LMFDB - Embedded newform 504.2.c.d.253.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(253,504)]

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([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("504.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.c (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:	$4$
Coefficient field:	4.0.2312.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x + 4 $ x^4 - x^3 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			253.3
Root			$1.28078 - 0.599676i$ of defining polynomial
Character	$\chi$	$=$	504.253
Dual form			504.2.c.d.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28078 - 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} -3.33513i q^{5} -1.00000 q^{7} +(0.719224 - 2.73546i) q^{8} +O(q^{10})$	\(q+(1.28078 - 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} -3.33513i q^{5} -1.00000 q^{7} +(0.719224 - 2.73546i) q^{8} +(-2.00000 - 4.27156i) q^{10} +4.27156i q^{11} -3.33513i q^{13} +(-1.28078 + 0.599676i) q^{14} +(-0.719224 - 3.93481i) q^{16} -2.00000 q^{17} +0.936426i q^{19} +(-5.12311 - 4.27156i) q^{20} +(2.56155 + 5.47091i) q^{22} +3.12311 q^{23} -6.12311 q^{25} +(-2.00000 - 4.27156i) q^{26} +(-1.28078 + 1.53610i) q^{28} +1.87285i q^{29} +6.24621 q^{31} +(-3.28078 - 4.60831i) q^{32} +(-2.56155 + 1.19935i) q^{34} +3.33513i q^{35} +1.87285i q^{37} +(0.561553 + 1.19935i) q^{38} +(-9.12311 - 2.39871i) q^{40} +12.2462 q^{41} -4.27156i q^{43} +(6.56155 + 5.47091i) q^{44} +(4.00000 - 1.87285i) q^{46} +1.00000 q^{49} +(-7.84233 + 3.67188i) q^{50} +(-5.12311 - 4.27156i) q^{52} +8.54312i q^{53} +14.2462 q^{55} +(-0.719224 + 2.73546i) q^{56} +(1.12311 + 2.39871i) q^{58} -7.60669i q^{59} -3.33513i q^{61} +(8.00000 - 3.74571i) q^{62} +(-6.96543 - 3.93481i) q^{64} -11.1231 q^{65} +15.7392i q^{67} +(-2.56155 + 3.07221i) q^{68} +(2.00000 + 4.27156i) q^{70} +8.00000 q^{71} -6.00000 q^{73} +(1.12311 + 2.39871i) q^{74} +(1.43845 + 1.19935i) q^{76} -4.27156i q^{77} +(-13.1231 + 2.39871i) q^{80} +(15.6847 - 7.34376i) q^{82} +9.47954i q^{83} +6.67026i q^{85} +(-2.56155 - 5.47091i) q^{86} +(11.6847 + 3.07221i) q^{88} -0.246211 q^{89} +3.33513i q^{91} +(4.00000 - 4.79741i) q^{92} +3.12311 q^{95} -4.24621 q^{97} +(1.28078 - 0.599676i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} - 4 q^{7} + 7 q^{8}+O(q^{10}) $ 4 * q + q^2 + q^4 - 4 * q^7 + 7 * q^8	$ 4 q + q^{2} + q^{4} - 4 q^{7} + 7 q^{8} - 8 q^{10} - q^{14} - 7 q^{16} - 8 q^{17} - 4 q^{20} + 2 q^{22} - 4 q^{23} - 8 q^{25} - 8 q^{26} - q^{28} - 8 q^{31} - 9 q^{32} - 2 q^{34} - 6 q^{38} - 20 q^{40} + 16 q^{41} + 18 q^{44} + 16 q^{46} + 4 q^{49} - 19 q^{50} - 4 q^{52} + 24 q^{55} - 7 q^{56} - 12 q^{58} + 32 q^{62} + q^{64} - 28 q^{65} - 2 q^{68} + 8 q^{70} + 32 q^{71} - 24 q^{73} - 12 q^{74} + 14 q^{76} - 36 q^{80} + 38 q^{82} - 2 q^{86} + 22 q^{88} + 32 q^{89} + 16 q^{92} - 4 q^{95} + 16 q^{97} + q^{98}+O(q^{100}) $ 4 * q + q^2 + q^4 - 4 * q^7 + 7 * q^8 - 8 * q^10 - q^14 - 7 * q^16 - 8 * q^17 - 4 * q^20 + 2 * q^22 - 4 * q^23 - 8 * q^25 - 8 * q^26 - q^28 - 8 * q^31 - 9 * q^32 - 2 * q^34 - 6 * q^38 - 20 * q^40 + 16 * q^41 + 18 * q^44 + 16 * q^46 + 4 * q^49 - 19 * q^50 - 4 * q^52 + 24 * q^55 - 7 * q^56 - 12 * q^58 + 32 * q^62 + q^64 - 28 * q^65 - 2 * q^68 + 8 * q^70 + 32 * q^71 - 24 * q^73 - 12 * q^74 + 14 * q^76 - 36 * q^80 + 38 * q^82 - 2 * q^86 + 22 * q^88 + 32 * q^89 + 16 * q^92 - 4 * q^95 + 16 * q^97 + 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 $

$2$	1.28078	−	0.599676i	0.905646	−	0.424035i
$2$	1.28078	−	0.599676i	0.905646	−	0.424035i
$3$		0			0
$3$		0			0
$4$	1.28078	−	1.53610i	0.640388	−	0.768051i
$5$		−	3.33513i		−	1.49152i	−0.666217	−	0.745758i	$-0.732087\pi$
$5$		−	3.33513i		−	1.49152i	0.666217	−	0.745758i	$-0.267913\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.719224	−	2.73546i	0.254284	−	0.967130i
$9$		0			0
$10$	−2.00000	−	4.27156i	−0.632456	−	1.35079i
$11$			4.27156i			1.28792i	0.765058	+	0.643962i	$0.222710\pi$
$11$			4.27156i			1.28792i	−0.765058	+	0.643962i	$0.777290\pi$
$12$		0			0
$13$		−	3.33513i		−	0.924999i	−0.886619	−	0.462500i	$-0.846953\pi$
$13$		−	3.33513i		−	0.924999i	0.886619	−	0.462500i	$-0.153047\pi$
$14$	−1.28078	+	0.599676i	−0.342302	+	0.160270i
$15$		0			0
$16$	−0.719224	−	3.93481i	−0.179806	−	0.983702i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$			0.936426i			0.214831i	0.994214	+	0.107415i	$0.0342575\pi$
$19$			0.936426i			0.214831i	−0.994214	+	0.107415i	$0.965742\pi$
$20$	−5.12311	−	4.27156i	−1.14556	−	0.955149i
$21$		0			0
$22$	2.56155	+	5.47091i	0.546125	+	1.16640i
$23$	3.12311			0.651213			0.325606	−	0.945505i	$-0.394432\pi$
$23$	3.12311			0.651213			0.325606	+	0.945505i	$0.394432\pi$
$24$		0			0
$25$	−6.12311			−1.22462
$26$	−2.00000	−	4.27156i	−0.392232	−	0.837722i
$27$		0			0
$28$	−1.28078	+	1.53610i	−0.242044	+	0.290296i
$29$			1.87285i			0.347780i	0.984765	+	0.173890i	$0.0556337\pi$
$29$			1.87285i			0.347780i	−0.984765	+	0.173890i	$0.944366\pi$
$30$		0			0
$31$	6.24621			1.12185			0.560926	−	0.827866i	$-0.310445\pi$
$31$	6.24621			1.12185			0.560926	+	0.827866i	$0.310445\pi$
$32$	−3.28078	−	4.60831i	−0.579965	−	0.814642i
$33$		0			0
$34$	−2.56155	+	1.19935i	−0.439303	+	0.205687i
$35$			3.33513i			0.563740i
$36$		0			0
$37$			1.87285i			0.307895i	0.988079	+	0.153948i	$0.0491987\pi$
$37$			1.87285i			0.307895i	−0.988079	+	0.153948i	$0.950801\pi$
$38$	0.561553	+	1.19935i	0.0910959	+	0.194561i
$39$		0			0
$40$	−9.12311	−	2.39871i	−1.44249	−	0.379269i
$41$	12.2462			1.91254			0.956268	−	0.292490i	$-0.0944840\pi$
$41$	12.2462			1.91254			0.956268	+	0.292490i	$0.0944840\pi$
$42$		0			0
$43$		−	4.27156i		−	0.651407i	−0.945472	−	0.325703i	$-0.894399\pi$
$43$		−	4.27156i		−	0.651407i	0.945472	−	0.325703i	$-0.105601\pi$
$44$	6.56155	+	5.47091i	0.989191	+	0.824771i
$45$		0			0
$46$	4.00000	−	1.87285i	0.589768	−	0.276137i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−7.84233	+	3.67188i	−1.10907	+	0.519283i
$51$		0			0
$52$	−5.12311	−	4.27156i	−0.710447	−	0.592359i
$53$			8.54312i			1.17349i	0.809773	+	0.586744i	$0.199590\pi$
$53$			8.54312i			1.17349i	−0.809773	+	0.586744i	$0.800410\pi$
$54$		0			0
$55$	14.2462			1.92096
$56$	−0.719224	+	2.73546i	−0.0961103	+	0.365541i
$57$		0			0
$58$	1.12311	+	2.39871i	0.147471	+	0.314965i
$59$		−	7.60669i		−	0.990307i	−0.868806	−	0.495153i	$-0.835112\pi$
$59$		−	7.60669i		−	0.990307i	0.868806	−	0.495153i	$-0.164888\pi$
$60$		0			0
$61$		−	3.33513i		−	0.427020i	−0.976941	−	0.213510i	$-0.931510\pi$
$61$		−	3.33513i		−	0.427020i	0.976941	−	0.213510i	$-0.0684896\pi$
$62$	8.00000	−	3.74571i	1.01600	−	0.475705i
$63$		0			0
$64$	−6.96543	−	3.93481i	−0.870679	−	0.491851i
$65$	−11.1231			−1.37965
$66$		0			0
$67$			15.7392i			1.92285i	0.275061	+	0.961427i	$0.411302\pi$
$67$			15.7392i			1.92285i	−0.275061	+	0.961427i	$0.588698\pi$
$68$	−2.56155	+	3.07221i	−0.310634	+	0.372560i
$69$		0			0
$70$	2.00000	+	4.27156i	0.239046	+	0.510549i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	1.12311	+	2.39871i	0.130558	+	0.278844i
$75$		0			0
$76$	1.43845	+	1.19935i	0.165001	+	0.137575i
$77$		−	4.27156i		−	0.486789i
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−13.1231	+	2.39871i	−1.46721	+	0.268183i
$81$		0			0
$82$	15.6847	−	7.34376i	1.73208	−	0.810983i
$83$			9.47954i			1.04052i	0.854009	+	0.520258i	$0.174164\pi$
$83$			9.47954i			1.04052i	−0.854009	+	0.520258i	$0.825836\pi$
$84$		0			0
$85$			6.67026i			0.723492i
$86$	−2.56155	−	5.47091i	−0.276219	−	0.589944i
$87$		0			0
$88$	11.6847	+	3.07221i	1.24559	+	0.327498i
$89$	−0.246211			−0.0260983			−0.0130492	−	0.999915i	$-0.504154\pi$
$89$	−0.246211			−0.0260983			−0.0130492	+	0.999915i	$0.504154\pi$
$90$		0			0
$91$			3.33513i			0.349617i
$92$	4.00000	−	4.79741i	0.417029	−	0.500165i
$93$		0			0
$94$		0			0
$95$	3.12311			0.320424
$96$		0			0
$97$	−4.24621			−0.431137			−0.215569	−	0.976489i	$-0.569161\pi$
$97$	−4.24621			−0.431137			−0.215569	+	0.976489i	$0.569161\pi$
$98$	1.28078	−	0.599676i	0.129378	−	0.0605765i
$99$		0			0
$100$	−7.84233	+	9.40572i	−0.784233	+	0.940572i
$101$			7.08084i			0.704570i	0.935893	+	0.352285i	$0.114595\pi$
$101$			7.08084i			0.704570i	−0.935893	+	0.352285i	$0.885405\pi$
$102$		0			0
$103$	−14.2462			−1.40372			−0.701860	−	0.712314i	$-0.747647\pi$
$103$	−14.2462			−1.40372			−0.701860	+	0.712314i	$0.747647\pi$
$104$	−9.12311	−	2.39871i	−0.894594	−	0.235212i
$105$		0			0
$106$	5.12311	+	10.9418i	0.497600	+	1.06276i
$107$			7.19612i			0.695675i	0.937555	+	0.347837i	$0.113084\pi$
$107$			7.19612i			0.695675i	−0.937555	+	0.347837i	$0.886916\pi$
$108$		0			0
$109$			5.61856i			0.538160i	0.963118	+	0.269080i	$0.0867197\pi$
$109$			5.61856i			0.538160i	−0.963118	+	0.269080i	$0.913280\pi$
$110$	18.2462	−	8.54312i	1.73971	−	0.814554i
$111$		0			0
$112$	0.719224	+	3.93481i	0.0679602	+	0.371804i
$113$	−13.1231			−1.23452			−0.617259	−	0.786760i	$-0.711757\pi$
$113$	−13.1231			−1.23452			−0.617259	+	0.786760i	$0.711757\pi$
$114$		0			0
$115$		−	10.4160i		−	0.971294i
$116$	2.87689	+	2.39871i	0.267113	+	0.222714i
$117$		0			0
$118$	−4.56155	−	9.74247i	−0.419925	−	0.896867i
$119$	2.00000			0.183340
$120$		0			0
$121$	−7.24621			−0.658746
$122$	−2.00000	−	4.27156i	−0.181071	−	0.386729i
$123$		0			0
$124$	8.00000	−	9.59482i	0.718421	−	0.861641i
$125$			3.74571i			0.335026i
$126$		0			0
$127$	4.87689			0.432754			0.216377	−	0.976310i	$-0.430576\pi$
$127$	4.87689			0.432754			0.216377	+	0.976310i	$0.430576\pi$
$128$	−11.2808	−	0.862603i	−0.997089	−	0.0762440i
$129$		0			0
$130$	−14.2462	+	6.67026i	−1.24948	+	0.585021i
$131$		−	3.86098i		−	0.337336i	−0.985673	−	0.168668i	$-0.946053\pi$
$131$		−	3.86098i		−	0.337336i	0.985673	−	0.168668i	$-0.0539465\pi$
$132$		0			0
$133$		−	0.936426i		−	0.0811985i
$134$	9.43845	+	20.1584i	0.815358	+	1.74142i
$135$		0			0
$136$	−1.43845	+	5.47091i	−0.123346	+	0.469127i
$137$	−0.246211			−0.0210352			−0.0105176	−	0.999945i	$-0.503348\pi$
$137$	−0.246211			−0.0210352			−0.0105176	+	0.999945i	$0.503348\pi$
$138$		0			0
$139$			18.0227i			1.52866i	0.644824	+	0.764331i	$0.276931\pi$
$139$			18.0227i			1.52866i	−0.644824	+	0.764331i	$0.723069\pi$
$140$	5.12311	+	4.27156i	0.432981	+	0.361013i
$141$		0			0
$142$	10.2462	−	4.79741i	0.859843	−	0.402590i
$143$	14.2462			1.19133
$144$		0			0
$145$	6.24621			0.518720
$146$	−7.68466	+	3.59806i	−0.635987	+	0.297777i
$147$		0			0
$148$	2.87689	+	2.39871i	0.236479	+	0.197172i
$149$		−	12.2888i		−	1.00674i	−0.864071	−	0.503370i	$-0.832093\pi$
$149$		−	12.2888i		−	1.00674i	0.864071	−	0.503370i	$-0.167907\pi$
$150$		0			0
$151$	19.1231			1.55622			0.778108	−	0.628130i	$-0.216180\pi$
$151$	19.1231			1.55622			0.778108	+	0.628130i	$0.216180\pi$
$152$	2.56155	+	0.673500i	0.207769	+	0.0546281i
$153$		0			0
$154$	−2.56155	−	5.47091i	−0.206416	−	0.440859i
$155$		−	20.8319i		−	1.67326i
$156$		0			0
$157$		−	16.6757i		−	1.33086i	−0.746459	−	0.665431i	$-0.768248\pi$
$157$		−	16.6757i		−	1.33086i	0.746459	−	0.665431i	$-0.231752\pi$
$158$		0			0
$159$		0			0
$160$	−15.3693	+	10.9418i	−1.21505	+	0.865027i
$161$	−3.12311			−0.246135
$162$		0			0
$163$		−	8.01726i		−	0.627961i	−0.949430	−	0.313980i	$-0.898337\pi$
$163$		−	8.01726i		−	0.627961i	0.949430	−	0.313980i	$-0.101663\pi$
$164$	15.6847	−	18.8114i	1.22477	−	1.46893i
$165$		0			0
$166$	5.68466	+	12.1412i	0.441215	+	0.942338i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	1.87689			0.144376
$170$	4.00000	+	8.54312i	0.306786	+	0.655227i
$171$		0			0
$172$	−6.56155	−	5.47091i	−0.500314	−	0.417153i
$173$		−	17.4968i		−	1.33026i	−0.746729	−	0.665129i	$-0.768377\pi$
$173$		−	17.4968i		−	1.33026i	0.746729	−	0.665129i	$-0.231623\pi$
$174$		0			0
$175$	6.12311			0.462863
$176$	16.8078	−	3.07221i	1.26693	−	0.231576i
$177$		0			0
$178$	−0.315342	+	0.147647i	−0.0236358	+	0.0110666i
$179$		−	2.39871i		−	0.179288i	−0.995974	−	0.0896438i	$-0.971427\pi$
$179$		−	2.39871i		−	0.179288i	0.995974	−	0.0896438i	$-0.0285729\pi$
$180$		0			0
$181$			13.7511i			1.02211i	0.859548	+	0.511056i	$0.170745\pi$
$181$			13.7511i			1.02211i	−0.859548	+	0.511056i	$0.829255\pi$
$182$	2.00000	+	4.27156i	0.148250	+	0.316629i
$183$		0			0
$184$	2.24621	−	8.54312i	0.165593	−	0.629807i
$185$	6.24621			0.459231
$186$		0			0
$187$		−	8.54312i		−	0.624735i
$188$		0			0
$189$		0			0
$190$	4.00000	−	1.87285i	0.290191	−	0.135871i
$191$	−16.0000			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$192$		0			0
$193$	−2.87689			−0.207083			−0.103542	−	0.994625i	$-0.533018\pi$
$193$	−2.87689			−0.207083			−0.103542	+	0.994625i	$0.533018\pi$
$194$	−5.43845	+	2.54635i	−0.390458	+	0.182817i
$195$		0			0
$196$	1.28078	−	1.53610i	0.0914840	−	0.109722i
$197$			1.05171i			0.0749309i	0.999298	+	0.0374655i	$0.0119284\pi$
$197$			1.05171i			0.0749309i	−0.999298	+	0.0374655i	$0.988072\pi$
$198$		0			0
$199$	−1.75379			−0.124323			−0.0621614	−	0.998066i	$-0.519799\pi$
$199$	−1.75379			−0.124323			−0.0621614	+	0.998066i	$0.519799\pi$
$200$	−4.40388	+	16.7495i	−0.311401	+	1.18437i
$201$		0			0
$202$	4.24621	+	9.06897i	0.298762	+	0.638090i
$203$		−	1.87285i		−	0.131448i
$204$		0			0
$205$		−	40.8427i		−	2.85258i
$206$	−18.2462	+	8.54312i	−1.27127	+	0.595227i
$207$		0			0
$208$	−13.1231	+	2.39871i	−0.909924	+	0.166320i
$209$	−4.00000			−0.276686
$210$		0			0
$211$			2.39871i			0.165134i	0.996586	+	0.0825669i	$0.0263118\pi$
$211$			2.39871i			0.165134i	−0.996586	+	0.0825669i	$0.973688\pi$
$212$	13.1231	+	10.9418i	0.901299	+	0.751487i
$213$		0			0
$214$	4.31534	+	9.21662i	0.294991	+	0.630035i
$215$	−14.2462			−0.971584
$216$		0			0
$217$	−6.24621			−0.424020
$218$	3.36932	+	7.19612i	0.228199	+	0.487383i
$219$		0			0
$220$	18.2462	−	21.8836i	1.23016	−	1.47540i
$221$			6.67026i			0.448691i
$222$		0			0
$223$	−22.2462			−1.48972			−0.744858	−	0.667223i	$-0.767483\pi$
$223$	−22.2462			−1.48972			−0.744858	+	0.667223i	$0.767483\pi$
$224$	3.28078	+	4.60831i	0.219206	+	0.307906i
$225$		0			0
$226$	−16.8078	+	7.86962i	−1.11804	+	0.523479i
$227$			12.4041i			0.823289i	0.911344	+	0.411645i	$0.135045\pi$
$227$			12.4041i			0.823289i	−0.911344	+	0.411645i	$0.864955\pi$
$228$		0			0
$229$		−	4.15628i		−	0.274655i	−0.990526	−	0.137327i	$-0.956149\pi$
$229$		−	4.15628i		−	0.274655i	0.990526	−	0.137327i	$-0.0438512\pi$
$230$	−6.24621	−	13.3405i	−0.411863	−	0.879648i
$231$		0			0
$232$	5.12311	+	1.34700i	0.336348	+	0.0884349i
$233$	−0.246211			−0.0161298			−0.00806492	−	0.999967i	$-0.502567\pi$
$233$	−0.246211			−0.0161298			−0.00806492	+	0.999967i	$0.502567\pi$
$234$		0			0
$235$		0			0
$236$	−11.6847	−	9.74247i	−0.760606	−	0.634181i
$237$		0			0
$238$	2.56155	−	1.19935i	0.166041	−	0.0777425i
$239$	−23.6155			−1.52756			−0.763781	−	0.645476i	$-0.776659\pi$
$239$	−23.6155			−1.52756			−0.763781	+	0.645476i	$0.776659\pi$
$240$		0			0
$241$	−20.2462			−1.30417			−0.652087	−	0.758145i	$-0.726106\pi$
$241$	−20.2462			−1.30417			−0.652087	+	0.758145i	$0.726106\pi$
$242$	−9.28078	+	4.34538i	−0.596591	+	0.279332i
$243$		0			0
$244$	−5.12311	−	4.27156i	−0.327973	−	0.273459i
$245$		−	3.33513i		−	0.213074i
$246$		0			0
$247$	3.12311			0.198718
$248$	4.49242	−	17.0862i	0.285269	−	1.08498i
$249$		0			0
$250$	2.24621	+	4.79741i	0.142063	+	0.303415i
$251$			26.5658i			1.67682i	0.545042	+	0.838408i	$0.316514\pi$
$251$			26.5658i			1.67682i	−0.545042	+	0.838408i	$0.683486\pi$
$252$		0			0
$253$			13.3405i			0.838712i
$254$	6.24621	−	2.92456i	0.391922	−	0.183503i
$255$		0			0
$256$	−14.9654	+	5.66001i	−0.935340	+	0.353751i
$257$	10.4924			0.654499			0.327250	−	0.944938i	$-0.393878\pi$
$257$	10.4924			0.654499			0.327250	+	0.944938i	$0.393878\pi$
$258$		0			0
$259$		−	1.87285i		−	0.116373i
$260$	−14.2462	+	17.0862i	−0.883513	+	1.05964i
$261$		0			0
$262$	−2.31534	−	4.94506i	−0.143042	−	0.305507i
$263$	20.4924			1.26362			0.631808	−	0.775125i	$-0.282313\pi$
$263$	20.4924			1.26362			0.631808	+	0.775125i	$0.282313\pi$
$264$		0			0
$265$	28.4924			1.75028
$266$	−0.561553	−	1.19935i	−0.0344310	−	0.0735370i
$267$		0			0
$268$	24.1771	+	20.1584i	1.47685	+	1.23137i
$269$		−	23.3459i		−	1.42343i	−0.702470	−	0.711713i	$-0.747920\pi$
$269$		−	23.3459i		−	1.42343i	0.702470	−	0.711713i	$-0.252080\pi$
$270$		0			0
$271$	−6.24621			−0.379430			−0.189715	−	0.981839i	$-0.560756\pi$
$271$	−6.24621			−0.379430			−0.189715	+	0.981839i	$0.560756\pi$
$272$	1.43845	+	7.86962i	0.0872187	+	0.477166i
$273$		0			0
$274$	−0.315342	+	0.147647i	−0.0190505	+	0.00891969i
$275$		−	26.1552i		−	1.57722i
$276$		0			0
$277$		−	8.54312i		−	0.513306i	−0.966504	−	0.256653i	$-0.917380\pi$
$277$		−	8.54312i		−	0.513306i	0.966504	−	0.256653i	$-0.0826198\pi$
$278$	10.8078	+	23.0830i	0.648207	+	1.38443i
$279$		0			0
$280$	9.12311	+	2.39871i	0.545210	+	0.143350i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$		−	8.65840i		−	0.514688i	−0.966320	−	0.257344i	$-0.917153\pi$
$283$		−	8.65840i		−	0.514688i	0.966320	−	0.257344i	$-0.0828474\pi$
$284$	10.2462	−	12.2888i	0.608001	−	0.729207i
$285$		0			0
$286$	18.2462	−	8.54312i	1.07892	−	0.505165i
$287$	−12.2462			−0.722871
$288$		0			0
$289$	−13.0000			−0.764706
$290$	8.00000	−	3.74571i	0.469776	−	0.219955i
$291$		0			0
$292$	−7.68466	+	9.21662i	−0.449711	+	0.539362i
$293$			7.08084i			0.413667i	0.978376	+	0.206833i	$0.0663158\pi$
$293$			7.08084i			0.413667i	−0.978376	+	0.206833i	$0.933684\pi$
$294$		0			0
$295$	−25.3693			−1.47706
$296$	5.12311	+	1.34700i	0.297774	+	0.0782928i
$297$		0			0
$298$	−7.36932	−	15.7392i	−0.426893	−	0.911749i
$299$		−	10.4160i		−	0.602371i
$300$		0			0
$301$			4.27156i			0.246209i
$302$	24.4924	−	11.4677i	1.40938	−	0.659891i
$303$		0			0
$304$	3.68466	−	0.673500i	0.211330	−	0.0386279i
$305$	−11.1231			−0.636907
$306$		0			0
$307$		−	15.3287i		−	0.874853i	−0.899254	−	0.437426i	$-0.855890\pi$
$307$		−	15.3287i		−	0.874853i	0.899254	−	0.437426i	$-0.144110\pi$
$308$	−6.56155	−	5.47091i	−0.373879	−	0.311734i
$309$		0			0
$310$	−12.4924	−	26.6811i	−0.709522	−	1.51538i
$311$	−20.4924			−1.16202			−0.581009	−	0.813897i	$-0.697342\pi$
$311$	−20.4924			−1.16202			−0.581009	+	0.813897i	$0.697342\pi$
$312$		0			0
$313$	28.7386			1.62440			0.812202	−	0.583377i	$-0.198269\pi$
$313$	28.7386			1.62440			0.812202	+	0.583377i	$0.198269\pi$
$314$	−10.0000	−	21.3578i	−0.564333	−	1.20529i
$315$		0			0
$316$		0			0
$317$		−	21.8836i		−	1.22911i	−0.788875	−	0.614554i	$-0.789336\pi$
$317$		−	21.8836i		−	1.22911i	0.788875	−	0.614554i	$-0.210664\pi$
$318$		0			0
$319$	−8.00000			−0.447914
$320$	−13.1231	+	23.2306i	−0.733604	+	1.29863i
$321$		0			0
$322$	−4.00000	+	1.87285i	−0.222911	+	0.104370i
$323$		−	1.87285i		−	0.104208i
$324$		0			0
$325$			20.4214i			1.13277i
$326$	−4.80776	−	10.2683i	−0.266277	−	0.568710i
$327$		0			0
$328$	8.80776	−	33.4990i	0.486327	−	1.84967i
$329$		0			0
$330$		0			0
$331$			22.4095i			1.23174i	0.787849	+	0.615869i	$0.211195\pi$
$331$			22.4095i			1.23174i	−0.787849	+	0.615869i	$0.788805\pi$
$332$	14.5616	+	12.1412i	0.799169	+	0.666334i
$333$		0			0
$334$	−10.2462	+	4.79741i	−0.560648	+	0.262503i
$335$	52.4924			2.86797
$336$		0			0
$337$	−9.12311			−0.496967			−0.248484	−	0.968636i	$-0.579932\pi$
$337$	−9.12311			−0.496967			−0.248484	+	0.968636i	$0.579932\pi$
$338$	2.40388	−	1.12553i	0.130754	−	0.0612207i
$339$		0			0
$340$	10.2462	+	8.54312i	0.555679	+	0.463316i
$341$			26.6811i			1.44486i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−11.6847	−	3.07221i	−0.629995	−	0.165642i
$345$		0			0
$346$	−10.4924	−	22.4095i	−0.564076	−	1.20474i
$347$		−	9.06897i		−	0.486848i	−0.969920	−	0.243424i	$-0.921729\pi$
$347$		−	9.06897i		−	0.486848i	0.969920	−	0.243424i	$-0.0782706\pi$
$348$		0			0
$349$			26.2705i			1.40623i	0.711078	+	0.703113i	$0.248207\pi$
$349$			26.2705i			1.40623i	−0.711078	+	0.703113i	$0.751793\pi$
$350$	7.84233	−	3.67188i	0.419190	−	0.196270i
$351$		0			0
$352$	19.6847	−	14.0140i	1.04920	−	0.746950i
$353$	−24.2462			−1.29050			−0.645248	−	0.763973i	$-0.723246\pi$
$353$	−24.2462			−1.29050			−0.645248	+	0.763973i	$0.723246\pi$
$354$		0			0
$355$		−	26.6811i		−	1.41608i
$356$	−0.315342	+	0.378206i	−0.0167131	+	0.0200449i
$357$		0			0
$358$	−1.43845	−	3.07221i	−0.0760243	−	0.162371i
$359$	6.63068			0.349954			0.174977	−	0.984573i	$-0.444015\pi$
$359$	6.63068			0.349954			0.174977	+	0.984573i	$0.444015\pi$
$360$		0			0
$361$	18.1231			0.953848
$362$	8.24621	+	17.6121i	0.433411	+	0.925671i
$363$		0			0
$364$	5.12311	+	4.27156i	0.268524	+	0.223890i
$365$			20.0108i			1.04741i
$366$		0			0
$367$	−6.24621			−0.326050			−0.163025	−	0.986622i	$-0.552125\pi$
$367$	−6.24621			−0.326050			−0.163025	+	0.986622i	$0.552125\pi$
$368$	−2.24621	−	12.2888i	−0.117092	−	0.640599i
$369$		0			0
$370$	8.00000	−	3.74571i	0.415900	−	0.194730i
$371$		−	8.54312i		−	0.443537i
$372$		0			0
$373$			12.2888i			0.636291i	0.948042	+	0.318146i	$0.103060\pi$
$373$			12.2888i			0.636291i	−0.948042	+	0.318146i	$0.896940\pi$
$374$	−5.12311	−	10.9418i	−0.264909	−	0.565788i
$375$		0			0
$376$		0			0
$377$	6.24621			0.321696
$378$		0			0
$379$		−	23.4612i		−	1.20512i	−0.798073	−	0.602561i	$-0.794147\pi$
$379$		−	23.4612i		−	1.20512i	0.798073	−	0.602561i	$-0.205853\pi$
$380$	4.00000	−	4.79741i	0.205196	−	0.246102i
$381$		0			0
$382$	−20.4924	+	9.59482i	−1.04848	+	0.490914i
$383$	−28.4924			−1.45589			−0.727947	−	0.685633i	$-0.759526\pi$
$383$	−28.4924			−1.45589			−0.727947	+	0.685633i	$0.759526\pi$
$384$		0			0
$385$	−14.2462			−0.726054
$386$	−3.68466	+	1.72521i	−0.187544	+	0.0878107i
$387$		0			0
$388$	−5.43845	+	6.52262i	−0.276095	+	0.331136i
$389$		−	7.72197i		−	0.391519i	−0.980652	−	0.195760i	$-0.937283\pi$
$389$		−	7.72197i		−	0.391519i	0.980652	−	0.195760i	$-0.0627173\pi$
$390$		0			0
$391$	−6.24621			−0.315884
$392$	0.719224	−	2.73546i	0.0363263	−	0.138161i
$393$		0			0
$394$	0.630683	+	1.34700i	0.0317734	+	0.0678609i
$395$		0			0
$396$		0			0
$397$			12.9300i			0.648936i	0.945897	+	0.324468i	$0.105185\pi$
$397$			12.9300i			0.648936i	−0.945897	+	0.324468i	$0.894815\pi$
$398$	−2.24621	+	1.05171i	−0.112592	+	0.0527172i
$399$		0			0
$400$	4.40388	+	24.0932i	0.220194	+	1.20466i
$401$	9.12311			0.455586			0.227793	−	0.973710i	$-0.426849\pi$
$401$	9.12311			0.455586			0.227793	+	0.973710i	$0.426849\pi$
$402$		0			0
$403$		−	20.8319i		−	1.03771i
$404$	10.8769	+	9.06897i	0.541146	+	0.451198i
$405$		0			0
$406$	−1.12311	−	2.39871i	−0.0557388	−	0.119046i
$407$	−8.00000			−0.396545
$408$		0			0
$409$	26.0000			1.28562			0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000			1.28562			0.642809	+	0.766027i	$0.277769\pi$
$410$	−24.4924	−	52.3104i	−1.20959	−	2.58343i
$411$		0			0
$412$	−18.2462	+	21.8836i	−0.898926	+	1.07813i
$413$			7.60669i			0.374301i
$414$		0			0
$415$	31.6155			1.55195
$416$	−15.3693	+	10.9418i	−0.753543	+	0.536467i
$417$		0			0
$418$	−5.12311	+	2.39871i	−0.250579	+	0.117325i
$419$		−	6.78554i		−	0.331495i	−0.986168	−	0.165748i	$-0.946996\pi$
$419$		−	6.78554i		−	0.331495i	0.986168	−	0.165748i	$-0.0530038\pi$
$420$		0			0
$421$		−	16.0345i		−	0.781475i	−0.920502	−	0.390738i	$-0.872220\pi$
$421$		−	16.0345i		−	0.781475i	0.920502	−	0.390738i	$-0.127780\pi$
$422$	1.43845	+	3.07221i	0.0700225	+	0.149553i
$423$		0			0
$424$	23.3693	+	6.14441i	1.13491	+	0.298399i
$425$	12.2462			0.594029
$426$		0			0
$427$			3.33513i			0.161398i
$428$	11.0540	+	9.21662i	0.534314	+	0.445502i
$429$		0			0
$430$	−18.2462	+	8.54312i	−0.879910	+	0.411986i
$431$	23.6155			1.13752			0.568760	−	0.822504i	$-0.307423\pi$
$431$	23.6155			1.13752			0.568760	+	0.822504i	$0.307423\pi$
$432$		0			0
$433$	14.4924			0.696461			0.348231	−	0.937409i	$-0.386783\pi$
$433$	14.4924			0.696461			0.348231	+	0.937409i	$0.386783\pi$
$434$	−8.00000	+	3.74571i	−0.384012	+	0.179800i
$435$		0			0
$436$	8.63068	+	7.19612i	0.413335	+	0.344631i
$437$			2.92456i			0.139901i
$438$		0			0
$439$	−26.7386			−1.27617			−0.638083	−	0.769968i	$-0.720272\pi$
$439$	−26.7386			−1.27617			−0.638083	+	0.769968i	$0.720272\pi$
$440$	10.2462	−	38.9699i	0.488469	−	1.85782i
$441$		0			0
$442$	4.00000	+	8.54312i	0.190261	+	0.406355i
$443$		−	6.14441i		−	0.291930i	−0.989290	−	0.145965i	$-0.953371\pi$
$443$		−	6.14441i		−	0.291930i	0.989290	−	0.145965i	$-0.0466287\pi$
$444$		0			0
$445$			0.821147i			0.0389261i
$446$	−28.4924	+	13.3405i	−1.34916	+	0.631692i
$447$		0			0
$448$	6.96543	+	3.93481i	0.329086	+	0.185902i
$449$	32.7386			1.54503			0.772516	−	0.634996i	$-0.218998\pi$
$449$	32.7386			1.54503			0.772516	+	0.634996i	$0.218998\pi$
$450$		0			0
$451$			52.3104i			2.46320i
$452$	−16.8078	+	20.1584i	−0.790571	+	0.948173i
$453$		0			0
$454$	7.43845	+	15.8869i	0.349104	+	0.745608i
$455$	11.1231			0.521459
$456$		0			0
$457$	−7.36932			−0.344722			−0.172361	−	0.985034i	$-0.555140\pi$
$457$	−7.36932			−0.344722			−0.172361	+	0.985034i	$0.555140\pi$
$458$	−2.49242	−	5.32326i	−0.116463	−	0.248740i
$459$		0			0
$460$	−16.0000	−	13.3405i	−0.746004	−	0.622005i
$461$			34.5830i			1.61069i	0.592805	+	0.805346i	$0.298021\pi$
$461$			34.5830i			1.61069i	−0.592805	+	0.805346i	$0.701979\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	7.36932	−	1.34700i	0.342112	−	0.0625329i
$465$		0			0
$466$	−0.315342	+	0.147647i	−0.0146079	+	0.00683962i
$467$		−	0.936426i		−	0.0433326i	−0.999765	−	0.0216663i	$-0.993103\pi$
$467$		−	0.936426i		−	0.0433326i	0.999765	−	0.0216663i	$-0.00689714\pi$
$468$		0			0
$469$		−	15.7392i		−	0.726770i
$470$		0			0
$471$		0			0
$472$	−20.8078	−	5.47091i	−0.957755	−	0.251819i
$473$	18.2462			0.838962
$474$		0			0
$475$		−	5.73384i		−	0.263087i
$476$	2.56155	−	3.07221i	0.117409	−	0.140814i
$477$		0			0
$478$	−30.2462	+	14.1617i	−1.38343	+	0.647740i
$479$	6.24621			0.285397			0.142698	−	0.989766i	$-0.454422\pi$
$479$	6.24621			0.285397			0.142698	+	0.989766i	$0.454422\pi$
$480$		0			0
$481$	6.24621			0.284803
$482$	−25.9309	+	12.1412i	−1.18112	+	0.553015i
$483$		0			0
$484$	−9.28078	+	11.1309i	−0.421853	+	0.505951i
$485$			14.1617i			0.643049i
$486$		0			0
$487$	25.3693			1.14959			0.574797	−	0.818296i	$-0.305081\pi$
$487$	25.3693			1.14959			0.574797	+	0.818296i	$0.305081\pi$
$488$	−9.12311	−	2.39871i	−0.412984	−	0.108584i
$489$		0			0
$490$	−2.00000	−	4.27156i	−0.0903508	−	0.192969i
$491$			22.1789i			1.00092i	0.865759	+	0.500461i	$0.166836\pi$
$491$			22.1789i			1.00092i	−0.865759	+	0.500461i	$0.833164\pi$
$492$		0			0
$493$		−	3.74571i		−	0.168698i
$494$	4.00000	−	1.87285i	0.179969	−	0.0842636i
$495$		0			0
$496$	−4.49242	−	24.5776i	−0.201716	−	1.10357i
$497$	−8.00000			−0.358849
$498$		0			0
$499$		−	24.2824i		−	1.08703i	−0.839400	−	0.543514i	$-0.817094\pi$
$499$		−	24.2824i		−	1.08703i	0.839400	−	0.543514i	$-0.182906\pi$
$500$	5.75379	+	4.79741i	0.257317	+	0.214547i
$501$		0			0
$502$	15.9309	+	34.0248i	0.711030	+	1.51860i
$503$	−30.2462			−1.34861			−0.674306	−	0.738452i	$-0.735557\pi$
$503$	−30.2462			−1.34861			−0.674306	+	0.738452i	$0.735557\pi$
$504$		0			0
$505$	23.6155			1.05088
$506$	8.00000	+	17.0862i	0.355643	+	0.759576i
$507$		0			0
$508$	6.24621	−	7.49141i	0.277131	−	0.332378i
$509$			32.9407i			1.46007i	0.683408	+	0.730036i	$0.260497\pi$
$509$			32.9407i			1.46007i	−0.683408	+	0.730036i	$0.739503\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$	−15.7732	+	16.2236i	−0.697083	+	0.716990i
$513$		0			0
$514$	13.4384	−	6.29206i	0.592744	−	0.277531i
$515$			47.5130i			2.09367i
$516$		0			0
$517$		0			0
$518$	−1.12311	−	2.39871i	−0.0493464	−	0.105393i
$519$		0			0
$520$	−8.00000	+	30.4268i	−0.350823	+	1.33430i
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$		0			0
$523$			35.9300i			1.57111i	0.618791	+	0.785555i	$0.287623\pi$
$523$			35.9300i			1.57111i	−0.618791	+	0.785555i	$0.712377\pi$
$524$	−5.93087	−	4.94506i	−0.259091	−	0.216026i
$525$		0			0
$526$	26.2462	−	12.2888i	1.14439	−	0.535818i
$527$	−12.4924			−0.544178
$528$		0			0
$529$	−13.2462			−0.575922
$530$	36.4924	−	17.0862i	1.58513	−	0.742179i
$531$		0			0
$532$	−1.43845	−	1.19935i	−0.0623646	−	0.0519985i
$533$		−	40.8427i		−	1.76910i
$534$		0			0
$535$	24.0000			1.03761
$536$	43.0540	+	11.3200i	1.85965	+	0.488951i
$537$		0			0
$538$	−14.0000	−	29.9009i	−0.603583	−	1.28912i
$539$			4.27156i			0.183989i
$540$		0			0
$541$			42.7156i			1.83649i	0.396017	+	0.918243i	$0.370392\pi$
$541$			42.7156i			1.83649i	−0.396017	+	0.918243i	$0.629608\pi$
$542$	−8.00000	+	3.74571i	−0.343629	+	0.160892i
$543$		0			0
$544$	6.56155	+	9.21662i	0.281324	+	0.395159i
$545$	18.7386			0.802675
$546$		0			0
$547$			39.4957i			1.68872i	0.535780	+	0.844358i	$0.320018\pi$
$547$			39.4957i			1.68872i	−0.535780	+	0.844358i	$0.679982\pi$
$548$	−0.315342	+	0.378206i	−0.0134707	+	0.0161562i
$549$		0			0
$550$	−15.6847	−	33.4990i	−0.668796	−	1.42840i
$551$	−1.75379			−0.0747139
$552$		0			0
$553$		0			0
$554$	−5.12311	−	10.9418i	−0.217660	−	0.464873i
$555$		0			0
$556$	27.6847	+	23.0830i	1.17409	+	0.978937i
$557$		−	8.54312i		−	0.361983i	−0.983485	−	0.180992i	$-0.942069\pi$
$557$		−	8.54312i		−	0.361983i	0.983485	−	0.180992i	$-0.0579307\pi$
$558$		0			0
$559$	−14.2462			−0.602551
$560$	13.1231	−	2.39871i	0.554552	−	0.101364i
$561$		0			0
$562$	7.68466	−	3.59806i	0.324158	−	0.151775i
$563$			16.9710i			0.715240i	0.933867	+	0.357620i	$0.116412\pi$
$563$			16.9710i			0.715240i	−0.933867	+	0.357620i	$0.883588\pi$
$564$		0			0
$565$			43.7673i			1.84130i
$566$	−5.19224	−	11.0895i	−0.218246	−	0.466125i
$567$		0			0
$568$	5.75379	−	21.8836i	0.241424	−	0.918217i
$569$	−11.3693			−0.476627			−0.238313	−	0.971188i	$-0.576595\pi$
$569$	−11.3693			−0.476627			−0.238313	+	0.971188i	$0.576595\pi$
$570$		0			0
$571$			29.9009i			1.25131i	0.780098	+	0.625657i	$0.215169\pi$
$571$			29.9009i			1.25131i	−0.780098	+	0.625657i	$0.784831\pi$
$572$	18.2462	−	21.8836i	0.762912	−	0.915001i
$573$		0			0
$574$	−15.6847	+	7.34376i	−0.654665	+	0.306523i
$575$	−19.1231			−0.797489
$576$		0			0
$577$	24.2462			1.00938			0.504691	−	0.863300i	$-0.331606\pi$
$577$	24.2462			1.00938			0.504691	+	0.863300i	$0.331606\pi$
$578$	−16.6501	+	7.79579i	−0.692553	+	0.324262i
$579$		0			0
$580$	8.00000	−	9.59482i	0.332182	−	0.398403i
$581$		−	9.47954i		−	0.393278i
$582$		0			0
$583$	−36.4924			−1.51136
$584$	−4.31534	+	16.4127i	−0.178570	+	0.679164i
$585$		0			0
$586$	4.24621	+	9.06897i	0.175409	+	0.374636i
$587$			8.65840i			0.357370i	0.983906	+	0.178685i	$0.0571843\pi$
$587$			8.65840i			0.357370i	−0.983906	+	0.178685i	$0.942816\pi$
$588$		0			0
$589$			5.84912i			0.241009i
$590$	−32.4924	+	15.2134i	−1.33769	+	0.626325i
$591$		0			0
$592$	7.36932	−	1.34700i	0.302877	−	0.0553614i
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$		0			0
$595$		−	6.67026i		−	0.273454i
$596$	−18.8769	−	15.7392i	−0.773228	−	0.644704i
$597$		0			0
$598$	−6.24621	−	13.3405i	−0.255427	−	0.545535i
$599$	−20.4924			−0.837298			−0.418649	−	0.908148i	$-0.637496\pi$
$599$	−20.4924			−0.837298			−0.418649	+	0.908148i	$0.637496\pi$
$600$		0			0
$601$	0.246211			0.0100432			0.00502158	−	0.999987i	$-0.498402\pi$
$601$	0.246211			0.0100432			0.00502158	+	0.999987i	$0.498402\pi$
$602$	2.56155	+	5.47091i	0.104401	+	0.222978i
$603$		0			0
$604$	24.4924	−	29.3751i	0.996583	−	1.19525i
$605$			24.1671i			0.982531i
$606$		0			0
$607$	−24.9848			−1.01410			−0.507052	−	0.861916i	$-0.669265\pi$
$607$	−24.9848			−1.01410			−0.507052	+	0.861916i	$0.669265\pi$
$608$	4.31534	−	3.07221i	0.175010	−	0.124594i
$609$		0			0
$610$	−14.2462	+	6.67026i	−0.576812	+	0.270071i
$611$		0			0
$612$		0			0
$613$		−	45.6401i		−	1.84339i	−0.387918	−	0.921694i	$-0.626806\pi$
$613$		−	45.6401i		−	1.84339i	0.387918	−	0.921694i	$-0.373194\pi$
$614$	−9.19224	−	19.6326i	−0.370968	−	0.792307i
$615$		0			0
$616$	−11.6847	−	3.07221i	−0.470788	−	0.123783i
$617$	4.63068			0.186424			0.0932121	−	0.995646i	$-0.470287\pi$
$617$	4.63068			0.186424			0.0932121	+	0.995646i	$0.470287\pi$
$618$		0			0
$619$		−	36.9817i		−	1.48642i	−0.669057	−	0.743211i	$-0.733302\pi$
$619$		−	36.9817i		−	1.48642i	0.669057	−	0.743211i	$-0.266698\pi$
$620$	−32.0000	−	26.6811i	−1.28515	−	1.07154i
$621$		0			0
$622$	−26.2462	+	12.2888i	−1.05238	+	0.492737i
$623$	0.246211			0.00986425
$624$		0			0
$625$	−18.1231			−0.724924
$626$	36.8078	−	17.2339i	1.47113	−	0.688804i
$627$		0			0
$628$	−25.6155	−	21.3578i	−1.02217	−	0.852269i
$629$		−	3.74571i		−	0.149351i
$630$		0			0
$631$	−36.4924			−1.45274			−0.726370	−	0.687304i	$-0.758794\pi$
$631$	−36.4924			−1.45274			−0.726370	+	0.687304i	$0.758794\pi$
$632$		0			0
$633$		0			0
$634$	−13.1231	−	28.0281i	−0.521185	−	1.11314i
$635$		−	16.2651i		−	0.645460i
$636$		0			0
$637$		−	3.33513i		−	0.132143i
$638$	−10.2462	+	4.79741i	−0.405651	+	0.189931i
$639$		0			0
$640$	−2.87689	+	37.6229i	−0.113719	+	1.48717i
$641$	−19.3693			−0.765042			−0.382521	−	0.923947i	$-0.624944\pi$
$641$	−19.3693			−0.765042			−0.382521	+	0.923947i	$0.624944\pi$
$642$		0			0
$643$		−	9.47954i		−	0.373837i	−0.982375	−	0.186918i	$-0.940150\pi$
$643$		−	9.47954i		−	0.373837i	0.982375	−	0.186918i	$-0.0598500\pi$
$644$	−4.00000	+	4.79741i	−0.157622	+	0.189044i
$645$		0			0
$646$	−1.12311	−	2.39871i	−0.0441880	−	0.0943758i
$647$	39.2311			1.54233			0.771166	−	0.636634i	$-0.219674\pi$
$647$	39.2311			1.54233			0.771166	+	0.636634i	$0.219674\pi$
$648$		0			0
$649$	32.4924			1.27544
$650$	12.2462	+	26.1552i	0.480336	+	1.02589i
$651$		0			0
$652$	−12.3153	−	10.2683i	−0.482306	−	0.402139i
$653$			21.0625i			0.824239i	0.911130	+	0.412120i	$0.135211\pi$
$653$			21.0625i			0.824239i	−0.911130	+	0.412120i	$0.864789\pi$
$654$		0			0
$655$	−12.8769			−0.503142
$656$	−8.80776	−	48.1865i	−0.343885	−	1.88137i
$657$		0			0
$658$		0			0
$659$			21.3578i			0.831981i	0.909369	+	0.415991i	$0.136565\pi$
$659$			21.3578i			0.831981i	−0.909369	+	0.415991i	$0.863435\pi$
$660$		0			0
$661$		−	5.43854i		−	0.211535i	−0.994391	−	0.105767i	$-0.966270\pi$
$661$		−	5.43854i		−	0.211535i	0.994391	−	0.105767i	$-0.0337299\pi$
$662$	13.4384	+	28.7016i	0.522300	+	1.11552i
$663$		0			0
$664$	25.9309	+	6.81791i	1.00631	+	0.264586i
$665$	−3.12311			−0.121109
$666$		0			0
$667$			5.84912i			0.226479i
$668$	−10.2462	+	12.2888i	−0.396438	+	0.475469i
$669$		0			0
$670$	67.2311	−	31.4785i	2.59736	−	1.21612i
$671$	14.2462			0.549969
$672$		0			0
$673$	26.9848			1.04019			0.520095	−	0.854109i	$-0.325897\pi$
$673$	26.9848			1.04019			0.520095	+	0.854109i	$0.325897\pi$
$674$	−11.6847	+	5.47091i	−0.450076	+	0.210732i
$675$		0			0
$676$	2.40388	−	2.88310i	0.0924570	−	0.110889i
$677$		−	6.25969i		−	0.240579i	−0.992739	−	0.120290i	$-0.961618\pi$
$677$		−	6.25969i		−	0.240579i	0.992739	−	0.120290i	$-0.0383824\pi$
$678$		0			0
$679$	4.24621			0.162955
$680$	18.2462	+	4.79741i	0.699710	+	0.183972i
$681$		0			0
$682$	16.0000	+	34.1725i	0.612672	+	1.30853i
$683$		−	19.4849i		−	0.745570i	−0.927918	−	0.372785i	$-0.878403\pi$
$683$		−	19.4849i		−	0.745570i	0.927918	−	0.372785i	$-0.121597\pi$
$684$		0			0
$685$			0.821147i			0.0313744i
$686$	−1.28078	+	0.599676i	−0.0489003	+	0.0228958i
$687$		0			0
$688$	−16.8078	+	3.07221i	−0.640790	+	0.117127i
$689$	28.4924			1.08547
$690$		0			0
$691$		−	42.0097i		−	1.59812i	−0.601248	−	0.799062i	$-0.705330\pi$
$691$		−	42.0097i		−	1.59812i	0.601248	−	0.799062i	$-0.294670\pi$
$692$	−26.8769	−	22.4095i	−1.02171	−	0.851881i
$693$		0			0
$694$	−5.43845	−	11.6153i	−0.206441	−	0.440912i
$695$	60.1080			2.28002
$696$		0			0
$697$	−24.4924			−0.927717
$698$	15.7538	+	33.6466i	0.596290	+	1.27354i
$699$		0			0
$700$	7.84233	−	9.40572i	0.296412	−	0.355503i
$701$		−	45.6401i		−	1.72380i	−0.507075	−	0.861902i	$-0.669273\pi$
$701$		−	45.6401i		−	1.72380i	0.507075	−	0.861902i	$-0.330727\pi$
$702$		0			0
$703$	−1.75379			−0.0661454
$704$	16.8078	−	29.7533i	0.633466	−	1.12137i
$705$		0			0
$706$	−31.0540	+	14.5399i	−1.16873	+	0.547216i
$707$		−	7.08084i		−	0.266302i
$708$		0			0
$709$		−	39.7910i		−	1.49438i	−0.664609	−	0.747192i	$-0.731402\pi$
$709$		−	39.7910i		−	1.49438i	0.664609	−	0.747192i	$-0.268598\pi$
$710$	−16.0000	−	34.1725i	−0.600469	−	1.28247i
$711$		0			0
$712$	−0.177081	+	0.673500i	−0.00663639	+	0.0252405i
$713$	19.5076			0.730565
$714$		0			0
$715$		−	47.5130i		−	1.77689i
$716$	−3.68466	−	3.07221i	−0.137702	−	0.114814i
$717$		0			0
$718$	8.49242	−	3.97626i	0.316934	−	0.148393i
$719$	19.5076			0.727510			0.363755	−	0.931495i	$-0.381495\pi$
$719$	19.5076			0.727510			0.363755	+	0.931495i	$0.381495\pi$
$720$		0			0
$721$	14.2462			0.530557
$722$	23.2116	−	10.8680i	0.863848	−	0.404465i
$723$		0			0
$724$	21.1231	+	17.6121i	0.785034	+	0.654548i
$725$		−	11.4677i		−	0.425899i
$726$		0			0
$727$	48.9848			1.81675			0.908374	−	0.418159i	$-0.137325\pi$
$727$	48.9848			1.81675			0.908374	+	0.418159i	$0.137325\pi$
$728$	9.12311	+	2.39871i	0.338125	+	0.0889019i
$729$		0			0
$730$	12.0000	+	25.6294i	0.444140	+	0.948585i
$731$			8.54312i			0.315979i
$732$		0			0
$733$			2.51398i			0.0928562i	0.998922	+	0.0464281i	$0.0147838\pi$
$733$			2.51398i			0.0928562i	−0.998922	+	0.0464281i	$0.985216\pi$
$734$	−8.00000	+	3.74571i	−0.295285	+	0.138257i
$735$		0			0
$736$	−10.2462	−	14.3922i	−0.377680	−	0.530505i
$737$	−67.2311			−2.47649
$738$		0			0
$739$			33.6466i			1.23771i	0.785505	+	0.618855i	$0.212403\pi$
$739$			33.6466i			1.23771i	−0.785505	+	0.618855i	$0.787597\pi$
$740$	8.00000	−	9.59482i	0.294086	−	0.352713i
$741$		0			0
$742$	−5.12311	−	10.9418i	−0.188075	−	0.401687i
$743$	−25.3693			−0.930710			−0.465355	−	0.885124i	$-0.654073\pi$
$743$	−25.3693			−0.930710			−0.465355	+	0.885124i	$0.654073\pi$
$744$		0			0
$745$	−40.9848			−1.50157
$746$	7.36932	+	15.7392i	0.269810	+	0.576254i
$747$		0			0
$748$	−13.1231	−	10.9418i	−0.479828	−	0.400073i
$749$		−	7.19612i		−	0.262940i
$750$		0			0
$751$	33.3693			1.21766			0.608832	−	0.793299i	$-0.291638\pi$
$751$	33.3693			1.21766			0.608832	+	0.793299i	$0.291638\pi$
$752$		0			0
$753$		0			0
$754$	8.00000	−	3.74571i	0.291343	−	0.136411i
$755$		−	63.7781i		−	2.32112i
$756$		0			0
$757$		−	38.1487i		−	1.38654i	−0.720678	−	0.693270i	$-0.756170\pi$
$757$		−	38.1487i		−	1.38654i	0.720678	−	0.693270i	$-0.243830\pi$
$758$	−14.0691	−	30.0486i	−0.511014	−	1.09141i
$759$		0			0
$760$	2.24621	−	8.54312i	0.0814786	−	0.309891i
$761$	40.7386			1.47677			0.738387	−	0.674377i	$-0.235588\pi$
$761$	40.7386			1.47677			0.738387	+	0.674377i	$0.235588\pi$
$762$		0			0
$763$		−	5.61856i		−	0.203405i
$764$	−20.4924	+	24.5776i	−0.741390	+	0.889188i
$765$		0			0
$766$	−36.4924	+	17.0862i	−1.31852	+	0.617351i
$767$	−25.3693			−0.916033
$768$		0			0
$769$	−23.7538			−0.856584			−0.428292	−	0.903641i	$-0.640884\pi$
$769$	−23.7538			−0.856584			−0.428292	+	0.903641i	$0.640884\pi$
$770$	−18.2462	+	8.54312i	−0.657548	+	0.307873i
$771$		0			0
$772$	−3.68466	+	4.41921i	−0.132614	+	0.159051i
$773$		−	3.33513i		−	0.119956i	−0.998200	−	0.0599782i	$-0.980897\pi$
$773$		−	3.33513i		−	0.119956i	0.998200	−	0.0599782i	$-0.0191031\pi$
$774$		0			0
$775$	−38.2462			−1.37384
$776$	−3.05398	+	11.6153i	−0.109631	+	0.416966i
$777$		0			0
$778$	−4.63068	−	9.89012i	−0.166018	−	0.354578i
$779$			11.4677i			0.410872i
$780$		0			0
$781$			34.1725i			1.22279i
$782$	−8.00000	+	3.74571i	−0.286079	+	0.133946i
$783$		0			0
$784$	−0.719224	−	3.93481i	−0.0256866	−	0.140529i
$785$	−55.6155			−1.98500
$786$		0			0
$787$			27.6175i			0.984457i	0.870466	+	0.492228i	$0.163818\pi$
$787$			27.6175i			0.984457i	−0.870466	+	0.492228i	$0.836182\pi$
$788$	1.61553	+	1.34700i	0.0575508	+	0.0479849i
$789$		0			0
$790$		0			0
$791$	13.1231			0.466604
$792$		0			0
$793$	−11.1231			−0.394993
$794$	7.75379	+	16.5604i	0.275172	+	0.587706i
$795$		0			0
$796$	−2.24621	+	2.69400i	−0.0796148	+	0.0954863i
$797$		−	4.15628i		−	0.147223i	−0.997287	−	0.0736115i	$-0.976548\pi$
$797$		−	4.15628i		−	0.147223i	0.997287	−	0.0736115i	$-0.0234525\pi$
$798$		0			0
$799$		0			0
$800$	20.0885	+	28.2172i	0.710237	+	0.997627i
$801$		0			0
$802$	11.6847	−	5.47091i	0.412600	−	0.193185i
$803$		−	25.6294i		−	0.904440i
$804$		0			0
$805$			10.4160i			0.367115i
$806$	−12.4924	−	26.6811i	−0.440027	−	0.939800i
$807$		0			0
$808$	19.3693	+	5.09271i	0.681410	+	0.179161i
$809$	19.8617			0.698302			0.349151	−	0.937067i	$-0.386470\pi$
$809$	19.8617			0.698302			0.349151	+	0.937067i	$0.386470\pi$
$810$		0			0
$811$			10.5312i			0.369802i	0.982757	+	0.184901i	$0.0591965\pi$
$811$			10.5312i			0.369802i	−0.982757	+	0.184901i	$0.940804\pi$
$812$	−2.87689	−	2.39871i	−0.100959	−	0.0841781i
$813$		0			0
$814$	−10.2462	+	4.79741i	−0.359130	+	0.168149i
$815$	−26.7386			−0.936613
$816$		0			0
$817$	4.00000			0.139942
$818$	33.3002	−	15.5916i	1.16431	−	0.545147i
$819$		0			0
$820$	−62.7386	−	52.3104i	−2.19093	−	1.82676i
$821$			2.69400i			0.0940212i	0.998894	+	0.0470106i	$0.0149695\pi$
$821$			2.69400i			0.0940212i	−0.998894	+	0.0470106i	$0.985031\pi$
$822$		0			0
$823$	32.9848			1.14978			0.574890	−	0.818231i	$-0.305045\pi$
$823$	32.9848			1.14978			0.574890	+	0.818231i	$0.305045\pi$
$824$	−10.2462	+	38.9699i	−0.356944	+	1.35758i
$825$		0			0
$826$	4.56155	+	9.74247i	0.158717	+	0.338984i
$827$		−	32.8255i		−	1.14145i	−0.821140	−	0.570727i	$-0.806662\pi$
$827$		−	32.8255i		−	1.14145i	0.821140	−	0.570727i	$-0.193338\pi$
$828$		0			0
$829$		−	18.3180i		−	0.636209i	−0.948056	−	0.318104i	$-0.896954\pi$
$829$		−	18.3180i		−	0.636209i	0.948056	−	0.318104i	$-0.103046\pi$
$830$	40.4924	−	18.9591i	1.40551	−	0.658079i
$831$		0			0
$832$	−13.1231	+	23.2306i	−0.454962	+	0.805378i
$833$	−2.00000			−0.0692959
$834$		0			0
$835$			26.6811i			0.923336i
$836$	−5.12311	+	6.14441i	−0.177186	+	0.212509i
$837$		0			0
$838$	−4.06913	−	8.69076i	−0.140566	−	0.300217i
$839$	−42.7386			−1.47550			−0.737751	−	0.675073i	$-0.764112\pi$
$839$	−42.7386			−1.47550			−0.737751	+	0.675073i	$0.764112\pi$
$840$		0			0
$841$	25.4924			0.879049
$842$	−9.61553	−	20.5366i	−0.331373	−	0.707740i
$843$		0			0
$844$	3.68466	+	3.07221i	0.126831	+	0.105750i
$845$		−	6.25969i		−	0.215340i
$846$		0			0
$847$	7.24621			0.248983
$848$	33.6155	−	6.14441i	1.15436	−	0.211000i
$849$		0			0
$850$	15.6847	−	7.34376i	0.537979	−	0.251889i
$851$			5.84912i			0.200505i
$852$		0			0
$853$		−	50.0270i		−	1.71289i	−0.516237	−	0.856446i	$-0.672668\pi$
$853$		−	50.0270i		−	1.71289i	0.516237	−	0.856446i	$-0.327332\pi$
$854$	2.00000	+	4.27156i	0.0684386	+	0.146170i
$855$		0			0
$856$	19.6847	+	5.17562i	0.672808	+	0.176899i
$857$	−18.9848			−0.648510			−0.324255	−	0.945970i	$-0.605114\pi$
$857$	−18.9848			−0.648510			−0.324255	+	0.945970i	$0.605114\pi$
$858$		0			0
$859$		−	47.3977i		−	1.61719i	−0.588366	−	0.808595i	$-0.700229\pi$
$859$		−	47.3977i		−	1.61719i	0.588366	−	0.808595i	$-0.299771\pi$
$860$	−18.2462	+	21.8836i	−0.622191	+	0.746226i
$861$		0			0
$862$	30.2462	−	14.1617i	1.03019	−	0.482349i
$863$	−3.50758			−0.119399			−0.0596997	−	0.998216i	$-0.519014\pi$
$863$	−3.50758			−0.119399			−0.0596997	+	0.998216i	$0.519014\pi$
$864$		0			0
$865$	−58.3542			−1.98410
$866$	18.5616	−	8.69076i	0.630747	−	0.295324i
$867$		0			0
$868$	−8.00000	+	9.59482i	−0.271538	+	0.325669i
$869$		0			0
$870$		0			0
$871$	52.4924			1.77864
$872$	15.3693	+	4.04100i	0.520471	+	0.136846i
$873$		0			0
$874$	1.75379	+	3.74571i	0.0593228	+	0.126700i
$875$		−	3.74571i		−	0.126628i
$876$		0			0
$877$			26.4505i			0.893170i	0.894741	+	0.446585i	$0.147360\pi$
$877$			26.4505i			0.893170i	−0.894741	+	0.446585i	$0.852640\pi$
$878$	−34.2462	+	16.0345i	−1.15575	+	0.541139i
$879$		0			0
$880$	−10.2462	−	56.0561i	−0.345400	−	1.88965i
$881$	−27.7538			−0.935049			−0.467524	−	0.883980i	$-0.654854\pi$
$881$	−27.7538			−0.935049			−0.467524	+	0.883980i	$0.654854\pi$
$882$		0			0
$883$			2.39871i			0.0807229i	0.999185	+	0.0403614i	$0.0128509\pi$
$883$			2.39871i			0.0807229i	−0.999185	+	0.0403614i	$0.987149\pi$
$884$	10.2462	+	8.54312i	0.344617	+	0.287336i
$885$		0			0
$886$	−3.68466	−	7.86962i	−0.123789	−	0.264385i
$887$	−4.49242			−0.150841			−0.0754204	−	0.997152i	$-0.524030\pi$
$887$	−4.49242			−0.150841			−0.0754204	+	0.997152i	$0.524030\pi$
$888$		0			0
$889$	−4.87689			−0.163566
$890$	0.492423	+	1.05171i	0.0165060	+	0.0352533i
$891$		0			0
$892$	−28.4924	+	34.1725i	−0.953997	+	1.14418i
$893$		0			0
$894$		0			0
$895$	−8.00000			−0.267411
$896$	11.2808	+	0.862603i	0.376864	+	0.0288175i
$897$		0			0
$898$	41.9309	−	19.6326i	1.39925	−	0.655148i
$899$			11.6982i			0.390158i
$900$		0			0
$901$		−	17.0862i		−	0.569225i
$902$	31.3693	+	66.9979i	1.04448	+	2.23079i
$903$		0			0
$904$	−9.43845	+	35.8977i	−0.313918	+	1.19394i
$905$	45.8617			1.52450
$906$		0			0
$907$		−	43.0109i		−	1.42815i	−0.700068	−	0.714076i	$-0.746847\pi$
$907$		−	43.0109i		−	1.42815i	0.700068	−	0.714076i	$-0.253153\pi$
$908$	19.0540	+	15.8869i	0.632328	+	0.527225i
$909$		0			0
$910$	14.2462	−	6.67026i	0.472257	−	0.221117i
$911$	45.8617			1.51947			0.759734	−	0.650234i	$-0.225329\pi$
$911$	45.8617			1.51947			0.759734	+	0.650234i	$0.225329\pi$
$912$		0			0
$913$	−40.4924			−1.34010
$914$	−9.43845	+	4.41921i	−0.312196	+	0.146174i
$915$		0			0
$916$	−6.38447	−	5.32326i	−0.210949	−	0.175886i
$917$			3.86098i			0.127501i
$918$		0			0
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$	−28.4924	−	7.49141i	−0.939367	−	0.246985i
$921$		0			0
$922$	20.7386	+	44.2931i	0.682991	+	1.45872i
$923$		−	26.6811i		−	0.878218i
$924$		0			0
$925$		−	11.4677i		−	0.377055i
$926$		0			0
$927$		0			0
$928$	8.63068	−	6.14441i	0.283316	−	0.201700i
$929$	−30.4924			−1.00042			−0.500212	−	0.865903i	$-0.666745\pi$
$929$	−30.4924			−1.00042			−0.500212	+	0.865903i	$0.666745\pi$
$930$		0			0
$931$			0.936426i			0.0306901i
$932$	−0.315342	+	0.378206i	−0.0103294	+	0.0123885i
$933$		0			0
$934$	−0.561553	−	1.19935i	−0.0183746	−	0.0392440i
$935$	−28.4924			−0.931802
$936$		0			0
$937$	−30.9848			−1.01223			−0.506115	−	0.862466i	$-0.668919\pi$
$937$	−30.9848			−1.01223			−0.506115	+	0.862466i	$0.668919\pi$
$938$	−9.43845	−	20.1584i	−0.308176	−	0.658196i
$939$		0			0
$940$		0			0
$941$			32.9407i			1.07384i	0.843634	+	0.536919i	$0.180412\pi$
$941$			32.9407i			1.07384i	−0.843634	+	0.536919i	$0.819588\pi$
$942$		0			0
$943$	38.2462			1.24547
$944$	−29.9309	+	5.47091i	−0.974167	+	0.178063i
$945$		0			0
$946$	23.3693	−	10.9418i	0.759802	−	0.355749i
$947$			6.37497i			0.207159i	0.994621	+	0.103579i	$0.0330296\pi$
$947$			6.37497i			0.207159i	−0.994621	+	0.103579i	$0.966970\pi$
$948$		0			0
$949$			20.0108i			0.649578i
$950$	−3.43845	−	7.34376i	−0.111558	−	0.238263i
$951$		0			0
$952$	1.43845	−	5.47091i	0.0466203	−	0.177313i
$953$	50.4924			1.63561			0.817805	−	0.575495i	$-0.195191\pi$
$953$	50.4924			1.63561			0.817805	+	0.575495i	$0.195191\pi$
$954$		0			0
$955$			53.3621i			1.72676i
$956$	−30.2462	+	36.2759i	−0.978232	+	1.17325i
$957$		0			0
$958$	8.00000	−	3.74571i	0.258468	−	0.121018i
$959$	0.246211			0.00795058
$960$		0			0
$961$	8.01515			0.258553
$962$	8.00000	−	3.74571i	0.257930	−	0.120766i
$963$		0			0
$964$	−25.9309	+	31.1003i	−0.835177	+	1.00167i
$965$			9.59482i			0.308868i
$966$		0			0
$967$	−19.1231			−0.614958			−0.307479	−	0.951555i	$-0.599485\pi$
$967$	−19.1231			−0.614958			−0.307479	+	0.951555i	$0.599485\pi$
$968$	−5.21165	+	19.8217i	−0.167509	+	0.637093i
$969$		0			0
$970$	8.49242	+	18.1379i	0.272675	+	0.582374i
$971$			26.5658i			0.852536i	0.904597	+	0.426268i	$0.140172\pi$
$971$			26.5658i			0.852536i	−0.904597	+	0.426268i	$0.859828\pi$
$972$		0			0
$973$		−	18.0227i		−	0.577780i
$974$	32.4924	−	15.2134i	1.04112	−	0.487468i
$975$		0			0
$976$	−13.1231	+	2.39871i	−0.420060	+	0.0767807i
$977$	−40.2462			−1.28759			−0.643795	−	0.765198i	$-0.722641\pi$
$977$	−40.2462			−1.28759			−0.643795	+	0.765198i	$0.722641\pi$
$978$		0			0
$979$		−	1.05171i		−	0.0336127i
$980$	−5.12311	−	4.27156i	−0.163652	−	0.136450i
$981$		0			0
$982$	13.3002	+	28.4063i	0.424426	+	0.906480i
$983$	17.7538			0.566258			0.283129	−	0.959082i	$-0.408628\pi$
$983$	17.7538			0.566258			0.283129	+	0.959082i	$0.408628\pi$
$984$		0			0
$985$	3.50758			0.111761
$986$	−2.24621	−	4.79741i	−0.0715339	−	0.152781i
$987$		0			0
$988$	4.00000	−	4.79741i	0.127257	−	0.152626i
$989$		−	13.3405i		−	0.424204i
$990$		0			0
$991$	−3.50758			−0.111422			−0.0557109	−	0.998447i	$-0.517743\pi$
$991$	−3.50758			−0.111422			−0.0557109	+	0.998447i	$0.517743\pi$
$992$	−20.4924	−	28.7845i	−0.650635	−	0.913908i
$993$		0			0
$994$	−10.2462	+	4.79741i	−0.324990	+	0.152165i
$995$			5.84912i			0.185429i
$996$		0			0
$997$			44.9990i			1.42513i	0.701605	+	0.712566i	$0.252467\pi$
$997$			44.9990i			1.42513i	−0.701605	+	0.712566i	$0.747533\pi$
$998$	−14.5616	−	31.1003i	−0.460938	−	0.984462i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.c.d.253.3		4
3.2	odd	2		56.2.b.b.29.2	yes	4
4.3	odd	2		2016.2.c.c.1009.1		4
8.3	odd	2		2016.2.c.c.1009.4		4
8.5	even	2	inner	504.2.c.d.253.4		4
12.11	even	2		224.2.b.b.113.2		4
21.2	odd	6		392.2.p.f.165.4		8
21.5	even	6		392.2.p.e.165.4		8
21.11	odd	6		392.2.p.f.373.2		8
21.17	even	6		392.2.p.e.373.2		8
21.20	even	2		392.2.b.c.197.2		4
24.5	odd	2		56.2.b.b.29.1	✓	4
24.11	even	2		224.2.b.b.113.3		4
48.5	odd	4		1792.2.a.x.1.3		4
48.11	even	4		1792.2.a.v.1.2		4
48.29	odd	4		1792.2.a.x.1.2		4
48.35	even	4		1792.2.a.v.1.3		4
84.11	even	6		1568.2.t.d.177.2		8
84.23	even	6		1568.2.t.d.753.3		8
84.47	odd	6		1568.2.t.e.753.2		8
84.59	odd	6		1568.2.t.e.177.3		8
84.83	odd	2		1568.2.b.d.785.3		4
168.5	even	6		392.2.p.e.165.2		8
168.11	even	6		1568.2.t.d.177.3		8
168.53	odd	6		392.2.p.f.373.4		8
168.59	odd	6		1568.2.t.e.177.2		8
168.83	odd	2		1568.2.b.d.785.2		4
168.101	even	6		392.2.p.e.373.4		8
168.107	even	6		1568.2.t.d.753.2		8
168.125	even	2		392.2.b.c.197.1		4
168.131	odd	6		1568.2.t.e.753.3		8
168.149	odd	6		392.2.p.f.165.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.b.b.29.1	✓	4	24.5	odd	2
56.2.b.b.29.2	yes	4	3.2	odd	2
224.2.b.b.113.2		4	12.11	even	2
224.2.b.b.113.3		4	24.11	even	2
392.2.b.c.197.1		4	168.125	even	2
392.2.b.c.197.2		4	21.20	even	2
392.2.p.e.165.2		8	168.5	even	6
392.2.p.e.165.4		8	21.5	even	6
392.2.p.e.373.2		8	21.17	even	6
392.2.p.e.373.4		8	168.101	even	6
392.2.p.f.165.2		8	168.149	odd	6
392.2.p.f.165.4		8	21.2	odd	6
392.2.p.f.373.2		8	21.11	odd	6
392.2.p.f.373.4		8	168.53	odd	6
504.2.c.d.253.3		4	1.1	even	1	trivial
504.2.c.d.253.4		4	8.5	even	2	inner
1568.2.b.d.785.2		4	168.83	odd	2
1568.2.b.d.785.3		4	84.83	odd	2
1568.2.t.d.177.2		8	84.11	even	6
1568.2.t.d.177.3		8	168.11	even	6
1568.2.t.d.753.2		8	168.107	even	6
1568.2.t.d.753.3		8	84.23	even	6
1568.2.t.e.177.2		8	168.59	odd	6
1568.2.t.e.177.3		8	84.59	odd	6
1568.2.t.e.753.2		8	84.47	odd	6
1568.2.t.e.753.3		8	168.131	odd	6
1792.2.a.v.1.2		4	48.11	even	4
1792.2.a.v.1.3		4	48.35	even	4
1792.2.a.x.1.2		4	48.29	odd	4
1792.2.a.x.1.3		4	48.5	odd	4
2016.2.c.c.1009.1		4	4.3	odd	2
2016.2.c.c.1009.4		4	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.28078 - 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} -3.33513i q^{5} -1.00000 q^{7} +(0.719224 - 2.73546i) q^{8} +O(q^{10})\)	\(q+(1.28078 - 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} -3.33513i q^{5} -1.00000 q^{7} +(0.719224 - 2.73546i) q^{8} +(-2.00000 - 4.27156i) q^{10} +4.27156i q^{11} -3.33513i q^{13} +(-1.28078 + 0.599676i) q^{14} +(-0.719224 - 3.93481i) q^{16} -2.00000 q^{17} +0.936426i q^{19} +(-5.12311 - 4.27156i) q^{20} +(2.56155 + 5.47091i) q^{22} +3.12311 q^{23} -6.12311 q^{25} +(-2.00000 - 4.27156i) q^{26} +(-1.28078 + 1.53610i) q^{28} +1.87285i q^{29} +6.24621 q^{31} +(-3.28078 - 4.60831i) q^{32} +(-2.56155 + 1.19935i) q^{34} +3.33513i q^{35} +1.87285i q^{37} +(0.561553 + 1.19935i) q^{38} +(-9.12311 - 2.39871i) q^{40} +12.2462 q^{41} -4.27156i q^{43} +(6.56155 + 5.47091i) q^{44} +(4.00000 - 1.87285i) q^{46} +1.00000 q^{49} +(-7.84233 + 3.67188i) q^{50} +(-5.12311 - 4.27156i) q^{52} +8.54312i q^{53} +14.2462 q^{55} +(-0.719224 + 2.73546i) q^{56} +(1.12311 + 2.39871i) q^{58} -7.60669i q^{59} -3.33513i q^{61} +(8.00000 - 3.74571i) q^{62} +(-6.96543 - 3.93481i) q^{64} -11.1231 q^{65} +15.7392i q^{67} +(-2.56155 + 3.07221i) q^{68} +(2.00000 + 4.27156i) q^{70} +8.00000 q^{71} -6.00000 q^{73} +(1.12311 + 2.39871i) q^{74} +(1.43845 + 1.19935i) q^{76} -4.27156i q^{77} +(-13.1231 + 2.39871i) q^{80} +(15.6847 - 7.34376i) q^{82} +9.47954i q^{83} +6.67026i q^{85} +(-2.56155 - 5.47091i) q^{86} +(11.6847 + 3.07221i) q^{88} -0.246211 q^{89} +3.33513i q^{91} +(4.00000 - 4.79741i) q^{92} +3.12311 q^{95} -4.24621 q^{97} +(1.28078 - 0.599676i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} - 4 q^{7} + 7 q^{8}+O(q^{10}) \) 4 * q + q^2 + q^4 - 4 * q^7 + 7 * q^8	\( 4 q + q^{2} + q^{4} - 4 q^{7} + 7 q^{8} - 8 q^{10} - q^{14} - 7 q^{16} - 8 q^{17} - 4 q^{20} + 2 q^{22} - 4 q^{23} - 8 q^{25} - 8 q^{26} - q^{28} - 8 q^{31} - 9 q^{32} - 2 q^{34} - 6 q^{38} - 20 q^{40} + 16 q^{41} + 18 q^{44} + 16 q^{46} + 4 q^{49} - 19 q^{50} - 4 q^{52} + 24 q^{55} - 7 q^{56} - 12 q^{58} + 32 q^{62} + q^{64} - 28 q^{65} - 2 q^{68} + 8 q^{70} + 32 q^{71} - 24 q^{73} - 12 q^{74} + 14 q^{76} - 36 q^{80} + 38 q^{82} - 2 q^{86} + 22 q^{88} + 32 q^{89} + 16 q^{92} - 4 q^{95} + 16 q^{97} + q^{98}+O(q^{100}) \) 4 * q + q^2 + q^4 - 4 * q^7 + 7 * q^8 - 8 * q^10 - q^14 - 7 * q^16 - 8 * q^17 - 4 * q^20 + 2 * q^22 - 4 * q^23 - 8 * q^25 - 8 * q^26 - q^28 - 8 * q^31 - 9 * q^32 - 2 * q^34 - 6 * q^38 - 20 * q^40 + 16 * q^41 + 18 * q^44 + 16 * q^46 + 4 * q^49 - 19 * q^50 - 4 * q^52 + 24 * q^55 - 7 * q^56 - 12 * q^58 + 32 * q^62 + q^64 - 28 * q^65 - 2 * q^68 + 8 * q^70 + 32 * q^71 - 24 * q^73 - 12 * q^74 + 14 * q^76 - 36 * q^80 + 38 * q^82 - 2 * q^86 + 22 * q^88 + 32 * q^89 + 16 * q^92 - 4 * q^95 + 16 * q^97 + q^98

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