LMFDB - Embedded newform 532.2.v.e.341.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [532,2,Mod(341,532)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(532, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("532.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 532 = 2^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	532.v (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 413x^{12} + 3916x^{10} + 26956x^{8} + 112304x^{6} + 333008x^{4} + 476096x^{2} + 473344 $ x^16 + 25x^14 + 413x^12 + 3916x^10 + 26956x^8 + 112304x^6 + 333008x^4 + 476096*x^2 + 473344
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.1
Root			$-1.61383 + 2.79524i$ of defining polynomial
Character	$\chi$	$=$	532.341
Dual form			532.2.v.e.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61383 - 2.79524i) q^{3} +(-3.48366 - 2.01129i) q^{5} +(-1.80346 - 1.93585i) q^{7} +(-3.70889 + 6.42399i) q^{9} +O(q^{10})$	\(q+(-1.61383 - 2.79524i) q^{3} +(-3.48366 - 2.01129i) q^{5} +(-1.80346 - 1.93585i) q^{7} +(-3.70889 + 6.42399i) q^{9} +(-1.40543 - 2.43428i) q^{11} +5.18661 q^{13} +12.9835i q^{15} +(1.38169 - 0.797720i) q^{17} +(0.268274 - 4.35064i) q^{19} +(-2.50068 + 8.16524i) q^{21} +(-0.405431 + 0.702226i) q^{23} +(5.59059 + 9.68318i) q^{25} +14.2591 q^{27} -5.10348i q^{29} +(-1.61383 - 2.79524i) q^{31} +(-4.53625 + 7.85702i) q^{33} +(2.38909 + 10.3711i) q^{35} +(3.32029 + 1.91697i) q^{37} +(-8.37031 - 14.4978i) q^{39} -6.45532 q^{41} +1.26133 q^{43} +(25.8410 - 14.9193i) q^{45} +(-1.21629 - 0.702226i) q^{47} +(-0.495041 + 6.98247i) q^{49} +(-4.45963 - 2.57477i) q^{51} +(-9.72286 + 5.61350i) q^{53} +11.3069i q^{55} +(-12.5940 + 6.27130i) q^{57} +(5.72834 + 9.92177i) q^{59} +(-7.52471 - 4.34440i) q^{61} +(19.1247 - 4.40557i) q^{63} +(-18.0684 - 10.4318i) q^{65} +(-1.94295 + 1.12176i) q^{67} +2.61718 q^{69} -7.83399i q^{71} +(-8.46732 + 4.88861i) q^{73} +(18.0445 - 31.2540i) q^{75} +(-2.17776 + 7.11083i) q^{77} +(7.88389 + 4.55177i) q^{79} +(-11.8851 - 20.5856i) q^{81} -4.14493i q^{83} -6.41779 q^{85} +(-14.2654 + 8.23615i) q^{87} +(3.13503 - 5.43003i) q^{89} +(-9.35386 - 10.0405i) q^{91} +(-5.20889 + 9.02207i) q^{93} +(-9.68497 + 14.6166i) q^{95} +12.8052 q^{97} +20.8504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{5} - 14 q^{7} - 26 q^{9}+O(q^{10}) $ 16 * q - 6 * q^5 - 14 * q^7 - 26 * q^9	$ 16 q - 6 q^{5} - 14 q^{7} - 26 q^{9} - 4 q^{11} - 24 q^{17} + 21 q^{19} + 12 q^{23} + 10 q^{25} - 30 q^{35} - 12 q^{39} + 16 q^{43} + 72 q^{45} + 36 q^{47} - 34 q^{49} - 2 q^{57} - 24 q^{61} + 20 q^{63} - 36 q^{73} + 4 q^{77} - 24 q^{81} - 36 q^{85} - 48 q^{87} - 50 q^{93} + 31 q^{95} + 156 q^{99}+O(q^{100}) $ 16 * q - 6 * q^5 - 14 * q^7 - 26 * q^9 - 4 * q^11 - 24 * q^17 + 21 * q^19 + 12 * q^23 + 10 * q^25 - 30 * q^35 - 12 * q^39 + 16 * q^43 + 72 * q^45 + 36 * q^47 - 34 * q^49 - 2 * q^57 - 24 * q^61 + 20 * q^63 - 36 * q^73 + 4 * q^77 - 24 * q^81 - 36 * q^85 - 48 * q^87 - 50 * q^93 + 31 * q^95 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$.

$n$	$267$	$381$	$477$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.61383	−	2.79524i	−0.931745	−	1.61383i	−0.780338	−	0.625358i	$-0.784953\pi$
$3$	−1.61383	−	2.79524i	−0.931745	−	1.61383i	−0.151407	−	0.988471i	$-0.548381\pi$
$4$		0			0
$5$	−3.48366	−	2.01129i	−1.55794	−	0.899477i	−0.997454	−	0.0713125i	$-0.977281\pi$
$5$	−3.48366	−	2.01129i	−1.55794	−	0.899477i	−0.560485	−	0.828164i	$-0.689385\pi$
$6$		0			0
$7$	−1.80346	−	1.93585i	−0.681645	−	0.731683i
$7$	−1.80346	−	1.93585i	−0.681645	−	0.731683i
$8$		0			0
$9$	−3.70889	+	6.42399i	−1.23630	+	2.14133i
$10$		0			0
$11$	−1.40543	−	2.43428i	−0.423753	−	0.733962i	0.572550	−	0.819870i	$-0.305954\pi$
$11$	−1.40543	−	2.43428i	−0.423753	−	0.733962i	−0.996303	+	0.0859077i	$0.972621\pi$
$12$		0			0
$13$	5.18661			1.43851			0.719254	−	0.694748i	$-0.244484\pi$
$13$	5.18661			1.43851			0.719254	+	0.694748i	$0.244484\pi$
$14$		0			0
$15$			12.9835i			3.35233i
$16$		0			0
$17$	1.38169	−	0.797720i	0.335109	−	0.193475i	−0.322998	−	0.946400i	$-0.604691\pi$
$17$	1.38169	−	0.797720i	0.335109	−	0.193475i	0.658107	+	0.752924i	$0.271357\pi$
$18$		0			0
$19$	0.268274	−	4.35064i	0.0615463	−	0.998104i
$19$	0.268274	−	4.35064i	0.0615463	−	0.998104i
$20$		0			0
$21$	−2.50068	+	8.16524i	−0.545693	+	1.78180i
$22$		0			0
$23$	−0.405431	+	0.702226i	−0.0845381	+	0.146424i	−0.905194	−	0.424998i	$-0.860275\pi$
$23$	−0.405431	+	0.702226i	−0.0845381	+	0.146424i	0.820656	+	0.571422i	$0.193608\pi$
$24$		0			0
$25$	5.59059	+	9.68318i	1.11812	+	1.93664i
$26$		0			0
$27$	14.2591			2.74417
$28$		0			0
$29$		−	5.10348i		−	0.947693i	−0.880608	−	0.473846i	$-0.842865\pi$
$29$		−	5.10348i		−	0.947693i	0.880608	−	0.473846i	$-0.157135\pi$
$30$		0			0
$31$	−1.61383	−	2.79524i	−0.289852	−	0.502039i	0.683922	−	0.729555i	$-0.260273\pi$
$31$	−1.61383	−	2.79524i	−0.289852	−	0.502039i	−0.973774	+	0.227516i	$0.926940\pi$
$32$		0			0
$33$	−4.53625	+	7.85702i	−0.789660	+	1.36773i
$34$		0			0
$35$	2.38909	+	10.3711i	0.403830	+	1.75304i
$36$		0			0
$37$	3.32029	+	1.91697i	0.545852	+	0.315148i	0.747447	−	0.664321i	$-0.231279\pi$
$37$	3.32029	+	1.91697i	0.545852	+	0.315148i	−0.201595	+	0.979469i	$0.564613\pi$
$38$		0			0
$39$	−8.37031	−	14.4978i	−1.34032	−	2.32151i
$40$		0			0
$41$	−6.45532			−1.00815			−0.504076	−	0.863659i	$-0.668167\pi$
$41$	−6.45532			−1.00815			−0.504076	+	0.863659i	$0.668167\pi$
$42$		0			0
$43$	1.26133			0.192351			0.0961756	−	0.995364i	$-0.469339\pi$
$43$	1.26133			0.192351			0.0961756	+	0.995364i	$0.469339\pi$
$44$		0			0
$45$	25.8410	−	14.9193i	3.85215	−	2.22404i
$46$		0			0
$47$	−1.21629	−	0.702226i	−0.177414	−	0.102430i	0.408663	−	0.912685i	$-0.365995\pi$
$47$	−1.21629	−	0.702226i	−0.177414	−	0.102430i	−0.586077	+	0.810255i	$0.699329\pi$
$48$		0			0
$49$	−0.495041	+	6.98247i	−0.0707201	+	0.997496i
$50$		0			0
$51$	−4.45963	−	2.57477i	−0.624473	−	0.360540i
$52$		0			0
$53$	−9.72286	+	5.61350i	−1.33554	+	0.771073i	−0.986142	−	0.165902i	$-0.946946\pi$
$53$	−9.72286	+	5.61350i	−1.33554	+	0.771073i	−0.349396	+	0.936975i	$0.613613\pi$
$54$		0			0
$55$			11.3069i			1.52462i
$56$		0			0
$57$	−12.5940	+	6.27130i	−1.66812	+	0.830654i
$58$		0			0
$59$	5.72834	+	9.92177i	0.745766	+	1.29170i	0.949836	+	0.312748i	$0.101250\pi$
$59$	5.72834	+	9.92177i	0.745766	+	1.29170i	−0.204070	+	0.978956i	$0.565417\pi$
$60$		0			0
$61$	−7.52471	−	4.34440i	−0.963441	−	0.556243i	−0.0662106	−	0.997806i	$-0.521091\pi$
$61$	−7.52471	−	4.34440i	−0.963441	−	0.556243i	−0.897230	+	0.441563i	$0.854424\pi$
$62$		0			0
$63$	19.1247	−	4.40557i	2.40949	−	0.555049i
$64$		0			0
$65$	−18.0684	−	10.4318i	−2.24111	−	1.29390i
$66$		0			0
$67$	−1.94295	+	1.12176i	−0.237369	+	0.137045i	−0.613967	−	0.789332i	$-0.710427\pi$
$67$	−1.94295	+	1.12176i	−0.237369	+	0.137045i	0.376598	+	0.926377i	$0.377094\pi$
$68$		0			0
$69$	2.61718			0.315072
$70$		0			0
$71$		−	7.83399i		−	0.929724i	−0.885383	−	0.464862i	$-0.846104\pi$
$71$		−	7.83399i		−	0.929724i	0.885383	−	0.464862i	$-0.153896\pi$
$72$		0			0
$73$	−8.46732	+	4.88861i	−0.991025	+	0.572168i	−0.905580	−	0.424175i	$-0.860564\pi$
$73$	−8.46732	+	4.88861i	−0.991025	+	0.572168i	−0.0854441	+	0.996343i	$0.527231\pi$
$74$		0			0
$75$	18.0445	−	31.2540i	2.08360	−	3.60890i
$76$		0			0
$77$	−2.17776	+	7.11083i	−0.248178	+	0.810355i
$78$		0			0
$79$	7.88389	+	4.55177i	0.887007	+	0.512114i	0.872962	−	0.487788i	$-0.162196\pi$
$79$	7.88389	+	4.55177i	0.887007	+	0.512114i	0.0140448	+	0.999901i	$0.495529\pi$
$80$		0			0
$81$	−11.8851	−	20.5856i	−1.32057	−	2.28729i
$82$		0			0
$83$		−	4.14493i		−	0.454965i	−0.973782	−	0.227482i	$-0.926951\pi$
$83$		−	4.14493i		−	0.454965i	0.973782	−	0.227482i	$-0.0730494\pi$
$84$		0			0
$85$	−6.41779			−0.696107
$86$		0			0
$87$	−14.2654	+	8.23615i	−1.52942	+	0.883008i
$88$		0			0
$89$	3.13503	−	5.43003i	0.332313	−	0.575582i	−0.650652	−	0.759376i	$-0.725504\pi$
$89$	3.13503	−	5.43003i	0.332313	−	0.575582i	0.982965	+	0.183793i	$0.0588378\pi$
$90$		0			0
$91$	−9.35386	−	10.0405i	−0.980551	−	1.05253i
$92$		0			0
$93$	−5.20889	+	9.02207i	−0.540137	+	0.935545i
$94$		0			0
$95$	−9.68497	+	14.6166i	−0.993657	+	1.49963i
$96$		0			0
$97$	12.8052			1.30017			0.650083	−	0.759863i	$-0.274734\pi$
$97$	12.8052			1.30017			0.650083	+	0.759863i	$0.274734\pi$
$98$		0			0
$99$	20.8504			2.09554
$100$		0			0
$101$	0.646538	−	0.373279i	0.0643329	−	0.0371426i	−0.467489	−	0.883999i	$-0.654841\pi$
$101$	0.646538	−	0.373279i	0.0643329	−	0.0371426i	0.531821	+	0.846857i	$0.321508\pi$
$102$		0			0
$103$	2.50068	−	4.33130i	0.246399	−	0.426776i	−0.716125	−	0.697972i	$-0.754086\pi$
$103$	2.50068	−	4.33130i	0.246399	−	0.426776i	0.962524	+	0.271196i	$0.0874193\pi$
$104$		0			0
$105$	25.1342	−	23.4153i	2.45284	−	2.28510i
$106$		0			0
$107$	−2.40457	−	1.38828i	−0.232459	−	0.134210i	0.379247	−	0.925295i	$-0.376183\pi$
$107$	−2.40457	−	1.38828i	−0.232459	−	0.134210i	−0.611706	+	0.791085i	$0.709516\pi$
$108$		0			0
$109$	1.94295	−	1.12176i	0.186100	−	0.107445i	−0.404055	−	0.914735i	$-0.632400\pi$
$109$	1.94295	−	1.12176i	0.186100	−	0.107445i	0.590156	+	0.807289i	$0.299066\pi$
$110$		0			0
$111$		−	12.3746i		−	1.17455i
$112$		0			0
$113$			9.95745i			0.936718i	0.883538	+	0.468359i	$0.155155\pi$
$113$			9.95745i			0.936718i	−0.883538	+	0.468359i	$0.844845\pi$
$114$		0			0
$115$	2.82476	−	1.63088i	0.263411	−	0.152080i
$116$		0			0
$117$	−19.2366	+	33.3188i	−1.77842	+	3.08032i
$118$		0			0
$119$	−4.03610	−	1.23609i	−0.369988	−	0.113312i
$120$		0			0
$121$	1.54953	−	2.68386i	0.140866	−	0.243988i
$122$		0			0
$123$	10.4178	+	18.0441i	0.939340	+	1.62699i
$124$		0			0
$125$		−	24.8643i		−	2.22393i
$126$		0			0
$127$		−	10.7400i		−	0.953022i	−0.879169	−	0.476511i	$-0.841901\pi$
$127$		−	10.7400i		−	0.953022i	0.879169	−	0.476511i	$-0.158099\pi$
$128$		0			0
$129$	−2.03557	−	3.52572i	−0.179222	−	0.310422i
$130$		0			0
$131$	−17.6103	−	10.1673i	−1.53862	−	0.888324i	−0.998920	−	0.0464685i	$-0.985203\pi$
$131$	−17.6103	−	10.1673i	−1.53862	−	0.888324i	−0.539703	−	0.841856i	$-0.681463\pi$
$132$		0			0
$133$	−8.90601	+	7.32687i	−0.772249	+	0.635320i
$134$		0			0
$135$	−49.6739	−	28.6792i	−4.27525	−	2.46832i
$136$		0			0
$137$	4.46732	+	7.73762i	0.381669	+	0.661070i	0.991301	−	0.131615i	$-0.0420162\pi$
$137$	4.46732	+	7.73762i	0.381669	+	0.661070i	−0.609632	+	0.792684i	$0.708683\pi$
$138$		0			0
$139$			5.56365i			0.471902i	0.971765	+	0.235951i	$0.0758205\pi$
$139$			5.56365i			0.471902i	−0.971765	+	0.235951i	$0.924179\pi$
$140$		0			0
$141$			4.53310i			0.381756i
$142$		0			0
$143$	−7.28942	−	12.6257i	−0.609572	−	1.05581i
$144$		0			0
$145$	−10.2646	+	17.7788i	−0.852428	+	1.47645i
$146$		0			0
$147$	20.3166	−	9.88477i	1.67568	−	0.815282i
$148$		0			0
$149$	6.35192	−	11.0018i	0.520369	−	0.901306i	−0.479350	−	0.877624i	$-0.659128\pi$
$149$	6.35192	−	11.0018i	0.520369	−	0.901306i	0.999720	−	0.0236823i	$-0.00753903\pi$
$150$		0			0
$151$	4.37986	−	2.52871i	0.356428	−	0.205784i	−0.311085	−	0.950382i	$-0.600692\pi$
$151$	4.37986	−	2.52871i	0.356428	−	0.205784i	0.667513	+	0.744598i	$0.267359\pi$
$152$		0			0
$153$			11.8346i			0.956773i
$154$		0			0
$155$			12.9835i			1.04286i
$156$		0			0
$157$	2.72865	−	1.57539i	0.217770	−	0.125729i	−0.387147	−	0.922018i	$-0.626540\pi$
$157$	2.72865	−	1.57539i	0.217770	−	0.125729i	0.604917	+	0.796288i	$0.293206\pi$
$158$		0			0
$159$	31.3821	+	18.1185i	2.48876	+	1.43689i
$160$		0			0
$161$	2.09059	−	0.481586i	0.164761	−	0.0379543i
$162$		0			0
$163$	−1.34803	+	2.33486i	−0.105586	+	0.182881i	−0.913978	−	0.405765i	$-0.867005\pi$
$163$	−1.34803	+	2.33486i	−0.105586	+	0.182881i	0.808391	+	0.588645i	$0.200339\pi$
$164$		0			0
$165$	31.6055	−	18.2474i	2.46049	−	1.42056i
$166$		0			0
$167$	−5.79709			−0.448592			−0.224296	−	0.974521i	$-0.572008\pi$
$167$	−5.79709			−0.448592			−0.224296	+	0.974521i	$0.572008\pi$
$168$		0			0
$169$	13.9009			1.06930
$170$		0			0
$171$	26.9534	+	17.8594i	2.06118	+	1.36575i
$172$		0			0
$173$	3.76939	−	6.52877i	0.286581	−	0.496373i	−0.686410	−	0.727214i	$-0.740815\pi$
$173$	3.76939	−	6.52877i	0.286581	−	0.496373i	0.972991	+	0.230842i	$0.0741479\pi$
$174$		0			0
$175$	8.66278	−	28.2858i	0.654844	−	2.13821i
$176$		0			0
$177$	18.4891	−	32.0241i	1.38973	−	2.40708i
$178$		0			0
$179$	14.1426	−	8.16524i	1.05707	−	0.610299i	0.132448	−	0.991190i	$-0.457716\pi$
$179$	14.1426	−	8.16524i	1.05707	−	0.610299i	0.924620	+	0.380891i	$0.124383\pi$
$180$		0			0
$181$	7.98905			0.593822			0.296911	−	0.954905i	$-0.404044\pi$
$181$	7.98905			0.593822			0.296911	+	0.954905i	$0.404044\pi$
$182$		0			0
$183$			28.0445i			2.07311i
$184$		0			0
$185$	−7.71117	−	13.3561i	−0.566936	−	0.981962i
$186$		0			0
$187$	−3.88374	−	2.24228i	−0.284007	−	0.163972i
$188$		0			0
$189$	−25.7158	−	27.6035i	−1.87055	−	2.00786i
$190$		0			0
$191$	−2.16044	+	3.74199i	−0.156324	+	0.270761i	−0.933540	−	0.358472i	$-0.883298\pi$
$191$	−2.16044	+	3.74199i	−0.156324	+	0.270761i	0.777216	+	0.629233i	$0.216631\pi$
$192$		0			0
$193$	−12.7653	+	7.37003i	−0.918864	+	0.530506i	−0.883272	−	0.468860i	$-0.844665\pi$
$193$	−12.7653	+	7.37003i	−0.918864	+	0.530506i	−0.0355915	+	0.999366i	$0.511332\pi$
$194$		0			0
$195$			67.3405i			4.82235i
$196$		0			0
$197$	9.99418			0.712056			0.356028	−	0.934475i	$-0.384131\pi$
$197$	9.99418			0.712056			0.356028	+	0.934475i	$0.384131\pi$
$198$		0			0
$199$	−9.48600	+	5.47674i	−0.672444	+	0.388236i	−0.797002	−	0.603976i	$-0.793582\pi$
$199$	−9.48600	+	5.47674i	−0.672444	+	0.388236i	0.124558	+	0.992212i	$0.460249\pi$
$200$		0			0
$201$	6.27117	+	3.62066i	0.442334	+	0.255382i
$202$		0			0
$203$	−9.87958	+	9.20394i	−0.693411	+	0.645990i
$204$		0			0
$205$	22.4881	+	12.9835i	1.57064	+	0.906809i
$206$		0			0
$207$	−3.00740	−	5.20897i	−0.209029	−	0.362048i
$208$		0			0
$209$	−10.9677	+	5.46146i	−0.758651	+	0.377777i
$210$		0			0
$211$			22.1792i			1.52688i	0.645880	+	0.763439i	$0.276490\pi$
$211$			22.1792i			1.52688i	−0.645880	+	0.763439i	$0.723510\pi$
$212$		0			0
$213$	−21.8978	+	12.6427i	−1.50042	+	0.866266i
$214$		0			0
$215$	−4.39405	−	2.53690i	−0.299672	−	0.173015i
$216$		0			0
$217$	−2.50068	+	8.16524i	−0.169757	+	0.554293i
$218$		0			0
$219$	27.3296	+	15.7788i	1.84676	+	1.06623i
$220$		0			0
$221$	7.16630	−	4.13746i	0.482057	−	0.278316i
$222$		0			0
$223$	−14.6843			−0.983336			−0.491668	−	0.870783i	$-0.663613\pi$
$223$	−14.6843			−0.983336			−0.491668	+	0.870783i	$0.663613\pi$
$224$		0			0
$225$	−82.9395			−5.52930
$226$		0			0
$227$	−0.212609	−	0.368250i	−0.0141114	−	0.0244416i	0.858883	−	0.512171i	$-0.171159\pi$
$227$	−0.212609	−	0.368250i	−0.0141114	−	0.0244416i	−0.872995	+	0.487729i	$0.837825\pi$
$228$		0			0
$229$	−10.6183	−	6.13048i	−0.701678	−	0.405114i	0.106294	−	0.994335i	$-0.466101\pi$
$229$	−10.6183	−	6.13048i	−0.701678	−	0.405114i	−0.807972	+	0.589221i	$0.799435\pi$
$230$		0			0
$231$	23.3910	−	5.38833i	1.53901	−	0.354526i
$232$		0			0
$233$	0.381691	−	0.661109i	0.0250054	−	0.0433107i	−0.853252	−	0.521499i	$-0.825373\pi$
$233$	0.381691	−	0.661109i	0.0250054	−	0.0433107i	0.878257	+	0.478188i	$0.158706\pi$
$234$		0			0
$235$	2.82476	+	4.89263i	0.184267	+	0.319160i
$236$		0			0
$237$		−	29.3831i		−	1.90864i
$238$		0			0
$239$	−24.3950			−1.57798			−0.788991	−	0.614404i	$-0.789396\pi$
$239$	−24.3950			−1.57798			−0.788991	+	0.614404i	$0.789396\pi$
$240$		0			0
$241$	−11.5493	−	20.0040i	−0.743956	−	1.28857i	−0.950681	−	0.310170i	$-0.899614\pi$
$241$	−11.5493	−	20.0040i	−0.743956	−	1.28857i	0.206725	−	0.978399i	$-0.433719\pi$
$242$		0			0
$243$	−16.9724	+	29.3971i	−1.08878	+	1.88582i
$244$		0			0
$245$	15.7683	−	23.3289i	1.00740	−	1.49043i
$246$		0			0
$247$	1.39143	−	22.5651i	0.0885348	−	1.43578i
$248$		0			0
$249$	−11.5860	+	6.68920i	−0.734236	+	0.423911i
$250$		0			0
$251$			13.2893i			0.838811i	0.907799	+	0.419406i	$0.137761\pi$
$251$			13.2893i			0.838811i	−0.907799	+	0.419406i	$0.862239\pi$
$252$		0			0
$253$	2.27922			0.143293
$254$		0			0
$255$	10.3572	+	17.9392i	0.648594	+	1.12340i
$256$		0			0
$257$	−10.3045	+	17.8479i	−0.642775	+	1.11332i	0.342035	+	0.939687i	$0.388884\pi$
$257$	−10.3045	+	17.8479i	−0.642775	+	1.11332i	−0.984811	+	0.173632i	$0.944450\pi$
$258$		0			0
$259$	−2.27705	−	9.88477i	−0.141489	−	0.614210i
$260$		0			0
$261$	32.7847	+	18.9283i	2.02932	+	1.17163i
$262$		0			0
$263$	−0.414374	−	0.717717i	−0.0255514	−	0.0442563i	0.852967	−	0.521965i	$-0.174801\pi$
$263$	−0.414374	−	0.717717i	−0.0255514	−	0.0442563i	−0.878518	+	0.477709i	$0.841467\pi$
$264$		0			0
$265$	45.1615			2.77425
$266$		0			0
$267$	−20.2376			−1.23852
$268$		0			0
$269$	−12.3162	−	21.3322i	−0.750930	−	1.30065i	−0.947372	−	0.320134i	$-0.896272\pi$
$269$	−12.3162	−	21.3322i	−0.750930	−	1.30065i	0.196442	−	0.980515i	$-0.437061\pi$
$270$		0			0
$271$	−8.06975	−	4.65907i	−0.490203	−	0.283019i	0.234456	−	0.972127i	$-0.424669\pi$
$271$	−8.06975	−	4.65907i	−0.490203	−	0.283019i	−0.724659	+	0.689108i	$0.758002\pi$
$272$		0			0
$273$	−12.9700	+	42.3499i	−0.784983	+	2.56313i
$274$		0			0
$275$	15.7144	−	27.2181i	0.947611	−	1.64131i
$276$		0			0
$277$	7.06433	+	12.2358i	0.424454	+	0.735176i	0.996369	−	0.0851366i	$-0.0271327\pi$
$277$	7.06433	+	12.2358i	0.424454	+	0.735176i	−0.571915	+	0.820313i	$0.693799\pi$
$278$		0			0
$279$	23.9421			1.43338
$280$		0			0
$281$			20.1644i			1.20291i	0.798907	+	0.601454i	$0.205412\pi$
$281$			20.1644i			1.20291i	−0.798907	+	0.601454i	$0.794588\pi$
$282$		0			0
$283$	−18.8415	+	10.8782i	−1.12001	+	0.646639i	−0.941404	−	0.337281i	$-0.890493\pi$
$283$	−18.8415	+	10.8782i	−1.12001	+	0.646639i	−0.178608	+	0.983920i	$0.557159\pi$
$284$		0			0
$285$	56.4866	+	3.48314i	3.34598	+	0.206324i
$286$		0			0
$287$	11.6419	+	12.4965i	0.687201	+	0.737647i
$288$		0			0
$289$	−7.22729	+	12.5180i	−0.425134	+	0.736355i
$290$		0			0
$291$	−20.6653	−	35.7934i	−1.21142	−	2.09825i
$292$		0			0
$293$	−6.45532			−0.377124			−0.188562	−	0.982061i	$-0.560383\pi$
$293$	−6.45532			−0.377124			−0.188562	+	0.982061i	$0.560383\pi$
$294$		0			0
$295$		−	46.0854i		−	2.68320i
$296$		0			0
$297$	−20.0402	−	34.7106i	−1.16285	−	2.01412i
$298$		0			0
$299$	−2.10281	+	3.64218i	−0.121609	+	0.210632i
$300$		0			0
$301$	−2.27476	−	2.44175i	−0.131115	−	0.140740i
$302$		0			0
$303$	−2.08681	−	1.20482i	−0.119884	−	0.0692150i
$304$		0			0
$305$	17.4757	+	30.2688i	1.00066	+	1.73319i
$306$		0			0
$307$	2.80244			0.159944			0.0799719	−	0.996797i	$-0.474517\pi$
$307$	2.80244			0.159944			0.0799719	+	0.996797i	$0.474517\pi$
$308$		0			0
$309$	−16.1427			−0.918324
$310$		0			0
$311$	−16.4558	+	9.50078i	−0.933125	+	0.538740i	−0.887798	−	0.460232i	$-0.847766\pi$
$311$	−16.4558	+	9.50078i	−0.933125	+	0.538740i	−0.0453262	+	0.998972i	$0.514433\pi$
$312$		0			0
$313$	29.2801	+	16.9049i	1.65501	+	0.955521i	0.974967	+	0.222349i	$0.0713725\pi$
$313$	29.2801	+	16.9049i	1.65501	+	0.955521i	0.680044	+	0.733172i	$0.261961\pi$
$314$		0			0
$315$	−75.4850	−	23.1179i	−4.25310	−	1.30255i
$316$		0			0
$317$	−19.4856	−	11.2500i	−1.09442	−	0.631864i	−0.159671	−	0.987170i	$-0.551043\pi$
$317$	−19.4856	−	11.2500i	−1.09442	−	0.631864i	−0.934750	+	0.355306i	$0.884377\pi$
$318$		0			0
$319$	−12.4233	+	7.17259i	−0.695571	+	0.401588i
$320$		0			0
$321$			8.96180i			0.500199i
$322$		0			0
$323$	−3.09992	−	6.22524i	−0.172484	−	0.346382i
$324$		0			0
$325$	28.9962	+	50.2229i	1.60842	+	2.78586i
$326$		0			0
$327$	−6.27117	−	3.62066i	−0.346796	−	0.200223i
$328$		0			0
$329$	0.834132	+	3.62100i	0.0459872	+	0.199632i
$330$		0			0
$331$	−14.1426	−	8.16524i	−0.777348	−	0.448802i	0.0581415	−	0.998308i	$-0.481483\pi$
$331$	−14.1426	−	8.16524i	−0.777348	−	0.448802i	−0.835490	+	0.549506i	$0.814816\pi$
$332$		0			0
$333$	−24.6292	+	14.2197i	−1.34967	+	0.779233i
$334$		0			0
$335$	9.02475			0.493075
$336$		0			0
$337$			3.26355i			0.177777i	0.996042	+	0.0888885i	$0.0283315\pi$
$337$			3.26355i			0.177777i	−0.996042	+	0.0888885i	$0.971669\pi$
$338$		0			0
$339$	27.8334	−	16.0696i	1.51170	−	0.872783i
$340$		0			0
$341$	−4.53625	+	7.85702i	−0.245652	+	0.425481i
$342$		0			0
$343$	14.4098	−	11.6343i	0.778057	−	0.628194i
$344$		0			0
$345$	−9.11738	−	5.26392i	−0.490863	−	0.283400i
$346$		0			0
$347$	−1.29003	−	2.23440i	−0.0692524	−	0.119949i	0.829320	−	0.558774i	$-0.188728\pi$
$347$	−1.29003	−	2.23440i	−0.0692524	−	0.119949i	−0.898572	+	0.438825i	$0.855395\pi$
$348$		0			0
$349$		−	24.7341i		−	1.32399i	−0.749510	−	0.661993i	$-0.769711\pi$
$349$		−	24.7341i		−	1.32399i	0.749510	−	0.661993i	$-0.230289\pi$
$350$		0			0
$351$	73.9565			3.94751
$352$		0			0
$353$	19.2682	−	11.1245i	1.02554	−	0.592099i	0.109840	−	0.993949i	$-0.464966\pi$
$353$	19.2682	−	11.1245i	1.02554	−	0.592099i	0.915705	+	0.401851i	$0.131633\pi$
$354$		0			0
$355$	−15.7564	+	27.2910i	−0.836265	+	1.44845i
$356$		0			0
$357$	3.05841	+	13.2767i	0.161868	+	0.702676i
$358$		0			0
$359$	5.52920	−	9.57686i	0.291820	−	0.505447i	−0.682420	−	0.730960i	$-0.739072\pi$
$359$	5.52920	−	9.57686i	0.291820	−	0.505447i	0.974240	+	0.225513i	$0.0724058\pi$
$360$		0			0
$361$	−18.8561	−	2.33432i	−0.992424	−	0.122859i
$362$		0			0
$363$	−10.0027			−0.525006
$364$		0			0
$365$	39.3297			2.05861
$366$		0			0
$367$	−16.2385	+	9.37529i	−0.847642	+	0.489386i	−0.859855	−	0.510539i	$-0.829446\pi$
$367$	−16.2385	+	9.37529i	−0.847642	+	0.489386i	0.0122125	+	0.999925i	$0.496113\pi$
$368$		0			0
$369$	23.9421	−	41.4689i	1.24638	−	2.15879i
$370$		0			0
$371$	28.4017	+	8.69828i	1.47454	+	0.451592i
$372$		0			0
$373$	24.7488	+	14.2888i	1.28145	+	0.739844i	0.977113	−	0.212722i	$-0.0682328\pi$
$373$	24.7488	+	14.2888i	1.28145	+	0.739844i	0.304334	+	0.952565i	$0.401566\pi$
$374$		0			0
$375$	−69.5015	+	40.1267i	−3.58904	+	2.07213i
$376$		0			0
$377$		−	26.4698i		−	1.36326i
$378$		0			0
$379$			2.98002i			0.153073i	0.997067	+	0.0765367i	$0.0243862\pi$
$379$			2.98002i			0.153073i	−0.997067	+	0.0765367i	$0.975614\pi$
$380$		0			0
$381$	−30.0208	+	17.3325i	−1.53801	+	0.887973i
$382$		0			0
$383$	−1.18861	+	2.05873i	−0.0607352	+	0.105196i	−0.894794	−	0.446479i	$-0.852678\pi$
$383$	−1.18861	+	2.05873i	−0.0607352	+	0.105196i	0.834059	+	0.551675i	$0.186011\pi$
$384$		0			0
$385$	21.8885	−	20.3916i	1.11554	−	1.03925i
$386$		0			0
$387$	−4.67814	+	8.10278i	−0.237803	+	0.411888i
$388$		0			0
$389$	−9.93122	−	17.2014i	−0.503533	−	0.872145i	−0.999992	−	0.00408425i	$-0.998700\pi$
$389$	−9.93122	−	17.2014i	−0.503533	−	0.872145i	0.496459	−	0.868060i	$-0.334633\pi$
$390$		0			0
$391$			1.29368i			0.0654242i
$392$		0			0
$393$			65.6334i			3.31077i
$394$		0			0
$395$	−18.3099	−	31.7136i	−0.921269	−	1.59568i
$396$		0			0
$397$	−4.00650	−	2.31316i	−0.201081	−	0.116094i	0.396079	−	0.918217i	$-0.370371\pi$
$397$	−4.00650	−	2.31316i	−0.201081	−	0.116094i	−0.597159	+	0.802123i	$0.703704\pi$
$398$		0			0
$399$	34.8531	+	13.0701i	1.74484	+	0.654321i
$400$		0			0
$401$	23.8256	+	13.7557i	1.18979	+	0.686927i	0.958260	−	0.285900i	$-0.0922924\pi$
$401$	23.8256	+	13.7557i	1.18979	+	0.686927i	0.231533	+	0.972827i	$0.425626\pi$
$402$		0			0
$403$	−8.37031	−	14.4978i	−0.416955	−	0.722187i
$404$		0			0
$405$			95.6176i			4.75128i
$406$		0			0
$407$		−	10.7767i		−	0.534180i
$408$		0			0
$409$	0.594470	+	1.02965i	0.0293946	+	0.0509130i	0.880349	−	0.474327i	$-0.157309\pi$
$409$	0.594470	+	1.02965i	0.0293946	+	0.0509130i	−0.850954	+	0.525240i	$0.823975\pi$
$410$		0			0
$411$	14.4190	−	24.9744i	0.711236	−	1.23190i
$412$		0			0
$413$	8.87623	−	28.9828i	0.436771	−	1.42615i
$414$		0			0
$415$	−8.33665	+	14.4395i	−0.409230	+	0.708807i
$416$		0			0
$417$	15.5517	−	8.97878i	0.761570	−	0.439693i
$418$		0			0
$419$		−	25.4257i		−	1.24212i	−0.783761	−	0.621062i	$-0.786701\pi$
$419$		−	25.4257i		−	1.24212i	0.783761	−	0.621062i	$-0.213299\pi$
$420$		0			0
$421$		−	38.7384i		−	1.88799i	−0.329953	−	0.943997i	$-0.607033\pi$
$421$		−	38.7384i		−	1.88799i	0.329953	−	0.943997i	$-0.392967\pi$
$422$		0			0
$423$	9.02219	−	5.20897i	0.438674	−	0.253269i
$424$		0			0
$425$	15.4489	+	8.91944i	0.749383	+	0.432656i
$426$		0			0
$427$	5.16044	+	22.4017i	0.249731	+	1.08409i
$428$		0			0
$429$	−23.5278	+	40.7513i	−1.13593	+	1.96749i
$430$		0			0
$431$	17.8049	−	10.2796i	0.857631	−	0.495153i	−0.00558755	−	0.999984i	$-0.501779\pi$
$431$	17.8049	−	10.2796i	0.857631	−	0.495153i	0.863218	+	0.504831i	$0.168445\pi$
$432$		0			0
$433$	5.13886			0.246958			0.123479	−	0.992347i	$-0.460595\pi$
$433$	5.13886			0.246958			0.123479	+	0.992347i	$0.460595\pi$
$434$		0			0
$435$	66.2612			3.17698
$436$		0			0
$437$	2.94636	+	1.95227i	0.140944	+	0.0933897i
$438$		0			0
$439$	9.74674	−	16.8819i	0.465187	−	0.805727i	−0.534023	−	0.845470i	$-0.679321\pi$
$439$	9.74674	−	16.8819i	0.465187	−	0.805727i	0.999210	+	0.0397429i	$0.0126539\pi$
$440$		0			0
$441$	−43.0193	−	29.0774i	−2.04854	−	1.38464i
$442$		0			0
$443$	3.92130	−	6.79190i	0.186307	−	0.322693i	−0.757709	−	0.652592i	$-0.773682\pi$
$443$	3.92130	−	6.79190i	0.186307	−	0.322693i	0.944016	+	0.329899i	$0.107015\pi$
$444$		0			0
$445$	−21.8428	+	12.6109i	−1.03545	+	0.597815i
$446$		0			0
$447$	−41.0037			−1.93941
$448$		0			0
$449$		−	3.97210i		−	0.187455i	−0.995598	−	0.0937275i	$-0.970122\pi$
$449$		−	3.97210i		−	0.187455i	0.995598	−	0.0937275i	$-0.0298783\pi$
$450$		0			0
$451$	9.07250	+	15.7140i	0.427208	+	0.739945i
$452$		0			0
$453$	−14.1367	−	8.16183i	−0.664200	−	0.383476i
$454$		0			0
$455$	12.3913	+	53.7911i	0.580912	+	2.52176i
$456$		0			0
$457$	5.13164	−	8.88826i	0.240048	−	0.415775i	−0.720680	−	0.693268i	$-0.756170\pi$
$457$	5.13164	−	8.88826i	0.240048	−	0.415775i	0.960728	+	0.277493i	$0.0895035\pi$
$458$		0			0
$459$	19.7017	−	11.3748i	0.919596	−	0.530929i
$460$		0			0
$461$			5.99418i			0.279177i	0.990210	+	0.139588i	$0.0445779\pi$
$461$			5.99418i			0.279177i	−0.990210	+	0.139588i	$0.955422\pi$
$462$		0			0
$463$	−10.1296			−0.470762			−0.235381	−	0.971903i	$-0.575634\pi$
$463$	−10.1296			−0.470762			−0.235381	+	0.971903i	$0.575634\pi$
$464$		0			0
$465$	36.2920	−	20.9532i	1.68300	−	0.971682i
$466$		0			0
$467$	28.2657	+	16.3192i	1.30798	+	0.755163i	0.981759	−	0.190130i	$-0.0608908\pi$
$467$	28.2657	+	16.3192i	1.30798	+	0.755163i	0.326223	+	0.945293i	$0.394224\pi$
$468$		0			0
$469$	5.67559	+	1.73820i	0.262075	+	0.0802627i
$470$		0			0
$471$	−8.80715	−	5.08481i	−0.405812	−	0.234296i
$472$		0			0
$473$	−1.77271	−	3.07043i	−0.0815095	−	0.141179i
$474$		0			0
$475$	43.6278	−	21.7249i	2.00178	−	0.996805i
$476$		0			0
$477$		−	83.2795i		−	3.81310i
$478$		0			0
$479$	−22.6857	+	13.0976i	−1.03653	+	0.598443i	−0.918850	−	0.394608i	$-0.870881\pi$
$479$	−22.6857	+	13.0976i	−1.03653	+	0.598443i	−0.117685	+	0.993051i	$0.537547\pi$
$480$		0			0
$481$	17.2210	+	9.94258i	0.785212	+	0.453342i
$482$		0			0
$483$	−4.72000	−	5.06648i	−0.214767	−	0.230533i
$484$		0			0
$485$	−44.6088	−	25.7549i	−2.02558	−	1.16947i
$486$		0			0
$487$	32.5853	−	18.8131i	1.47658	−	0.852505i	0.476931	−	0.878941i	$-0.341749\pi$
$487$	32.5853	−	18.8131i	1.47658	−	0.852505i	0.999651	+	0.0264362i	$0.00841588\pi$
$488$		0			0
$489$	8.70199			0.393518
$490$		0			0
$491$	−39.1633			−1.76741			−0.883707	−	0.468040i	$-0.844960\pi$
$491$	−39.1633			−1.76741			−0.883707	+	0.468040i	$0.844960\pi$
$492$		0			0
$493$	−4.07115	−	7.05144i	−0.183355	−	0.317581i
$494$		0			0
$495$	−72.6356	−	41.9362i	−3.26473	−	1.88489i
$496$		0			0
$497$	−15.1654	+	14.1283i	−0.680263	+	0.633742i
$498$		0			0
$499$	12.3891	−	21.4585i	0.554612	−	0.960616i	−0.443322	−	0.896363i	$-0.646200\pi$
$499$	12.3891	−	21.4585i	0.554612	−	0.960616i	0.997934	−	0.0642533i	$-0.0204666\pi$
$500$		0			0
$501$	9.35551	+	16.2042i	0.417973	+	0.723951i
$502$		0			0
$503$		−	27.3235i		−	1.21829i	−0.793058	−	0.609147i	$-0.791512\pi$
$503$		−	27.3235i		−	1.21829i	0.793058	−	0.609147i	$-0.208488\pi$
$504$		0			0
$505$	−3.00309			−0.133636
$506$		0			0
$507$	−22.4338	−	38.8564i	−0.996318	−	1.72567i
$508$		0			0
$509$	5.67559	−	9.83042i	0.251566	−	0.435725i	−0.712391	−	0.701783i	$-0.752388\pi$
$509$	5.67559	−	9.83042i	0.251566	−	0.435725i	0.963957	+	0.266057i	$0.0857210\pi$
$510$		0			0
$511$	24.7341	+	7.57504i	1.09417	+	0.335100i
$512$		0			0
$513$	3.82535	−	62.0362i	0.168893	−	2.73897i
$514$		0			0
$515$	−17.4230	+	10.0592i	−0.767750	+	0.443260i
$516$		0			0
$517$			3.94772i			0.173621i
$518$		0			0
$519$	−24.3326			−1.06808
$520$		0			0
$521$	8.18913	+	14.1840i	0.358772	+	0.621412i	0.987756	−	0.156007i	$-0.0498621\pi$
$521$	8.18913	+	14.1840i	0.358772	+	0.621412i	−0.628984	+	0.777418i	$0.716529\pi$
$522$		0			0
$523$	5.17061	−	8.95575i	0.226095	−	0.391608i	−0.730553	−	0.682856i	$-0.760737\pi$
$523$	5.17061	−	8.95575i	0.226095	−	0.391608i	0.956647	+	0.291249i	$0.0940708\pi$
$524$		0			0
$525$	−93.0457	+	21.4340i	−4.06085	+	0.935455i
$526$		0			0
$527$	−4.45963	−	2.57477i	−0.194265	−	0.112159i
$528$		0			0
$529$	11.1713	+	19.3492i	0.485707	+	0.841269i
$530$		0			0
$531$	−84.9832			−3.68796
$532$		0			0
$533$	−33.4812			−1.45023
$534$		0			0
$535$	5.58448	+	9.67260i	0.241438	+	0.418183i
$536$		0			0
$537$	−45.6475	−	26.3546i	−1.96984	−	1.13729i
$538$		0			0
$539$	17.6930	−	8.60831i	0.762092	−	0.370786i
$540$		0			0
$541$	−15.0826	+	26.1239i	−0.648452	+	1.12315i	0.335040	+	0.942204i	$0.391250\pi$
$541$	−15.0826	+	26.1239i	−0.648452	+	1.12315i	−0.983493	+	0.180949i	$0.942083\pi$
$542$		0			0
$543$	−12.8930	−	22.3313i	−0.553290	−	0.958327i
$544$		0			0
$545$	−9.02475			−0.386578
$546$		0			0
$547$		−	36.7992i		−	1.57342i	−0.617323	−	0.786709i	$-0.711783\pi$
$547$		−	36.7992i		−	1.57342i	0.617323	−	0.786709i	$-0.288217\pi$
$548$		0			0
$549$	55.8167	−	32.2258i	2.38220	−	1.37536i
$550$		0			0
$551$	−22.2034	−	1.36913i	−0.945896	−	0.0583270i
$552$		0			0
$553$	−5.40676	−	23.4710i	−0.229919	−	0.998088i
$554$		0			0
$555$	−24.8890	+	43.1091i	−1.05648	+	1.82988i
$556$		0			0
$557$	2.37878	+	4.12017i	0.100792	+	0.174577i	0.912011	−	0.410165i	$-0.134529\pi$
$557$	2.37878	+	4.12017i	0.100792	+	0.174577i	−0.811219	+	0.584742i	$0.801196\pi$
$558$		0			0
$559$	6.54204			0.276699
$560$		0			0
$561$			14.4746i			0.611119i
$562$		0			0
$563$	1.69360	+	2.93340i	0.0713767	+	0.123628i	0.899505	−	0.436911i	$-0.143927\pi$
$563$	1.69360	+	2.93340i	0.0713767	+	0.123628i	−0.828128	+	0.560539i	$0.810594\pi$
$564$		0			0
$565$	20.0273	−	34.6884i	0.842556	−	1.45935i
$566$		0			0
$567$	−18.4163	+	60.1332i	−0.773413	+	2.52536i
$568$		0			0
$569$	−15.3039	−	8.83569i	−0.641571	−	0.370411i	0.143648	−	0.989629i	$-0.454117\pi$
$569$	−15.3039	−	8.83569i	−0.641571	−	0.370411i	−0.785220	+	0.619217i	$0.787450\pi$
$570$		0			0
$571$	−12.6193	−	21.8572i	−0.528101	−	0.914697i	−0.999463	−	0.0327576i	$-0.989571\pi$
$571$	−12.6193	−	21.8572i	−0.528101	−	0.914697i	0.471363	−	0.881939i	$-0.343762\pi$
$572$		0			0
$573$	13.9463			0.582616
$574$		0			0
$575$	−9.06638			−0.378094
$576$		0			0
$577$	29.6059	−	17.0930i	1.23251	−	0.711590i	0.264957	−	0.964260i	$-0.414642\pi$
$577$	29.6059	−	17.0930i	1.23251	−	0.711590i	0.967552	+	0.252671i	$0.0813089\pi$
$578$		0			0
$579$	41.2019	+	23.7879i	1.71229	+	0.988593i
$580$		0			0
$581$	−8.02396	+	7.47522i	−0.332890	+	0.310124i
$582$		0			0
$583$	27.3296	+	15.7788i	1.13188	+	0.653490i
$584$		0			0
$585$	134.027	−	77.3808i	5.54135	−	3.19930i
$586$		0			0
$587$			17.4627i			0.720764i	0.932805	+	0.360382i	$0.117354\pi$
$587$			17.4627i			0.720764i	−0.932805	+	0.360382i	$0.882646\pi$
$588$		0			0
$589$	−12.5940	+	6.27130i	−0.518927	+	0.258404i
$590$		0			0
$591$	−16.1289	−	27.9361i	−0.663455	−	1.14914i
$592$		0			0
$593$	−21.8396	−	12.6091i	−0.896844	−	0.517793i	−0.0206690	−	0.999786i	$-0.506580\pi$
$593$	−21.8396	−	12.6091i	−0.896844	−	0.517793i	−0.876175	+	0.481993i	$0.839913\pi$
$594$		0			0
$595$	11.5742	+	12.4239i	0.474498	+	0.509330i
$596$		0			0
$597$	30.6176	+	17.6771i	1.25309	+	0.723474i
$598$		0			0
$599$	−25.8009	+	14.8961i	−1.05420	+	0.608640i	−0.923821	−	0.382825i	$-0.874951\pi$
$599$	−25.8009	+	14.8961i	−1.05420	+	0.608640i	−0.130374	+	0.991465i	$0.541618\pi$
$600$		0			0
$601$	−21.9097			−0.893714			−0.446857	−	0.894605i	$-0.647457\pi$
$601$	−21.9097			−0.893714			−0.446857	+	0.894605i	$0.647457\pi$
$602$		0			0
$603$		−	16.6420i		−	0.677713i
$604$		0			0
$605$	−10.7961	+	6.23311i	−0.438922	+	0.253412i
$606$		0			0
$607$	−22.9387	+	39.7311i	−0.931055	+	1.61263i	−0.149532	+	0.988757i	$0.547777\pi$
$607$	−22.9387	+	39.7311i	−0.931055	+	1.61263i	−0.781522	+	0.623877i	$0.785556\pi$
$608$		0			0
$609$	41.6712	+	12.7622i	1.68860	+	0.517149i
$610$		0			0
$611$	−6.30843	−	3.64218i	−0.255212	−	0.147347i
$612$		0			0
$613$	−16.6847	−	28.8987i	−0.673888	−	1.16721i	−0.976793	−	0.214188i	$-0.931290\pi$
$613$	−16.6847	−	28.8987i	−0.673888	−	1.16721i	0.302904	−	0.953021i	$-0.402044\pi$
$614$		0			0
$615$		−	83.8128i		−	3.37966i
$616$		0			0
$617$	20.5990			0.829283			0.414641	−	0.909985i	$-0.363907\pi$
$617$	20.5990			0.829283			0.414641	+	0.909985i	$0.363907\pi$
$618$		0			0
$619$	−26.6977	+	15.4139i	−1.07307	+	0.619539i	−0.929019	−	0.370031i	$-0.879347\pi$
$619$	−26.6977	+	15.4139i	−1.07307	+	0.619539i	−0.144053	+	0.989570i	$0.546014\pi$
$620$		0			0
$621$	−5.78108	+	10.0131i	−0.231987	+	0.401813i
$622$		0			0
$623$	−16.1657	+	3.72391i	−0.647663	+	0.149195i
$624$		0			0
$625$	−22.0564	+	38.2027i	−0.882254	+	1.52811i
$626$		0			0
$627$	32.9661	+	21.8434i	1.31654	+	0.872342i
$628$		0			0
$629$	6.11682			0.243893
$630$		0			0
$631$	39.1800			1.55973			0.779866	−	0.625946i	$-0.215287\pi$
$631$	39.1800			1.55973			0.779866	+	0.625946i	$0.215287\pi$
$632$		0			0
$633$	61.9960	−	35.7934i	2.46412	−	1.42266i
$634$		0			0
$635$	−21.6013	+	37.4145i	−0.857221	+	1.48475i
$636$		0			0
$637$	−2.56759	+	36.2154i	−0.101731	+	1.43491i
$638$		0			0
$639$	50.3255	+	29.0554i	1.99085	+	1.14942i
$640$		0			0
$641$	23.9851	−	13.8478i	0.947355	−	0.546956i	0.0550970	−	0.998481i	$-0.482453\pi$
$641$	23.9851	−	13.8478i	0.947355	−	0.546956i	0.892258	+	0.451525i	$0.149120\pi$
$642$		0			0
$643$			43.4733i			1.71442i	0.514967	+	0.857210i	$0.327804\pi$
$643$			43.4733i			1.71442i	−0.514967	+	0.857210i	$0.672196\pi$
$644$		0			0
$645$			16.3765i			0.644825i
$646$		0			0
$647$	3.89013	−	2.24597i	0.152937	−	0.0882981i	−0.421579	−	0.906792i	$-0.638524\pi$
$647$	3.89013	−	2.24597i	0.152937	−	0.0882981i	0.574515	+	0.818494i	$0.305191\pi$
$648$		0			0
$649$	16.1016	−	27.8887i	0.632042	−	1.09473i
$650$		0			0
$651$	26.8594	−	6.18732i	1.05270	−	0.242500i
$652$		0			0
$653$	−21.2272	+	36.7666i	−0.830684	+	1.43879i	0.0668128	+	0.997766i	$0.478717\pi$
$653$	−21.2272	+	36.7666i	−0.830684	+	1.43879i	−0.897497	+	0.441021i	$0.854616\pi$
$654$		0			0
$655$	40.8989	+	70.8390i	1.59805	+	2.76791i
$656$		0			0
$657$		−	72.5253i		−	2.82948i
$658$		0			0
$659$		−	8.01821i		−	0.312345i	−0.987730	−	0.156173i	$-0.950084\pi$
$659$		−	8.01821i		−	0.312345i	0.987730	−	0.156173i	$-0.0499156\pi$
$660$		0			0
$661$	−24.8324	−	43.0110i	−0.965869	−	1.67293i	−0.707262	−	0.706952i	$-0.750070\pi$
$661$	−24.8324	−	43.0110i	−0.965869	−	1.67293i	−0.258607	−	0.965983i	$-0.583264\pi$
$662$		0			0
$663$	−23.1304	−	13.3543i	−0.898309	−	0.518639i
$664$		0			0
$665$	45.7620	−	7.61175i	1.77457	−	0.295171i
$666$		0			0
$667$	3.58380	+	2.06911i	0.138765	+	0.0801162i
$668$		0			0
$669$	23.6980	+	41.0462i	0.916218	+	1.58694i
$670$		0			0
$671$			24.4230i			0.942839i
$672$		0			0
$673$			18.2992i			0.705381i	0.935740	+	0.352691i	$0.114733\pi$
$673$			18.2992i			0.705381i	−0.935740	+	0.352691i	$0.885267\pi$
$674$		0			0
$675$	79.7168	+	138.074i	3.06830	+	5.31445i
$676$		0			0
$677$	−1.94295	+	3.36528i	−0.0746735	+	0.129338i	−0.900944	−	0.433935i	$-0.857125\pi$
$677$	−1.94295	+	3.36528i	−0.0746735	+	0.129338i	0.826271	+	0.563273i	$0.190458\pi$
$678$		0			0
$679$	−23.0936	−	24.7889i	−0.886252	−	0.951309i
$680$		0			0
$681$	−0.686231	+	1.18859i	−0.0262964	+	0.0455467i
$682$		0			0
$683$	2.26072	−	1.30522i	0.0865039	−	0.0499430i	−0.456124	−	0.889916i	$-0.650763\pi$
$683$	2.26072	−	1.30522i	0.0865039	−	0.0499430i	0.542628	+	0.839973i	$0.317429\pi$
$684$		0			0
$685$		−	35.9403i		−	1.37321i
$686$		0			0
$687$			39.5742i			1.50985i
$688$		0			0
$689$	−50.4287	+	29.1150i	−1.92118	+	1.10919i
$690$		0			0
$691$	−35.1321	−	20.2835i	−1.33649	−	0.771621i	−0.350202	−	0.936674i	$-0.613887\pi$
$691$	−35.1321	−	20.2835i	−1.33649	−	0.771621i	−0.986285	+	0.165053i	$0.947220\pi$
$692$		0			0
$693$	−37.6029	−	40.3632i	−1.42842	−	1.53327i
$694$		0			0
$695$	11.1901	−	19.3818i	0.424465	−	0.735195i
$696$		0			0
$697$	−8.91926	+	5.14954i	−0.337841	+	0.195053i
$698$		0			0
$699$	−2.46394			−0.0931947
$700$		0			0
$701$	27.8296			1.05111			0.525554	−	0.850760i	$-0.323858\pi$
$701$	27.8296			1.05111			0.525554	+	0.850760i	$0.323858\pi$
$702$		0			0
$703$	9.23078	−	13.9311i	0.348146	−	0.525421i
$704$		0			0
$705$	9.11738	−	15.7918i	0.343380	−	0.594752i
$706$		0			0
$707$	−1.88862	−	0.578407i	−0.0710289	−	0.0217532i
$708$		0			0
$709$	−17.3276	+	30.0123i	−0.650752	+	1.12714i	0.332189	+	0.943213i	$0.392213\pi$
$709$	−17.3276	+	30.0123i	−0.650752	+	1.12714i	−0.982941	+	0.183922i	$0.941120\pi$
$710$		0			0
$711$	−58.4810	+	33.7640i	−2.19321	+	1.26625i
$712$		0			0
$713$	2.61718			0.0980143
$714$		0			0
$715$			58.6446i			2.19318i
$716$		0			0
$717$	39.3694	+	68.1898i	1.47028	+	2.54660i
$718$		0			0
$719$	16.7816	+	9.68886i	0.625848	+	0.361333i	0.779142	−	0.626847i	$-0.215655\pi$
$719$	16.7816	+	9.68886i	0.625848	+	0.361333i	−0.153294	+	0.988181i	$0.548988\pi$
$720$		0			0
$721$	−12.8946	+	2.97040i	−0.480221	+	0.110624i
$722$		0			0
$723$	−37.2772	+	64.5660i	−1.38635	+	2.40124i
$724$		0			0
$725$	49.4179	−	28.5315i	1.83534	−	1.05963i
$726$		0			0
$727$		−	34.1207i		−	1.26547i	−0.774370	−	0.632733i	$-0.781933\pi$
$727$		−	34.1207i		−	1.26547i	0.774370	−	0.632733i	$-0.218067\pi$
$728$		0			0
$729$	38.2516			1.41673
$730$		0			0
$731$	1.74277	−	1.00619i	0.0644587	−	0.0372152i
$732$		0			0
$733$	−19.3373	−	11.1644i	−0.714241	−	0.412367i	0.0983883	−	0.995148i	$-0.468631\pi$
$733$	−19.3373	−	11.1644i	−0.714241	−	0.412367i	−0.812629	+	0.582781i	$0.801965\pi$
$734$		0			0
$735$	−90.6571	−	6.42738i	−3.34394	−	0.237077i
$736$		0			0
$737$	5.46135	+	3.15311i	0.201171	+	0.116146i
$738$		0			0
$739$	−6.30153	−	10.9146i	−0.231806	−	0.401499i	0.726534	−	0.687131i	$-0.241130\pi$
$739$	−6.30153	−	10.9146i	−0.231806	−	0.401499i	−0.958339	+	0.285632i	$0.907797\pi$
$740$		0			0
$741$	−65.3202	+	32.5268i	−2.39960	+	1.19490i
$742$		0			0
$743$		−	14.5279i		−	0.532977i	−0.963838	−	0.266488i	$-0.914137\pi$
$743$		−	14.5279i		−	0.532977i	0.963838	−	0.266488i	$-0.0858634\pi$
$744$		0			0
$745$	−44.2558	+	25.5511i	−1.62141	+	0.936120i
$746$		0			0
$747$	26.6270	+	15.3731i	0.974230	+	0.562472i
$748$		0			0
$749$	1.64905	+	7.15861i	0.0602551	+	0.261570i
$750$		0			0
$751$	−30.7539	−	17.7558i	−1.12223	−	0.647917i	−0.180257	−	0.983620i	$-0.557693\pi$
$751$	−30.7539	−	17.7558i	−1.12223	−	0.647917i	−0.941968	+	0.335703i	$0.891026\pi$
$752$		0			0
$753$	37.1466	−	21.4466i	1.35370	−	0.781558i
$754$		0			0
$755$	−20.3439			−0.740391
$756$		0			0
$757$	25.3427			0.921095			0.460547	−	0.887635i	$-0.347653\pi$
$757$	25.3427			0.921095			0.460547	+	0.887635i	$0.347653\pi$
$758$		0			0
$759$	−3.67827	−	6.37095i	−0.133513	−	0.231251i
$760$		0			0
$761$	10.7818	+	6.22486i	0.390839	+	0.225651i	0.682524	−	0.730864i	$-0.260882\pi$
$761$	10.7818	+	6.22486i	0.390839	+	0.225651i	−0.291685	+	0.956515i	$0.594216\pi$
$762$		0			0
$763$	−5.67559	−	1.73820i	−0.205470	−	0.0629271i
$764$		0			0
$765$	23.8029	−	41.2278i	0.860595	−	1.49059i
$766$		0			0
$767$	29.7107	+	51.4604i	1.07279	+	1.85813i
$768$		0			0
$769$		−	20.2616i		−	0.730651i	−0.930880	−	0.365325i	$-0.880958\pi$
$769$		−	20.2616i		−	0.730651i	0.930880	−	0.365325i	$-0.119042\pi$
$770$		0			0
$771$	66.5187			2.39561
$772$		0			0
$773$	0.597616	+	1.03510i	0.0214947	+	0.0372300i	0.876573	−	0.481269i	$-0.159824\pi$
$773$	0.597616	+	1.03510i	0.0214947	+	0.0372300i	−0.855078	+	0.518499i	$0.826491\pi$
$774$		0			0
$775$	18.0445	−	31.2540i	0.648178	−	1.12268i
$776$		0			0
$777$	−23.9555	+	22.3172i	−0.859398	+	0.800626i
$778$		0			0
$779$	−1.73179	+	28.0847i	−0.0620480	+	1.00624i
$780$		0			0
$781$	−19.0701	+	11.0101i	−0.682382	+	0.393973i
$782$		0			0
$783$		−	72.7711i		−	2.60063i
$784$		0			0
$785$	−12.6742			−0.452363
$786$		0			0
$787$	14.6042	+	25.2953i	0.520585	+	0.901679i	0.999714	+	0.0239347i	$0.00761938\pi$
$787$	14.6042	+	25.2953i	0.520585	+	0.901679i	−0.479129	+	0.877745i	$0.659047\pi$
$788$		0			0
$789$	−1.33746	+	2.31655i	−0.0476148	+	0.0824712i
$790$		0			0
$791$	19.2761	−	17.9579i	0.685381	−	0.638509i
$792$		0			0
$793$	−39.0278	−	22.5327i	−1.38592	−	0.800159i
$794$		0			0
$795$	−72.8830	−	126.237i	−2.58489	−	4.47717i
$796$		0			0
$797$	51.2783			1.81637			0.908186	−	0.418567i	$-0.137468\pi$
$797$	51.2783			1.81637			0.908186	+	0.418567i	$0.137468\pi$
$798$		0			0
$799$	−2.24072			−0.0792710
$800$		0			0
$801$	23.2550	+	40.2788i	0.821675	+	1.42318i
$802$		0			0
$803$	23.8005	+	13.7412i	0.839900	+	0.484916i
$804$		0			0
$805$	−8.25149	−	2.52709i	−0.290827	−	0.0890684i
$806$		0			0
$807$	−39.7524	+	68.8532i	−1.39935	+	2.42375i
$808$		0			0
$809$	17.1400	+	29.6874i	0.602611	+	1.04375i	0.992424	+	0.122859i	$0.0392062\pi$
$809$	17.1400	+	29.6874i	0.602611	+	1.04375i	−0.389813	+	0.920894i	$0.627461\pi$
$810$		0			0
$811$	−27.6678			−0.971548			−0.485774	−	0.874085i	$-0.661462\pi$
$811$	−27.6678			−0.971548			−0.485774	+	0.874085i	$0.661462\pi$
$812$		0			0
$813$			30.0758i			1.05480i
$814$		0			0
$815$	9.39218	−	5.42258i	0.328994	−	0.189945i
$816$		0			0
$817$	0.338382	−	5.48759i	0.0118385	−	0.191987i
$818$		0			0
$819$	99.1926	−	22.8500i	3.46607	−	0.798442i
$820$		0			0
$821$	20.7654	−	35.9668i	0.724719	−	1.25525i	−0.234371	−	0.972147i	$-0.575303\pi$
$821$	20.7654	−	35.9668i	0.724719	−	1.25525i	0.959090	−	0.283102i	$-0.0913636\pi$
$822$		0			0
$823$	0.552907	+	0.957662i	0.0192731	+	0.0333820i	0.875501	−	0.483216i	$-0.160531\pi$
$823$	0.552907	+	0.957662i	0.0192731	+	0.0333820i	−0.856228	+	0.516598i	$0.827198\pi$
$824$		0			0
$825$	−101.441			−3.53173
$826$		0			0
$827$		−	34.0019i		−	1.18236i	−0.806539	−	0.591180i	$-0.798662\pi$
$827$		−	34.0019i		−	1.18236i	0.806539	−	0.591180i	$-0.201338\pi$
$828$		0			0
$829$	−22.0519	−	38.1950i	−0.765894	−	1.32657i	−0.939773	−	0.341800i	$-0.888963\pi$
$829$	−22.0519	−	38.1950i	−0.765894	−	1.32657i	0.173879	−	0.984767i	$-0.444370\pi$
$830$		0			0
$831$	22.8012	−	39.4929i	0.790966	−	1.36999i
$832$		0			0
$833$	4.88606	+	10.0425i	0.169292	+	0.347953i
$834$		0			0
$835$	20.1951	+	11.6596i	0.698879	+	0.403498i
$836$		0			0
$837$	−23.0118	−	39.8576i	−0.795404	−	1.37768i
$838$		0			0
$839$	26.8313			0.926318			0.463159	−	0.886275i	$-0.346716\pi$
$839$	26.8313			0.926318			0.463159	+	0.886275i	$0.346716\pi$
$840$		0			0
$841$	2.95447			0.101878
$842$		0			0
$843$	56.3643	−	32.5419i	1.94129	−	1.12080i
$844$		0			0
$845$	−48.4261	−	27.9588i	−1.66591	−	0.961813i
$846$		0			0
$847$	−7.99008	+	1.84059i	−0.274542	+	0.0632435i
$848$		0			0
$849$	60.8140	+	35.1110i	2.08713	+	1.20501i
$850$		0			0
$851$	−2.69229	+	1.55440i	−0.0922906	+	0.0532840i
$852$		0			0
$853$			11.2933i			0.386676i	0.981132	+	0.193338i	$0.0619314\pi$
$853$			11.2933i			0.386676i	−0.981132	+	0.193338i	$0.938069\pi$
$854$		0			0
$855$	−57.9761	−	116.427i	−1.98274	−	3.98173i
$856$		0			0
$857$	7.79278	+	13.4975i	0.266196	+	0.461065i	0.967876	−	0.251427i	$-0.0808998\pi$
$857$	7.79278	+	13.4975i	0.266196	+	0.461065i	−0.701680	+	0.712492i	$0.747566\pi$
$858$		0			0
$859$	−4.17617	−	2.41112i	−0.142489	−	0.0822662i	0.427061	−	0.904223i	$-0.359549\pi$
$859$	−4.17617	−	2.41112i	−0.142489	−	0.0822662i	−0.569550	+	0.821957i	$0.692882\pi$
$860$		0			0
$861$	16.1427	−	52.7092i	0.550141	−	1.79633i
$862$		0			0
$863$	36.0109	+	20.7909i	1.22582	+	0.707730i	0.966154	−	0.257967i	$-0.0830526\pi$
$863$	36.0109	+	20.7909i	1.22582	+	0.707730i	0.259671	+	0.965697i	$0.416386\pi$
$864$		0			0
$865$	−26.2625	+	15.1627i	−0.892952	+	0.515546i
$866$		0			0
$867$	46.6544			1.58447
$868$		0			0
$869$		−	25.5888i		−	0.868040i
$870$		0			0
$871$	−10.0773	+	5.81814i	−0.341456	+	0.197140i
$872$		0			0
$873$	−47.4929	+	82.2602i	−1.60739	+	2.78409i
$874$		0			0
$875$	−48.1335	+	44.8418i	−1.62721	+	1.51593i
$876$		0			0
$877$	−27.9276	−	16.1240i	−0.943047	−	0.544468i	−0.0521327	−	0.998640i	$-0.516602\pi$
$877$	−27.9276	−	16.1240i	−0.943047	−	0.544468i	−0.890914	+	0.454172i	$0.849935\pi$
$878$		0			0
$879$	10.4178	+	18.0441i	0.351383	+	0.608614i
$880$		0			0
$881$			54.5320i			1.83723i	0.395153	+	0.918615i	$0.370692\pi$
$881$			54.5320i			1.83723i	−0.395153	+	0.918615i	$0.629308\pi$
$882$		0			0
$883$	−54.2600			−1.82599			−0.912997	−	0.407966i	$-0.866238\pi$
$883$	−54.2600			−1.82599			−0.912997	+	0.407966i	$0.866238\pi$
$884$		0			0
$885$	−128.820	+	74.3740i	−4.33022	+	2.50006i
$886$		0			0
$887$	−18.4010	+	31.8714i	−0.617844	+	1.07014i	0.372034	+	0.928219i	$0.378660\pi$
$887$	−18.4010	+	31.8714i	−0.617844	+	1.07014i	−0.989878	+	0.141919i	$0.954673\pi$
$888$		0			0
$889$	−20.7911	+	19.3692i	−0.697310	+	0.649622i
$890$		0			0
$891$	−33.4074	+	57.8633i	−1.11919	+	1.93849i
$892$		0			0
$893$	−3.38143	+	5.10325i	−0.113155	+	0.170774i
$894$		0			0
$895$	−65.6907			−2.19580
$896$		0			0
$897$	13.5743			0.453233
$898$		0			0
$899$	−14.2654	+	8.23615i	−0.475779	+	0.274691i
$900$		0			0
$901$	−8.95600	+	15.5122i	−0.298368	+	0.516788i
$902$		0			0
$903$	−3.15418	+	10.2991i	−0.104965	+	0.342732i
$904$		0			0
$905$	−27.8311	−	16.0683i	−0.925138	−	0.534129i
$906$		0			0
$907$	4.92126	−	2.84129i	0.163408	−	0.0943435i	−0.416066	−	0.909334i	$-0.636591\pi$
$907$	4.92126	−	2.84129i	0.163408	−	0.0943435i	0.579474	+	0.814991i	$0.303258\pi$
$908$		0			0
$909$			5.53781i			0.183677i
$910$		0			0
$911$			23.6688i			0.784181i	0.919927	+	0.392091i	$0.128248\pi$
$911$			23.6688i			0.784181i	−0.919927	+	0.392091i	$0.871752\pi$
$912$		0			0
$913$	−10.0899	+	5.82540i	−0.333927	+	0.192793i
$914$		0			0
$915$	56.4056	−	97.6973i	1.86471	−	3.22977i
$916$		0			0
$917$	12.0772	+	52.4274i	0.398823	+	1.73131i
$918$		0			0
$919$	25.2182	−	43.6793i	0.831873	−	1.44085i	−0.0646782	−	0.997906i	$-0.520602\pi$
$919$	25.2182	−	43.6793i	0.831873	−	1.44085i	0.896551	−	0.442940i	$-0.146065\pi$
$920$		0			0
$921$	−4.52266	−	7.83348i	−0.149027	−	0.258122i
$922$		0			0
$923$		−	40.6319i		−	1.33741i
$924$		0			0
$925$			42.8679i			1.40949i
$926$		0			0
$927$	18.5495	+	32.1287i	0.609245	+	1.05524i
$928$		0			0
$929$	−43.4625	−	25.0931i	−1.42596	−	0.823278i	−0.429160	−	0.903228i	$-0.641190\pi$
$929$	−43.4625	−	25.0931i	−1.42596	−	0.823278i	−0.996799	+	0.0799508i	$0.974524\pi$
$930$		0			0
$931$	30.2454	+	4.02696i	0.991253	+	0.131978i
$932$		0			0
$933$	53.1138	+	30.6653i	1.73887	+	1.00394i
$934$		0			0
$935$	9.01975	+	15.6227i	0.294978	+	0.510916i
$936$		0			0
$937$			1.38951i			0.0453932i	0.999742	+	0.0226966i	$0.00722517\pi$
$937$			1.38951i			0.0453932i	−0.999742	+	0.0226966i	$0.992775\pi$
$938$		0			0
$939$		−	109.126i		−	3.56121i
$940$		0			0
$941$	11.6020	+	20.0953i	0.378216	+	0.655089i	0.990803	−	0.135314i	$-0.0432044\pi$
$941$	11.6020	+	20.0953i	0.378216	+	0.655089i	−0.612587	+	0.790403i	$0.709871\pi$
$942$		0			0
$943$	2.61718	−	4.53310i	0.0852272	−	0.147618i
$944$		0			0
$945$	34.0663	+	147.883i	1.10818	+	4.81064i
$946$		0			0
$947$	6.54652	−	11.3389i	0.212733	−	0.368465i	−0.739836	−	0.672788i	$-0.765097\pi$
$947$	6.54652	−	11.3389i	0.212733	−	0.368465i	0.952569	+	0.304323i	$0.0984301\pi$
$948$		0			0
$949$	−43.9167	+	25.3553i	−1.42560	+	0.823068i
$950$		0			0
$951$			72.6225i			2.35495i
$952$		0			0
$953$		−	51.2256i		−	1.65936i	−0.558240	−	0.829679i	$-0.688523\pi$
$953$		−	51.2256i		−	1.65936i	0.558240	−	0.829679i	$-0.311477\pi$
$954$		0			0
$955$	15.0525	−	8.69055i	0.487087	−	0.281220i
$956$		0			0
$957$	40.0982	+	23.1507i	1.29619	+	0.748355i
$958$		0			0
$959$	6.92224	−	22.6026i	0.223531	−	0.729875i
$960$		0			0
$961$	10.2911	−	17.8247i	0.331971	−	0.574991i
$962$		0			0
$963$	17.8366	−	10.2980i	0.574777	−	0.331848i
$964$		0			0
$965$	59.2931			1.90871
$966$		0			0
$967$	−50.5857			−1.62673			−0.813364	−	0.581755i	$-0.802366\pi$
$967$	−50.5857			−1.62673			−0.813364	+	0.581755i	$0.802366\pi$
$968$		0			0
$969$	−12.3983	+	18.7115i	−0.398290	+	0.601099i
$970$		0			0
$971$	−20.3166	+	35.1893i	−0.651990	+	1.12928i	0.330650	+	0.943754i	$0.392732\pi$
$971$	−20.3166	+	35.1893i	−0.651990	+	1.12928i	−0.982639	+	0.185526i	$0.940601\pi$
$972$		0			0
$973$	10.7704	−	10.0338i	0.345283	−	0.321670i
$974$		0			0
$975$	93.5898	−	162.102i	2.99727	−	5.19143i
$976$		0			0
$977$	36.7903	−	21.2409i	1.17703	−	0.679556i	0.221701	−	0.975115i	$-0.428839\pi$
$977$	36.7903	−	21.2409i	1.17703	−	0.679556i	0.955324	+	0.295559i	$0.0955059\pi$
$978$		0			0
$979$	−17.6243			−0.563274
$980$		0			0
$981$			16.6420i			0.531337i
$982$		0			0
$983$	23.7408	+	41.1203i	0.757215	+	1.31153i	0.944266	+	0.329184i	$0.106774\pi$
$983$	23.7408	+	41.1203i	0.757215	+	1.31153i	−0.187051	+	0.982350i	$0.559893\pi$
$984$		0			0
$985$	−34.8163	−	20.1012i	−1.10934	−	0.640478i
$986$		0			0
$987$	8.77540	−	8.17527i	0.279324	−	0.260222i
$988$		0			0
$989$	−0.511382	+	0.885740i	−0.0162610	+	0.0281649i
$990$		0			0
$991$	−8.13757	+	4.69823i	−0.258498	+	0.149244i	−0.623649	−	0.781704i	$-0.714351\pi$
$991$	−8.13757	+	4.69823i	−0.258498	+	0.149244i	0.365151	+	0.930948i	$0.381017\pi$
$992$		0			0
$993$			52.7092i			1.67268i
$994$		0			0
$995$	44.0613			1.39684
$996$		0			0
$997$	32.4764	−	18.7503i	1.02854	−	0.593827i	0.111973	−	0.993711i	$-0.464283\pi$
$997$	32.4764	−	18.7503i	1.02854	−	0.593827i	0.916566	+	0.399884i	$0.130950\pi$
$998$		0			0
$999$	47.3444	+	27.3343i	1.49791	+	0.864819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.v.e.341.1	✓	16
7.2	even	3		3724.2.g.f.1861.16		16
7.3	odd	6	inner	532.2.v.e.493.8	yes	16
7.5	odd	6		3724.2.g.f.1861.1		16
19.18	odd	2	inner	532.2.v.e.341.8	yes	16
133.37	odd	6		3724.2.g.f.1861.2		16
133.75	even	6		3724.2.g.f.1861.15		16
133.94	even	6	inner	532.2.v.e.493.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.v.e.341.1	✓	16	1.1	even	1	trivial
532.2.v.e.341.8	yes	16	19.18	odd	2	inner
532.2.v.e.493.1	yes	16	133.94	even	6	inner
532.2.v.e.493.8	yes	16	7.3	odd	6	inner
3724.2.g.f.1861.1		16	7.5	odd	6
3724.2.g.f.1861.2		16	133.37	odd	6
3724.2.g.f.1861.15		16	133.75	even	6
3724.2.g.f.1861.16		16	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61383 - 2.79524i) q^{3} +(-3.48366 - 2.01129i) q^{5} +(-1.80346 - 1.93585i) q^{7} +(-3.70889 + 6.42399i) q^{9} +O(q^{10})\)	\(q+(-1.61383 - 2.79524i) q^{3} +(-3.48366 - 2.01129i) q^{5} +(-1.80346 - 1.93585i) q^{7} +(-3.70889 + 6.42399i) q^{9} +(-1.40543 - 2.43428i) q^{11} +5.18661 q^{13} +12.9835i q^{15} +(1.38169 - 0.797720i) q^{17} +(0.268274 - 4.35064i) q^{19} +(-2.50068 + 8.16524i) q^{21} +(-0.405431 + 0.702226i) q^{23} +(5.59059 + 9.68318i) q^{25} +14.2591 q^{27} -5.10348i q^{29} +(-1.61383 - 2.79524i) q^{31} +(-4.53625 + 7.85702i) q^{33} +(2.38909 + 10.3711i) q^{35} +(3.32029 + 1.91697i) q^{37} +(-8.37031 - 14.4978i) q^{39} -6.45532 q^{41} +1.26133 q^{43} +(25.8410 - 14.9193i) q^{45} +(-1.21629 - 0.702226i) q^{47} +(-0.495041 + 6.98247i) q^{49} +(-4.45963 - 2.57477i) q^{51} +(-9.72286 + 5.61350i) q^{53} +11.3069i q^{55} +(-12.5940 + 6.27130i) q^{57} +(5.72834 + 9.92177i) q^{59} +(-7.52471 - 4.34440i) q^{61} +(19.1247 - 4.40557i) q^{63} +(-18.0684 - 10.4318i) q^{65} +(-1.94295 + 1.12176i) q^{67} +2.61718 q^{69} -7.83399i q^{71} +(-8.46732 + 4.88861i) q^{73} +(18.0445 - 31.2540i) q^{75} +(-2.17776 + 7.11083i) q^{77} +(7.88389 + 4.55177i) q^{79} +(-11.8851 - 20.5856i) q^{81} -4.14493i q^{83} -6.41779 q^{85} +(-14.2654 + 8.23615i) q^{87} +(3.13503 - 5.43003i) q^{89} +(-9.35386 - 10.0405i) q^{91} +(-5.20889 + 9.02207i) q^{93} +(-9.68497 + 14.6166i) q^{95} +12.8052 q^{97} +20.8504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} - 14 q^{7} - 26 q^{9}+O(q^{10}) \) 16 * q - 6 * q^5 - 14 * q^7 - 26 * q^9	\( 16 q - 6 q^{5} - 14 q^{7} - 26 q^{9} - 4 q^{11} - 24 q^{17} + 21 q^{19} + 12 q^{23} + 10 q^{25} - 30 q^{35} - 12 q^{39} + 16 q^{43} + 72 q^{45} + 36 q^{47} - 34 q^{49} - 2 q^{57} - 24 q^{61} + 20 q^{63} - 36 q^{73} + 4 q^{77} - 24 q^{81} - 36 q^{85} - 48 q^{87} - 50 q^{93} + 31 q^{95} + 156 q^{99}+O(q^{100}) \) 16 * q - 6 * q^5 - 14 * q^7 - 26 * q^9 - 4 * q^11 - 24 * q^17 + 21 * q^19 + 12 * q^23 + 10 * q^25 - 30 * q^35 - 12 * q^39 + 16 * q^43 + 72 * q^45 + 36 * q^47 - 34 * q^49 - 2 * q^57 - 24 * q^61 + 20 * q^63 - 36 * q^73 + 4 * q^77 - 24 * q^81 - 36 * q^85 - 48 * q^87 - 50 * q^93 + 31 * q^95 + 156 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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