LMFDB - Embedded newform 1716.2.z.g.313.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1716,2,Mod(157,1716)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1716, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8, 0]))

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

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

chi := DirichletCharacter("1716.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1716.z (of order $5$, degree $4$, 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:	$13.7023289869$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			313.2
Character	$\chi$	$=$	1716.313
Dual form			1716.2.z.g.625.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{3} +(-0.558385 + 1.71853i) q^{5} +(-2.68818 + 1.95307i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{3} +(-0.558385 + 1.71853i) q^{5} +(-2.68818 + 1.95307i) q^{7} +(0.309017 + 0.951057i) q^{9} +(-3.05862 - 1.28251i) q^{11} +(0.309017 + 0.951057i) q^{13} +(1.46187 - 1.06211i) q^{15} +(-0.849050 + 2.61311i) q^{17} +(-5.23270 - 3.80178i) q^{19} +3.32277 q^{21} +0.621071 q^{23} +(1.40352 + 1.01972i) q^{25} +(0.309017 - 0.951057i) q^{27} +(5.95788 - 4.32865i) q^{29} +(-0.498339 - 1.53373i) q^{31} +(1.72064 + 2.83539i) q^{33} +(-1.85539 - 5.71029i) q^{35} +(6.24151 - 4.53472i) q^{37} +(0.309017 - 0.951057i) q^{39} +(-6.59347 - 4.79043i) q^{41} +3.09012 q^{43} -1.80697 q^{45} +(-0.130333 - 0.0946921i) q^{47} +(1.24867 - 3.84302i) q^{49} +(2.22284 - 1.61499i) q^{51} +(2.36992 + 7.29386i) q^{53} +(3.91193 - 4.54021i) q^{55} +(1.99871 + 6.15140i) q^{57} +(0.303052 - 0.220180i) q^{59} +(3.42939 - 10.5546i) q^{61} +(-2.68818 - 1.95307i) q^{63} -1.80697 q^{65} +6.97404 q^{67} +(-0.502457 - 0.365057i) q^{69} +(-0.348429 + 1.07235i) q^{71} +(4.17594 - 3.03400i) q^{73} +(-0.536098 - 1.64994i) q^{75} +(10.7270 - 2.52610i) q^{77} +(-0.406480 - 1.25102i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(3.61582 - 11.1284i) q^{83} +(-4.01662 - 2.91824i) q^{85} -7.36434 q^{87} -5.66105 q^{89} +(-2.68818 - 1.95307i) q^{91} +(-0.498339 + 1.53373i) q^{93} +(9.45534 - 6.86971i) q^{95} +(-2.60340 - 8.01243i) q^{97} +(0.274575 - 3.30524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 7 q^{3} - 2 q^{5} - 5 q^{7} - 7 q^{9}+O(q^{10}) $ 28 * q - 7 * q^3 - 2 * q^5 - 5 * q^7 - 7 * q^9	$ 28 q - 7 q^{3} - 2 q^{5} - 5 q^{7} - 7 q^{9} + 8 q^{11} - 7 q^{13} - 2 q^{15} + 4 q^{17} + 10 q^{21} + 26 q^{23} - 13 q^{25} - 7 q^{27} + 16 q^{29} - 16 q^{31} + 3 q^{33} - 24 q^{37} - 7 q^{39} - 16 q^{41} + 12 q^{43} + 8 q^{45} - 24 q^{47} - 52 q^{49} - q^{51} + 13 q^{53} + 6 q^{55} - 10 q^{57} - 19 q^{59} + 4 q^{61} - 5 q^{63} + 8 q^{65} + 40 q^{67} - 14 q^{69} - 68 q^{71} + 13 q^{73} - 13 q^{75} + 20 q^{77} - 11 q^{79} - 7 q^{81} + 4 q^{83} - 26 q^{85} - 4 q^{87} - 18 q^{89} - 5 q^{91} - 16 q^{93} + 27 q^{95} + 2 q^{97} - 2 q^{99}+O(q^{100}) $ 28 * q - 7 * q^3 - 2 * q^5 - 5 * q^7 - 7 * q^9 + 8 * q^11 - 7 * q^13 - 2 * q^15 + 4 * q^17 + 10 * q^21 + 26 * q^23 - 13 * q^25 - 7 * q^27 + 16 * q^29 - 16 * q^31 + 3 * q^33 - 24 * q^37 - 7 * q^39 - 16 * q^41 + 12 * q^43 + 8 * q^45 - 24 * q^47 - 52 * q^49 - q^51 + 13 * q^53 + 6 * q^55 - 10 * q^57 - 19 * q^59 + 4 * q^61 - 5 * q^63 + 8 * q^65 + 40 * q^67 - 14 * q^69 - 68 * q^71 + 13 * q^73 - 13 * q^75 + 20 * q^77 - 11 * q^79 - 7 * q^81 + 4 * q^83 - 26 * q^85 - 4 * q^87 - 18 * q^89 - 5 * q^91 - 16 * q^93 + 27 * q^95 + 2 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1716\mathbb{Z}\right)^\times$.

$n$	$859$	$925$	$937$	$1145$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$		0			0
$5$	−0.558385	+	1.71853i	−0.249718	+	0.768551i	0.745107	+	0.666945i	$0.232398\pi$
$5$	−0.558385	+	1.71853i	−0.249718	+	0.768551i	−0.994825	+	0.101607i	$0.967602\pi$
$6$		0			0
$7$	−2.68818	+	1.95307i	−1.01604	+	0.738193i	−0.965466	−	0.260528i	$-0.916103\pi$
$7$	−2.68818	+	1.95307i	−1.01604	+	0.738193i	−0.0505689	+	0.998721i	$0.516103\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−3.05862	−	1.28251i	−0.922209	−	0.386692i
$11$	−3.05862	−	1.28251i	−0.922209	−	0.386692i
$12$		0			0
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$		0			0
$15$	1.46187	−	1.06211i	0.377454	−	0.274236i
$16$		0			0
$17$	−0.849050	+	2.61311i	−0.205925	+	0.633772i	0.793749	+	0.608245i	$0.208126\pi$
$17$	−0.849050	+	2.61311i	−0.205925	+	0.633772i	−0.999674	+	0.0255267i	$0.991874\pi$
$18$		0			0
$19$	−5.23270	−	3.80178i	−1.20046	−	0.872187i	−0.206133	−	0.978524i	$-0.566088\pi$
$19$	−5.23270	−	3.80178i	−1.20046	−	0.872187i	−0.994330	+	0.106337i	$0.966088\pi$
$20$		0			0
$21$	3.32277			0.725088
$22$		0			0
$23$	0.621071			0.129502			0.0647512	−	0.997901i	$-0.479375\pi$
$23$	0.621071			0.129502			0.0647512	+	0.997901i	$0.479375\pi$
$24$		0			0
$25$	1.40352	+	1.01972i	0.280704	+	0.203944i
$26$		0			0
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$		0			0
$29$	5.95788	−	4.32865i	1.10635	−	0.803811i	0.124265	−	0.992249i	$-0.460343\pi$
$29$	5.95788	−	4.32865i	1.10635	−	0.803811i	0.982085	+	0.188438i	$0.0603426\pi$
$30$		0			0
$31$	−0.498339	−	1.53373i	−0.0895043	−	0.275466i	0.896278	−	0.443492i	$-0.146261\pi$
$31$	−0.498339	−	1.53373i	−0.0895043	−	0.275466i	−0.985783	+	0.168026i	$0.946261\pi$
$32$		0			0
$33$	1.72064	+	2.83539i	0.299524	+	0.493577i
$34$		0			0
$35$	−1.85539	−	5.71029i	−0.313617	−	0.965215i
$36$		0			0
$37$	6.24151	−	4.53472i	1.02610	−	0.745503i	0.0585733	−	0.998283i	$-0.481345\pi$
$37$	6.24151	−	4.53472i	1.02610	−	0.745503i	0.967524	+	0.252780i	$0.0813449\pi$
$38$		0			0
$39$	0.309017	−	0.951057i	0.0494823	−	0.152291i
$40$		0			0
$41$	−6.59347	−	4.79043i	−1.02973	−	0.748140i	−0.0614725	−	0.998109i	$-0.519580\pi$
$41$	−6.59347	−	4.79043i	−1.02973	−	0.748140i	−0.968254	+	0.249969i	$0.919580\pi$
$42$		0			0
$43$	3.09012			0.471239			0.235619	−	0.971845i	$-0.424288\pi$
$43$	3.09012			0.471239			0.235619	+	0.971845i	$0.424288\pi$
$44$		0			0
$45$	−1.80697			−0.269368
$46$		0			0
$47$	−0.130333	−	0.0946921i	−0.0190110	−	0.0138123i	0.578239	−	0.815867i	$-0.303740\pi$
$47$	−0.130333	−	0.0946921i	−0.0190110	−	0.0138123i	−0.597250	+	0.802055i	$0.703740\pi$
$48$		0			0
$49$	1.24867	−	3.84302i	0.178382	−	0.549003i
$50$		0			0
$51$	2.22284	−	1.61499i	0.311260	−	0.226144i
$52$		0			0
$53$	2.36992	+	7.29386i	0.325533	+	1.00189i	0.971199	+	0.238269i	$0.0765798\pi$
$53$	2.36992	+	7.29386i	0.325533	+	1.00189i	−0.645666	+	0.763620i	$0.723420\pi$
$54$		0			0
$55$	3.91193	−	4.54021i	0.527484	−	0.612201i
$56$		0			0
$57$	1.99871	+	6.15140i	0.264736	+	0.814773i
$58$		0			0
$59$	0.303052	−	0.220180i	0.0394541	−	0.0286650i	−0.567883	−	0.823109i	$-0.692238\pi$
$59$	0.303052	−	0.220180i	0.0394541	−	0.0286650i	0.607338	+	0.794444i	$0.292238\pi$
$60$		0			0
$61$	3.42939	−	10.5546i	0.439089	−	1.35138i	−0.449749	−	0.893155i	$-0.648487\pi$
$61$	3.42939	−	10.5546i	0.439089	−	1.35138i	0.888838	−	0.458222i	$-0.151513\pi$
$62$		0			0
$63$	−2.68818	−	1.95307i	−0.338678	−	0.246064i
$64$		0			0
$65$	−1.80697			−0.224127
$66$		0			0
$67$	6.97404			0.852015			0.426007	−	0.904720i	$-0.359920\pi$
$67$	6.97404			0.852015			0.426007	+	0.904720i	$0.359920\pi$
$68$		0			0
$69$	−0.502457	−	0.365057i	−0.0604887	−	0.0439476i
$70$		0			0
$71$	−0.348429	+	1.07235i	−0.0413509	+	0.127265i	−0.969601	−	0.244692i	$-0.921313\pi$
$71$	−0.348429	+	1.07235i	−0.0413509	+	0.127265i	0.928250	+	0.371957i	$0.121313\pi$
$72$		0			0
$73$	4.17594	−	3.03400i	0.488757	−	0.355103i	−0.315949	−	0.948776i	$-0.602323\pi$
$73$	4.17594	−	3.03400i	0.488757	−	0.355103i	0.804706	+	0.593673i	$0.202323\pi$
$74$		0			0
$75$	−0.536098	−	1.64994i	−0.0619032	−	0.190519i
$76$		0			0
$77$	10.7270	−	2.52610i	1.22245	−	0.287876i
$78$		0			0
$79$	−0.406480	−	1.25102i	−0.0457326	−	0.140751i	0.925583	−	0.378545i	$-0.123576\pi$
$79$	−0.406480	−	1.25102i	−0.0457326	−	0.140751i	−0.971315	+	0.237795i	$0.923576\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	3.61582	−	11.1284i	0.396888	−	1.22150i	−0.530593	−	0.847627i	$-0.678031\pi$
$83$	3.61582	−	11.1284i	0.396888	−	1.22150i	0.927481	−	0.373870i	$-0.121969\pi$
$84$		0			0
$85$	−4.01662	−	2.91824i	−0.435663	−	0.316528i
$86$		0			0
$87$	−7.36434			−0.789541
$88$		0			0
$89$	−5.66105			−0.600070			−0.300035	−	0.953928i	$-0.596998\pi$
$89$	−5.66105			−0.600070			−0.300035	+	0.953928i	$0.596998\pi$
$90$		0			0
$91$	−2.68818	−	1.95307i	−0.281797	−	0.204738i
$92$		0			0
$93$	−0.498339	+	1.53373i	−0.0516753	+	0.159040i
$94$		0			0
$95$	9.45534	−	6.86971i	0.970098	−	0.704817i
$96$		0			0
$97$	−2.60340	−	8.01243i	−0.264335	−	0.813539i	−0.991846	−	0.127443i	$-0.959323\pi$
$97$	−2.60340	−	8.01243i	−0.264335	−	0.813539i	0.727511	−	0.686096i	$-0.240677\pi$
$98$		0			0
$99$	0.274575	−	3.30524i	0.0275958	−	0.332189i
$100$		0			0
$101$	1.14085	+	3.51119i	0.113519	+	0.349376i	0.991635	−	0.129071i	$-0.0411996\pi$
$101$	1.14085	+	3.51119i	0.113519	+	0.349376i	−0.878116	+	0.478448i	$0.841200\pi$
$102$		0			0
$103$	−1.40624	+	1.02169i	−0.138561	+	0.100670i	−0.654906	−	0.755710i	$-0.727292\pi$
$103$	−1.40624	+	1.02169i	−0.138561	+	0.100670i	0.516346	+	0.856380i	$0.327292\pi$
$104$		0			0
$105$	−1.85539	+	5.71029i	−0.181067	+	0.557267i
$106$		0			0
$107$	3.52724	+	2.56269i	0.340991	+	0.247744i	0.745080	−	0.666975i	$-0.232411\pi$
$107$	3.52724	+	2.56269i	0.340991	+	0.247744i	−0.404089	+	0.914720i	$0.632411\pi$
$108$		0			0
$109$	2.10583			0.201702			0.100851	−	0.994902i	$-0.467844\pi$
$109$	2.10583			0.201702			0.100851	+	0.994902i	$0.467844\pi$
$110$		0			0
$111$	−7.71492			−0.732268
$112$		0			0
$113$	−13.0492	−	9.48083i	−1.22757	−	0.891881i	−0.230864	−	0.972986i	$-0.574155\pi$
$113$	−13.0492	−	9.48083i	−1.22757	−	0.891881i	−0.996706	+	0.0811047i	$0.974155\pi$
$114$		0			0
$115$	−0.346797	+	1.06733i	−0.0323390	+	0.0995292i
$116$		0			0
$117$	−0.809017	+	0.587785i	−0.0747936	+	0.0543408i
$118$		0			0
$119$	−2.82120	−	8.68276i	−0.258619	−	0.795947i
$120$		0			0
$121$	7.71033	+	7.84543i	0.700939	+	0.713221i
$122$		0			0
$123$	2.51848	+	7.75108i	0.227084	+	0.698892i
$124$		0			0
$125$	−9.84549	+	7.15316i	−0.880607	+	0.639798i
$126$		0			0
$127$	4.20193	−	12.9322i	0.372861	−	1.14755i	−0.572049	−	0.820220i	$-0.693851\pi$
$127$	4.20193	−	12.9322i	0.372861	−	1.14755i	0.944910	−	0.327330i	$-0.106149\pi$
$128$		0			0
$129$	−2.49996	−	1.81633i	−0.220109	−	0.159919i
$130$		0			0
$131$	−18.8480			−1.64676			−0.823378	−	0.567493i	$-0.807913\pi$
$131$	−18.8480			−1.64676			−0.823378	+	0.567493i	$0.807913\pi$
$132$		0			0
$133$	21.4916			1.86356
$134$		0			0
$135$	1.46187	+	1.06211i	0.125818	+	0.0914120i
$136$		0			0
$137$	−0.428105	+	1.31757i	−0.0365755	+	0.112568i	−0.967677	−	0.252191i	$-0.918849\pi$
$137$	−0.428105	+	1.31757i	−0.0365755	+	0.112568i	0.931102	+	0.364759i	$0.118849\pi$
$138$		0			0
$139$	−4.97970	+	3.61796i	−0.422372	+	0.306872i	−0.778592	−	0.627531i	$-0.784066\pi$
$139$	−4.97970	+	3.61796i	−0.422372	+	0.306872i	0.356219	+	0.934402i	$0.384066\pi$
$140$		0			0
$141$	0.0497826	+	0.153215i	0.00419245	+	0.0129030i
$142$		0			0
$143$	0.274575	−	3.30524i	0.0229611	−	0.276398i
$144$		0			0
$145$	4.11214	+	12.6559i	0.341495	+	1.05101i
$146$		0			0
$147$	−3.26907	+	2.37512i	−0.269628	+	0.195897i
$148$		0			0
$149$	0.844443	−	2.59893i	0.0691795	−	0.212913i	−0.910490	−	0.413531i	$-0.864295\pi$
$149$	0.844443	−	2.59893i	0.0691795	−	0.212913i	0.979669	+	0.200619i	$0.0642952\pi$
$150$		0			0
$151$	−13.8536	−	10.0652i	−1.12739	−	0.819098i	−0.142078	−	0.989855i	$-0.545378\pi$
$151$	−13.8536	−	10.0652i	−1.12739	−	0.819098i	−0.985313	+	0.170758i	$0.945378\pi$
$152$		0			0
$153$	−2.74759			−0.222129
$154$		0			0
$155$	2.91403			0.234061
$156$		0			0
$157$	2.21753	+	1.61113i	0.176978	+	0.128582i	0.672748	−	0.739872i	$-0.265114\pi$
$157$	2.21753	+	1.61113i	0.176978	+	0.128582i	−0.495769	+	0.868454i	$0.665114\pi$
$158$		0			0
$159$	2.36992	−	7.29386i	0.187947	−	0.578441i
$160$		0			0
$161$	−1.66955	+	1.21300i	−0.131579	+	0.0955977i
$162$		0			0
$163$	−0.946857	−	2.91413i	−0.0741636	−	0.228252i	0.907102	−	0.420910i	$-0.138289\pi$
$163$	−0.946857	−	2.91413i	−0.0741636	−	0.228252i	−0.981266	+	0.192658i	$0.938289\pi$
$164$		0			0
$165$	−5.83348	+	1.37373i	−0.454136	+	0.106945i
$166$		0			0
$167$	−3.36904	−	10.3688i	−0.260704	−	0.802364i	−0.992652	−	0.121004i	$-0.961389\pi$
$167$	−3.36904	−	10.3688i	−0.260704	−	0.802364i	0.731948	−	0.681360i	$-0.238611\pi$
$168$		0			0
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$		0			0
$171$	1.99871	−	6.15140i	0.152845	−	0.470410i
$172$		0			0
$173$	−10.7542	−	7.81335i	−0.817623	−	0.594038i	0.0984075	−	0.995146i	$-0.468625\pi$
$173$	−10.7542	−	7.81335i	−0.817623	−	0.594038i	−0.916031	+	0.401108i	$0.868625\pi$
$174$		0			0
$175$	−5.76450			−0.435755
$176$		0			0
$177$	−0.374593			−0.0281562
$178$		0			0
$179$	10.7986	+	7.84561i	0.807122	+	0.586408i	0.912995	−	0.407971i	$-0.133764\pi$
$179$	10.7986	+	7.84561i	0.807122	+	0.586408i	−0.105873	+	0.994380i	$0.533764\pi$
$180$		0			0
$181$	5.10397	−	15.7084i	0.379375	−	1.16760i	−0.561104	−	0.827745i	$-0.689623\pi$
$181$	5.10397	−	15.7084i	0.379375	−	1.16760i	0.940479	−	0.339851i	$-0.110377\pi$
$182$		0			0
$183$	−8.97827	+	6.52309i	−0.663693	+	0.482201i
$184$		0			0
$185$	4.30790	+	13.2584i	0.316723	+	0.974774i
$186$		0			0
$187$	5.94827	−	6.90359i	0.434980	−	0.504841i
$188$		0			0
$189$	1.02679	+	3.16014i	0.0746881	+	0.229866i
$190$		0			0
$191$	−15.3464	+	11.1498i	−1.11043	+	0.806775i	−0.982731	−	0.185038i	$-0.940759\pi$
$191$	−15.3464	+	11.1498i	−1.11043	+	0.806775i	−0.127699	+	0.991813i	$0.540759\pi$
$192$		0			0
$193$	6.20061	−	19.0835i	0.446330	−	1.37366i	−0.434689	−	0.900581i	$-0.643142\pi$
$193$	6.20061	−	19.0835i	0.446330	−	1.37366i	0.881019	−	0.473081i	$-0.156858\pi$
$194$		0			0
$195$	1.46187	+	1.06211i	0.104687	+	0.0760594i
$196$		0			0
$197$	−10.6870			−0.761416			−0.380708	−	0.924695i	$-0.624320\pi$
$197$	−10.6870			−0.761416			−0.380708	+	0.924695i	$0.624320\pi$
$198$		0			0
$199$	19.1948			1.36068			0.680341	−	0.732896i	$-0.261832\pi$
$199$	19.1948			1.36068			0.680341	+	0.732896i	$0.261832\pi$
$200$		0			0
$201$	−5.64212	−	4.09924i	−0.397964	−	0.289138i
$202$		0			0
$203$	−7.56165	+	23.2724i	−0.530724	+	1.63340i
$204$		0			0
$205$	11.9142	−	8.65618i	0.832125	−	0.604574i
$206$		0			0
$207$	0.191922	+	0.590674i	0.0133395	+	0.0410547i
$208$		0			0
$209$	11.1290	+	18.3392i	0.769810	+	1.26855i
$210$		0			0
$211$	3.14549	+	9.68083i	0.216545	+	0.666456i	0.999040	+	0.0437997i	$0.0139463\pi$
$211$	3.14549	+	9.68083i	0.216545	+	0.666456i	−0.782496	+	0.622656i	$0.786054\pi$
$212$		0			0
$213$	0.912199	−	0.662751i	0.0625028	−	0.0454110i
$214$		0			0
$215$	−1.72548	+	5.31047i	−0.117677	+	0.362171i
$216$		0			0
$217$	4.33511	+	3.14964i	0.294287	+	0.213812i
$218$		0			0
$219$	−5.16175			−0.348799
$220$		0			0
$221$	−2.74759			−0.184823
$222$		0			0
$223$	−16.7505	−	12.1700i	−1.12170	−	0.814960i	−0.137231	−	0.990539i	$-0.543820\pi$
$223$	−16.7505	−	12.1700i	−1.12170	−	0.814960i	−0.984465	+	0.175579i	$0.943820\pi$
$224$		0			0
$225$	−0.536098	+	1.64994i	−0.0357399	+	0.109996i
$226$		0			0
$227$	21.5995	−	15.6930i	1.43361	−	1.04158i	0.444280	−	0.895888i	$-0.353460\pi$
$227$	21.5995	−	15.6930i	1.43361	−	1.04158i	0.989330	−	0.145691i	$-0.0465404\pi$
$228$		0			0
$229$	−3.34644	−	10.2993i	−0.221139	−	0.680595i	−0.998661	−	0.0517392i	$-0.983524\pi$
$229$	−3.34644	−	10.2993i	−0.221139	−	0.680595i	0.777522	−	0.628856i	$-0.216476\pi$
$230$		0			0
$231$	−10.1631	−	4.26149i	−0.668682	−	0.280385i
$232$		0			0
$233$	4.65563	+	14.3286i	0.305001	+	0.938696i	0.979677	+	0.200582i	$0.0642833\pi$
$233$	4.65563	+	14.3286i	0.305001	+	0.938696i	−0.674676	+	0.738114i	$0.735717\pi$
$234$		0			0
$235$	0.235507	−	0.171106i	0.0153628	−	0.0111617i
$236$		0			0
$237$	−0.406480	+	1.25102i	−0.0264037	+	0.0812623i
$238$		0			0
$239$	4.14969	+	3.01493i	0.268421	+	0.195019i	0.713851	−	0.700297i	$-0.246949\pi$
$239$	4.14969	+	3.01493i	0.268421	+	0.195019i	−0.445430	+	0.895317i	$0.646949\pi$
$240$		0			0
$241$	19.0228			1.22536			0.612682	−	0.790329i	$-0.290091\pi$
$241$	19.0228			1.22536			0.612682	+	0.790329i	$0.290091\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	5.90712	+	4.29178i	0.377392	+	0.274191i
$246$		0			0
$247$	1.99871	−	6.15140i	0.127175	−	0.391404i
$248$		0			0
$249$	−9.46635	+	6.87771i	−0.599906	+	0.435857i
$250$		0			0
$251$	3.63045	+	11.1734i	0.229152	+	0.705257i	0.997844	+	0.0656376i	$0.0209081\pi$
$251$	3.63045	+	11.1734i	0.229152	+	0.705257i	−0.768692	+	0.639620i	$0.779092\pi$
$252$		0			0
$253$	−1.89962	−	0.796531i	−0.119428	−	0.0500775i
$254$		0			0
$255$	1.53421	+	4.72182i	0.0960760	+	0.295692i
$256$		0			0
$257$	7.59593	−	5.51876i	0.473821	−	0.344251i	−0.325108	−	0.945677i	$-0.605401\pi$
$257$	7.59593	−	5.51876i	0.473821	−	0.344251i	0.798929	+	0.601426i	$0.205401\pi$
$258$		0			0
$259$	−7.92162	+	24.3803i	−0.492226	+	1.51492i
$260$		0			0
$261$	5.95788	+	4.32865i	0.368783	+	0.267937i
$262$		0			0
$263$	−12.4760			−0.769302			−0.384651	−	0.923062i	$-0.625678\pi$
$263$	−12.4760			−0.769302			−0.384651	+	0.923062i	$0.625678\pi$
$264$		0			0
$265$	−13.8581			−0.851294
$266$		0			0
$267$	4.57988	+	3.32748i	0.280284	+	0.203638i
$268$		0			0
$269$	−6.43379	+	19.8012i	−0.392275	+	1.20730i	0.538788	+	0.842441i	$0.318882\pi$
$269$	−6.43379	+	19.8012i	−0.392275	+	1.20730i	−0.931063	+	0.364858i	$0.881118\pi$
$270$		0			0
$271$	17.2665	−	12.5449i	1.04887	−	0.762046i	0.0768701	−	0.997041i	$-0.475507\pi$
$271$	17.2665	−	12.5449i	1.04887	−	0.762046i	0.971997	+	0.234995i	$0.0755073\pi$
$272$		0			0
$273$	1.02679	+	3.16014i	0.0621443	+	0.191260i
$274$		0			0
$275$	−2.98504	−	4.91897i	−0.180005	−	0.296625i
$276$		0			0
$277$	6.74024	+	20.7443i	0.404982	+	1.24641i	0.920911	+	0.389774i	$0.127447\pi$
$277$	6.74024	+	20.7443i	0.404982	+	1.24641i	−0.515929	+	0.856631i	$0.672553\pi$
$278$		0			0
$279$	1.30467	−	0.947897i	0.0781084	−	0.0567491i
$280$		0			0
$281$	−4.79524	+	14.7582i	−0.286060	+	0.880403i	0.700019	+	0.714125i	$0.253175\pi$
$281$	−4.79524	+	14.7582i	−0.286060	+	0.880403i	−0.986079	+	0.166278i	$0.946825\pi$
$282$		0			0
$283$	8.15280	+	5.92335i	0.484633	+	0.352107i	0.803117	−	0.595822i	$-0.203174\pi$
$283$	8.15280	+	5.92335i	0.484633	+	0.352107i	−0.318483	+	0.947928i	$0.603174\pi$
$284$		0			0
$285$	−11.6874			−0.692304
$286$		0			0
$287$	27.0805			1.59851
$288$		0			0
$289$	7.64584	+	5.55503i	0.449755	+	0.326766i
$290$		0			0
$291$	−2.60340	+	8.01243i	−0.152614	+	0.469697i
$292$		0			0
$293$	−3.04346	+	2.21120i	−0.177801	+	0.129180i	−0.673126	−	0.739528i	$-0.735049\pi$
$293$	−3.04346	+	2.21120i	−0.177801	+	0.129180i	0.495325	+	0.868708i	$0.335049\pi$
$294$		0			0
$295$	0.209167	+	0.643751i	0.0121782	+	0.0374806i
$296$		0			0
$297$	−2.16491	+	2.51260i	−0.125621	+	0.145796i
$298$		0			0
$299$	0.191922	+	0.590674i	0.0110991	+	0.0341596i
$300$		0			0
$301$	−8.30678	+	6.03523i	−0.478795	+	0.347865i
$302$		0			0
$303$	1.14085	−	3.51119i	0.0655404	−	0.201713i
$304$		0			0
$305$	16.2235	+	11.7871i	0.928954	+	0.674925i
$306$		0			0
$307$	−15.2828			−0.872235			−0.436117	−	0.899890i	$-0.643647\pi$
$307$	−15.2828			−0.872235			−0.436117	+	0.899890i	$0.643647\pi$
$308$		0			0
$309$	1.73820			0.0988829
$310$		0			0
$311$	−15.7053	−	11.4106i	−0.890566	−	0.647034i	0.0454595	−	0.998966i	$-0.485525\pi$
$311$	−15.7053	−	11.4106i	−0.890566	−	0.647034i	−0.936026	+	0.351932i	$0.885525\pi$
$312$		0			0
$313$	7.80865	−	24.0326i	0.441371	−	1.35840i	−0.445044	−	0.895509i	$-0.646812\pi$
$313$	7.80865	−	24.0326i	0.441371	−	1.35840i	0.886415	−	0.462892i	$-0.153188\pi$
$314$		0			0
$315$	4.85746	−	3.52915i	0.273687	−	0.198845i
$316$		0			0
$317$	3.77861	+	11.6294i	0.212228	+	0.653170i	0.999339	+	0.0363587i	$0.0115759\pi$
$317$	3.77861	+	11.6294i	0.212228	+	0.653170i	−0.787111	+	0.616811i	$0.788424\pi$
$318$		0			0
$319$	−23.7744	+	5.59866i	−1.33111	+	0.313465i
$320$		0			0
$321$	−1.34728	−	4.14652i	−0.0751981	−	0.231436i
$322$		0			0
$323$	14.3773	−	10.4457i	0.799973	−	0.581215i
$324$		0			0
$325$	−0.536098	+	1.64994i	−0.0297374	+	0.0915222i
$326$		0			0
$327$	−1.70365	−	1.23777i	−0.0942120	−	0.0684490i
$328$		0			0
$329$	0.535298			0.0295119
$330$		0			0
$331$	0.705228			0.0387628			0.0193814	−	0.999812i	$-0.493830\pi$
$331$	0.705228			0.0387628			0.0193814	+	0.999812i	$0.493830\pi$
$332$		0			0
$333$	6.24151	+	4.53472i	0.342032	+	0.248501i
$334$		0			0
$335$	−3.89420	+	11.9851i	−0.212763	+	0.654817i
$336$		0			0
$337$	−9.45772	+	6.87144i	−0.515195	+	0.374311i	−0.814791	−	0.579755i	$-0.803148\pi$
$337$	−9.45772	+	6.87144i	−0.515195	+	0.374311i	0.299596	+	0.954066i	$0.403148\pi$
$338$		0			0
$339$	4.98437	+	15.3403i	0.270714	+	0.833171i
$340$		0			0
$341$	−0.442796	+	5.33022i	−0.0239787	+	0.288648i
$342$		0			0
$343$	−3.03849	−	9.35151i	−0.164063	−	0.504934i
$344$		0			0
$345$	0.907927	−	0.659647i	0.0488811	−	0.0355142i
$346$		0			0
$347$	−2.72355	+	8.38223i	−0.146208	+	0.449982i	−0.997164	−	0.0752545i	$-0.976023\pi$
$347$	−2.72355	+	8.38223i	−0.146208	+	0.449982i	0.850956	+	0.525236i	$0.176023\pi$
$348$		0			0
$349$	−0.0924685	−	0.0671823i	−0.00494973	−	0.00359619i	0.585308	−	0.810811i	$-0.300974\pi$
$349$	−0.0924685	−	0.0671823i	−0.00494973	−	0.00359619i	−0.590257	+	0.807215i	$0.700974\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$		0			0
$353$	−22.9660			−1.22236			−0.611179	−	0.791492i	$-0.709305\pi$
$353$	−22.9660			−1.22236			−0.611179	+	0.791492i	$0.709305\pi$
$354$		0			0
$355$	−1.64832	−	1.19757i	−0.0874837	−	0.0635606i
$356$		0			0
$357$	−2.82120	+	8.68276i	−0.149314	+	0.459540i
$358$		0			0
$359$	5.89594	−	4.28365i	0.311176	−	0.226083i	−0.421225	−	0.906956i	$-0.638400\pi$
$359$	5.89594	−	4.28365i	0.311176	−	0.226083i	0.732401	+	0.680874i	$0.238400\pi$
$360$		0			0
$361$	7.05629	+	21.7170i	0.371383	+	1.14300i
$362$		0			0
$363$	−1.62636	−	10.8791i	−0.0853615	−	0.571005i
$364$		0			0
$365$	2.88224	+	8.87064i	0.150864	+	0.464310i
$366$		0			0
$367$	16.3071	−	11.8478i	0.851225	−	0.618451i	−0.0742582	−	0.997239i	$-0.523659\pi$
$367$	16.3071	−	11.8478i	0.851225	−	0.618451i	0.925484	+	0.378788i	$0.123659\pi$
$368$		0			0
$369$	2.51848	−	7.75108i	0.131107	−	0.403505i
$370$		0			0
$371$	−20.6162	−	14.9786i	−1.07034	−	0.777648i
$372$		0			0
$373$	−23.5255			−1.21811			−0.609053	−	0.793129i	$-0.708450\pi$
$373$	−23.5255			−1.21811			−0.609053	+	0.793129i	$0.708450\pi$
$374$		0			0
$375$	12.1697			0.628440
$376$		0			0
$377$	5.95788	+	4.32865i	0.306846	+	0.222937i
$378$		0			0
$379$	−4.48522	+	13.8041i	−0.230390	+	0.709069i	0.767309	+	0.641278i	$0.221595\pi$
$379$	−4.48522	+	13.8041i	−0.230390	+	0.709069i	−0.997700	+	0.0677915i	$0.978405\pi$
$380$		0			0
$381$	−11.0008	+	7.99255i	−0.563588	+	0.409471i
$382$		0			0
$383$	−1.96146	−	6.03677i	−0.100226	−	0.308464i	0.888354	−	0.459159i	$-0.151849\pi$
$383$	−1.96146	−	6.03677i	−0.100226	−	0.308464i	−0.988580	+	0.150694i	$0.951849\pi$
$384$		0			0
$385$	−1.64859	+	19.8452i	−0.0840200	+	1.01140i
$386$		0			0
$387$	0.954899	+	2.93888i	0.0485402	+	0.149392i
$388$		0			0
$389$	6.49032	−	4.71549i	0.329072	−	0.239085i	−0.410965	−	0.911651i	$-0.634808\pi$
$389$	6.49032	−	4.71549i	0.329072	−	0.239085i	0.740037	+	0.672566i	$0.234808\pi$
$390$		0			0
$391$	−0.527321	+	1.62293i	−0.0266678	+	0.0820749i
$392$		0			0
$393$	15.2483	+	11.0786i	0.769177	+	0.558840i
$394$		0			0
$395$	2.37689			0.119594
$396$		0			0
$397$	37.3609			1.87509			0.937545	−	0.347864i	$-0.113093\pi$
$397$	37.3609			1.87509			0.937545	+	0.347864i	$0.113093\pi$
$398$		0			0
$399$	−17.3870	−	12.6324i	−0.870441	−	0.632412i
$400$		0			0
$401$	−6.05957	+	18.6494i	−0.302601	+	0.931309i	0.677961	+	0.735098i	$0.262864\pi$
$401$	−6.05957	+	18.6494i	−0.302601	+	0.931309i	−0.980562	+	0.196211i	$0.937136\pi$
$402$		0			0
$403$	1.30467	−	0.947897i	0.0649902	−	0.0472181i
$404$		0			0
$405$	−0.558385	−	1.71853i	−0.0277464	−	0.0853946i
$406$		0			0
$407$	−24.9062	+	5.86518i	−1.23456	+	0.290726i
$408$		0			0
$409$	2.26006	+	6.95576i	0.111753	+	0.343940i	0.991256	−	0.131953i	$-0.0421249\pi$
$409$	2.26006	+	6.95576i	0.111753	+	0.343940i	−0.879503	+	0.475893i	$0.842125\pi$
$410$		0			0
$411$	1.12079	−	0.814305i	0.0552847	−	0.0401667i
$412$		0			0
$413$	−0.384629	+	1.18377i	−0.0189264	+	0.0582494i
$414$		0			0
$415$	17.1054	+	12.4278i	0.839673	+	0.610058i
$416$		0			0
$417$	6.15525			0.301424
$418$		0			0
$419$	−0.545056			−0.0266277			−0.0133139	−	0.999911i	$-0.504238\pi$
$419$	−0.545056			−0.0266277			−0.0133139	+	0.999911i	$0.504238\pi$
$420$		0			0
$421$	−29.2388	−	21.2432i	−1.42501	−	1.03533i	−0.990919	−	0.134464i	$-0.957069\pi$
$421$	−29.2388	−	21.2432i	−1.42501	−	1.03533i	−0.434093	−	0.900868i	$-0.642931\pi$
$422$		0			0
$423$	0.0497826	−	0.153215i	0.00242051	−	0.00744957i
$424$		0			0
$425$	−3.85630	+	2.80176i	−0.187058	+	0.135905i
$426$		0			0
$427$	11.3951	+	35.0705i	0.551447	+	1.69718i
$428$		0			0
$429$	−2.16491	+	2.51260i	−0.104523	+	0.121310i
$430$		0			0
$431$	3.82568	+	11.7742i	0.184276	+	0.567144i	0.999935	−	0.0113889i	$-0.00362527\pi$
$431$	3.82568	+	11.7742i	0.184276	+	0.567144i	−0.815659	+	0.578533i	$0.803625\pi$
$432$		0			0
$433$	−24.3466	+	17.6889i	−1.17002	+	0.850072i	−0.991012	−	0.133775i	$-0.957290\pi$
$433$	−24.3466	+	17.6889i	−1.17002	+	0.850072i	−0.179012	+	0.983847i	$0.557290\pi$
$434$		0			0
$435$	4.11214	−	12.6559i	0.197162	−	0.606803i
$436$		0			0
$437$	−3.24988	−	2.36117i	−0.155463	−	0.112950i
$438$		0			0
$439$	−16.0409			−0.765589			−0.382794	−	0.923834i	$-0.625038\pi$
$439$	−16.0409			−0.765589			−0.382794	+	0.923834i	$0.625038\pi$
$440$		0			0
$441$	4.04079			0.192419
$442$		0			0
$443$	−10.0935	−	7.33336i	−0.479557	−	0.348418i	0.321597	−	0.946877i	$-0.395780\pi$
$443$	−10.0935	−	7.33336i	−0.479557	−	0.348418i	−0.801154	+	0.598458i	$0.795780\pi$
$444$		0			0
$445$	3.16105	−	9.72870i	0.149848	−	0.461185i
$446$		0			0
$447$	−2.21078	+	1.60623i	−0.104566	+	0.0759719i
$448$		0			0
$449$	4.85505	+	14.9423i	0.229124	+	0.705171i	0.997847	+	0.0655891i	$0.0208927\pi$
$449$	4.85505	+	14.9423i	0.229124	+	0.705171i	−0.768723	+	0.639582i	$0.779107\pi$
$450$		0			0
$451$	14.0231	+	23.1083i	0.660323	+	1.08813i
$452$		0			0
$453$	5.29161	+	16.2859i	0.248622	+	0.765178i
$454$		0			0
$455$	4.85746	−	3.52915i	0.227721	−	0.165449i
$456$		0			0
$457$	−1.82801	+	5.62602i	−0.0855105	+	0.263174i	−0.984665	−	0.174458i	$-0.944183\pi$
$457$	−1.82801	+	5.62602i	−0.0855105	+	0.263174i	0.899154	+	0.437632i	$0.144183\pi$
$458$		0			0
$459$	2.22284	+	1.61499i	0.103753	+	0.0753813i
$460$		0			0
$461$	−0.867224			−0.0403906			−0.0201953	−	0.999796i	$-0.506429\pi$
$461$	−0.867224			−0.0403906			−0.0201953	+	0.999796i	$0.506429\pi$
$462$		0			0
$463$	23.2126			1.07878			0.539390	−	0.842056i	$-0.318655\pi$
$463$	23.2126			1.07878			0.539390	+	0.842056i	$0.318655\pi$
$464$		0			0
$465$	−2.35750	−	1.71282i	−0.109326	−	0.0794303i
$466$		0			0
$467$	0.830138	−	2.55490i	0.0384142	−	0.118227i	−0.930011	−	0.367533i	$-0.880203\pi$
$467$	0.830138	−	2.55490i	0.0384142	−	0.118227i	0.968425	+	0.249306i	$0.0802025\pi$
$468$		0			0
$469$	−18.7475	+	13.6208i	−0.865677	+	0.628951i
$470$		0			0
$471$	−0.847022	−	2.60687i	−0.0390287	−	0.120118i
$472$		0			0
$473$	−9.45150	−	3.96311i	−0.434580	−	0.182224i
$474$		0			0
$475$	−3.46746	−	10.6718i	−0.159098	−	0.489654i
$476$		0			0
$477$	−6.20453	+	4.50785i	−0.284086	+	0.206400i
$478$		0			0
$479$	7.12326	−	21.9231i	0.325470	−	1.00169i	−0.645758	−	0.763542i	$-0.723459\pi$
$479$	7.12326	−	21.9231i	0.325470	−	1.00169i	0.971228	−	0.238151i	$-0.0765415\pi$
$480$		0			0
$481$	6.24151	+	4.53472i	0.284588	+	0.206765i
$482$		0			0
$483$	2.06368			0.0939005
$484$		0			0
$485$	15.2233			0.691255
$486$		0			0
$487$	−17.1936	−	12.4919i	−0.779117	−	0.566061i	0.125597	−	0.992081i	$-0.459915\pi$
$487$	−17.1936	−	12.4919i	−0.779117	−	0.566061i	−0.904714	+	0.426020i	$0.859915\pi$
$488$		0			0
$489$	−0.946857	+	2.91413i	−0.0428184	+	0.131781i
$490$		0			0
$491$	26.0157	−	18.9015i	1.17407	−	0.853013i	0.182581	−	0.983191i	$-0.441555\pi$
$491$	26.0157	−	18.9015i	1.17407	−	0.853013i	0.991491	+	0.130178i	$0.0415547\pi$
$492$		0			0
$493$	6.25270	+	19.2438i	0.281607	+	0.866699i
$494$		0			0
$495$	5.52685	+	2.31746i	0.248413	+	0.104162i
$496$		0			0
$497$	−1.15775	−	3.56318i	−0.0519321	−	0.159831i
$498$		0			0
$499$	10.0951	−	7.33448i	0.451917	−	0.328337i	−0.338435	−	0.940990i	$-0.609898\pi$
$499$	10.0951	−	7.33448i	0.451917	−	0.328337i	0.790352	+	0.612653i	$0.209898\pi$
$500$		0			0
$501$	−3.36904	+	10.3688i	−0.150518	+	0.463245i
$502$		0			0
$503$	−5.15939	−	3.74852i	−0.230046	−	0.167138i	0.466791	−	0.884368i	$-0.345410\pi$
$503$	−5.15939	−	3.74852i	−0.230046	−	0.167138i	−0.696837	+	0.717229i	$0.745410\pi$
$504$		0			0
$505$	−6.67113			−0.296861
$506$		0			0
$507$	1.00000			0.0444116
$508$		0			0
$509$	−19.6705	−	14.2915i	−0.871880	−	0.633458i	0.0592109	−	0.998245i	$-0.481142\pi$
$509$	−19.6705	−	14.2915i	−0.871880	−	0.633458i	−0.931091	+	0.364788i	$0.881142\pi$
$510$		0			0
$511$	−5.30004	+	16.3119i	−0.234460	+	0.721594i
$512$		0			0
$513$	−5.23270	+	3.80178i	−0.231029	+	0.167853i
$514$		0			0
$515$	−0.970587	−	2.98716i	−0.0427692	−	0.131630i
$516$		0			0
$517$	0.277194	+	0.456780i	0.0121910	+	0.0200892i
$518$		0			0
$519$	4.10772	+	12.6423i	0.180309	+	0.554934i
$520$		0			0
$521$	0.737526	−	0.535844i	0.0323116	−	0.0234758i	−0.571512	−	0.820594i	$-0.693643\pi$
$521$	0.737526	−	0.535844i	0.0323116	−	0.0234758i	0.603824	+	0.797118i	$0.293643\pi$
$522$		0			0
$523$	1.31559	−	4.04898i	0.0575269	−	0.177050i	−0.918164	−	0.396200i	$-0.870329\pi$
$523$	1.31559	−	4.04898i	0.0575269	−	0.177050i	0.975691	+	0.219151i	$0.0703286\pi$
$524$		0			0
$525$	4.66358	+	3.38829i	0.203535	+	0.147877i
$526$		0			0
$527$	4.43092			0.193014
$528$		0			0
$529$	−22.6143			−0.983229
$530$		0			0
$531$	0.303052	+	0.220180i	0.0131514	+	0.00955502i
$532$		0			0
$533$	2.51848	−	7.75108i	0.109087	−	0.335737i
$534$		0			0
$535$	−6.37362	+	4.63071i	−0.275556	+	0.200203i
$536$		0			0
$537$	−4.12468	−	12.6945i	−0.177993	−	0.547806i
$538$		0			0
$539$	−8.74794	+	10.1529i	−0.376801	+	0.437317i
$540$		0			0
$541$	−14.1616	−	43.5850i	−0.608856	−	1.87387i	−0.467719	−	0.883877i	$-0.654924\pi$
$541$	−14.1616	−	43.5850i	−0.608856	−	1.87387i	−0.141137	−	0.989990i	$-0.545076\pi$
$542$		0			0
$543$	−13.3624	+	9.70833i	−0.573434	+	0.416624i
$544$		0			0
$545$	−1.17586	+	3.61893i	−0.0503684	+	0.155018i
$546$		0			0
$547$	−35.3616	−	25.6917i	−1.51195	−	1.09850i	−0.965301	−	0.261138i	$-0.915902\pi$
$547$	−35.3616	−	25.6917i	−1.51195	−	1.09850i	−0.546652	−	0.837360i	$-0.684098\pi$
$548$		0			0
$549$	11.0978			0.473641
$550$		0			0
$551$	−47.6323			−2.02921
$552$		0			0
$553$	3.53602	+	2.56907i	0.150367	+	0.109248i
$554$		0			0
$555$	4.30790	−	13.2584i	0.182860	−	0.562786i
$556$		0			0
$557$	7.27514	−	5.28570i	0.308258	−	0.223962i	−0.422891	−	0.906181i	$-0.638985\pi$
$557$	7.27514	−	5.28570i	0.308258	−	0.223962i	0.731149	+	0.682218i	$0.238985\pi$
$558$		0			0
$559$	0.954899	+	2.93888i	0.0403879	+	0.124301i
$560$		0			0
$561$	−8.87008	+	2.08882i	−0.374495	+	0.0881901i
$562$		0			0
$563$	−11.6818	−	35.9527i	−0.492327	−	1.51523i	−0.821081	−	0.570812i	$-0.806629\pi$
$563$	−11.6818	−	35.9527i	−0.492327	−	1.51523i	0.328754	−	0.944416i	$-0.393371\pi$
$564$		0			0
$565$	23.5796	−	17.1316i	0.992002	−	0.720732i
$566$		0			0
$567$	1.02679	−	3.16014i	0.0431212	−	0.132713i
$568$		0			0
$569$	−28.0942	−	20.4116i	−1.17777	−	0.855701i	−0.185853	−	0.982578i	$-0.559505\pi$
$569$	−28.0942	−	20.4116i	−1.17777	−	0.855701i	−0.991918	+	0.126877i	$0.959505\pi$
$570$		0			0
$571$	43.9191			1.83796			0.918980	−	0.394305i	$-0.129015\pi$
$571$	43.9191			1.83796			0.918980	+	0.394305i	$0.129015\pi$
$572$		0			0
$573$	18.9693			0.792452
$574$		0			0
$575$	0.871687	+	0.633318i	0.0363519	+	0.0264112i
$576$		0			0
$577$	7.60280	−	23.3990i	0.316509	−	0.974113i	−0.658620	−	0.752475i	$-0.728860\pi$
$577$	7.60280	−	23.3990i	0.316509	−	0.974113i	0.975129	−	0.221638i	$-0.0711403\pi$
$578$		0			0
$579$	−16.2334	+	11.7943i	−0.674638	+	0.490153i
$580$		0			0
$581$	12.0145	+	36.9770i	0.498447	+	1.53406i
$582$		0			0
$583$	2.10578	−	25.3486i	0.0872123	−	1.04983i
$584$		0			0
$585$	−0.558385	−	1.71853i	−0.0230864	−	0.0710526i
$586$		0			0
$587$	−4.86158	+	3.53214i	−0.200659	+	0.145787i	−0.683577	−	0.729878i	$-0.739577\pi$
$587$	−4.86158	+	3.53214i	−0.200659	+	0.145787i	0.482918	+	0.875665i	$0.339577\pi$
$588$		0			0
$589$	−3.22324	+	9.92011i	−0.132811	+	0.408751i
$590$		0			0
$591$	8.64595	+	6.28165i	0.355647	+	0.258393i
$592$		0			0
$593$	34.8417			1.43078			0.715389	−	0.698726i	$-0.246249\pi$
$593$	34.8417			1.43078			0.715389	+	0.698726i	$0.246249\pi$
$594$		0			0
$595$	16.4969			0.676308
$596$		0			0
$597$	−15.5289	−	11.2824i	−0.635555	−	0.461758i
$598$		0			0
$599$	2.01765	−	6.20968i	0.0824389	−	0.253721i	−0.901338	−	0.433116i	$-0.857414\pi$
$599$	2.01765	−	6.20968i	0.0824389	−	0.253721i	0.983777	+	0.179395i	$0.0574141\pi$
$600$		0			0
$601$	31.0484	−	22.5580i	1.26649	−	0.920160i	0.267434	−	0.963576i	$-0.413824\pi$
$601$	31.0484	−	22.5580i	1.26649	−	0.920160i	0.999057	+	0.0434166i	$0.0138243\pi$
$602$		0			0
$603$	2.15510	+	6.63271i	0.0877624	+	0.270105i
$604$		0			0
$605$	−17.7880	+	8.86968i	−0.723184	+	0.360604i
$606$		0			0
$607$	−3.53532	−	10.8806i	−0.143494	−	0.441629i	0.853320	−	0.521387i	$-0.174585\pi$
$607$	−3.53532	−	10.8806i	−0.143494	−	0.441629i	−0.996814	+	0.0797579i	$0.974585\pi$
$608$		0			0
$609$	19.7967	−	14.3831i	0.802201	−	0.582833i
$610$		0			0
$611$	0.0497826	−	0.153215i	0.00201399	−	0.00619842i
$612$		0			0
$613$	−15.8806	−	11.5379i	−0.641412	−	0.466013i	0.218923	−	0.975742i	$-0.429746\pi$
$613$	−15.8806	−	11.5379i	−0.641412	−	0.466013i	−0.860335	+	0.509729i	$0.829746\pi$
$614$		0			0
$615$	−14.7268			−0.593841
$616$		0			0
$617$	2.43592			0.0980666			0.0490333	−	0.998797i	$-0.484386\pi$
$617$	2.43592			0.0980666			0.0490333	+	0.998797i	$0.484386\pi$
$618$		0			0
$619$	0.834469	+	0.606277i	0.0335401	+	0.0243683i	0.604429	−	0.796659i	$-0.293401\pi$
$619$	0.834469	+	0.606277i	0.0335401	+	0.0243683i	−0.570889	+	0.821027i	$0.693401\pi$
$620$		0			0
$621$	0.191922	−	0.590674i	0.00770155	−	0.0237029i
$622$		0			0
$623$	15.2179	−	11.0564i	0.609692	−	0.442967i
$624$		0			0
$625$	−4.11489	−	12.6643i	−0.164595	−	0.506573i
$626$		0			0
$627$	1.77594	−	21.3782i	0.0709243	−	0.853763i
$628$		0			0
$629$	6.55036	+	20.1599i	0.261180	+	0.803829i
$630$		0			0
$631$	−28.4721	+	20.6862i	−1.13346	+	0.823503i	−0.986194	−	0.165594i	$-0.947046\pi$
$631$	−28.4721	+	20.6862i	−1.13346	+	0.823503i	−0.147261	+	0.989098i	$0.547046\pi$
$632$		0			0
$633$	3.14549	−	9.68083i	0.125022	−	0.384778i
$634$		0			0
$635$	19.8782	+	14.4423i	0.788841	+	0.573126i
$636$		0			0
$637$	4.04079			0.160102
$638$		0			0
$639$	−1.12754			−0.0446048
$640$		0			0
$641$	−16.0429	−	11.6559i	−0.633657	−	0.460379i	0.224008	−	0.974587i	$-0.428086\pi$
$641$	−16.0429	−	11.6559i	−0.633657	−	0.460379i	−0.857665	+	0.514209i	$0.828086\pi$
$642$		0			0
$643$	−5.32361	+	16.3844i	−0.209943	+	0.646137i	0.789531	+	0.613710i	$0.210324\pi$
$643$	−5.32361	+	16.3844i	−0.209943	+	0.646137i	−0.999474	+	0.0324270i	$0.989676\pi$
$644$		0			0
$645$	4.51736	−	3.28205i	0.177871	−	0.129231i
$646$		0			0
$647$	−3.26040	−	10.0345i	−0.128180	−	0.394496i	0.866287	−	0.499546i	$-0.166500\pi$
$647$	−3.26040	−	10.0345i	−0.128180	−	0.394496i	−0.994467	+	0.105050i	$0.966500\pi$
$648$		0			0
$649$	−1.20931	+	0.284780i	−0.0474694	+	0.0111786i
$650$		0			0
$651$	−1.65587	−	5.09623i	−0.0648985	−	0.199737i
$652$		0			0
$653$	32.0455	−	23.2824i	1.25404	−	0.911112i	0.255590	−	0.966785i	$-0.417730\pi$
$653$	32.0455	−	23.2824i	1.25404	−	0.911112i	0.998449	+	0.0556730i	$0.0177304\pi$
$654$		0			0
$655$	10.5244	−	32.3909i	0.411224	−	1.26562i
$656$		0			0
$657$	4.17594	+	3.03400i	0.162919	+	0.118368i
$658$		0			0
$659$	−14.5386			−0.566342			−0.283171	−	0.959070i	$-0.591386\pi$
$659$	−14.5386			−0.566342			−0.283171	+	0.959070i	$0.591386\pi$
$660$		0			0
$661$	35.7583			1.39084			0.695418	−	0.718606i	$-0.255219\pi$
$661$	35.7583			1.39084			0.695418	+	0.718606i	$0.255219\pi$
$662$		0			0
$663$	2.22284	+	1.61499i	0.0863281	+	0.0627210i
$664$		0			0
$665$	−12.0006	+	36.9340i	−0.465362	+	1.43224i
$666$		0			0
$667$	3.70027	−	2.68840i	0.143275	−	0.104095i
$668$		0			0
$669$	6.39812	+	19.6914i	0.247366	+	0.761313i
$670$		0			0
$671$	−24.0256	+	27.8843i	−0.927498	+	1.07646i
$672$		0			0
$673$	−4.73231	−	14.5646i	−0.182417	−	0.561422i	0.817477	−	0.575961i	$-0.195372\pi$
$673$	−4.73231	−	14.5646i	−0.182417	−	0.561422i	−0.999894	+	0.0145387i	$0.995372\pi$
$674$		0			0
$675$	1.40352	−	1.01972i	0.0540216	−	0.0392490i
$676$		0			0
$677$	−4.33500	+	13.3417i	−0.166607	+	0.512765i	−0.999151	−	0.0411944i	$-0.986884\pi$
$677$	−4.33500	+	13.3417i	−0.166607	+	0.512765i	0.832544	+	0.553959i	$0.186884\pi$
$678$		0			0
$679$	22.6473	+	16.4542i	0.869122	+	0.631454i
$680$		0			0
$681$	−26.6985			−1.02309
$682$		0			0
$683$	29.5345			1.13011			0.565053	−	0.825055i	$-0.308856\pi$
$683$	29.5345			1.13011			0.565053	+	0.825055i	$0.308856\pi$
$684$		0			0
$685$	−2.02525	−	1.47143i	−0.0773807	−	0.0562203i
$686$		0			0
$687$	−3.34644	+	10.2993i	−0.127675	+	0.392942i
$688$		0			0
$689$	−6.20453	+	4.50785i	−0.236374	+	0.171735i
$690$		0			0
$691$	13.2498	+	40.7787i	0.504047	+	1.55130i	0.802367	+	0.596831i	$0.203574\pi$
$691$	13.2498	+	40.7787i	0.504047	+	1.55130i	−0.298321	+	0.954466i	$0.596426\pi$
$692$		0			0
$693$	5.71727	+	9.42133i	0.217181	+	0.357887i
$694$		0			0
$695$	−3.43700	−	10.5780i	−0.130373	−	0.401246i
$696$		0			0
$697$	18.1161	−	13.1621i	0.686197	−	0.498551i
$698$		0			0
$699$	4.65563	−	14.3286i	0.176092	−	0.541956i
$700$		0			0
$701$	−30.5061	−	22.1640i	−1.15220	−	0.837123i	−0.163429	−	0.986555i	$-0.552255\pi$
$701$	−30.5061	−	22.1640i	−1.15220	−	0.837123i	−0.988772	+	0.149432i	$0.952255\pi$
$702$		0			0
$703$	−49.8999			−1.88201
$704$		0			0
$705$	−0.291103			−0.0109636
$706$		0			0
$707$	−9.92443	−	7.21052i	−0.373247	−	0.271180i
$708$		0			0
$709$	−0.716923	+	2.20646i	−0.0269246	+	0.0828654i	−0.963616	−	0.267291i	$-0.913872\pi$
$709$	−0.716923	+	2.20646i	−0.0269246	+	0.0828654i	0.936691	+	0.350156i	$0.113872\pi$
$710$		0			0
$711$	1.06418	−	0.773172i	0.0399098	−	0.0289962i
$712$		0			0
$713$	−0.309504	−	0.952555i	−0.0115910	−	0.0356735i
$714$		0			0
$715$	5.52685	+	2.31746i	0.206692	+	0.0866682i
$716$		0			0
$717$	−1.58504	−	4.87825i	−0.0591944	−	0.182182i
$718$		0			0
$719$	−21.5259	+	15.6395i	−0.802779	+	0.583253i	−0.911728	−	0.410794i	$-0.865252\pi$
$719$	−21.5259	+	15.6395i	−0.802779	+	0.583253i	0.108949	+	0.994047i	$0.465252\pi$
$720$		0			0
$721$	1.78477	−	5.49297i	0.0664684	−	0.204569i
$722$		0			0
$723$	−15.3897	−	11.1813i	−0.572351	−	0.415837i
$724$		0			0
$725$	12.7760			0.474490
$726$		0			0
$727$	30.1643			1.11873			0.559367	−	0.828920i	$-0.311044\pi$
$727$	30.1643			1.11873			0.559367	+	0.828920i	$0.311044\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−2.62367	+	8.07481i	−0.0970398	+	0.298658i
$732$		0			0
$733$	−38.5765	+	28.0275i	−1.42486	+	1.03522i	−0.433912	+	0.900955i	$0.642867\pi$
$733$	−38.5765	+	28.0275i	−1.42486	+	1.03522i	−0.990946	+	0.134264i	$0.957133\pi$
$734$		0			0
$735$	−2.25632	−	6.94424i	−0.0832256	−	0.256142i
$736$		0			0
$737$	−21.3310	−	8.94429i	−0.785736	−	0.329467i
$738$		0			0
$739$	13.9759	+	43.0135i	0.514113	+	1.58228i	0.784890	+	0.619635i	$0.212719\pi$
$739$	13.9759	+	43.0135i	0.514113	+	1.58228i	−0.270778	+	0.962642i	$0.587281\pi$
$740$		0			0
$741$	−5.23270	+	3.80178i	−0.192228	+	0.139662i
$742$		0			0
$743$	0.726194	−	2.23500i	0.0266415	−	0.0819941i	−0.936852	−	0.349727i	$-0.886274\pi$
$743$	0.726194	−	2.23500i	0.0266415	−	0.0819941i	0.963493	+	0.267733i	$0.0862744\pi$
$744$		0			0
$745$	3.99482	+	2.90241i	0.146359	+	0.106336i
$746$		0			0
$747$	11.7011			0.428119
$748$		0			0
$749$	−14.4870			−0.529342
$750$		0			0
$751$	27.4167	+	19.9194i	1.00045	+	0.726869i	0.962184	−	0.272399i	$-0.0878170\pi$
$751$	27.4167	+	19.9194i	1.00045	+	0.726869i	0.0382648	+	0.999268i	$0.487817\pi$
$752$		0			0
$753$	3.63045	−	11.1734i	0.132301	−	0.407180i
$754$		0			0
$755$	25.0331	−	18.1876i	0.911048	−	0.661915i
$756$		0			0
$757$	0.306060	+	0.941957i	0.0111239	+	0.0342360i	0.956464	−	0.291849i	$-0.0942705\pi$
$757$	0.306060	+	0.941957i	0.0111239	+	0.0342360i	−0.945340	+	0.326085i	$0.894270\pi$
$758$		0			0
$759$	1.06864	+	1.76098i	0.0387891	+	0.0639194i
$760$		0			0
$761$	−12.2278	−	37.6333i	−0.443258	−	1.36421i	−0.884383	−	0.466761i	$-0.845421\pi$
$761$	−12.2278	−	37.6333i	−0.443258	−	1.36421i	0.441126	−	0.897445i	$-0.354579\pi$
$762$		0			0
$763$	−5.66083	+	4.11283i	−0.204936	+	0.148895i
$764$		0			0
$765$	1.53421	−	4.72182i	0.0554695	−	0.170718i
$766$		0			0
$767$	0.303052	+	0.220180i	0.0109426	+	0.00795025i
$768$		0			0
$769$	−48.4024			−1.74544			−0.872718	−	0.488224i	$-0.837645\pi$
$769$	−48.4024			−1.74544			−0.872718	+	0.488224i	$0.837645\pi$
$770$		0			0
$771$	−9.38908			−0.338140
$772$		0			0
$773$	38.3268	+	27.8460i	1.37852	+	1.00155i	0.997017	+	0.0771840i	$0.0245929\pi$
$773$	38.3268	+	27.8460i	1.37852	+	1.00155i	0.381502	+	0.924368i	$0.375407\pi$
$774$		0			0
$775$	0.864543	−	2.66079i	0.0310553	−	0.0955784i
$776$		0			0
$777$	20.7391	−	15.0678i	0.744010	−	0.540555i
$778$		0			0
$779$	16.2894	+	50.1338i	0.583630	+	1.79623i
$780$		0			0
$781$	2.44102	−	2.83306i	0.0873465	−	0.101375i
$782$		0			0
$783$	−2.27571	−	7.00391i	−0.0813271	−	0.250299i
$784$		0			0
$785$	−4.00702	+	2.91127i	−0.143017	+	0.103908i
$786$		0			0
$787$	−5.77449	+	17.7721i	−0.205838	+	0.633505i	0.793840	+	0.608127i	$0.208079\pi$
$787$	−5.77449	+	17.7721i	−0.205838	+	0.633505i	−0.999678	+	0.0253780i	$0.991921\pi$
$788$		0			0
$789$	10.0933	+	7.33319i	0.359330	+	0.261069i
$790$		0			0
$791$	53.5954			1.90563
$792$		0			0
$793$	11.0978			0.394093
$794$		0			0
$795$	11.2114	+	8.14557i	0.397628	+	0.288893i
$796$		0			0
$797$	16.1667	−	49.7561i	0.572655	−	1.76245i	−0.0713735	−	0.997450i	$-0.522738\pi$
$797$	16.1667	−	49.7561i	0.572655	−	1.76245i	0.644029	−	0.765001i	$-0.277262\pi$
$798$		0			0
$799$	0.358100	−	0.260175i	0.0126687	−	0.00920432i
$800$		0			0
$801$	−1.74936	−	5.38398i	−0.0618106	−	0.190233i
$802$		0			0
$803$	−16.6638	+	3.92416i	−0.588051	+	0.138481i
$804$		0			0
$805$	−1.15233	−	3.54650i	−0.0406142	−	0.124998i
$806$		0			0
$807$	16.8439	−	12.2378i	0.592933	−	0.430791i
$808$		0			0
$809$	9.33206	−	28.7211i	0.328098	−	1.00978i	−0.641925	−	0.766767i	$-0.721864\pi$
$809$	9.33206	−	28.7211i	0.328098	−	1.00978i	0.970023	−	0.243014i	$-0.0781360\pi$
$810$		0			0
$811$	11.9875	+	8.70945i	0.420939	+	0.305830i	0.778016	−	0.628245i	$-0.216226\pi$
$811$	11.9875	+	8.70945i	0.420939	+	0.305830i	−0.357077	+	0.934075i	$0.616226\pi$
$812$		0			0
$813$	−21.3426			−0.748518
$814$		0			0
$815$	5.53674			0.193943
$816$		0			0
$817$	−16.1697	−	11.7479i	−0.565704	−	0.411008i
$818$		0			0
$819$	1.02679	−	3.16014i	0.0358790	−	0.110424i
$820$		0			0
$821$	39.3423	−	28.5838i	1.37306	−	0.997583i	0.375564	−	0.926796i	$-0.377449\pi$
$821$	39.3423	−	28.5838i	1.37306	−	0.997583i	0.997491	−	0.0707868i	$-0.0225510\pi$
$822$		0			0
$823$	−13.7398	−	42.2867i	−0.478939	−	1.47402i	−0.840571	−	0.541702i	$-0.817780\pi$
$823$	−13.7398	−	42.2867i	−0.478939	−	1.47402i	0.361631	−	0.932321i	$-0.382220\pi$
$824$		0			0
$825$	−0.476346	+	5.73409i	−0.0165843	+	0.199635i
$826$		0			0
$827$	0.530144	+	1.63162i	0.0184349	+	0.0567368i	0.959851	−	0.280511i	$-0.0905039\pi$
$827$	0.530144	+	1.63162i	0.0184349	+	0.0567368i	−0.941416	+	0.337248i	$0.890504\pi$
$828$		0			0
$829$	−8.73771	+	6.34832i	−0.303473	+	0.220486i	−0.729091	−	0.684417i	$-0.760057\pi$
$829$	−8.73771	+	6.34832i	−0.303473	+	0.220486i	0.425618	+	0.904903i	$0.360057\pi$
$830$		0			0
$831$	6.74024	−	20.7443i	0.233816	−	0.719612i
$832$		0			0
$833$	8.98205	+	6.52584i	0.311210	+	0.226107i
$834$		0			0
$835$	19.7004			0.681761
$836$		0			0
$837$	−1.61266			−0.0557416
$838$		0			0
$839$	−31.4190	−	22.8272i	−1.08470	−	0.788083i	−0.106207	−	0.994344i	$-0.533870\pi$
$839$	−31.4190	−	22.8272i	−1.08470	−	0.788083i	−0.978497	+	0.206261i	$0.933870\pi$
$840$		0			0
$841$	7.79760	−	23.9985i	0.268883	−	0.827536i
$842$		0			0
$843$	12.5541	−	9.12110i	0.432387	−	0.314147i
$844$		0			0
$845$	−0.558385	−	1.71853i	−0.0192090	−	0.0591193i
$846$		0			0
$847$	−36.0494	−	6.03107i	−1.23867	−	0.207230i
$848$		0			0
$849$	−3.11409	−	9.58419i	−0.106875	−	0.328928i
$850$		0			0
$851$	3.87642	−	2.81638i	0.132882	−	0.0965444i
$852$		0			0
$853$	2.89925	−	8.92299i	0.0992686	−	0.305517i	−0.889074	−	0.457763i	$-0.848651\pi$
$853$	2.89925	−	8.92299i	0.0992686	−	0.305517i	0.988343	+	0.152246i	$0.0486507\pi$
$854$		0			0
$855$	9.45534	+	6.86971i	0.323366	+	0.234939i
$856$		0			0
$857$	−7.59150			−0.259321			−0.129660	−	0.991558i	$-0.541389\pi$
$857$	−7.59150			−0.259321			−0.129660	+	0.991558i	$0.541389\pi$
$858$		0			0
$859$	12.6504			0.431627			0.215814	−	0.976435i	$-0.430760\pi$
$859$	12.6504			0.431627			0.215814	+	0.976435i	$0.430760\pi$
$860$		0			0
$861$	−21.9086	−	15.9175i	−0.746642	−	0.542467i
$862$		0			0
$863$	−8.75664	+	26.9502i	−0.298079	+	0.917394i	0.684090	+	0.729397i	$0.260199\pi$
$863$	−8.75664	+	26.9502i	−0.298079	+	0.917394i	−0.982170	+	0.187997i	$0.939801\pi$
$864$		0			0
$865$	19.4325	−	14.1185i	0.660724	−	0.480044i
$866$		0			0
$867$	−2.92045	−	8.98822i	−0.0991837	−	0.305256i
$868$		0			0
$869$	−0.361176	+	4.34771i	−0.0122520	+	0.147486i
$870$		0			0
$871$	2.15510	+	6.63271i	0.0730227	+	0.224741i
$872$		0			0
$873$	6.81578	−	4.95195i	0.230679	−	0.167598i
$874$		0			0
$875$	12.4957	−	38.4579i	0.422433	−	1.30012i
$876$		0			0
$877$	15.0813	+	10.9572i	0.509258	+	0.369998i	0.812542	−	0.582902i	$-0.198083\pi$
$877$	15.0813	+	10.9572i	0.509258	+	0.369998i	−0.303284	+	0.952900i	$0.598083\pi$
$878$		0			0
$879$	3.76192			0.126886
$880$		0			0
$881$	5.24538			0.176721			0.0883607	−	0.996089i	$-0.471837\pi$
$881$	5.24538			0.176721			0.0883607	+	0.996089i	$0.471837\pi$
$882$		0			0
$883$	−3.69133	−	2.68190i	−0.124223	−	0.0902533i	0.523939	−	0.851756i	$-0.324462\pi$
$883$	−3.69133	−	2.68190i	−0.124223	−	0.0902533i	−0.648162	+	0.761503i	$0.724462\pi$
$884$		0			0
$885$	0.209167	−	0.643751i	0.00703109	−	0.0216395i
$886$		0			0
$887$	39.0195	−	28.3493i	1.31015	−	0.951877i	0.310147	−	0.950689i	$-0.399622\pi$
$887$	39.0195	−	28.3493i	1.31015	−	0.951877i	0.999999	−	0.00118818i	$-0.000378208\pi$
$888$		0			0
$889$	13.9621	+	42.9708i	0.468272	+	1.44119i
$890$		0			0
$891$	3.22832	−	0.760239i	0.108153	−	0.0254690i
$892$		0			0
$893$	0.321992	+	0.990990i	0.0107751	+	0.0331622i
$894$		0			0
$895$	−19.5127	+	14.1768i	−0.652237	+	0.473878i
$896$		0			0
$897$	0.191922	−	0.590674i	0.00640807	−	0.0197220i
$898$		0			0
$899$	−9.60802	−	6.98064i	−0.320446	−	0.232817i
$900$		0			0
$901$	−21.0718			−0.702004
$902$		0			0
$903$	10.2677			0.341689
$904$		0			0
$905$	24.1454	+	17.5427i	0.802621	+	0.583139i
$906$		0			0
$907$	−5.51275	+	16.9665i	−0.183048	+	0.563363i	−0.999909	−	0.0134706i	$-0.995712\pi$
$907$	−5.51275	+	16.9665i	−0.183048	+	0.563363i	0.816861	+	0.576834i	$0.195712\pi$
$908$		0			0
$909$	−2.98680	+	2.17003i	−0.0990658	+	0.0719755i
$910$		0			0
$911$	−6.70046	−	20.6219i	−0.221996	−	0.683234i	−0.998583	−	0.0532232i	$-0.983051\pi$
$911$	−6.70046	−	20.6219i	−0.221996	−	0.683234i	0.776587	−	0.630011i	$-0.216949\pi$
$912$		0			0
$913$	−25.3317	+	29.4001i	−0.838356	+	0.973001i
$914$		0			0
$915$	−6.19682	−	19.0719i	−0.204861	−	0.630496i
$916$		0			0
$917$	50.6667	−	36.8115i	1.67316	−	1.21562i
$918$		0			0
$919$	−9.05776	+	27.8769i	−0.298788	+	0.919575i	0.683135	+	0.730293i	$0.260616\pi$
$919$	−9.05776	+	27.8769i	−0.298788	+	0.919575i	−0.981923	+	0.189283i	$0.939384\pi$
$920$		0			0
$921$	12.3640	+	8.98299i	0.407409	+	0.296000i
$922$		0			0
$923$	−1.12754			−0.0371134
$924$		0			0
$925$	13.3842			0.440071
$926$		0			0
$927$	−1.40624	−	1.02169i	−0.0461868	−	0.0335567i
$928$		0			0
$929$	5.04027	−	15.5124i	0.165366	−	0.508944i	−0.833697	−	0.552222i	$-0.813780\pi$
$929$	5.04027	−	15.5124i	0.165366	−	0.508944i	0.999063	+	0.0432777i	$0.0137800\pi$
$930$		0			0
$931$	−21.1442	+	15.3622i	−0.692975	+	0.503476i
$932$		0			0
$933$	5.99889	+	18.4627i	0.196395	+	0.604441i
$934$		0			0
$935$	8.54263	+	14.0772i	0.279374	+	0.460372i
$936$		0			0
$937$	−16.8187	−	51.7625i	−0.549442	−	1.69101i	−0.710188	−	0.704012i	$-0.751390\pi$
$937$	−16.8187	−	51.7625i	−0.549442	−	1.69101i	0.160747	−	0.986996i	$-0.448610\pi$
$938$		0			0
$939$	−20.4433	+	14.8529i	−0.667142	+	0.484707i
$940$		0			0
$941$	6.65547	−	20.4834i	0.216962	−	0.667740i	−0.782046	−	0.623220i	$-0.785824\pi$
$941$	6.65547	−	20.4834i	0.216962	−	0.667740i	0.999008	−	0.0445203i	$-0.0141759\pi$
$942$		0			0
$943$	−4.09501	−	2.97520i	−0.133352	−	0.0968859i
$944$		0			0
$945$	−6.00415			−0.195315
$946$		0			0
$947$	35.5276			1.15449			0.577246	−	0.816570i	$-0.304127\pi$
$947$	35.5276			1.15449			0.577246	+	0.816570i	$0.304127\pi$
$948$		0			0
$949$	4.17594	+	3.03400i	0.135557	+	0.0984878i
$950$		0			0
$951$	3.77861	−	11.6294i	0.122530	−	0.377108i
$952$		0			0
$953$	−22.9008	+	16.6384i	−0.741830	+	0.538971i	−0.893284	−	0.449493i	$-0.851605\pi$
$953$	−22.9008	+	16.6384i	−0.741830	+	0.538971i	0.151454	+	0.988464i	$0.451605\pi$
$954$		0			0
$955$	−10.5922	−	32.5993i	−0.342754	−	1.05489i
$956$		0			0
$957$	22.5247	+	9.44486i	0.728121	+	0.305309i
$958$		0			0
$959$	−1.42250	−	4.37799i	−0.0459348	−	0.141373i
$960$		0			0
$961$	22.9755	−	16.6927i	0.741147	−	0.538474i
$962$		0			0
$963$	−1.34728	+	4.14652i	−0.0434156	+	0.133620i
$964$		0			0
$965$	29.3333	+	21.3119i	0.944274	+	0.686055i
$966$		0			0
$967$	−45.8004			−1.47284			−0.736421	−	0.676523i	$-0.763486\pi$
$967$	−45.8004			−1.47284			−0.736421	+	0.676523i	$0.763486\pi$
$968$		0			0
$969$	−17.7713			−0.570896
$970$		0			0
$971$	−44.8727	−	32.6019i	−1.44003	−	1.04624i	−0.988036	−	0.154225i	$-0.950712\pi$
$971$	−44.8727	−	32.6019i	−1.44003	−	1.04624i	−0.451997	−	0.892020i	$-0.649288\pi$
$972$		0			0
$973$	6.32016	−	19.4514i	0.202615	−	0.623585i
$974$		0			0
$975$	1.40352	−	1.01972i	0.0449487	−	0.0326571i
$976$		0			0
$977$	−17.5126	−	53.8981i	−0.560276	−	1.72435i	−0.681586	−	0.731738i	$-0.738709\pi$
$977$	−17.5126	−	53.8981i	−0.560276	−	1.72435i	0.121310	−	0.992615i	$-0.461291\pi$
$978$		0			0
$979$	17.3150	+	7.26036i	0.553390	+	0.232042i
$980$		0			0
$981$	0.650736	+	2.00276i	0.0207764	+	0.0639432i
$982$		0			0
$983$	−40.7725	+	29.6229i	−1.30044	+	0.944824i	−0.999960	−	0.00896387i	$-0.997147\pi$
$983$	−40.7725	+	29.6229i	−1.30044	+	0.944824i	−0.300479	+	0.953788i	$0.597147\pi$
$984$		0			0
$985$	5.96745	−	18.3659i	0.190139	−	0.585187i
$986$		0			0
$987$	−0.433065	−	0.314640i	−0.0137846	−	0.0100151i
$988$		0			0
$989$	1.91918			0.0610265
$990$		0			0
$991$	−33.5073			−1.06439			−0.532197	−	0.846621i	$-0.678633\pi$
$991$	−33.5073			−1.06439			−0.532197	+	0.846621i	$0.678633\pi$
$992$		0			0
$993$	−0.570541	−	0.414523i	−0.0181056	−	0.0131545i
$994$		0			0
$995$	−10.7181	+	32.9869i	−0.339786	+	1.04575i
$996$		0			0
$997$	−21.6475	+	15.7278i	−0.685584	+	0.498106i	−0.875206	−	0.483751i	$-0.839274\pi$
$997$	−21.6475	+	15.7278i	−0.685584	+	0.498106i	0.189621	+	0.981857i	$0.439274\pi$
$998$		0			0
$999$	−2.38404	−	7.33733i	−0.0754278	−	0.232143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1716.2.z.g.313.2	✓	28
11.9	even	5	inner	1716.2.z.g.625.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1716.2.z.g.313.2	✓	28	1.1	even	1	trivial
1716.2.z.g.625.2	yes	28	11.9	even	5	inner

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:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1716.z (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{3} +(-0.558385 + 1.71853i) q^{5} +(-2.68818 + 1.95307i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{3} +(-0.558385 + 1.71853i) q^{5} +(-2.68818 + 1.95307i) q^{7} +(0.309017 + 0.951057i) q^{9} +(-3.05862 - 1.28251i) q^{11} +(0.309017 + 0.951057i) q^{13} +(1.46187 - 1.06211i) q^{15} +(-0.849050 + 2.61311i) q^{17} +(-5.23270 - 3.80178i) q^{19} +3.32277 q^{21} +0.621071 q^{23} +(1.40352 + 1.01972i) q^{25} +(0.309017 - 0.951057i) q^{27} +(5.95788 - 4.32865i) q^{29} +(-0.498339 - 1.53373i) q^{31} +(1.72064 + 2.83539i) q^{33} +(-1.85539 - 5.71029i) q^{35} +(6.24151 - 4.53472i) q^{37} +(0.309017 - 0.951057i) q^{39} +(-6.59347 - 4.79043i) q^{41} +3.09012 q^{43} -1.80697 q^{45} +(-0.130333 - 0.0946921i) q^{47} +(1.24867 - 3.84302i) q^{49} +(2.22284 - 1.61499i) q^{51} +(2.36992 + 7.29386i) q^{53} +(3.91193 - 4.54021i) q^{55} +(1.99871 + 6.15140i) q^{57} +(0.303052 - 0.220180i) q^{59} +(3.42939 - 10.5546i) q^{61} +(-2.68818 - 1.95307i) q^{63} -1.80697 q^{65} +6.97404 q^{67} +(-0.502457 - 0.365057i) q^{69} +(-0.348429 + 1.07235i) q^{71} +(4.17594 - 3.03400i) q^{73} +(-0.536098 - 1.64994i) q^{75} +(10.7270 - 2.52610i) q^{77} +(-0.406480 - 1.25102i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(3.61582 - 11.1284i) q^{83} +(-4.01662 - 2.91824i) q^{85} -7.36434 q^{87} -5.66105 q^{89} +(-2.68818 - 1.95307i) q^{91} +(-0.498339 + 1.53373i) q^{93} +(9.45534 - 6.86971i) q^{95} +(-2.60340 - 8.01243i) q^{97} +(0.274575 - 3.30524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{3} - 2 q^{5} - 5 q^{7} - 7 q^{9}+O(q^{10}) \) 28 * q - 7 * q^3 - 2 * q^5 - 5 * q^7 - 7 * q^9	\( 28 q - 7 q^{3} - 2 q^{5} - 5 q^{7} - 7 q^{9} + 8 q^{11} - 7 q^{13} - 2 q^{15} + 4 q^{17} + 10 q^{21} + 26 q^{23} - 13 q^{25} - 7 q^{27} + 16 q^{29} - 16 q^{31} + 3 q^{33} - 24 q^{37} - 7 q^{39} - 16 q^{41} + 12 q^{43} + 8 q^{45} - 24 q^{47} - 52 q^{49} - q^{51} + 13 q^{53} + 6 q^{55} - 10 q^{57} - 19 q^{59} + 4 q^{61} - 5 q^{63} + 8 q^{65} + 40 q^{67} - 14 q^{69} - 68 q^{71} + 13 q^{73} - 13 q^{75} + 20 q^{77} - 11 q^{79} - 7 q^{81} + 4 q^{83} - 26 q^{85} - 4 q^{87} - 18 q^{89} - 5 q^{91} - 16 q^{93} + 27 q^{95} + 2 q^{97} - 2 q^{99}+O(q^{100}) \) 28 * q - 7 * q^3 - 2 * q^5 - 5 * q^7 - 7 * q^9 + 8 * q^11 - 7 * q^13 - 2 * q^15 + 4 * q^17 + 10 * q^21 + 26 * q^23 - 13 * q^25 - 7 * q^27 + 16 * q^29 - 16 * q^31 + 3 * q^33 - 24 * q^37 - 7 * q^39 - 16 * q^41 + 12 * q^43 + 8 * q^45 - 24 * q^47 - 52 * q^49 - q^51 + 13 * q^53 + 6 * q^55 - 10 * q^57 - 19 * q^59 + 4 * q^61 - 5 * q^63 + 8 * q^65 + 40 * q^67 - 14 * q^69 - 68 * q^71 + 13 * q^73 - 13 * q^75 + 20 * q^77 - 11 * q^79 - 7 * q^81 + 4 * q^83 - 26 * q^85 - 4 * q^87 - 18 * q^89 - 5 * q^91 - 16 * q^93 + 27 * q^95 + 2 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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