LMFDB - Embedded newform 532.2.v.e.341.8

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			341.8
Root			$1.61383 - 2.79524i$ of defining polynomial
Character	$\chi$	$=$	532.341
Dual form			532.2.v.e.493.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61383 + 2.79524i) q^{3} +(-3.48366 - 2.01129i) q^{5} +(-1.80346 - 1.93585i) q^{7} +(-3.70889 + 6.42399i) q^{9} +O(q^{10})$	\(q+(1.61383 + 2.79524i) q^{3} +(-3.48366 - 2.01129i) q^{5} +(-1.80346 - 1.93585i) q^{7} +(-3.70889 + 6.42399i) q^{9} +(-1.40543 - 2.43428i) q^{11} -5.18661 q^{13} -12.9835i q^{15} +(1.38169 - 0.797720i) q^{17} +(-3.63362 + 2.40765i) q^{19} +(2.50068 - 8.16524i) q^{21} +(-0.405431 + 0.702226i) q^{23} +(5.59059 + 9.68318i) q^{25} -14.2591 q^{27} +5.10348i q^{29} +(1.61383 + 2.79524i) q^{31} +(4.53625 - 7.85702i) q^{33} +(2.38909 + 10.3711i) q^{35} +(-3.32029 - 1.91697i) q^{37} +(-8.37031 - 14.4978i) q^{39} +6.45532 q^{41} +1.26133 q^{43} +(25.8410 - 14.9193i) q^{45} +(-1.21629 - 0.702226i) q^{47} +(-0.495041 + 6.98247i) q^{49} +(4.45963 + 2.57477i) q^{51} +(9.72286 - 5.61350i) q^{53} +11.3069i q^{55} +(-12.5940 - 6.27130i) q^{57} +(-5.72834 - 9.92177i) q^{59} +(-7.52471 - 4.34440i) q^{61} +(19.1247 - 4.40557i) q^{63} +(18.0684 + 10.4318i) q^{65} +(1.94295 - 1.12176i) q^{67} -2.61718 q^{69} +7.83399i q^{71} +(-8.46732 + 4.88861i) q^{73} +(-18.0445 + 31.2540i) q^{75} +(-2.17776 + 7.11083i) q^{77} +(-7.88389 - 4.55177i) q^{79} +(-11.8851 - 20.5856i) q^{81} -4.14493i q^{83} -6.41779 q^{85} +(-14.2654 + 8.23615i) q^{87} +(-3.13503 + 5.43003i) q^{89} +(9.35386 + 10.0405i) q^{91} +(-5.20889 + 9.02207i) q^{93} +(17.5008 - 1.07915i) q^{95} -12.8052 q^{97} +20.8504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.215047\pi$
$3$	1.61383	+	2.79524i	0.931745	+	1.61383i	0.151407	+	0.988471i	$0.451619\pi$
$4$		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	$-0.755516\pi$
$13$	−5.18661			−1.43851			−0.719254	+	0.694748i	$0.755516\pi$
$14$		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
$19$	−3.63362	+	2.40765i	−0.833610	+	0.552353i
$19$	−3.63362	+	2.40765i	−0.833610	+	0.552353i
$20$		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	$0.157135\pi$
$29$			5.10348i			0.947693i	−0.880608	+	0.473846i	$0.842865\pi$
$30$		0			0
$31$	1.61383	+	2.79524i	0.289852	+	0.502039i	0.973774	−	0.227516i	$-0.0730604\pi$
$31$	1.61383	+	2.79524i	0.289852	+	0.502039i	−0.683922	+	0.729555i	$0.739727\pi$
$32$		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	0.201595	−	0.979469i	$-0.435387\pi$
$37$	−3.32029	−	1.91697i	−0.545852	−	0.315148i	−0.747447	+	0.664321i	$0.768721\pi$
$38$		0			0
$39$	−8.37031	−	14.4978i	−1.34032	−	2.32151i
$40$		0			0
$41$	6.45532			1.00815			0.504076	−	0.863659i	$-0.331833\pi$
$41$	6.45532			1.00815			0.504076	+	0.863659i	$0.331833\pi$
$42$		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	0.349396	−	0.936975i	$-0.386387\pi$
$53$	9.72286	−	5.61350i	1.33554	−	0.771073i	0.986142	+	0.165902i	$0.0530535\pi$
$54$		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	$-0.898750\pi$
$59$	−5.72834	−	9.92177i	−0.745766	−	1.29170i	0.204070	−	0.978956i	$-0.434583\pi$
$60$		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	−0.376598	−	0.926377i	$-0.622906\pi$
$67$	1.94295	−	1.12176i	0.237369	−	0.137045i	0.613967	+	0.789332i	$0.289573\pi$
$68$		0			0
$69$	−2.61718			−0.315072
$70$		0			0
$71$			7.83399i			0.929724i	0.885383	+	0.464862i	$0.153896\pi$
$71$			7.83399i			0.929724i	−0.885383	+	0.464862i	$0.846104\pi$
$72$		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	−0.0140448	−	0.999901i	$-0.504471\pi$
$79$	−7.88389	−	4.55177i	−0.887007	−	0.512114i	−0.872962	+	0.487788i	$0.837804\pi$
$80$		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	−0.982965	−	0.183793i	$-0.941162\pi$
$89$	−3.13503	+	5.43003i	−0.332313	+	0.575582i	0.650652	+	0.759376i	$0.274496\pi$
$90$		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
$95$	17.5008	−	1.07915i	1.79554	−	0.110719i
$96$		0			0
$97$	−12.8052			−1.30017			−0.650083	−	0.759863i	$-0.725266\pi$
$97$	−12.8052			−1.30017			−0.650083	+	0.759863i	$0.725266\pi$
$98$		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	−0.962524	−	0.271196i	$-0.912581\pi$
$103$	−2.50068	+	4.33130i	−0.246399	+	0.426776i	0.716125	+	0.697972i	$0.245914\pi$
$104$		0			0
$105$	−25.1342	+	23.4153i	−2.45284	+	2.28510i
$106$		0			0
$107$	2.40457	+	1.38828i	0.232459	+	0.134210i	0.611706	−	0.791085i	$-0.290484\pi$
$107$	2.40457	+	1.38828i	0.232459	+	0.134210i	−0.379247	+	0.925295i	$0.623817\pi$
$108$		0			0
$109$	−1.94295	+	1.12176i	−0.186100	+	0.107445i	−0.590156	−	0.807289i	$-0.700934\pi$
$109$	−1.94295	+	1.12176i	−0.186100	+	0.107445i	0.404055	+	0.914735i	$0.367600\pi$
$110$		0			0
$111$		−	12.3746i		−	1.17455i
$112$		0			0
$113$		−	9.95745i		−	0.936718i	−0.883538	−	0.468359i	$-0.844845\pi$
$113$		−	9.95745i		−	0.936718i	0.883538	−	0.468359i	$-0.155155\pi$
$114$		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	$0.158099\pi$
$127$			10.7400i			0.953022i	−0.879169	+	0.476511i	$0.841901\pi$
$128$		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
$133$	11.2140	+	2.69205i	0.972374	+	0.233430i
$134$		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	−0.667513	−	0.744598i	$-0.732641\pi$
$151$	−4.37986	+	2.52871i	−0.356428	+	0.205784i	0.311085	+	0.950382i	$0.399308\pi$
$152$		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	$-0.427992\pi$
$167$	5.79709			0.448592			0.224296	+	0.974521i	$0.427992\pi$
$168$		0			0
$169$	13.9009			1.06930
$170$		0			0
$171$	−1.99000	−	32.2721i	−0.152179	−	2.46791i
$172$		0			0
$173$	−3.76939	+	6.52877i	−0.286581	+	0.496373i	−0.972991	−	0.230842i	$-0.925852\pi$
$173$	−3.76939	+	6.52877i	−0.286581	+	0.496373i	0.686410	+	0.727214i	$0.259185\pi$
$174$		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	−0.924620	−	0.380891i	$-0.875617\pi$
$179$	−14.1426	+	8.16524i	−1.05707	+	0.610299i	−0.132448	+	0.991190i	$0.542284\pi$
$180$		0			0
$181$	−7.98905			−0.593822			−0.296911	−	0.954905i	$-0.595956\pi$
$181$	−7.98905			−0.593822			−0.296911	+	0.954905i	$0.595956\pi$
$182$		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	0.0355915	−	0.999366i	$-0.488668\pi$
$193$	12.7653	−	7.37003i	0.918864	−	0.530506i	0.883272	+	0.468860i	$0.155335\pi$
$194$		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	$-0.723510\pi$
$211$		−	22.1792i		−	1.52688i	0.645880	−	0.763439i	$-0.276490\pi$
$212$		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	$-0.336387\pi$
$223$	14.6843			0.983336			0.491668	+	0.870783i	$0.336387\pi$
$224$		0			0
$225$	−82.9395			−5.52930
$226$		0			0
$227$	0.212609	+	0.368250i	0.0141114	+	0.0244416i	0.872995	−	0.487729i	$-0.162175\pi$
$227$	0.212609	+	0.368250i	0.0141114	+	0.0244416i	−0.858883	+	0.512171i	$0.828841\pi$
$228$		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	$0.100386\pi$
$241$	11.5493	+	20.0040i	0.743956	+	1.28857i	−0.206725	+	0.978399i	$0.566281\pi$
$242$		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
$247$	18.8462	−	12.4875i	1.19915	−	0.794563i
$248$		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	$-0.611116\pi$
$257$	10.3045	−	17.8479i	0.642775	−	1.11332i	0.984811	−	0.173632i	$-0.0555505\pi$
$258$		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	$0.103728\pi$
$269$	12.3162	+	21.3322i	0.750930	+	1.30065i	−0.196442	+	0.980515i	$0.562939\pi$
$270$		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	$-0.794588\pi$
$281$		−	20.1644i		−	1.20291i	0.798907	−	0.601454i	$-0.205412\pi$
$282$		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
$285$	31.2598	+	47.1773i	1.85167	+	2.79454i
$286$		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	$-0.439617\pi$
$293$	6.45532			0.377124			0.188562	+	0.982061i	$0.439617\pi$
$294$		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	$-0.525483\pi$
$307$	−2.80244			−0.159944			−0.0799719	+	0.996797i	$0.525483\pi$
$308$		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	0.934750	−	0.355306i	$-0.115623\pi$
$317$	19.4856	+	11.2500i	1.09442	+	0.631864i	0.159671	+	0.987170i	$0.448957\pi$
$318$		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	0.835490	−	0.549506i	$-0.185184\pi$
$331$	14.1426	+	8.16524i	0.777348	+	0.448802i	−0.0581415	+	0.998308i	$0.518517\pi$
$332$		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	$-0.971669\pi$
$337$		−	3.26355i		−	0.177777i	0.996042	−	0.0888885i	$-0.0283315\pi$
$338$		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
$361$	7.40644	−	17.4970i	0.389813	−	0.920894i
$362$		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	−0.304334	−	0.952565i	$-0.598434\pi$
$373$	−24.7488	−	14.2888i	−1.28145	−	0.739844i	−0.977113	+	0.212722i	$0.931767\pi$
$374$		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	$-0.975614\pi$
$379$		−	2.98002i		−	0.153073i	0.997067	−	0.0765367i	$-0.0243862\pi$
$380$		0			0
$381$	−30.0208	+	17.3325i	−1.53801	+	0.887973i
$382$		0			0
$383$	1.18861	−	2.05873i	0.0607352	−	0.105196i	−0.834059	−	0.551675i	$-0.813989\pi$
$383$	1.18861	−	2.05873i	0.0607352	−	0.105196i	0.894794	+	0.446479i	$0.147322\pi$
$384$		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
$399$	10.5725	+	35.6902i	0.529288	+	1.78674i
$400$		0			0
$401$	−23.8256	−	13.7557i	−1.18979	−	0.686927i	−0.231533	−	0.972827i	$-0.574374\pi$
$401$	−23.8256	−	13.7557i	−1.18979	−	0.686927i	−0.958260	+	0.285900i	$0.907708\pi$
$402$		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	0.850954	−	0.525240i	$-0.176025\pi$
$409$	−0.594470	−	1.02965i	−0.0293946	−	0.0509130i	−0.880349	+	0.474327i	$0.842691\pi$
$410$		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	$0.392967\pi$
$421$			38.7384i			1.88799i	−0.329953	+	0.943997i	$0.607033\pi$
$422$		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	−0.863218	−	0.504831i	$-0.831555\pi$
$431$	−17.8049	+	10.2796i	−0.857631	+	0.495153i	0.00558755	+	0.999984i	$0.498221\pi$
$432$		0			0
$433$	−5.13886			−0.246958			−0.123479	−	0.992347i	$-0.539405\pi$
$433$	−5.13886			−0.246958			−0.123479	+	0.992347i	$0.539405\pi$
$434$		0			0
$435$	66.2612			3.17698
$436$		0			0
$437$	−0.217533	−	3.52776i	−0.0104060	−	0.168756i
$438$		0			0
$439$	−9.74674	+	16.8819i	−0.465187	+	0.805727i	−0.999210	−	0.0397429i	$-0.987346\pi$
$439$	−9.74674	+	16.8819i	−0.465187	+	0.805727i	0.534023	+	0.845470i	$0.320679\pi$
$440$		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	$0.0298783\pi$
$449$			3.97210i			0.187455i	−0.995598	+	0.0937275i	$0.970122\pi$
$450$		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	−0.999651	−	0.0264362i	$-0.991584\pi$
$487$	−32.5853	+	18.8131i	−1.47658	+	0.852505i	−0.476931	+	0.878941i	$0.658251\pi$
$488$		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	−0.963957	−	0.266057i	$-0.914279\pi$
$509$	−5.67559	+	9.83042i	−0.251566	+	0.435725i	0.712391	+	0.701783i	$0.247612\pi$
$510$		0			0
$511$	24.7341	+	7.57504i	1.09417	+	0.335100i
$512$		0			0
$513$	51.8123	−	34.3310i	2.28757	−	1.51575i
$514$		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	0.628984	−	0.777418i	$-0.283471\pi$
$521$	−8.18913	−	14.1840i	−0.358772	−	0.621412i	−0.987756	+	0.156007i	$0.950138\pi$
$522$		0			0
$523$	−5.17061	+	8.95575i	−0.226095	+	0.391608i	−0.956647	−	0.291249i	$-0.905929\pi$
$523$	−5.17061	+	8.95575i	−0.226095	+	0.391608i	0.730553	+	0.682856i	$0.239263\pi$
$524$		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	$0.288217\pi$
$547$			36.7992i			1.57342i	−0.617323	+	0.786709i	$0.711783\pi$
$548$		0			0
$549$	55.8167	−	32.2258i	2.38220	−	1.37536i
$550$		0			0
$551$	−12.2874	−	18.5441i	−0.523461	−	0.790007i
$552$		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	0.828128	−	0.560539i	$-0.189406\pi$
$563$	−1.69360	−	2.93340i	−0.0713767	−	0.123628i	−0.899505	+	0.436911i	$0.856073\pi$
$564$		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	0.785220	−	0.619217i	$-0.212550\pi$
$569$	15.3039	+	8.83569i	0.641571	+	0.370411i	−0.143648	+	0.989629i	$0.545883\pi$
$570$		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	0.130374	−	0.991465i	$-0.458382\pi$
$599$	25.8009	−	14.8961i	1.05420	−	0.608640i	0.923821	+	0.382825i	$0.125049\pi$
$600$		0			0
$601$	21.9097			0.893714			0.446857	−	0.894605i	$-0.352543\pi$
$601$	21.9097			0.893714			0.446857	+	0.894605i	$0.352543\pi$
$602$		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	$-0.452223\pi$
$607$	22.9387	−	39.7311i	0.931055	−	1.61263i	0.781522	−	0.623877i	$-0.214444\pi$
$608$		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
$627$	2.43392	+	39.4712i	0.0972013	+	1.57633i
$628$		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	−0.892258	−	0.451525i	$-0.850880\pi$
$641$	−23.9851	+	13.8478i	−0.947355	+	0.546956i	−0.0550970	+	0.998481i	$0.517547\pi$
$642$		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	$0.0499156\pi$
$659$			8.01821i			0.312345i	−0.987730	+	0.156173i	$0.950084\pi$
$660$		0			0
$661$	24.8324	+	43.0110i	0.965869	+	1.67293i	0.707262	+	0.706952i	$0.249930\pi$
$661$	24.8324	+	43.0110i	0.965869	+	1.67293i	0.258607	+	0.965983i	$0.416736\pi$
$662$		0			0
$663$	−23.1304	−	13.3543i	−0.898309	−	0.518639i
$664$		0			0
$665$	−33.6511	−	31.9327i	−1.30493	−	1.23830i
$666$		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	$-0.885267\pi$
$673$		−	18.2992i		−	0.705381i	0.935740	−	0.352691i	$-0.114733\pi$
$674$		0			0
$675$	−79.7168	−	138.074i	−3.06830	−	5.31445i
$676$		0			0
$677$	1.94295	−	3.36528i	0.0746735	−	0.129338i	−0.826271	−	0.563273i	$-0.809542\pi$
$677$	1.94295	−	3.36528i	0.0746735	−	0.129338i	0.900944	+	0.433935i	$0.142875\pi$
$678$		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	−0.542628	−	0.839973i	$-0.682571\pi$
$683$	−2.26072	+	1.30522i	−0.0865039	+	0.0499430i	0.456124	+	0.889916i	$0.349237\pi$
$684$		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
$703$	16.6801	−	1.02855i	0.629101	−	0.0387923i
$704$		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	$0.0858634\pi$
$743$			14.5279i			0.532977i	−0.963838	+	0.266488i	$0.914137\pi$
$744$		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	0.941968	−	0.335703i	$-0.108974\pi$
$751$	30.7539	+	17.7558i	1.12223	+	0.647917i	0.180257	+	0.983620i	$0.442307\pi$
$752$		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	0.855078	−	0.518499i	$-0.173509\pi$
$773$	−0.597616	−	1.03510i	−0.0214947	−	0.0372300i	−0.876573	+	0.481269i	$0.840176\pi$
$774$		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
$779$	−23.4562	+	15.5421i	−0.840406	+	0.556855i
$780$		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	$-0.992381\pi$
$787$	−14.6042	−	25.2953i	−0.520585	−	0.901679i	0.479129	−	0.877745i	$-0.340953\pi$
$788$		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	$-0.862532\pi$
$797$	−51.2783			−1.81637			−0.908186	+	0.418567i	$0.862532\pi$
$798$		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	$-0.338538\pi$
$811$	27.6678			0.971548			0.485774	+	0.874085i	$0.338538\pi$
$812$		0			0
$813$		−	30.0758i		−	1.05480i
$814$		0			0
$815$	9.39218	−	5.42258i	0.328994	−	0.189945i
$816$		0			0
$817$	−4.58320	+	3.03684i	−0.160346	+	0.106246i
$818$		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	$0.201338\pi$
$827$			34.0019i			1.18236i	−0.806539	+	0.591180i	$0.798662\pi$
$828$		0			0
$829$	22.0519	+	38.1950i	0.765894	+	1.32657i	0.939773	+	0.341800i	$0.111037\pi$
$829$	22.0519	+	38.1950i	0.765894	+	1.32657i	−0.173879	+	0.984767i	$0.555630\pi$
$830$		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	$-0.653284\pi$
$839$	−26.8313			−0.926318			−0.463159	+	0.886275i	$0.653284\pi$
$840$		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	0.701680	−	0.712492i	$-0.252434\pi$
$857$	−7.79278	−	13.4975i	−0.266196	−	0.461065i	−0.967876	+	0.251427i	$0.919100\pi$
$858$		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	−0.259671	−	0.965697i	$-0.583614\pi$
$863$	−36.0109	−	20.7909i	−1.22582	−	0.707730i	−0.966154	+	0.257967i	$0.916947\pi$
$864$		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	0.890914	−	0.454172i	$-0.150065\pi$
$877$	27.9276	+	16.1240i	0.943047	+	0.544468i	0.0521327	+	0.998640i	$0.483398\pi$
$878$		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	$-0.621340\pi$
$887$	18.4010	−	31.8714i	0.617844	−	1.07014i	0.989878	−	0.141919i	$-0.0453271\pi$
$888$		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
$893$	6.11026	−	0.376778i	0.204472	−	0.0126084i
$894$		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	−0.579474	−	0.814991i	$-0.696742\pi$
$907$	−4.92126	+	2.84129i	−0.163408	+	0.0943435i	0.416066	+	0.909334i	$0.363409\pi$
$908$		0			0
$909$			5.53781i			0.183677i
$910$		0			0
$911$		−	23.6688i		−	0.784181i	−0.919927	−	0.392091i	$-0.871752\pi$
$911$		−	23.6688i		−	0.784181i	0.919927	−	0.392091i	$-0.128248\pi$
$912$		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
$931$	−15.0126	−	26.5636i	−0.492017	−	0.870586i
$932$		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	0.612587	−	0.790403i	$-0.290129\pi$
$941$	−11.6020	−	20.0953i	−0.378216	−	0.655089i	−0.990803	+	0.135314i	$0.956796\pi$
$942$		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	$0.311477\pi$
$953$			51.2256i			1.65936i	−0.558240	+	0.829679i	$0.688523\pi$
$954$		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
$969$	−22.4038	+	1.38149i	−0.719712	+	0.0443797i
$970$		0			0
$971$	20.3166	−	35.1893i	0.651990	−	1.12928i	−0.330650	−	0.943754i	$-0.607268\pi$
$971$	20.3166	−	35.1893i	0.651990	−	1.12928i	0.982639	−	0.185526i	$-0.0593988\pi$
$972$		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	−0.955324	−	0.295559i	$-0.904494\pi$
$977$	−36.7903	+	21.2409i	−1.17703	+	0.679556i	−0.221701	+	0.975115i	$0.571161\pi$
$978$		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	$-0.893226\pi$
$983$	−23.7408	−	41.1203i	−0.757215	−	1.31153i	0.187051	−	0.982350i	$-0.440107\pi$
$984$		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	−0.365151	−	0.930948i	$-0.618983\pi$
$991$	8.13757	−	4.69823i	0.258498	−	0.149244i	0.623649	+	0.781704i	$0.285649\pi$
$992$		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.341.8	yes	16
7.2	even	3		3724.2.g.f.1861.2		16
7.3	odd	6	inner	532.2.v.e.493.1	yes	16
7.5	odd	6		3724.2.g.f.1861.15		16
19.18	odd	2	inner	532.2.v.e.341.1	✓	16
133.37	odd	6		3724.2.g.f.1861.16		16
133.75	even	6		3724.2.g.f.1861.1		16
133.94	even	6	inner	532.2.v.e.493.8	yes	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.61383 + 2.79524i) q^{3} +(-3.48366 - 2.01129i) q^{5} +(-1.80346 - 1.93585i) q^{7} +(-3.70889 + 6.42399i) q^{9} +O(q^{10})\)	\(q+(1.61383 + 2.79524i) q^{3} +(-3.48366 - 2.01129i) q^{5} +(-1.80346 - 1.93585i) q^{7} +(-3.70889 + 6.42399i) q^{9} +(-1.40543 - 2.43428i) q^{11} -5.18661 q^{13} -12.9835i q^{15} +(1.38169 - 0.797720i) q^{17} +(-3.63362 + 2.40765i) q^{19} +(2.50068 - 8.16524i) q^{21} +(-0.405431 + 0.702226i) q^{23} +(5.59059 + 9.68318i) q^{25} -14.2591 q^{27} +5.10348i q^{29} +(1.61383 + 2.79524i) q^{31} +(4.53625 - 7.85702i) q^{33} +(2.38909 + 10.3711i) q^{35} +(-3.32029 - 1.91697i) q^{37} +(-8.37031 - 14.4978i) q^{39} +6.45532 q^{41} +1.26133 q^{43} +(25.8410 - 14.9193i) q^{45} +(-1.21629 - 0.702226i) q^{47} +(-0.495041 + 6.98247i) q^{49} +(4.45963 + 2.57477i) q^{51} +(9.72286 - 5.61350i) q^{53} +11.3069i q^{55} +(-12.5940 - 6.27130i) q^{57} +(-5.72834 - 9.92177i) q^{59} +(-7.52471 - 4.34440i) q^{61} +(19.1247 - 4.40557i) q^{63} +(18.0684 + 10.4318i) q^{65} +(1.94295 - 1.12176i) q^{67} -2.61718 q^{69} +7.83399i q^{71} +(-8.46732 + 4.88861i) q^{73} +(-18.0445 + 31.2540i) q^{75} +(-2.17776 + 7.11083i) q^{77} +(-7.88389 - 4.55177i) q^{79} +(-11.8851 - 20.5856i) q^{81} -4.14493i q^{83} -6.41779 q^{85} +(-14.2654 + 8.23615i) q^{87} +(-3.13503 + 5.43003i) q^{89} +(9.35386 + 10.0405i) q^{91} +(-5.20889 + 9.02207i) q^{93} +(17.5008 - 1.07915i) q^{95} -12.8052 q^{97} +20.8504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} - 14 q^{7} - 26 q^{9}+O(q^{10}) \) 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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Database

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