11.4232	−	34.1629i	−0.363604	−	1.08742i
$988$		0			0
$989$	0.811730	+	0.468652i	0.0258115	+	0.0149023i
$990$		0			0
$991$	−4.25134	−	7.36353i	−0.135048	−	0.233910i	0.790568	−	0.612375i	$-0.209786\pi$
$991$	−4.25134	−	7.36353i	−0.135048	−	0.233910i	−0.925616	+	0.378464i	$0.876452\pi$
$992$		0			0
$993$	17.1850	+	5.56746i	0.545348	+	0.176678i
$994$		0			0
$995$	10.4437	+	6.02967i	0.331087	+	0.191153i
$996$		0			0
$997$	9.78395	+	5.64877i	0.309861	+	0.178898i	0.646864	−	0.762605i	$-0.276080\pi$
$997$	9.78395	+	5.64877i	0.309861	+	0.178898i	−0.337003	+	0.941503i	$0.609413\pi$
$998$		0			0
$999$	48.9454	−	5.27159i	1.54857	−	0.166786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.c.257.1		16
3.2	odd	2		3024.2.ca.c.2609.6		16
4.3	odd	2		126.2.l.a.5.8	✓	16
7.3	odd	6		1008.2.df.c.689.4		16
9.2	odd	6		1008.2.df.c.929.4		16
9.7	even	3		3024.2.df.c.1601.6		16
12.11	even	2		378.2.l.a.341.3		16
21.17	even	6		3024.2.df.c.17.6		16
28.3	even	6		126.2.t.a.59.3	yes	16
28.11	odd	6		882.2.t.a.815.2		16
28.19	even	6		882.2.m.a.293.8		16
28.23	odd	6		882.2.m.b.293.5		16
28.27	even	2		882.2.l.b.509.5		16
36.7	odd	6		378.2.t.a.89.7		16
36.11	even	6		126.2.t.a.47.3	yes	16
36.23	even	6		1134.2.k.b.971.7		16
36.31	odd	6		1134.2.k.a.971.2		16
63.38	even	6	inner	1008.2.ca.c.353.1		16
63.52	odd	6		3024.2.ca.c.2033.6		16
84.11	even	6		2646.2.t.b.2285.6		16
84.23	even	6		2646.2.m.b.881.3		16
84.47	odd	6		2646.2.m.a.881.2		16
84.59	odd	6		378.2.t.a.17.7		16
84.83	odd	2		2646.2.l.a.1097.2		16
252.11	even	6		882.2.l.b.227.1		16
252.31	even	6		1134.2.k.b.647.7		16
252.47	odd	6		882.2.m.b.587.5		16
252.59	odd	6		1134.2.k.a.647.2		16
252.79	odd	6		2646.2.m.a.1763.2		16
252.83	odd	6		882.2.t.a.803.2		16
252.115	even	6		378.2.l.a.143.7		16
252.151	odd	6		2646.2.l.a.521.6		16
252.187	even	6		2646.2.m.b.1763.3		16
252.191	even	6		882.2.m.a.587.8		16
252.223	even	6		2646.2.t.b.1979.6		16
252.227	odd	6		126.2.l.a.101.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.8	✓	16	4.3	odd	2
126.2.l.a.101.4	yes	16	252.227	odd	6
126.2.t.a.47.3	yes	16	36.11	even	6
126.2.t.a.59.3	yes	16	28.3	even	6
378.2.l.a.143.7		16	252.115	even	6
378.2.l.a.341.3		16	12.11	even	2
378.2.t.a.17.7		16	84.59	odd	6
378.2.t.a.89.7		16	36.7	odd	6
882.2.l.b.227.1		16	252.11	even	6
882.2.l.b.509.5		16	28.27	even	2
882.2.m.a.293.8		16	28.19	even	6
882.2.m.a.587.8		16	252.191	even	6
882.2.m.b.293.5		16	28.23	odd	6
882.2.m.b.587.5		16	252.47	odd	6
882.2.t.a.803.2		16	252.83	odd	6
882.2.t.a.815.2		16	28.11	odd	6
1008.2.ca.c.257.1		16	1.1	even	1	trivial
1008.2.ca.c.353.1		16	63.38	even	6	inner
1008.2.df.c.689.4		16	7.3	odd	6
1008.2.df.c.929.4		16	9.2	odd	6
1134.2.k.a.647.2		16	252.59	odd	6
1134.2.k.a.971.2		16	36.31	odd	6
1134.2.k.b.647.7		16	252.31	even	6
1134.2.k.b.971.7		16	36.23	even	6
2646.2.l.a.521.6		16	252.151	odd	6
2646.2.l.a.1097.2		16	84.83	odd	2
2646.2.m.a.881.2		16	84.47	odd	6
2646.2.m.a.1763.2		16	252.79	odd	6
2646.2.m.b.881.3		16	84.23	even	6
2646.2.m.b.1763.3		16	252.187	even	6
2646.2.t.b.1979.6		16	252.223	even	6
2646.2.t.b.2285.6		16	84.11	even	6
3024.2.ca.c.2033.6		16	63.52	odd	6
3024.2.ca.c.2609.6		16	3.2	odd	2
3024.2.df.c.17.6		16	21.17	even	6
3024.2.df.c.1601.6		16	9.7	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.64774 - 0.533822i) q^{3} +(-0.450129 - 0.779646i) q^{5} +(-1.57151 - 2.12847i) q^{7} +(2.43007 + 1.75919i) q^{9} +O(q^{10})\)	\(q+(-1.64774 - 0.533822i) q^{3} +(-0.450129 - 0.779646i) q^{5} +(-1.57151 - 2.12847i) q^{7} +(2.43007 + 1.75919i) q^{9} +(2.70900 + 1.56404i) q^{11} +(-1.99033 - 1.14912i) q^{13} +(0.325502 + 1.52494i) q^{15} +(-2.57638 - 4.46242i) q^{17} +(-2.38111 - 1.37474i) q^{19} +(1.45321 + 4.34605i) q^{21} +(1.48584 - 0.857850i) q^{23} +(2.09477 - 3.62824i) q^{25} +(-3.06502 - 4.19591i) q^{27} +(-1.85590 + 1.07151i) q^{29} +10.0032i q^{31} +(-3.62880 - 4.02326i) q^{33} +(-0.952070 + 2.18330i) q^{35} +(-4.73701 + 8.20475i) q^{37} +(2.66612 + 2.95593i) q^{39} +(1.22134 - 2.11542i) q^{41} +(0.273155 + 0.473119i) q^{43} +(0.277705 - 2.68646i) q^{45} -7.86068 q^{47} +(-2.06074 + 6.68980i) q^{49} +(1.86306 + 8.72821i) q^{51} +(-12.0733 + 6.97054i) q^{53} -2.81608i q^{55} +(3.18958 + 3.53629i) q^{57} -7.98443 q^{59} +7.25411i q^{61} +(-0.0744824 - 7.93690i) q^{63} +2.06901i q^{65} -3.67050 q^{67} +(-2.90621 + 0.620337i) q^{69} -14.1484i q^{71} +(-10.9190 + 6.30409i) q^{73} +(-5.38846 + 4.86016i) q^{75} +(-0.928202 - 8.22392i) q^{77} +6.54804 q^{79} +(2.81047 + 8.54993i) q^{81} +(-0.184437 - 0.319454i) q^{83} +(-2.31940 + 4.01733i) q^{85} +(3.63003 - 0.774838i) q^{87} +(6.00244 - 10.3965i) q^{89} +(0.681960 + 6.04220i) q^{91} +(5.33990 - 16.4826i) q^{93} +2.47523i q^{95} +(8.86815 - 5.12003i) q^{97} +(3.83161 + 8.56640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^7	\( 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49} - 6 q^{51} - 36 q^{53} + 6 q^{57} - 60 q^{59} - 36 q^{63} + 28 q^{67} - 42 q^{69} - 60 q^{75} - 42 q^{77} - 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{87} - 24 q^{89} + 12 q^{91} - 42 q^{93} + 6 q^{97} - 18 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Introduction

L-functions

Modular forms

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