LMFDB - Embedded newform 504.2.p.g.307.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(307,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.p (of order $2$, degree $1$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$16$
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} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 - 4x^12 - 4x^10 + 16x^8 - 16x^6 - 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			307.5
Root			$1.20933 + 0.733159i$ of defining polynomial
Character	$\chi$	$=$	504.307
Dual form			504.2.p.g.307.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733159 - 1.20933i) q^{2} +(-0.924955 + 1.77326i) q^{4} -1.12786 q^{5} +(2.11337 + 1.59175i) q^{7} +(2.82260 - 0.181508i) q^{8} +O(q^{10})$	\(q+(-0.733159 - 1.20933i) q^{2} +(-0.924955 + 1.77326i) q^{4} -1.12786 q^{5} +(2.11337 + 1.59175i) q^{7} +(2.82260 - 0.181508i) q^{8} +(0.826905 + 1.36396i) q^{10} -5.11151 q^{11} -5.88054 q^{13} +(0.375521 - 3.72277i) q^{14} +(-2.28892 - 3.28038i) q^{16} -3.31623i q^{17} -7.49510i q^{19} +(1.04322 - 2.00000i) q^{20} +(3.74755 + 6.18150i) q^{22} +1.73845i q^{23} -3.72792 q^{25} +(4.31137 + 7.11151i) q^{26} +(-4.77737 + 2.27525i) q^{28} +5.88054i q^{29} -6.04982 q^{31} +(-2.28892 + 5.17309i) q^{32} +(-4.01041 + 2.43132i) q^{34} +(-2.38359 - 1.79528i) q^{35} +1.65381i q^{37} +(-9.06405 + 5.49510i) q^{38} +(-3.18351 + 0.204716i) q^{40} -1.45096i q^{41} +1.79528 q^{43} +(4.72792 - 9.06405i) q^{44} +(2.10236 - 1.27456i) q^{46} -5.56335 q^{47} +(1.93264 + 6.72792i) q^{49} +(2.73316 + 4.50828i) q^{50} +(5.43924 - 10.4277i) q^{52} +3.62481i q^{53} +5.76510 q^{55} +(6.25410 + 4.10929i) q^{56} +(7.11151 - 4.31137i) q^{58} -0.767184i q^{59} -0.317194 q^{61} +(4.43548 + 7.31623i) q^{62} +(7.93411 - 1.02465i) q^{64} +6.63246 q^{65} -6.56247 q^{67} +(5.88054 + 3.06736i) q^{68} +(-0.423537 + 4.19878i) q^{70} -10.1919i q^{71} +6.63246i q^{73} +(2.00000 - 1.21251i) q^{74} +(13.2908 + 6.93264i) q^{76} +(-10.8025 - 8.13627i) q^{77} -3.01423i q^{79} +(2.58159 + 3.69982i) q^{80} +(-1.75468 + 1.06378i) q^{82} -16.0883i q^{83} +3.74026i q^{85} +(-1.31623 - 2.17109i) q^{86} +(-14.4277 + 0.927779i) q^{88} +8.08341i q^{89} +(-12.4277 - 9.36038i) q^{91} +(-3.08273 - 1.60799i) q^{92} +(4.07882 + 6.72792i) q^{94} +8.45347i q^{95} +0.357752i q^{97} +(6.71934 - 7.26983i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8	$ 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8} + 8 q^{11} + 14 q^{14} + 18 q^{16} + 8 q^{22} + 16 q^{25} - 10 q^{28} + 18 q^{32} - 24 q^{35} - 8 q^{43} + 52 q^{46} - 8 q^{49} + 34 q^{50} - 50 q^{56} + 24 q^{58} + 2 q^{64} - 40 q^{67} - 24 q^{70} + 32 q^{74} + 32 q^{86} - 88 q^{88} - 56 q^{91} - 44 q^{92} - 66 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8 + 8 * q^11 + 14 * q^14 + 18 * q^16 + 8 * q^22 + 16 * q^25 - 10 * q^28 + 18 * q^32 - 24 * q^35 - 8 * q^43 + 52 * q^46 - 8 * q^49 + 34 * q^50 - 50 * q^56 + 24 * q^58 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 32 * q^74 + 32 * q^86 - 88 * q^88 - 56 * q^91 - 44 * q^92 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.733159	−	1.20933i	−0.518422	−	0.855125i
$2$	−0.733159	−	1.20933i	−0.518422	−	0.855125i
$3$		0			0
$3$		0			0
$4$	−0.924955	+	1.77326i	−0.462478	+	0.886631i
$5$	−1.12786			−0.504397			−0.252198	−	0.967676i	$-0.581154\pi$
$5$	−1.12786			−0.504397			−0.252198	+	0.967676i	$0.581154\pi$
$6$		0			0
$7$	2.11337	+	1.59175i	0.798777	+	0.601627i
$7$	2.11337	+	1.59175i	0.798777	+	0.601627i
$8$	2.82260	−	0.181508i	0.997939	−	0.0641726i
$9$		0			0
$10$	0.826905	+	1.36396i	0.261490	+	0.431322i
$11$	−5.11151			−1.54118			−0.770590	−	0.637332i	$-0.780038\pi$
$11$	−5.11151			−1.54118			−0.770590	+	0.637332i	$0.780038\pi$
$12$		0			0
$13$	−5.88054			−1.63097			−0.815484	−	0.578779i	$-0.803529\pi$
$13$	−5.88054			−1.63097			−0.815484	+	0.578779i	$0.803529\pi$
$14$	0.375521	−	3.72277i	0.100362	−	0.994951i
$15$		0			0
$16$	−2.28892	−	3.28038i	−0.572229	−	0.820094i
$17$		−	3.31623i		−	0.804304i	−0.915573	−	0.402152i	$-0.868262\pi$
$17$		−	3.31623i		−	0.804304i	0.915573	−	0.402152i	$-0.131738\pi$
$18$		0			0
$19$		−	7.49510i		−	1.71949i	−0.510719	−	0.859747i	$-0.670621\pi$
$19$		−	7.49510i		−	1.71949i	0.510719	−	0.859747i	$-0.329379\pi$
$20$	1.04322	−	2.00000i	0.233272	−	0.447214i
$21$		0			0
$22$	3.74755	+	6.18150i	0.798981	+	1.31790i
$23$			1.73845i			0.362492i	0.983438	+	0.181246i	$0.0580130\pi$
$23$			1.73845i			0.362492i	−0.983438	+	0.181246i	$0.941987\pi$
$24$		0			0
$25$	−3.72792			−0.745584
$26$	4.31137	+	7.11151i	0.845530	+	1.39468i
$27$		0			0
$28$	−4.77737	+	2.27525i	−0.902837	+	0.429982i
$29$			5.88054i			1.09199i	0.837789	+	0.545995i	$0.183848\pi$
$29$			5.88054i			1.09199i	−0.837789	+	0.545995i	$0.816152\pi$
$30$		0			0
$31$	−6.04982			−1.08658			−0.543290	−	0.839545i	$-0.682822\pi$
$31$	−6.04982			−1.08658			−0.543290	+	0.839545i	$0.682822\pi$
$32$	−2.28892	+	5.17309i	−0.404627	+	0.914482i
$33$		0			0
$34$	−4.01041	+	2.43132i	−0.687780	+	0.416969i
$35$	−2.38359	−	1.79528i	−0.402901	−	0.303458i
$36$		0			0
$37$			1.65381i			0.271885i	0.990717	+	0.135942i	$0.0434062\pi$
$37$			1.65381i			0.271885i	−0.990717	+	0.135942i	$0.956594\pi$
$38$	−9.06405	+	5.49510i	−1.47038	+	0.891424i
$39$		0			0
$40$	−3.18351	+	0.204716i	−0.503357	+	0.0323685i
$41$		−	1.45096i		−	0.226601i	−0.993561	−	0.113301i	$-0.963858\pi$
$41$		−	1.45096i		−	0.226601i	0.993561	−	0.113301i	$-0.0361423\pi$
$42$		0			0
$43$	1.79528			0.273778			0.136889	−	0.990586i	$-0.456290\pi$
$43$	1.79528			0.273778			0.136889	+	0.990586i	$0.456290\pi$
$44$	4.72792	−	9.06405i	0.712761	−	1.36646i
$45$		0			0
$46$	2.10236	−	1.27456i	0.309976	−	0.187924i
$47$	−5.56335			−0.811498			−0.405749	−	0.913985i	$-0.632989\pi$
$47$	−5.56335			−0.811498			−0.405749	+	0.913985i	$0.632989\pi$
$48$		0			0
$49$	1.93264	+	6.72792i	0.276091	+	0.961132i
$50$	2.73316	+	4.50828i	0.386527	+	0.637568i
$51$		0			0
$52$	5.43924	−	10.4277i	0.754287	−	1.44607i
$53$			3.62481i			0.497906i	0.968516	+	0.248953i	$0.0800865\pi$
$53$			3.62481i			0.497906i	−0.968516	+	0.248953i	$0.919913\pi$
$54$		0			0
$55$	5.76510			0.777365
$56$	6.25410	+	4.10929i	0.835739	+	0.549127i
$57$		0			0
$58$	7.11151	−	4.31137i	0.933787	−	0.566111i
$59$		−	0.767184i		−	0.0998789i	−0.998752	−	0.0499394i	$-0.984097\pi$
$59$		−	0.767184i		−	0.0998789i	0.998752	−	0.0499394i	$-0.0159028\pi$
$60$		0			0
$61$	−0.317194			−0.0406125			−0.0203063	−	0.999794i	$-0.506464\pi$
$61$	−0.317194			−0.0406125			−0.0203063	+	0.999794i	$0.506464\pi$
$62$	4.43548	+	7.31623i	0.563307	+	0.929162i
$63$		0			0
$64$	7.93411	−	1.02465i	0.991764	−	0.128081i
$65$	6.63246			0.822655
$66$		0			0
$67$	−6.56247			−0.801733			−0.400867	−	0.916136i	$-0.631291\pi$
$67$	−6.56247			−0.801733			−0.400867	+	0.916136i	$0.631291\pi$
$68$	5.88054	+	3.06736i	0.713121	+	0.371972i
$69$		0			0
$70$	−0.423537	+	4.19878i	−0.0506224	+	0.501850i
$71$		−	10.1919i		−	1.20956i	−0.796393	−	0.604779i	$-0.793261\pi$
$71$		−	10.1919i		−	1.20956i	0.796393	−	0.604779i	$-0.206739\pi$
$72$		0			0
$73$			6.63246i			0.776270i	0.921602	+	0.388135i	$0.126881\pi$
$73$			6.63246i			0.776270i	−0.921602	+	0.388135i	$0.873119\pi$
$74$	2.00000	−	1.21251i	0.232495	−	0.140951i
$75$		0			0
$76$	13.2908	+	6.93264i	1.52456	+	0.795228i
$77$	−10.8025	−	8.13627i	−1.23106	−	0.927214i
$78$		0			0
$79$		−	3.01423i		−	0.339127i	−0.985519	−	0.169564i	$-0.945764\pi$
$79$		−	3.01423i		−	0.339127i	0.985519	−	0.169564i	$-0.0542358\pi$
$80$	2.58159	+	3.69982i	0.288630	+	0.413653i
$81$		0			0
$82$	−1.75468	+	1.06378i	−0.193772	+	0.117475i
$83$		−	16.0883i		−	1.76592i	−0.469448	−	0.882960i	$-0.655547\pi$
$83$		−	16.0883i		−	1.76592i	0.469448	−	0.882960i	$-0.344453\pi$
$84$		0			0
$85$			3.74026i			0.405688i
$86$	−1.31623	−	2.17109i	−0.141933	−	0.234115i
$87$		0			0
$88$	−14.4277	+	0.927779i	−1.53800	+	0.0989015i
$89$			8.08341i			0.856840i	0.903580	+	0.428420i	$0.140930\pi$
$89$			8.08341i			0.856840i	−0.903580	+	0.428420i	$0.859070\pi$
$90$		0			0
$91$	−12.4277	−	9.36038i	−1.30278	−	0.981234i
$92$	−3.08273	−	1.60799i	−0.321396	−	0.167644i
$93$		0			0
$94$	4.07882	+	6.72792i	0.420698	+	0.693932i
$95$			8.45347i			0.867307i
$96$		0			0
$97$			0.357752i			0.0363242i	0.999835	+	0.0181621i	$0.00578150\pi$
$97$			0.357752i			0.0363242i	−0.999835	+	0.0181621i	$0.994219\pi$
$98$	6.71934	−	7.26983i	0.678756	−	0.734364i
$99$		0			0
$100$	3.44816	−	6.61058i	0.344816	−	0.661058i
$101$	3.38359			0.336680			0.168340	−	0.985729i	$-0.446159\pi$
$101$	3.38359			0.336680			0.168340	+	0.985729i	$0.446159\pi$
$102$		0			0
$103$	14.5033			1.42905			0.714526	−	0.699609i	$-0.246643\pi$
$103$	14.5033			1.42905			0.714526	+	0.699609i	$0.246643\pi$
$104$	−16.5984	+	1.06736i	−1.62761	+	0.104664i
$105$		0			0
$106$	4.38359	−	2.65756i	0.425772	−	0.258125i
$107$	1.87870			0.181621			0.0908103	−	0.995868i	$-0.471054\pi$
$107$	1.87870			0.181621			0.0908103	+	0.995868i	$0.471054\pi$
$108$		0			0
$109$			13.6166i			1.30424i	0.758117	+	0.652119i	$0.226120\pi$
$109$			13.6166i			1.30424i	−0.758117	+	0.652119i	$0.773880\pi$
$110$	−4.22673	−	6.97190i	−0.403003	−	0.664745i
$111$		0			0
$112$	0.384235	−	10.5760i	0.0363068	−	0.999341i
$113$	−4.63246			−0.435785			−0.217892	−	0.975973i	$-0.569918\pi$
$113$	−4.63246			−0.435785			−0.217892	+	0.975973i	$0.569918\pi$
$114$		0			0
$115$		−	1.96074i		−	0.182840i
$116$	−10.4277	−	5.43924i	−0.968192	−	0.505021i
$117$		0			0
$118$	−0.927779	+	0.562468i	−0.0854089	+	0.0517794i
$119$	5.27862	−	7.00841i	0.483890	−	0.642460i
$120$		0			0
$121$	15.1276			1.37523
$122$	0.232554	+	0.383592i	0.0210544	+	0.0347288i
$123$		0			0
$124$	5.59582	−	10.7279i	0.502519	−	0.963396i
$125$	9.84392			0.880467
$126$		0			0
$127$		−	9.38124i		−	0.832451i	−0.909261	−	0.416225i	$-0.863353\pi$
$127$		−	9.38124i		−	0.832451i	0.909261	−	0.416225i	$-0.136647\pi$
$128$	−7.05610	−	8.84372i	−0.623677	−	0.781682i
$129$		0			0
$130$	−4.86265	−	8.02083i	−0.426482	−	0.703473i
$131$			6.22303i			0.543708i	0.962338	+	0.271854i	$0.0876368\pi$
$131$			6.22303i			0.543708i	−0.962338	+	0.271854i	$0.912363\pi$
$132$		0			0
$133$	11.9304	−	15.8399i	1.03449	−	1.37349i
$134$	4.81133	+	7.93619i	0.415636	+	0.685582i
$135$		0			0
$136$	−0.601921	−	9.36038i	−0.0516143	−	0.802646i
$137$	−7.45584			−0.636996			−0.318498	−	0.947924i	$-0.603178\pi$
$137$	−7.45584			−0.636996			−0.318498	+	0.947924i	$0.603178\pi$
$138$		0			0
$139$			2.27471i			0.192938i	0.995336	+	0.0964690i	$0.0307549\pi$
$139$			2.27471i			0.192938i	−0.995336	+	0.0964690i	$0.969245\pi$
$140$	5.38822	−	2.56618i	0.455388	−	0.216881i
$141$		0			0
$142$	−12.3254	+	7.47230i	−1.03432	+	0.627061i
$143$	30.0585			2.51362
$144$		0			0
$145$		−	6.63246i		−	0.550796i
$146$	8.02083	−	4.86265i	0.663808	−	0.402436i
$147$		0			0
$148$	−2.93264	−	1.52970i	−0.241061	−	0.125741i
$149$			4.19427i			0.343608i	0.985131	+	0.171804i	$0.0549595\pi$
$149$			4.19427i			0.343608i	−0.985131	+	0.171804i	$0.945040\pi$
$150$		0			0
$151$		−	9.79874i		−	0.797411i	−0.917079	−	0.398705i	$-0.869460\pi$
$151$		−	9.79874i		−	0.797411i	0.917079	−	0.398705i	$-0.130540\pi$
$152$	−1.36042	−	21.1557i	−0.110345	−	1.71595i
$153$		0			0
$154$	−1.91948	+	19.0290i	−0.154676	+	1.53340i
$155$	6.82338			0.548067
$156$		0			0
$157$	−4.82865			−0.385369			−0.192684	−	0.981261i	$-0.561719\pi$
$157$	−4.82865			−0.385369			−0.192684	+	0.981261i	$0.561719\pi$
$158$	−3.64519	+	2.20991i	−0.289996	+	0.175811i
$159$		0			0
$160$	2.58159	−	5.83455i	0.204092	−	0.461261i
$161$	−2.76718	+	3.67398i	−0.218085	+	0.289550i
$162$		0			0
$163$	−1.43753			−0.112596			−0.0562981	−	0.998414i	$-0.517930\pi$
$163$	−1.43753			−0.112596			−0.0562981	+	0.998414i	$0.517930\pi$
$164$	2.57292	+	1.34207i	0.200912	+	0.104798i
$165$		0			0
$166$	−19.4561	+	11.7953i	−1.51008	+	0.915492i
$167$	−16.0417			−1.24134			−0.620670	−	0.784072i	$-0.713139\pi$
$167$	−16.0417			−1.24134			−0.620670	+	0.784072i	$0.713139\pi$
$168$		0			0
$169$	21.5808			1.66006
$170$	4.52320	−	2.74220i	0.346914	−	0.210318i
$171$		0			0
$172$	−1.66056	+	3.18351i	−0.126616	+	0.242740i
$173$	−4.01798			−0.305482			−0.152741	−	0.988266i	$-0.548810\pi$
$173$	−4.01798			−0.305482			−0.152741	+	0.988266i	$0.548810\pi$
$174$		0			0
$175$	−7.87846	−	5.93393i	−0.595556	−	0.448563i
$176$	11.6998	+	16.7677i	0.881907	+	1.26391i
$177$		0			0
$178$	9.77551	−	5.92643i	0.732705	−	0.444205i
$179$	6.97679			0.521469			0.260735	−	0.965410i	$-0.416035\pi$
$179$	6.97679			0.521469			0.260735	+	0.965410i	$0.416035\pi$
$180$		0			0
$181$	−13.4687			−1.00112			−0.500561	−	0.865701i	$-0.666873\pi$
$181$	−13.4687			−1.00112			−0.500561	+	0.865701i	$0.666873\pi$
$182$	−2.20827	+	21.8919i	−0.163688	+	1.62273i
$183$		0			0
$184$	0.315542	+	4.90694i	0.0232621	+	0.361745i
$185$		−	1.86527i		−	0.137138i
$186$		0			0
$187$			16.9509i			1.23958i
$188$	5.14585	−	9.86527i	0.375300	−	0.719499i
$189$		0			0
$190$	10.2230	−	6.19774i	0.741656	−	0.449631i
$191$			21.0704i			1.52460i	0.647224	+	0.762300i	$0.275930\pi$
$191$			21.0704i			1.52460i	−0.647224	+	0.762300i	$0.724070\pi$
$192$		0			0
$193$	−5.13735			−0.369795			−0.184897	−	0.982758i	$-0.559195\pi$
$193$	−5.13735			−0.369795			−0.184897	+	0.982758i	$0.559195\pi$
$194$	0.432640	−	0.262289i	0.0310618	−	0.0188313i
$195$		0			0
$196$	−13.7180	−	2.79595i	−0.979855	−	0.199711i
$197$		−	26.4337i		−	1.88332i	−0.336566	−	0.941660i	$-0.609265\pi$
$197$		−	26.4337i		−	1.88332i	0.336566	−	0.941660i	$-0.390735\pi$
$198$		0			0
$199$	−10.8420			−0.768567			−0.384283	−	0.923215i	$-0.625551\pi$
$199$	−10.8420			−0.768567			−0.384283	+	0.923215i	$0.625551\pi$
$200$	−10.5224	+	0.676646i	−0.744047	+	0.0478461i
$201$		0			0
$202$	−2.48071	−	4.09188i	−0.174542	−	0.287904i
$203$	−9.36038	+	12.4277i	−0.656970	+	0.872256i
$204$		0			0
$205$			1.63648i			0.114297i
$206$	−10.6332	−	17.5393i	−0.740852	−	1.22202i
$207$		0			0
$208$	13.4601	+	19.2904i	0.933288	+	1.33755i
$209$			38.3113i			2.65005i
$210$		0			0
$211$	9.79528			0.674335			0.337168	−	0.941445i	$-0.390531\pi$
$211$	9.79528			0.674335			0.337168	+	0.941445i	$0.390531\pi$
$212$	−6.42774	−	3.35279i	−0.441459	−	0.230271i
$213$		0			0
$214$	−1.37738	−	2.27196i	−0.0941560	−	0.155308i
$215$	−2.02484			−0.138093
$216$		0			0
$217$	−12.7855	−	9.62983i	−0.867936	−	0.653716i
$218$	16.4670	−	9.98317i	1.11529	−	0.676145i
$219$		0			0
$220$	−5.33246	+	10.2230i	−0.359514	+	0.689236i
$221$			19.5012i			1.31179i
$222$		0			0
$223$	15.3534			1.02814			0.514071	−	0.857748i	$-0.328137\pi$
$223$	15.3534			1.02814			0.514071	+	0.857748i	$0.328137\pi$
$224$	−13.0716	+	7.28925i	−0.873383	+	0.487033i
$225$		0			0
$226$	3.39633	+	5.60217i	0.225920	+	0.372651i
$227$			5.86527i			0.389292i	0.980874	+	0.194646i	$0.0623558\pi$
$227$			5.86527i			0.389292i	−0.980874	+	0.194646i	$0.937644\pi$
$228$		0			0
$229$	2.57292			0.170024			0.0850118	−	0.996380i	$-0.472907\pi$
$229$	2.57292			0.170024			0.0850118	+	0.996380i	$0.472907\pi$
$230$	−2.37118	+	1.43753i	−0.156351	+	0.0947880i
$231$		0			0
$232$	1.06736	+	16.5984i	0.0700758	+	1.08974i
$233$	19.6227			1.28552			0.642762	−	0.766066i	$-0.277788\pi$
$233$	19.6227			1.28552			0.642762	+	0.766066i	$0.277788\pi$
$234$		0			0
$235$	6.27471			0.409317
$236$	1.36042	+	0.709611i	0.0885557	+	0.0461918i
$237$		0			0
$238$	−12.3455	−	1.24531i	−0.800243	−	0.0807217i
$239$			0.348000i			0.0225102i	0.999937	+	0.0112551i	$0.00358269\pi$
$239$			0.348000i			0.0225102i	−0.999937	+	0.0112551i	$0.996417\pi$
$240$		0			0
$241$			20.0883i			1.29400i	0.762490	+	0.647001i	$0.223977\pi$
$241$			20.0883i			1.29400i	−0.762490	+	0.647001i	$0.776023\pi$
$242$	−11.0909	−	18.2942i	−0.712951	−	1.17600i
$243$		0			0
$244$	0.293390	−	0.562468i	0.0187824	−	0.0360083i
$245$	−2.17975	−	7.58819i	−0.139259	−	0.484791i
$246$		0			0
$247$			44.0753i			2.80444i
$248$	−17.0762	+	1.09809i	−1.08434	+	0.0697287i
$249$		0			0
$250$	−7.21716	−	11.9045i	−0.456453	−	0.752909i
$251$			9.12494i			0.575961i	0.957636	+	0.287980i	$0.0929838\pi$
$251$			9.12494i			0.575961i	−0.957636	+	0.287980i	$0.907016\pi$
$252$		0			0
$253$		−	8.88611i		−	0.558665i
$254$	−11.3450	+	6.87795i	−0.711850	+	0.431561i
$255$		0			0
$256$	−5.52173	+	15.0170i	−0.345108	+	0.938563i
$257$		−	21.8970i		−	1.36590i	−0.730466	−	0.682949i	$-0.760697\pi$
$257$		−	21.8970i		−	1.36590i	0.730466	−	0.682949i	$-0.239303\pi$
$258$		0			0
$259$	−2.63246	+	3.49510i	−0.163573	+	0.217175i
$260$	−6.13473	+	11.7611i	−0.380460	+	0.729392i
$261$		0			0
$262$	7.52569	−	4.56247i	0.464939	−	0.281870i
$263$		−	28.1507i		−	1.73585i	−0.496696	−	0.867924i	$-0.665454\pi$
$263$		−	28.1507i		−	1.73585i	0.496696	−	0.867924i	$-0.334546\pi$
$264$		0			0
$265$		−	4.08830i		−	0.251142i
$266$	−27.9025	−	2.81457i	−1.71081	−	0.172572i
$267$		0			0
$268$	6.06999	−	11.6370i	0.370784	−	0.710841i
$269$	−25.6230			−1.56226			−0.781130	−	0.624368i	$-0.785357\pi$
$269$	−25.6230			−1.56226			−0.781130	+	0.624368i	$0.785357\pi$
$270$		0			0
$271$	−19.0147			−1.15506			−0.577532	−	0.816368i	$-0.695984\pi$
$271$	−19.0147			−1.15506			−0.577532	+	0.816368i	$0.695984\pi$
$272$	−10.8785	+	7.59057i	−0.659605	+	0.460246i
$273$		0			0
$274$	5.46632	+	9.01657i	0.330232	+	0.544711i
$275$	19.0553			1.14908
$276$		0			0
$277$			18.2649i			1.09743i	0.836009	+	0.548716i	$0.184883\pi$
$277$			18.2649i			1.09743i	−0.836009	+	0.548716i	$0.815117\pi$
$278$	2.75087	−	1.66772i	0.164986	−	0.100023i
$279$		0			0
$280$	−7.05378	−	4.63472i	−0.421544	−	0.276978i
$281$	19.8136			1.18198			0.590990	−	0.806679i	$-0.298737\pi$
$281$	19.8136			1.18198			0.590990	+	0.806679i	$0.298737\pi$
$282$		0			0
$283$		−	13.7698i		−	0.818530i	−0.912416	−	0.409265i	$-0.865785\pi$
$283$		−	13.7698i		−	0.818530i	0.912416	−	0.409265i	$-0.134215\pi$
$284$	18.0729	+	9.42707i	1.07243	+	0.559393i
$285$		0			0
$286$	−22.0376	−	36.3506i	−1.30311	−	2.14946i
$287$	2.30956	−	3.06640i	0.136329	−	0.181004i
$288$		0			0
$289$	6.00263			0.353096
$290$	−8.02083	+	4.86265i	−0.470999	+	0.285544i
$291$		0			0
$292$	−11.7611	−	6.13473i	−0.688265	−	0.359008i
$293$	25.2844			1.47713			0.738566	−	0.674181i	$-0.235503\pi$
$293$	25.2844			1.47713			0.738566	+	0.674181i	$0.235503\pi$
$294$		0			0
$295$			0.865280i			0.0503786i
$296$	0.300179	+	4.66804i	0.0174475	+	0.271324i
$297$		0			0
$298$	5.07225	−	3.07506i	0.293827	−	0.178134i
$299$		−	10.2230i		−	0.591213i
$300$		0			0
$301$	3.79409	+	2.85765i	0.218688	+	0.164712i
$302$	−11.8499	+	7.18404i	−0.681886	+	0.413395i
$303$		0			0
$304$	−24.5868	+	17.1557i	−1.41015	+	0.983945i
$305$	0.357752			0.0204848
$306$		0			0
$307$			5.96074i			0.340197i	0.985427	+	0.170099i	$0.0544086\pi$
$307$			5.96074i			0.340197i	−0.985427	+	0.170099i	$0.945591\pi$
$308$	24.4196	−	11.6300i	1.39143	−	0.662679i
$309$		0			0
$310$	−5.00263	−	8.25172i	−0.284130	−	0.468666i
$311$	−26.4123			−1.49770			−0.748852	−	0.662738i	$-0.769394\pi$
$311$	−26.4123			−1.49770			−0.748852	+	0.662738i	$0.769394\pi$
$312$		0			0
$313$			9.53437i			0.538914i	0.963012	+	0.269457i	$0.0868443\pi$
$313$			9.53437i			0.538914i	−0.963012	+	0.269457i	$0.913156\pi$
$314$	3.54017	+	5.83943i	0.199783	+	0.329538i
$315$		0			0
$316$	5.34502	+	2.78803i	0.300681	+	0.156839i
$317$			24.8123i			1.39360i	0.717266	+	0.696799i	$0.245393\pi$
$317$			24.8123i			1.39360i	−0.717266	+	0.696799i	$0.754607\pi$
$318$		0			0
$319$		−	30.0585i		−	1.68295i
$320$	−8.94860	+	1.15566i	−0.500242	+	0.0646035i
$321$		0			0
$322$	6.47184	+	0.652825i	0.360662	+	0.0363805i
$323$	−24.8555			−1.38300
$324$		0			0
$325$	21.9222			1.21602
$326$	1.05394	+	1.73845i	0.0583723	+	0.0962838i
$327$		0			0
$328$	−0.263359	−	4.09546i	−0.0145416	−	0.226134i
$329$	−11.7574	−	8.85548i	−0.648206	−	0.488219i
$330$		0			0
$331$	9.46438			0.520209			0.260105	−	0.965580i	$-0.416243\pi$
$331$	9.46438			0.520209			0.260105	+	0.965580i	$0.416243\pi$
$332$	28.5288	+	14.8810i	1.56572	+	0.816699i
$333$		0			0
$334$	11.7611	+	19.3996i	0.643538	+	1.06150i
$335$	7.40158			0.404391
$336$		0			0
$337$	−35.7110			−1.94530			−0.972650	−	0.232275i	$-0.925383\pi$
$337$	−35.7110			−1.94530			−0.972650	+	0.232275i	$0.925383\pi$
$338$	−15.8221	−	26.0983i	−0.860611	−	1.41956i
$339$		0			0
$340$	−6.63246	−	3.45957i	−0.359696	−	0.187622i
$341$	30.9237			1.67461
$342$		0			0
$343$	−6.62483	+	17.2948i	−0.357707	+	0.933834i
$344$	5.06736	−	0.325858i	0.273214	−	0.0175691i
$345$		0			0
$346$	2.94582	+	4.85907i	0.158368	+	0.261225i
$347$	26.3764			1.41596			0.707980	−	0.706232i	$-0.249606\pi$
$347$	26.3764			1.41596			0.707980	+	0.706232i	$0.249606\pi$
$348$		0			0
$349$	−7.90538			−0.423165			−0.211583	−	0.977360i	$-0.567862\pi$
$349$	−7.90538			−0.423165			−0.211583	+	0.977360i	$0.567862\pi$
$350$	−1.39991	+	13.8782i	−0.0748285	+	0.741820i
$351$		0			0
$352$	11.6998	−	26.4423i	0.623603	−	1.40938i
$353$		−	14.5490i		−	0.774368i	−0.922003	−	0.387184i	$-0.873448\pi$
$353$		−	14.5490i		−	0.774368i	0.922003	−	0.387184i	$-0.126552\pi$
$354$		0			0
$355$			11.4951i			0.610097i
$356$	−14.3340	−	7.47680i	−0.759701	−	0.396269i
$357$		0			0
$358$	−5.11509	−	8.43723i	−0.270341	−	0.445922i
$359$			21.3186i			1.12515i	0.826745	+	0.562577i	$0.190190\pi$
$359$			21.3186i			1.12515i	−0.826745	+	0.562577i	$0.809810\pi$
$360$		0			0
$361$	−37.1766			−1.95666
$362$	9.87472	+	16.2881i	0.519004	+	0.856085i
$363$		0			0
$364$	28.0935	−	13.3797i	1.47250	−	0.701287i
$365$		−	7.48052i		−	0.391548i
$366$		0			0
$367$	6.89996			0.360175			0.180088	−	0.983651i	$-0.442362\pi$
$367$	6.89996			0.360175			0.180088	+	0.983651i	$0.442362\pi$
$368$	5.70277	−	3.97916i	0.297277	−	0.207428i
$369$		0			0
$370$	−2.25573	+	1.36754i	−0.117270	+	0.0710951i
$371$	−5.76981	+	7.66056i	−0.299554	+	0.397716i
$372$		0			0
$373$		−	26.5816i		−	1.37634i	−0.725549	−	0.688171i	$-0.758414\pi$
$373$		−	26.5816i		−	1.37634i	0.725549	−	0.688171i	$-0.241586\pi$
$374$	20.4993	−	12.4277i	1.05999	−	0.642623i
$375$		0			0
$376$	−15.7031	+	1.00979i	−0.809825	+	0.0520760i
$377$		−	34.5808i		−	1.78100i
$378$		0			0
$379$	5.52583			0.283843			0.141921	−	0.989878i	$-0.454672\pi$
$379$	5.52583			0.283843			0.141921	+	0.989878i	$0.454672\pi$
$380$	−14.9902	−	7.81908i	−0.768982	−	0.401110i
$381$		0			0
$382$	25.4810	−	15.4480i	1.30372	−	0.790386i
$383$	−10.3706			−0.529915			−0.264957	−	0.964260i	$-0.585358\pi$
$383$	−10.3706			−0.529915			−0.264957	+	0.964260i	$0.585358\pi$
$384$		0			0
$385$	12.1838	+	9.17662i	0.620942	+	0.467684i
$386$	3.76650	+	6.21275i	0.191710	+	0.316221i
$387$		0			0
$388$	−0.634388	−	0.330905i	−0.0322062	−	0.0167991i
$389$		−	12.2302i		−	0.620097i	−0.950721	−	0.310049i	$-0.899655\pi$
$389$		−	12.2302i		−	0.620097i	0.950721	−	0.310049i	$-0.100345\pi$
$390$		0			0
$391$	5.76510			0.291553
$392$	6.67622	+	18.6394i	0.337200	+	0.941433i
$393$		0			0
$394$	−31.9670	+	19.3801i	−1.61047	+	0.976354i
$395$			3.39964i			0.171055i
$396$		0			0
$397$	−7.50188			−0.376509			−0.188254	−	0.982120i	$-0.560283\pi$
$397$	−7.50188			−0.376509			−0.188254	+	0.982120i	$0.560283\pi$
$398$	7.94889	+	13.1115i	0.398442	+	0.657221i
$399$		0			0
$400$	8.53290	+	12.2290i	0.426645	+	0.611449i
$401$	−11.4558			−0.572077			−0.286039	−	0.958218i	$-0.592339\pi$
$401$	−11.4558			−0.572077			−0.286039	+	0.958218i	$0.592339\pi$
$402$		0			0
$403$	35.5762			1.77218
$404$	−3.12967	+	6.00000i	−0.155707	+	0.298511i
$405$		0			0
$406$	21.8919	+	2.20827i	1.08648	+	0.109595i
$407$		−	8.45347i		−	0.419023i
$408$		0			0
$409$		−	29.6227i		−	1.46475i	−0.680903	−	0.732373i	$-0.738413\pi$
$409$		−	29.6227i		−	1.46475i	0.680903	−	0.732373i	$-0.261587\pi$
$410$	1.97905	−	1.19980i	0.0977381	−	0.0592540i
$411$		0			0
$412$	−13.4149	+	25.7181i	−0.660904	+	1.26704i
$413$	1.22117	−	1.62134i	0.0600898	−	0.0797810i
$414$		0			0
$415$			18.1454i			0.890724i
$416$	13.4601	−	30.4206i	0.659934	−	1.49149i
$417$		0			0
$418$	46.3310	−	28.0883i	2.26612	−	1.37384i
$419$			17.8136i			0.870251i	0.900370	+	0.435125i	$0.143296\pi$
$419$			17.8136i			0.870251i	−0.900370	+	0.435125i	$0.856704\pi$
$420$		0			0
$421$		−	13.4149i		−	0.653802i	−0.945059	−	0.326901i	$-0.893996\pi$
$421$		−	13.4149i		−	0.653802i	0.945059	−	0.326901i	$-0.106004\pi$
$422$	−7.18150	−	11.8457i	−0.349590	−	0.576641i
$423$		0			0
$424$	0.657931	+	10.2314i	0.0319520	+	0.496880i
$425$			12.3626i			0.599676i
$426$		0			0
$427$	−0.670347	−	0.504895i	−0.0324404	−	0.0244336i
$428$	−1.73771	+	3.33142i	−0.0839954	+	0.161030i
$429$		0			0
$430$	1.48453	+	2.44870i	0.0715903	+	0.118087i
$431$		−	17.6108i		−	0.848283i	−0.905596	−	0.424142i	$-0.860576\pi$
$431$		−	17.6108i		−	0.848283i	0.905596	−	0.424142i	$-0.139424\pi$
$432$		0			0
$433$		−	36.4461i		−	1.75149i	−0.482778	−	0.875743i	$-0.660372\pi$
$433$		−	36.4461i		−	1.75149i	0.482778	−	0.875743i	$-0.339628\pi$
$434$	−2.27184	+	22.5221i	−0.109052	+	1.08109i
$435$		0			0
$436$	−24.1459	−	12.5948i	−1.15638	−	0.603181i
$437$	13.0299			0.623303
$438$		0			0
$439$	4.79619			0.228909			0.114455	−	0.993428i	$-0.463488\pi$
$439$	4.79619			0.228909			0.114455	+	0.993428i	$0.463488\pi$
$440$	16.2725	−	1.04641i	0.775763	−	0.0498856i
$441$		0			0
$442$	23.5834	−	14.2975i	1.12175	−	0.680063i
$443$	−32.7021			−1.55372			−0.776861	−	0.629672i	$-0.783189\pi$
$443$	−32.7021			−1.55372			−0.776861	+	0.629672i	$0.783189\pi$
$444$		0			0
$445$		−	9.11700i		−	0.432187i
$446$	−11.2565	−	18.5674i	−0.533011	−	0.879190i
$447$		0			0
$448$	18.3987	+	10.4637i	0.869255	+	0.494363i
$449$	−25.3480			−1.19624			−0.598122	−	0.801405i	$-0.704086\pi$
$449$	−25.3480			−1.19624			−0.598122	+	0.801405i	$0.704086\pi$
$450$		0			0
$451$			7.41658i			0.349233i
$452$	4.28482	−	8.21456i	0.201541	−	0.386380i
$453$		0			0
$454$	7.09305	−	4.30018i	0.332893	−	0.201817i
$455$	14.0168	+	10.5572i	0.657118	+	0.494931i
$456$		0			0
$457$	−1.66910			−0.0780770			−0.0390385	−	0.999238i	$-0.512429\pi$
$457$	−1.66910			−0.0780770			−0.0390385	+	0.999238i	$0.512429\pi$
$458$	−1.88636	−	3.11151i	−0.0881439	−	0.145391i
$459$		0			0
$460$	3.47690	+	1.81359i	0.162111	+	0.0845592i
$461$	−33.0246			−1.53811			−0.769054	−	0.639184i	$-0.779272\pi$
$461$	−33.0246			−1.53811			−0.769054	+	0.639184i	$0.779272\pi$
$462$		0			0
$463$		−	15.6833i		−	0.728866i	−0.931230	−	0.364433i	$-0.881263\pi$
$463$		−	15.6833i		−	0.728866i	0.931230	−	0.364433i	$-0.118737\pi$
$464$	19.2904	−	13.4601i	0.895534	−	0.624868i
$465$		0			0
$466$	−14.3865	−	23.7303i	−0.666444	−	1.09928i
$467$		−	4.85548i		−	0.224685i	−0.993670	−	0.112342i	$-0.964165\pi$
$467$		−	4.85548i		−	0.224685i	0.993670	−	0.112342i	$-0.0358354\pi$
$468$		0			0
$469$	−13.8689	−	10.4458i	−0.640406	−	0.482344i
$470$	−4.60036	−	7.58819i	−0.212199	−	0.350017i
$471$		0			0
$472$	−0.139250	−	2.16545i	−0.00640949	−	0.0996730i
$473$	−9.17662			−0.421941
$474$		0			0
$475$			27.9412i			1.28203i
$476$	7.54525	+	15.8428i	0.345836	+	0.726155i
$477$		0			0
$478$	0.420846	−	0.255139i	0.0192491	−	0.0116698i
$479$	−7.10575			−0.324670			−0.162335	−	0.986736i	$-0.551903\pi$
$479$	−7.10575			−0.324670			−0.162335	+	0.986736i	$0.551903\pi$
$480$		0			0
$481$		−	9.72529i		−	0.443435i
$482$	24.2934	−	14.7279i	1.10653	−	0.670838i
$483$		0			0
$484$	−13.9923	+	26.8251i	−0.636014	+	1.21932i
$485$		−	0.403496i		−	0.0183218i
$486$		0			0
$487$			4.29701i			0.194716i	0.995249	+	0.0973580i	$0.0310392\pi$
$487$			4.29701i			0.194716i	−0.995249	+	0.0973580i	$0.968961\pi$
$488$	−0.895311	+	0.0575732i	−0.0405288	+	0.00260621i
$489$		0			0
$490$	−7.57851	+	8.19939i	−0.342362	+	0.370411i
$491$	19.3862			0.874888			0.437444	−	0.899246i	$-0.355884\pi$
$491$	19.3862			0.874888			0.437444	+	0.899246i	$0.355884\pi$
$492$		0			0
$493$	19.5012			0.878291
$494$	53.3015	−	32.3142i	2.39815	−	1.45388i
$495$		0			0
$496$	13.8475	+	19.8457i	0.621773	+	0.891098i
$497$	16.2230	−	21.5393i	0.727702	−	0.966168i
$498$		0			0
$499$	−30.5722			−1.36860			−0.684301	−	0.729200i	$-0.739892\pi$
$499$	−30.5722			−1.36860			−0.684301	+	0.729200i	$0.739892\pi$
$500$	−9.10518	+	17.4558i	−0.407196	+	0.780649i
$501$		0			0
$502$	11.0351	−	6.69003i	0.492519	−	0.298591i
$503$	−26.9817			−1.20306			−0.601528	−	0.798852i	$-0.705441\pi$
$503$	−26.9817			−1.20306			−0.601528	+	0.798852i	$0.705441\pi$
$504$		0			0
$505$	−3.81624			−0.169820
$506$	−10.7462	+	6.51493i	−0.477728	+	0.289624i
$507$		0			0
$508$	16.6354	+	8.67723i	0.738077	+	0.384990i
$509$	−14.1717			−0.628151			−0.314075	−	0.949398i	$-0.601694\pi$
$509$	−14.1717			−0.628151			−0.314075	+	0.949398i	$0.601694\pi$
$510$		0			0
$511$	−10.5572	+	14.0168i	−0.467025	+	0.620067i
$512$	22.2088	−	4.33226i	0.981500	−	0.191461i
$513$		0			0
$514$	−26.4807	+	16.0540i	−1.16801	+	0.708111i
$515$	−16.3578			−0.720809
$516$		0			0
$517$	28.4371			1.25066
$518$	6.15674	+	0.621040i	0.270512	+	0.0272869i
$519$		0			0
$520$	18.7208	−	1.20384i	0.820959	−	0.0527920i
$521$			25.9487i			1.13683i	0.822741	+	0.568416i	$0.192444\pi$
$521$			25.9487i			1.13683i	−0.822741	+	0.568416i	$0.807556\pi$
$522$		0			0
$523$		−	24.6370i		−	1.07730i	−0.842530	−	0.538650i	$-0.818935\pi$
$523$		−	24.6370i		−	1.07730i	0.842530	−	0.538650i	$-0.181065\pi$
$524$	−11.0351	−	5.75602i	−0.482069	−	0.251453i
$525$		0			0
$526$	−34.0435	+	20.6390i	−1.48437	+	0.899902i
$527$			20.0626i			0.873940i
$528$		0			0
$529$	19.9778			0.868600
$530$	−4.94410	+	2.99737i	−0.214758	+	0.130198i
$531$		0			0
$532$	17.0532	+	35.8069i	0.739352	+	1.55242i
$533$			8.53241i			0.369579i
$534$		0			0
$535$	−2.11892			−0.0916088
$536$	−18.5232	+	1.19114i	−0.800081	+	0.0514493i
$537$		0			0
$538$	18.7857	+	30.9866i	0.809910	+	1.33593i
$539$	−9.87870	−	34.3899i	−0.425506	−	1.48128i
$540$		0			0
$541$		−	5.59582i		−	0.240583i	−0.992739	−	0.120291i	$-0.961617\pi$
$541$		−	5.59582i		−	0.240583i	0.992739	−	0.120291i	$-0.0383829\pi$
$542$	13.9408	+	22.9951i	0.598810	+	0.987724i
$543$		0			0
$544$	17.1552	+	7.59057i	0.735521	+	0.325443i
$545$		−	15.3577i		−	0.657853i
$546$		0			0
$547$	−2.15304			−0.0920572			−0.0460286	−	0.998940i	$-0.514657\pi$
$547$	−2.15304			−0.0920572			−0.0460286	+	0.998940i	$0.514657\pi$
$548$	6.89632	−	13.2212i	0.294596	−	0.564780i
$549$		0			0
$550$	−13.9706	−	23.0442i	−0.595707	−	0.982606i
$551$	44.0753			1.87767
$552$		0			0
$553$	4.79791	−	6.37017i	0.204028	−	0.270887i
$554$	22.0883	−	13.3911i	0.938442	−	0.568933i
$555$		0			0
$556$	−4.03365	−	2.10400i	−0.171065	−	0.0892295i
$557$			31.1317i			1.31909i	0.751664	+	0.659547i	$0.229252\pi$
$557$			31.1317i			1.31909i	−0.751664	+	0.659547i	$0.770748\pi$
$558$		0			0
$559$	−10.5572			−0.446524
$560$	−0.433365	+	11.9283i	−0.0183130	+	0.504064i
$561$		0			0
$562$	−14.5265	−	23.9612i	−0.612764	−	1.01074i
$563$			17.6227i			0.742707i	0.928492	+	0.371353i	$0.121106\pi$
$563$			17.6227i			0.742707i	−0.928492	+	0.371353i	$0.878894\pi$
$564$		0			0
$565$	5.22479			0.219808
$566$	−16.6522	+	10.0955i	−0.699946	+	0.424344i
$567$		0			0
$568$	−1.84991	−	28.7677i	−0.0776205	−	1.20706i
$569$	−13.5389			−0.567580			−0.283790	−	0.958887i	$-0.591592\pi$
$569$	−13.5389			−0.567580			−0.283790	+	0.958887i	$0.591592\pi$
$570$		0			0
$571$	30.2145			1.26444			0.632218	−	0.774790i	$-0.282145\pi$
$571$	30.2145			1.26444			0.632218	+	0.774790i	$0.282145\pi$
$572$	−27.8027	+	53.3015i	−1.16249	+	2.22865i
$573$		0			0
$574$	−5.40157	−	0.544864i	−0.225457	−	0.0227422i
$575$		−	6.48080i		−	0.270268i
$576$		0			0
$577$		−	38.1570i		−	1.58850i	−0.607593	−	0.794249i	$-0.707865\pi$
$577$		−	38.1570i		−	1.58850i	0.607593	−	0.794249i	$-0.292135\pi$
$578$	−4.40088	−	7.25915i	−0.183052	−	0.301941i
$579$		0			0
$580$	11.7611	+	6.13473i	0.488352	+	0.254731i
$581$	25.6086	−	34.0005i	1.06242	−	1.41058i
$582$		0			0
$583$		−	18.5283i		−	0.767363i
$584$	1.20384	+	18.7208i	0.0498153	+	0.774670i
$585$		0			0
$586$	−18.5375	−	30.5772i	−0.765777	−	1.26313i
$587$		−	35.7057i		−	1.47373i	−0.676039	−	0.736866i	$-0.736305\pi$
$587$		−	35.7057i		−	1.47373i	0.676039	−	0.736866i	$-0.263695\pi$
$588$		0			0
$589$			45.3441i			1.86837i
$590$	1.04641	−	0.634388i	0.0430800	−	0.0261173i
$591$		0			0
$592$	5.42512	−	3.78543i	0.222971	−	0.155580i
$593$			16.9630i			0.696587i	0.937386	+	0.348293i	$0.113239\pi$
$593$			16.9630i			0.696587i	−0.937386	+	0.348293i	$0.886761\pi$
$594$		0			0
$595$	−5.95357	+	7.90454i	−0.244073	+	0.324054i
$596$	−7.43753	−	3.87951i	−0.304653	−	0.158911i
$597$		0			0
$598$	−12.3630	+	7.49510i	−0.505561	+	0.306498i
$599$			30.2372i			1.23546i	0.786391	+	0.617729i	$0.211947\pi$
$599$			30.2372i			1.23546i	−0.786391	+	0.617729i	$0.788053\pi$
$600$		0			0
$601$			29.4558i			1.20153i	0.799426	+	0.600764i	$0.205137\pi$
$601$			29.4558i			1.20153i	−0.799426	+	0.600764i	$0.794863\pi$
$602$	0.674167	−	6.68342i	0.0274770	−	0.272396i
$603$		0			0
$604$	17.3757	+	9.06340i	0.707009	+	0.368785i
$605$	−17.0618			−0.693663
$606$		0			0
$607$	−21.7031			−0.880902			−0.440451	−	0.897777i	$-0.645182\pi$
$607$	−21.7031			−0.880902			−0.440451	+	0.897777i	$0.645182\pi$
$608$	38.7729	+	17.1557i	1.57245	+	0.695754i
$609$		0			0
$610$	−0.262289	−	0.432640i	−0.0106198	−	0.0175171i
$611$	32.7155			1.32353
$612$		0			0
$613$			41.0159i			1.65662i	0.560273	+	0.828308i	$0.310696\pi$
$613$			41.0159i			1.65662i	−0.560273	+	0.828308i	$0.689304\pi$
$614$	7.20849	−	4.37017i	0.290911	−	0.176366i
$615$		0			0
$616$	−31.9679	−	21.0047i	−1.28802	−	0.846303i
$617$	−42.2551			−1.70113			−0.850564	−	0.525872i	$-0.823739\pi$
$617$	−42.2551			−1.70113			−0.850564	+	0.525872i	$0.823739\pi$
$618$		0			0
$619$			14.5442i			0.584579i	0.956330	+	0.292290i	$0.0944171\pi$
$619$			14.5442i			0.584579i	−0.956330	+	0.292290i	$0.905583\pi$
$620$	−6.31132	+	12.0996i	−0.253469	+	0.485933i
$621$		0			0
$622$	19.3644	+	31.9412i	0.776442	+	1.28072i
$623$	−12.8668	+	17.0832i	−0.515498	+	0.684425i
$624$		0			0
$625$	7.53699			0.301480
$626$	11.5302	−	6.99021i	0.460839	−	0.279385i
$627$		0			0
$628$	4.46629	−	8.56247i	0.178224	−	0.341680i
$629$	5.48441			0.218678
$630$		0			0
$631$		−	11.6986i		−	0.465713i	−0.972511	−	0.232857i	$-0.925193\pi$
$631$		−	11.6986i		−	0.465713i	0.972511	−	0.232857i	$-0.0748073\pi$
$632$	−0.547105	−	8.50795i	−0.0217627	−	0.338428i
$633$		0			0
$634$	30.0063	−	18.1914i	1.19170	−	0.722472i
$635$			10.5808i			0.419885i
$636$		0			0
$637$	−11.3650	−	39.5638i	−0.450296	−	1.56758i
$638$	−36.3506	+	22.0376i	−1.43913	+	0.872479i
$639$		0			0
$640$	7.95833	+	9.97453i	0.314581	+	0.394278i
$641$	11.5344			0.455580			0.227790	−	0.973710i	$-0.426850\pi$
$641$	11.5344			0.455580			0.227790	+	0.973710i	$0.426850\pi$
$642$		0			0
$643$		−	13.7698i		−	0.543028i	−0.962434	−	0.271514i	$-0.912476\pi$
$643$		−	13.7698i		−	0.543028i	0.962434	−	0.271514i	$-0.0875244\pi$
$644$	−3.95541	−	8.30521i	−0.155865	−	0.327271i
$645$		0			0
$646$	18.2230	+	30.0585i	0.716975	+	1.18263i
$647$	−18.7149			−0.735758			−0.367879	−	0.929874i	$-0.619916\pi$
$647$	−18.7149			−0.735758			−0.367879	+	0.929874i	$0.619916\pi$
$648$		0			0
$649$			3.92147i			0.153931i
$650$	−16.0725	−	26.5112i	−0.630414	−	1.03985i
$651$		0			0
$652$	1.32965	−	2.54912i	0.0520732	−	0.0998313i
$653$		−	19.5588i		−	0.765395i	−0.923874	−	0.382697i	$-0.874995\pi$
$653$		−	19.5588i		−	0.765395i	0.923874	−	0.382697i	$-0.125005\pi$
$654$		0			0
$655$		−	7.01873i		−	0.274245i
$656$	−4.75968	+	3.32111i	−0.185834	+	0.129668i
$657$		0			0
$658$	−2.08915	+	20.7110i	−0.0814437	+	0.807400i
$659$	2.56735			0.100010			0.0500050	−	0.998749i	$-0.484076\pi$
$659$	2.56735			0.100010			0.0500050	+	0.998749i	$0.484076\pi$
$660$		0			0
$661$	9.00155			0.350120			0.175060	−	0.984558i	$-0.443988\pi$
$661$	9.00155			0.350120			0.175060	+	0.984558i	$0.443988\pi$
$662$	−6.93890	−	11.4456i	−0.269688	−	0.444844i
$663$		0			0
$664$	−2.92015	−	45.4108i	−0.113324	−	1.76228i
$665$	−13.4558	+	17.8653i	−0.521795	+	0.692786i
$666$		0			0
$667$	−10.2230			−0.395837
$668$	14.8378	−	28.4461i	0.574092	−	1.10061i
$669$		0			0
$670$	−5.42653	−	8.95095i	−0.209645	−	0.345805i
$671$	1.62134			0.0625912
$672$		0			0
$673$	−28.7645			−1.10879			−0.554396	−	0.832253i	$-0.687051\pi$
$673$	−28.7645			−1.10879			−0.554396	+	0.832253i	$0.687051\pi$
$674$	26.1818	+	43.1863i	1.00849	+	1.66347i
$675$		0			0
$676$	−19.9613	+	38.2684i	−0.767741	+	1.47186i
$677$	−17.2485			−0.662912			−0.331456	−	0.943471i	$-0.607540\pi$
$677$	−17.2485			−0.662912			−0.331456	+	0.943471i	$0.607540\pi$
$678$		0			0
$679$	−0.569453	+	0.756061i	−0.0218536	+	0.0290150i
$680$	0.678885	+	10.5572i	0.0260341	+	0.404852i
$681$		0			0
$682$	−22.6720	−	37.3970i	−0.868157	−	1.43201i
$683$	26.2096			1.00288			0.501441	−	0.865192i	$-0.332803\pi$
$683$	26.2096			1.00288			0.501441	+	0.865192i	$0.332803\pi$
$684$		0			0
$685$	8.40918			0.321298
$686$	25.7722	−	4.66828i	0.983988	−	0.178236i
$687$		0			0
$688$	−4.10925	−	5.88921i	−0.156664	−	0.224524i
$689$		−	21.3159i		−	0.812070i
$690$		0			0
$691$			2.99021i			0.113753i	0.998381	+	0.0568765i	$0.0181141\pi$
$691$			2.99021i			0.113753i	−0.998381	+	0.0568765i	$0.981886\pi$
$692$	3.71645	−	7.12494i	0.141278	−	0.270849i
$693$		0			0
$694$	−19.3381	−	31.8978i	−0.734065	−	1.21082i
$695$		−	2.56556i		−	0.0973173i
$696$		0			0
$697$	−4.81170			−0.182256
$698$	5.79590	+	9.56021i	0.219378	+	0.361859i
$699$		0			0
$700$	17.8096	−	8.48195i	0.673141	−	0.320588i
$701$			18.1971i			0.687294i	0.939099	+	0.343647i	$0.111662\pi$
$701$			18.1971i			0.687294i	−0.939099	+	0.343647i	$0.888338\pi$
$702$		0			0
$703$	12.3955			0.467504
$704$	−40.5553	+	5.23749i	−1.52849	+	0.197395i
$705$		0			0
$706$	−17.5946	+	10.6668i	−0.662181	+	0.401449i
$707$	7.15078	+	5.38585i	0.268933	+	0.202556i
$708$		0			0
$709$		−	4.86735i		−	0.182797i	−0.995814	−	0.0913986i	$-0.970866\pi$
$709$		−	4.86735i		−	0.182797i	0.995814	−	0.0913986i	$-0.0291337\pi$
$710$	13.9014	−	8.42774i	0.521709	−	0.316288i
$711$		0			0
$712$	1.46720	+	22.8162i	0.0549857	+	0.855074i
$713$		−	10.5173i		−	0.393876i
$714$		0			0
$715$	−33.9019			−1.26786
$716$	−6.45322	+	12.3717i	−0.241168	+	0.462351i
$717$		0			0
$718$	25.7812	−	15.6299i	0.962147	−	0.583304i
$719$	−7.10575			−0.265000			−0.132500	−	0.991183i	$-0.542300\pi$
$719$	−7.10575			−0.265000			−0.132500	+	0.991183i	$0.542300\pi$
$720$		0			0
$721$	30.6508	+	23.0857i	1.14149	+	0.859755i
$722$	27.2564	+	44.9588i	1.01438	+	1.67319i
$723$		0			0
$724$	12.4580	−	23.8836i	0.462997	−	0.887626i
$725$		−	21.9222i		−	0.814170i
$726$		0			0
$727$	−42.5369			−1.57761			−0.788803	−	0.614645i	$-0.789299\pi$
$727$	−42.5369			−1.57761			−0.788803	+	0.614645i	$0.789299\pi$
$728$	−36.7775	−	24.1648i	−1.36306	−	0.895609i
$729$		0			0
$730$	−9.04641	+	5.48441i	−0.334823	+	0.202987i
$731$		−	5.95357i		−	0.220201i
$732$		0			0
$733$	−38.8291			−1.43419			−0.717093	−	0.696977i	$-0.754528\pi$
$733$	−38.8291			−1.43419			−0.717093	+	0.696977i	$0.754528\pi$
$734$	−5.05877	−	8.34433i	−0.186723	−	0.307995i
$735$		0			0
$736$	−8.99316	−	3.97916i	−0.331492	−	0.146674i
$737$	33.5441			1.23561
$738$		0			0
$739$	−27.0085			−0.993524			−0.496762	−	0.867887i	$-0.665478\pi$
$739$	−27.0085			−0.993524			−0.496762	+	0.867887i	$0.665478\pi$
$740$	3.30762	+	1.72529i	0.121590	+	0.0634231i
$741$		0			0
$742$	13.4943	+	1.36119i	0.495392	+	0.0499710i
$743$		−	28.0242i		−	1.02811i	−0.857758	−	0.514054i	$-0.828143\pi$
$743$		−	28.0242i		−	1.02811i	0.857758	−	0.514054i	$-0.171857\pi$
$744$		0			0
$745$		−	4.73057i		−	0.173315i
$746$	−32.1459	+	19.4885i	−1.17694	+	0.713525i
$747$		0			0
$748$	−30.0585	−	15.6789i	−1.09905	−	0.573276i
$749$	3.97038	+	2.99042i	0.145074	+	0.109268i
$750$		0			0
$751$			46.6071i			1.70072i	0.526204	+	0.850358i	$0.323615\pi$
$751$			46.6071i			1.70072i	−0.526204	+	0.850358i	$0.676385\pi$
$752$	12.7340	+	18.2499i	0.464362	+	0.665504i
$753$		0			0
$754$	−41.8196	+	25.3532i	−1.52298	+	0.923310i
$755$			11.0517i			0.402211i
$756$		0			0
$757$		−	18.9934i		−	0.690326i	−0.938543	−	0.345163i	$-0.887824\pi$
$757$		−	18.9934i		−	0.690326i	0.938543	−	0.345163i	$-0.112176\pi$
$758$	−4.05131	−	6.68255i	−0.147150	−	0.242721i
$759$		0			0
$760$	1.53437	+	23.8607i	0.0556574	+	0.865520i
$761$		−	25.9487i		−	0.940639i	−0.882496	−	0.470320i	$-0.844139\pi$
$761$		−	25.9487i		−	0.940639i	0.882496	−	0.470320i	$-0.155861\pi$
$762$		0			0
$763$	−21.6743	+	28.7770i	−0.784664	+	1.04180i
$764$	−37.3633	−	19.4892i	−1.35176	−	0.705093i
$765$		0			0
$766$	7.60333	+	12.5415i	0.274719	+	0.453143i
$767$			4.51146i			0.162899i
$768$		0			0
$769$		−	5.27924i		−	0.190374i	−0.995459	−	0.0951872i	$-0.969655\pi$
$769$		−	5.27924i		−	0.190374i	0.995459	−	0.0951872i	$-0.0303450\pi$
$770$	2.16492	−	21.4621i	0.0780181	−	0.773440i
$771$		0			0
$772$	4.75182	−	9.10987i	0.171022	−	0.327871i
$773$	5.30076			0.190655			0.0953276	−	0.995446i	$-0.469610\pi$
$773$	5.30076			0.190655			0.0953276	+	0.995446i	$0.469610\pi$
$774$		0			0
$775$	22.5533			0.810137
$776$	0.0649347	+	1.00979i	0.00233102	+	0.0362494i
$777$		0			0
$778$	−14.7904	+	8.96671i	−0.530261	+	0.321472i
$779$	−10.8751			−0.389640
$780$		0			0
$781$			52.0961i			1.86415i
$782$	−4.22673	−	6.97190i	−0.151148	−	0.249315i
$783$		0			0
$784$	17.6465	−	21.7394i	0.630231	−	0.776408i
$785$	5.44607			0.194379
$786$		0			0
$787$			15.7305i			0.560733i	0.959893	+	0.280367i	$0.0904561\pi$
$787$			15.7305i			0.560733i	−0.959893	+	0.280367i	$0.909544\pi$
$788$	46.8738	+	24.4499i	1.66981	+	0.870993i
$789$		0			0
$790$	4.11129	−	2.49248i	0.146273	−	0.0886784i
$791$	−9.79008	−	7.37373i	−0.348095	−	0.262180i
$792$		0			0
$793$	1.86527			0.0662378
$794$	5.50008	+	9.07225i	0.195190	+	0.321962i
$795$		0			0
$796$	10.0283	−	19.2257i	0.355445	−	0.681435i
$797$	−8.71605			−0.308738			−0.154369	−	0.988013i	$-0.549335\pi$
$797$	−8.71605			−0.308738			−0.154369	+	0.988013i	$0.549335\pi$
$798$		0			0
$799$			18.4493i			0.652691i
$800$	8.53290	−	19.2849i	0.301683	−	0.681823i
$801$		0			0
$802$	8.39896	+	13.8539i	0.296577	+	0.489198i
$803$		−	33.9019i		−	1.19637i
$804$		0			0
$805$	3.12101	−	4.14375i	0.110001	−	0.146048i
$806$	−26.0830	−	43.0234i	−0.918736	−	1.51543i
$807$		0			0
$808$	9.55053	−	0.614148i	0.335986	−	0.0216057i
$809$	−4.28448			−0.150634			−0.0753171	−	0.997160i	$-0.523997\pi$
$809$	−4.28448			−0.150634			−0.0753171	+	0.997160i	$0.523997\pi$
$810$		0			0
$811$		−	30.7208i		−	1.07875i	−0.842065	−	0.539376i	$-0.818660\pi$
$811$		−	30.7208i		−	1.07875i	0.842065	−	0.539376i	$-0.181340\pi$
$812$	−13.3797	−	28.0935i	−0.469536	−	0.985889i
$813$		0			0
$814$	−10.2230	+	6.19774i	−0.358317	+	0.217231i
$815$	1.62134			0.0567931
$816$		0			0
$817$		−	13.4558i		−	0.470760i
$818$	−35.8236	+	21.7181i	−1.25254	+	0.759357i
$819$		0			0
$820$	−2.90191	−	1.51367i	−0.101339	−	0.0528597i
$821$		−	27.1897i		−	0.948928i	−0.880275	−	0.474464i	$-0.842642\pi$
$821$		−	27.1897i		−	0.948928i	0.880275	−	0.474464i	$-0.157358\pi$
$822$		0			0
$823$		−	49.5318i		−	1.72657i	−0.504715	−	0.863286i	$-0.668403\pi$
$823$		−	49.5318i		−	1.72657i	0.504715	−	0.863286i	$-0.331597\pi$
$824$	40.9369	−	2.63246i	1.42611	−	0.0917060i
$825$		0			0
$826$	−2.85605	−	0.288094i	−0.0993746	−	0.0100241i
$827$	−27.4228			−0.953585			−0.476793	−	0.879016i	$-0.658201\pi$
$827$	−27.4228			−0.953585			−0.476793	+	0.879016i	$0.658201\pi$
$828$		0			0
$829$	−44.3135			−1.53907			−0.769536	−	0.638603i	$-0.779513\pi$
$829$	−44.3135			−1.53907			−0.769536	+	0.638603i	$0.779513\pi$
$830$	21.9438	−	13.3035i	0.761680	−	0.461771i
$831$		0			0
$832$	−46.6569	+	6.02547i	−1.61754	+	0.208896i
$833$	22.3113	−	6.40907i	0.773042	−	0.222061i
$834$		0			0
$835$	18.0928			0.626128
$836$	−67.9360	−	35.4363i	−2.34962	−	1.22559i
$837$		0			0
$838$	21.5425	−	13.0602i	0.744173	−	0.451157i
$839$	52.9322			1.82742			0.913712	−	0.406362i	$-0.133203\pi$
$839$	52.9322			1.82742			0.913712	+	0.406362i	$0.133203\pi$
$840$		0			0
$841$	−5.58078			−0.192441
$842$	−16.2230	+	9.83525i	−0.559082	+	0.338945i
$843$		0			0
$844$	−9.06020	+	17.3696i	−0.311865	+	0.597886i
$845$	−24.3402			−0.837328
$846$		0			0
$847$	31.9701	+	24.0794i	1.09851	+	0.827377i
$848$	11.8907	−	8.29689i	0.408330	−	0.284916i
$849$		0			0
$850$	14.9505	−	9.06378i	0.512798	−	0.310885i
$851$	−2.87506			−0.0985559
$852$		0			0
$853$	23.8821			0.817707			0.408854	−	0.912600i	$-0.365929\pi$
$853$	23.8821			0.817707			0.408854	+	0.912600i	$0.365929\pi$
$854$	−0.119113	+	1.18084i	−0.00407597	+	0.0404075i
$855$		0			0
$856$	5.30281	−	0.340998i	0.181246	−	0.0116551i
$857$			46.2279i			1.57912i	0.613676	+	0.789558i	$0.289690\pi$
$857$			46.2279i			1.57912i	−0.613676	+	0.789558i	$0.710310\pi$
$858$		0			0
$859$		−	18.2159i		−	0.621517i	−0.950489	−	0.310759i	$-0.899417\pi$
$859$		−	18.2159i		−	0.621517i	0.950489	−	0.310759i	$-0.100583\pi$
$860$	1.87288	−	3.59057i	0.0638648	−	0.122437i
$861$		0			0
$862$	−21.2973	+	12.9115i	−0.725388	+	0.439769i
$863$		−	3.72055i		−	0.126649i	−0.997993	−	0.0633245i	$-0.979830\pi$
$863$		−	3.72055i		−	0.126649i	0.997993	−	0.0633245i	$-0.0201703\pi$
$864$		0			0
$865$	4.53174			0.154084
$866$	−44.0753	+	26.7208i	−1.49774	+	0.908008i
$867$		0			0
$868$	28.9022	−	13.7649i	0.981005	−	0.467210i
$869$			15.4073i			0.522656i
$870$		0			0
$871$	38.5909			1.30760
$872$	2.47152	+	38.4343i	0.0836964	+	1.30155i
$873$		0			0
$874$	−9.55296	−	15.7574i	−0.323134	−	0.533002i
$875$	20.8038	+	15.6691i	0.703297	+	0.529712i
$876$		0			0
$877$			19.1011i			0.644997i	0.946570	+	0.322498i	$0.104523\pi$
$877$			19.1011i			0.644997i	−0.946570	+	0.322498i	$0.895477\pi$
$878$	−3.51637	−	5.80017i	−0.118672	−	0.195746i
$879$		0			0
$880$	−13.1958	−	18.9117i	−0.444831	−	0.637513i
$881$			29.3993i			0.990487i	0.868754	+	0.495243i	$0.164921\pi$
$881$			29.3993i			0.990487i	−0.868754	+	0.495243i	$0.835079\pi$
$882$		0			0
$883$	−4.33944			−0.146034			−0.0730169	−	0.997331i	$-0.523263\pi$
$883$	−4.33944			−0.146034			−0.0730169	+	0.997331i	$0.523263\pi$
$884$	−34.5808	−	18.0378i	−1.16308	−	0.606676i
$885$		0			0
$886$	23.9758	+	39.5476i	0.805484	+	1.32863i
$887$	−8.74929			−0.293773			−0.146886	−	0.989153i	$-0.546925\pi$
$887$	−8.74929			−0.293773			−0.146886	+	0.989153i	$0.546925\pi$
$888$		0			0
$889$	14.9326	−	19.8260i	0.500825	−	0.664943i
$890$	−11.0255	+	6.68421i	−0.369574	+	0.224055i
$891$		0			0
$892$	−14.2012	+	27.2257i	−0.475493	+	0.911582i
$893$			41.6979i			1.39537i
$894$		0			0
$895$	−7.86887			−0.263027
$896$	−0.835090	−	29.9216i	−0.0278984	−	0.999611i
$897$		0			0
$898$	18.5841	+	30.6540i	0.620159	+	1.02294i
$899$		−	35.5762i		−	1.18653i
$900$		0			0
$901$	12.0207			0.400468
$902$	8.96909	−	5.43753i	0.298638	−	0.181050i
$903$		0			0
$904$	−13.0756	+	0.840826i	−0.434887	+	0.0279655i
$905$	15.1909			0.504963
$906$		0			0
$907$	40.5946			1.34792			0.673960	−	0.738768i	$-0.264592\pi$
$907$	40.5946			1.34792			0.673960	+	0.738768i	$0.264592\pi$
$908$	−10.4007	−	5.42512i	−0.345158	−	0.180039i
$909$		0			0
$910$	2.49063	−	24.6911i	0.0825635	−	0.818502i
$911$		−	30.4887i		−	1.01014i	−0.863079	−	0.505068i	$-0.831467\pi$
$911$		−	30.4887i		−	1.01014i	0.863079	−	0.505068i	$-0.168533\pi$
$912$		0			0
$913$			82.2355i			2.72160i
$914$	1.22371	+	2.01849i	0.0404768	+	0.0667656i
$915$		0			0
$916$	−2.37984	+	4.56247i	−0.0786321	+	0.150748i
$917$	−9.90553	+	13.1515i	−0.327109	+	0.434302i
$918$		0			0
$919$		−	16.6925i		−	0.550634i	−0.961353	−	0.275317i	$-0.911217\pi$
$919$		−	16.6925i		−	0.550634i	0.961353	−	0.275317i	$-0.0887828\pi$
$920$	−0.355889	−	5.53437i	−0.0117333	−	0.182463i
$921$		0			0
$922$	24.2123	+	39.9376i	0.797388	+	1.31527i
$923$			59.9340i			1.97275i
$924$		0			0
$925$		−	6.16527i		−	0.202713i
$926$	−18.9663	+	11.4984i	−0.623272	+	0.377860i
$927$		0			0
$928$	−30.4206	−	13.4601i	−0.998604	−	0.441848i
$929$			44.6963i			1.46644i	0.679993	+	0.733219i	$0.261983\pi$
$929$			44.6963i			1.46644i	−0.679993	+	0.733219i	$0.738017\pi$
$930$		0			0
$931$	50.4265	−	14.4853i	1.65266	−	0.474737i
$932$	−18.1501	+	34.7961i	−0.594526	+	1.13979i
$933$		0			0
$934$	−5.87188	+	3.55984i	−0.192134	+	0.116482i
$935$		−	19.1184i		−	0.625238i
$936$		0			0
$937$			58.7208i			1.91832i	0.282858	+	0.959162i	$0.408717\pi$
$937$			58.7208i			1.91832i	−0.282858	+	0.959162i	$0.591283\pi$
$938$	−2.46435	+	24.4305i	−0.0804637	+	0.797685i
$939$		0			0
$940$	−5.80382	+	11.1267i	−0.189300	+	0.362913i
$941$	28.7137			0.936040			0.468020	−	0.883718i	$-0.344967\pi$
$941$	28.7137			0.936040			0.468020	+	0.883718i	$0.344967\pi$
$942$		0			0
$943$	2.52241			0.0821411
$944$	−2.51665	+	1.75602i	−0.0819101	+	0.0571536i
$945$		0			0
$946$	6.72792	+	11.0976i	0.218744	+	0.360813i
$947$	−40.7146			−1.32305			−0.661523	−	0.749925i	$-0.730090\pi$
$947$	−40.7146			−1.32305			−0.661523	+	0.749925i	$0.730090\pi$
$948$		0			0
$949$		−	39.0024i		−	1.26607i
$950$	33.7901	−	20.4853i	1.09629	−	0.664631i
$951$		0			0
$952$	13.6273	−	20.7400i	0.441665	−	0.672188i
$953$	25.5396			0.827309			0.413655	−	0.910434i	$-0.364252\pi$
$953$	25.5396			0.827309			0.413655	+	0.910434i	$0.364252\pi$
$954$		0			0
$955$		−	23.7646i		−	0.769003i
$956$	−0.617095	−	0.321884i	−0.0199583	−	0.0104105i
$957$		0			0
$958$	5.20965	+	8.59319i	0.168316	+	0.277633i
$959$	−15.7569	−	11.8679i	−0.508818	−	0.383233i
$960$		0			0
$961$	5.60036			0.180657
$962$	−11.7611	+	7.13019i	−0.379193	+	0.229887i
$963$		0			0
$964$	−35.6218	−	18.5808i	−1.14730	−	0.598447i
$965$	5.79424			0.186523
$966$		0			0
$967$		−	20.8465i		−	0.670378i	−0.942151	−	0.335189i	$-0.891200\pi$
$967$		−	20.8465i		−	0.670378i	0.942151	−	0.335189i	$-0.108800\pi$
$968$	42.6990	−	2.74577i	1.37240	−	0.0882523i
$969$		0			0
$970$	−0.487960	+	0.295827i	−0.0156674	+	0.00949843i
$971$			35.1302i			1.12738i	0.825986	+	0.563691i	$0.190619\pi$
$971$			35.1302i			1.12738i	−0.825986	+	0.563691i	$0.809381\pi$
$972$		0			0
$973$	−3.62077	+	4.80729i	−0.116077	+	0.154115i
$974$	5.19650	−	3.15039i	0.166507	−	0.100945i
$975$		0			0
$976$	0.726031	+	1.04052i	0.0232397	+	0.0333061i
$977$	−8.63246			−0.276177			−0.138088	−	0.990420i	$-0.544096\pi$
$977$	−8.63246			−0.276177			−0.138088	+	0.990420i	$0.544096\pi$
$978$		0			0
$979$		−	41.3185i		−	1.32054i
$980$	15.4720	+	3.15346i	0.494235	+	0.100734i
$981$		0			0
$982$	−14.2132	−	23.4443i	−0.453561	−	0.748138i
$983$	25.0646			0.799436			0.399718	−	0.916638i	$-0.369108\pi$
$983$	25.0646			0.799436			0.399718	+	0.916638i	$0.369108\pi$
$984$		0			0
$985$			29.8136i			0.949940i
$986$	−14.2975	−	23.5834i	−0.455325	−	0.751049i
$987$		0			0
$988$	−78.1570	−	40.7677i	−2.48651	−	1.29699i
$989$			3.12101i			0.0992424i
$990$		0			0
$991$		−	10.3855i		−	0.329907i	−0.986301	−	0.164954i	$-0.947253\pi$
$991$		−	10.3855i		−	0.329907i	0.986301	−	0.164954i	$-0.0527474\pi$
$992$	13.8475	−	31.2963i	0.439660	−	0.993658i
$993$		0			0
$994$	−37.9421	−	3.82728i	−1.20345	−	0.121394i
$995$	12.2283			0.387662
$996$		0			0
$997$	−50.1424			−1.58803			−0.794013	−	0.607900i	$-0.792012\pi$
$997$	−50.1424			−1.58803			−0.794013	+	0.607900i	$0.792012\pi$
$998$	22.4143	+	36.9719i	0.709513	+	1.17033i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.p.g.307.5		16
3.2	odd	2		168.2.p.a.139.11	yes	16
4.3	odd	2		2016.2.p.g.559.7		16
7.6	odd	2	inner	504.2.p.g.307.6		16
8.3	odd	2	inner	504.2.p.g.307.8		16
8.5	even	2		2016.2.p.g.559.10		16
12.11	even	2		672.2.p.a.559.13		16
21.20	even	2		168.2.p.a.139.12	yes	16
24.5	odd	2		672.2.p.a.559.12		16
24.11	even	2		168.2.p.a.139.9	✓	16
28.27	even	2		2016.2.p.g.559.9		16
56.13	odd	2		2016.2.p.g.559.8		16
56.27	even	2	inner	504.2.p.g.307.7		16
84.83	odd	2		672.2.p.a.559.4		16
168.83	odd	2		168.2.p.a.139.10	yes	16
168.125	even	2		672.2.p.a.559.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.p.a.139.9	✓	16	24.11	even	2
168.2.p.a.139.10	yes	16	168.83	odd	2
168.2.p.a.139.11	yes	16	3.2	odd	2
168.2.p.a.139.12	yes	16	21.20	even	2
504.2.p.g.307.5		16	1.1	even	1	trivial
504.2.p.g.307.6		16	7.6	odd	2	inner
504.2.p.g.307.7		16	56.27	even	2	inner
504.2.p.g.307.8		16	8.3	odd	2	inner
672.2.p.a.559.4		16	84.83	odd	2
672.2.p.a.559.5		16	168.125	even	2
672.2.p.a.559.12		16	24.5	odd	2
672.2.p.a.559.13		16	12.11	even	2
2016.2.p.g.559.7		16	4.3	odd	2
2016.2.p.g.559.8		16	56.13	odd	2
2016.2.p.g.559.9		16	28.27	even	2
2016.2.p.g.559.10		16	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.733159 - 1.20933i) q^{2} +(-0.924955 + 1.77326i) q^{4} -1.12786 q^{5} +(2.11337 + 1.59175i) q^{7} +(2.82260 - 0.181508i) q^{8} +O(q^{10})\)	\(q+(-0.733159 - 1.20933i) q^{2} +(-0.924955 + 1.77326i) q^{4} -1.12786 q^{5} +(2.11337 + 1.59175i) q^{7} +(2.82260 - 0.181508i) q^{8} +(0.826905 + 1.36396i) q^{10} -5.11151 q^{11} -5.88054 q^{13} +(0.375521 - 3.72277i) q^{14} +(-2.28892 - 3.28038i) q^{16} -3.31623i q^{17} -7.49510i q^{19} +(1.04322 - 2.00000i) q^{20} +(3.74755 + 6.18150i) q^{22} +1.73845i q^{23} -3.72792 q^{25} +(4.31137 + 7.11151i) q^{26} +(-4.77737 + 2.27525i) q^{28} +5.88054i q^{29} -6.04982 q^{31} +(-2.28892 + 5.17309i) q^{32} +(-4.01041 + 2.43132i) q^{34} +(-2.38359 - 1.79528i) q^{35} +1.65381i q^{37} +(-9.06405 + 5.49510i) q^{38} +(-3.18351 + 0.204716i) q^{40} -1.45096i q^{41} +1.79528 q^{43} +(4.72792 - 9.06405i) q^{44} +(2.10236 - 1.27456i) q^{46} -5.56335 q^{47} +(1.93264 + 6.72792i) q^{49} +(2.73316 + 4.50828i) q^{50} +(5.43924 - 10.4277i) q^{52} +3.62481i q^{53} +5.76510 q^{55} +(6.25410 + 4.10929i) q^{56} +(7.11151 - 4.31137i) q^{58} -0.767184i q^{59} -0.317194 q^{61} +(4.43548 + 7.31623i) q^{62} +(7.93411 - 1.02465i) q^{64} +6.63246 q^{65} -6.56247 q^{67} +(5.88054 + 3.06736i) q^{68} +(-0.423537 + 4.19878i) q^{70} -10.1919i q^{71} +6.63246i q^{73} +(2.00000 - 1.21251i) q^{74} +(13.2908 + 6.93264i) q^{76} +(-10.8025 - 8.13627i) q^{77} -3.01423i q^{79} +(2.58159 + 3.69982i) q^{80} +(-1.75468 + 1.06378i) q^{82} -16.0883i q^{83} +3.74026i q^{85} +(-1.31623 - 2.17109i) q^{86} +(-14.4277 + 0.927779i) q^{88} +8.08341i q^{89} +(-12.4277 - 9.36038i) q^{91} +(-3.08273 - 1.60799i) q^{92} +(4.07882 + 6.72792i) q^{94} +8.45347i q^{95} +0.357752i q^{97} +(6.71934 - 7.26983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8	\( 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8} + 8 q^{11} + 14 q^{14} + 18 q^{16} + 8 q^{22} + 16 q^{25} - 10 q^{28} + 18 q^{32} - 24 q^{35} - 8 q^{43} + 52 q^{46} - 8 q^{49} + 34 q^{50} - 50 q^{56} + 24 q^{58} + 2 q^{64} - 40 q^{67} - 24 q^{70} + 32 q^{74} + 32 q^{86} - 88 q^{88} - 56 q^{91} - 44 q^{92} - 66 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8 + 8 * q^11 + 14 * q^14 + 18 * q^16 + 8 * q^22 + 16 * q^25 - 10 * q^28 + 18 * q^32 - 24 * q^35 - 8 * q^43 + 52 * q^46 - 8 * q^49 + 34 * q^50 - 50 * q^56 + 24 * q^58 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 32 * q^74 + 32 * q^86 - 88 * q^88 - 56 * q^91 - 44 * q^92 - 66 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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