LMFDB - Embedded newform 570.2.x.b.217.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.6
Character	$\chi$	$=$	570.217
Dual form			570.2.x.b.373.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.17769 + 0.507589i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.55332 - 2.55332i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.17769 + 0.507589i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.55332 - 2.55332i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.05392 - 1.97212i) q^{10} -2.10070 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-0.0901556 + 0.336465i) q^{13} +(1.80547 - 3.12716i) q^{14} +(-1.97212 + 1.05392i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.16833 + 1.11690i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.05014 - 1.61133i) q^{19} +(1.63214 - 1.52843i) q^{20} +(-3.12716 - 1.80547i) q^{21} +(-0.543700 - 2.02912i) q^{22} +(-3.42206 - 0.916939i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(4.48471 - 2.21075i) q^{25} -0.348335 q^{26} +(0.707107 - 0.707107i) q^{27} +(3.48789 + 0.934578i) q^{28} +(0.205030 + 0.355122i) q^{29} +(-1.52843 - 1.63214i) q^{30} -9.24205i q^{31} +(0.965926 + 0.258819i) q^{32} +(-2.02912 + 0.543700i) q^{33} +(-2.15768 - 3.73722i) q^{34} +(6.85638 + 4.26431i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.61173 + 3.61173i) q^{37} +(0.508171 - 4.32918i) q^{38} +0.348335i q^{39} +(1.89878 + 1.18094i) q^{40} +(6.95086 + 4.01308i) q^{41} +(0.934578 - 3.48789i) q^{42} +(0.601718 + 2.24564i) q^{43} +(1.81926 - 1.05035i) q^{44} +(-1.63214 + 1.52843i) q^{45} -3.54278i q^{46} +(-1.74819 + 6.52433i) q^{47} +(0.258819 - 0.965926i) q^{48} +6.03884i q^{49} +(3.29615 + 3.75971i) q^{50} +(-3.73722 + 2.15768i) q^{51} +(-0.0901556 - 0.336465i) q^{52} +(3.33923 - 12.4622i) q^{53} +(0.866025 + 0.500000i) q^{54} +(4.57468 - 1.06629i) q^{55} +3.61093i q^{56} +(-4.32918 - 0.508171i) q^{57} +(-0.289956 + 0.289956i) q^{58} +(-6.55422 + 11.3522i) q^{59} +(1.18094 - 1.89878i) q^{60} +(0.171384 + 0.296845i) q^{61} +(8.92714 - 2.39202i) q^{62} +(-3.48789 - 0.934578i) q^{63} +1.00000i q^{64} +(0.0255453 - 0.778481i) q^{65} +(-1.05035 - 1.81926i) q^{66} +(-5.76524 - 1.54479i) q^{67} +(3.05143 - 3.05143i) q^{68} -3.54278 q^{69} +(-2.34444 + 7.72643i) q^{70} +(0.442835 + 0.255671i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(1.48064 + 5.52581i) q^{73} +(-4.42345 - 2.55388i) q^{74} +(3.75971 - 3.29615i) q^{75} +(4.31319 - 0.629617i) q^{76} +(5.36374 + 5.36374i) q^{77} +(-0.336465 + 0.0901556i) q^{78} +(4.99199 - 8.64638i) q^{79} +(-0.649262 + 2.13973i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.07732 + 7.75267i) q^{82} +(-4.69214 + 4.69214i) q^{83} +3.61093 q^{84} +(8.51041 - 4.54806i) q^{85} +(-2.01339 + 1.16243i) q^{86} +(0.289956 + 0.289956i) q^{87} +(1.48542 + 1.48542i) q^{88} +(8.24426 + 14.2795i) q^{89} +(-1.89878 - 1.18094i) q^{90} +(1.08930 - 0.628907i) q^{91} +(3.42206 - 0.916939i) q^{92} +(-2.39202 - 8.92714i) q^{93} -6.75448 q^{94} +(9.63786 + 1.45318i) q^{95} +1.00000 q^{96} +(-3.35662 - 12.5271i) q^{97} +(-5.83307 + 1.56297i) q^{98} +(-1.81926 + 1.05035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q + 20 * q^6 - 8 * q^7	$ 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−2.17769	+	0.507589i	−0.973895	+	0.227001i
$5$	−2.17769	+	0.507589i	−0.973895	+	0.227001i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−2.55332	−	2.55332i	−0.965063	−	0.965063i	0.0343474	−	0.999410i	$-0.489065\pi$
$7$	−2.55332	−	2.55332i	−0.965063	−	0.965063i	−0.999410	+	0.0343474i	$0.989065\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−1.05392	−	1.97212i	−0.333279	−	0.623638i
$11$	−2.10070			−0.633384			−0.316692	−	0.948528i	$-0.602572\pi$
$11$	−2.10070			−0.633384			−0.316692	+	0.948528i	$0.602572\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−0.0901556	+	0.336465i	−0.0250047	+	0.0933187i	−0.977301	−	0.211858i	$-0.932049\pi$
$13$	−0.0901556	+	0.336465i	−0.0250047	+	0.0933187i	0.952296	+	0.305176i	$0.0987154\pi$
$14$	1.80547	−	3.12716i	0.482531	−	0.835769i
$15$	−1.97212	+	1.05392i	−0.509199	+	0.272121i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−4.16833	+	1.11690i	−1.01097	+	0.270888i	−0.726034	−	0.687659i	$-0.758638\pi$
$17$	−4.16833	+	1.11690i	−1.01097	+	0.270888i	−0.284934	+	0.958547i	$0.591972\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−4.05014	−	1.61133i	−0.929165	−	0.369664i
$19$	−4.05014	−	1.61133i	−0.929165	−	0.369664i
$20$	1.63214	−	1.52843i	0.364959	−	0.341768i
$21$	−3.12716	−	1.80547i	−0.682402	−	0.393985i
$22$	−0.543700	−	2.02912i	−0.115917	−	0.432609i
$23$	−3.42206	−	0.916939i	−0.713549	−	0.191195i	−0.116258	−	0.993219i	$-0.537090\pi$
$23$	−3.42206	−	0.916939i	−0.713549	−	0.191195i	−0.597292	+	0.802024i	$0.703756\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	4.48471	−	2.21075i	0.896941	−	0.442149i
$26$	−0.348335			−0.0683140
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	3.48789	+	0.934578i	0.659150	+	0.176619i
$29$	0.205030	+	0.355122i	0.0380731	+	0.0659445i	0.884434	−	0.466665i	$-0.154545\pi$
$29$	0.205030	+	0.355122i	0.0380731	+	0.0659445i	−0.846361	+	0.532610i	$0.821211\pi$
$30$	−1.52843	−	1.63214i	−0.279052	−	0.297987i
$31$		−	9.24205i		−	1.65992i	−0.557822	−	0.829961i	$-0.688363\pi$
$31$		−	9.24205i		−	1.65992i	0.557822	−	0.829961i	$-0.311637\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−2.02912	+	0.543700i	−0.353224	+	0.0946461i
$34$	−2.15768	−	3.73722i	−0.370040	−	0.640928i
$35$	6.85638	+	4.26431i	1.15894	+	0.720799i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.61173	+	3.61173i	−0.593765	+	0.593765i	−0.938646	−	0.344881i	$-0.887919\pi$
$37$	−3.61173	+	3.61173i	−0.593765	+	0.593765i	0.344881	+	0.938646i	$0.387919\pi$
$38$	0.508171	−	4.32918i	0.0824363	−	0.702285i
$39$			0.348335i			0.0557782i
$40$	1.89878	+	1.18094i	0.300224	+	0.186723i
$41$	6.95086	+	4.01308i	1.08554	+	0.626738i	0.932386	−	0.361464i	$-0.117723\pi$
$41$	6.95086	+	4.01308i	1.08554	+	0.626738i	0.153156	+	0.988202i	$0.451056\pi$
$42$	0.934578	−	3.48789i	0.144209	−	0.538194i
$43$	0.601718	+	2.24564i	0.0917612	+	0.342457i	0.996509	−	0.0834913i	$-0.0266071\pi$
$43$	0.601718	+	2.24564i	0.0917612	+	0.342457i	−0.904747	+	0.425949i	$0.859940\pi$
$44$	1.81926	−	1.05035i	0.274263	−	0.158346i
$45$	−1.63214	+	1.52843i	−0.243306	+	0.227845i
$46$		−	3.54278i		−	0.522354i
$47$	−1.74819	+	6.52433i	−0.255000	+	0.951671i	0.713091	+	0.701071i	$0.247295\pi$
$47$	−1.74819	+	6.52433i	−0.255000	+	0.951671i	−0.968091	+	0.250600i	$0.919372\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$			6.03884i			0.862691i
$50$	3.29615	+	3.75971i	0.466145	+	0.531703i
$51$	−3.73722	+	2.15768i	−0.523315	+	0.302136i
$52$	−0.0901556	−	0.336465i	−0.0125023	−	0.0466594i
$53$	3.33923	−	12.4622i	0.458678	−	1.71181i	−0.218364	−	0.975867i	$-0.570072\pi$
$53$	3.33923	−	12.4622i	0.458678	−	1.71181i	0.677042	−	0.735944i	$-0.263261\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	4.57468	−	1.06629i	0.616849	−	0.143779i
$56$			3.61093i			0.482531i
$57$	−4.32918	−	0.508171i	−0.573413	−	0.0673090i
$58$	−0.289956	+	0.289956i	−0.0380731	+	0.0380731i
$59$	−6.55422	+	11.3522i	−0.853287	+	1.47794i	0.0249375	+	0.999689i	$0.492061\pi$
$59$	−6.55422	+	11.3522i	−0.853287	+	1.47794i	−0.878225	+	0.478248i	$0.841272\pi$
$60$	1.18094	−	1.89878i	0.152459	−	0.245132i
$61$	0.171384	+	0.296845i	0.0219434	+	0.0380071i	0.876789	−	0.480876i	$-0.159681\pi$
$61$	0.171384	+	0.296845i	0.0219434	+	0.0380071i	−0.854845	+	0.518883i	$0.826348\pi$
$62$	8.92714	−	2.39202i	1.13375	−	0.303787i
$63$	−3.48789	−	0.934578i	−0.439433	−	0.117746i
$64$			1.00000i			0.125000i
$65$	0.0255453	−	0.778481i	0.00316851	−	0.0965587i
$66$	−1.05035	−	1.81926i	−0.129289	−	0.223935i
$67$	−5.76524	−	1.54479i	−0.704336	−	0.188726i	−0.111164	−	0.993802i	$-0.535458\pi$
$67$	−5.76524	−	1.54479i	−0.704336	−	0.188726i	−0.593172	+	0.805076i	$0.702125\pi$
$68$	3.05143	−	3.05143i	0.370040	−	0.370040i
$69$	−3.54278			−0.426501
$70$	−2.34444	+	7.72643i	−0.280215	+	0.923486i
$71$	0.442835	+	0.255671i	0.0525548	+	0.0303425i	0.526047	−	0.850455i	$-0.323674\pi$
$71$	0.442835	+	0.255671i	0.0525548	+	0.0303425i	−0.473492	+	0.880798i	$0.657007\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	1.48064	+	5.52581i	0.173295	+	0.646748i	0.996836	+	0.0794897i	$0.0253291\pi$
$73$	1.48064	+	5.52581i	0.173295	+	0.646748i	−0.823540	+	0.567258i	$0.808004\pi$
$74$	−4.42345	−	2.55388i	−0.514216	−	0.296883i
$75$	3.75971	−	3.29615i	0.434134	−	0.380606i
$76$	4.31319	−	0.629617i	0.494756	−	0.0722220i
$77$	5.36374	+	5.36374i	0.611255	+	0.611255i
$78$	−0.336465	+	0.0901556i	−0.0380972	+	0.0102081i
$79$	4.99199	−	8.64638i	0.561643	−	0.972794i	−0.435711	−	0.900087i	$-0.643503\pi$
$79$	4.99199	−	8.64638i	0.561643	−	0.972794i	0.997353	−	0.0727070i	$-0.0231638\pi$
$80$	−0.649262	+	2.13973i	−0.0725897	+	0.239229i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.07732	+	7.75267i	−0.229402	+	0.856139i
$83$	−4.69214	+	4.69214i	−0.515029	+	0.515029i	−0.916063	−	0.401034i	$-0.868651\pi$
$83$	−4.69214	+	4.69214i	−0.515029	+	0.515029i	0.401034	+	0.916063i	$0.368651\pi$
$84$	3.61093			0.393985
$85$	8.51041	−	4.54806i	0.923084	−	0.493307i
$86$	−2.01339	+	1.16243i	−0.217109	+	0.125348i
$87$	0.289956	+	0.289956i	0.0310865	+	0.0310865i
$88$	1.48542	+	1.48542i	0.158346	+	0.158346i
$89$	8.24426	+	14.2795i	0.873890	+	1.51362i	0.857941	+	0.513749i	$0.171744\pi$
$89$	8.24426	+	14.2795i	0.873890	+	1.51362i	0.0159489	+	0.999873i	$0.494923\pi$
$90$	−1.89878	−	1.18094i	−0.200149	−	0.124482i
$91$	1.08930	−	0.628907i	0.114189	−	0.0659273i
$92$	3.42206	−	0.916939i	0.356775	−	0.0955975i
$93$	−2.39202	−	8.92714i	−0.248041	−	0.925701i
$94$	−6.75448			−0.696672
$95$	9.63786	+	1.45318i	0.988823	+	0.149093i
$96$	1.00000			0.102062
$97$	−3.35662	−	12.5271i	−0.340813	−	1.27193i	−0.897428	−	0.441161i	$-0.854567\pi$
$97$	−3.35662	−	12.5271i	−0.340813	−	1.27193i	0.556615	−	0.830770i	$-0.312100\pi$
$98$	−5.83307	+	1.56297i	−0.589229	+	0.157883i
$99$	−1.81926	+	1.05035i	−0.182842	+	0.105564i
$100$	−2.77850	+	4.15692i	−0.277850	+	0.415692i
$101$	2.04489	+	3.54184i	0.203474	+	0.352427i	0.949645	−	0.313327i	$-0.101444\pi$
$101$	2.04489	+	3.54184i	0.203474	+	0.352427i	−0.746172	+	0.665754i	$0.768110\pi$
$102$	−3.05143	−	3.05143i	−0.302136	−	0.302136i
$103$	−9.80360	−	9.80360i	−0.965977	−	0.965977i	0.0334625	−	0.999440i	$-0.489347\pi$
$103$	−9.80360	−	9.80360i	−0.965977	−	0.965977i	−0.999440	+	0.0334625i	$0.989347\pi$
$104$	0.301667	−	0.174167i	0.0295808	−	0.0170785i
$105$	7.72643	+	2.34444i	0.754023	+	0.228794i
$106$	12.9018			1.25313
$107$	2.94121	−	2.94121i	0.284338	−	0.284338i	−0.550498	−	0.834836i	$-0.685562\pi$
$107$	2.94121	−	2.94121i	0.284338	−	0.284338i	0.834836	+	0.550498i	$0.185562\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	−1.56833	+	2.71643i	−0.150219	+	0.260187i	−0.931308	−	0.364233i	$-0.881331\pi$
$109$	−1.56833	+	2.71643i	−0.150219	+	0.260187i	0.781089	+	0.624420i	$0.214665\pi$
$110$	2.21397	+	4.14282i	0.211094	+	0.395002i
$111$	−2.55388	+	4.42345i	−0.242404	+	0.419855i
$112$	−3.48789	+	0.934578i	−0.329575	+	0.0883094i
$113$	−12.7427	−	12.7427i	−1.19874	−	1.19874i	−0.974545	−	0.224190i	$-0.928026\pi$
$113$	−12.7427	−	12.7427i	−1.19874	−	1.19874i	−0.224190	−	0.974545i	$-0.571974\pi$
$114$	−0.629617	−	4.31319i	−0.0589691	−	0.403967i
$115$	7.91763	+	0.259812i	0.738323	+	0.0242276i
$116$	−0.355122	−	0.205030i	−0.0329722	−	0.0190365i
$117$	0.0901556	+	0.336465i	0.00833489	+	0.0311062i
$118$	−12.6618	−	3.39272i	−1.16561	−	0.312325i
$119$	13.4948	+	7.79125i	1.23707	+	0.714223i
$120$	2.13973	+	0.649262i	0.195330	+	0.0592693i
$121$	−6.58707			−0.598825
$122$	−0.242373	+	0.242373i	−0.0219434	+	0.0219434i
$123$	7.75267	+	2.07732i	0.699035	+	0.187306i
$124$	4.62103	+	8.00385i	0.414980	+	0.718767i
$125$	−8.64417	+	7.09072i	−0.773158	+	0.634213i
$126$		−	3.61093i		−	0.321688i
$127$	3.57208	+	0.957135i	0.316971	+	0.0849320i	0.413797	−	0.910369i	$-0.364202\pi$
$127$	3.57208	+	0.957135i	0.316971	+	0.0849320i	−0.0968262	+	0.995301i	$0.530869\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	1.16243	+	2.01339i	0.102346	+	0.177269i
$130$	0.758566	−	0.176811i	0.0665307	−	0.0155073i
$131$	6.97423	−	12.0797i	0.609341	−	1.05541i	−0.382008	−	0.924159i	$-0.624767\pi$
$131$	6.97423	−	12.0797i	0.609341	−	1.05541i	0.991349	−	0.131251i	$-0.0418995\pi$
$132$	1.48542	−	1.48542i	0.129289	−	0.129289i
$133$	6.22705	+	14.4555i	0.539954	+	1.25345i
$134$		−	5.96862i		−	0.515610i
$135$	−1.18094	+	1.89878i	−0.101639	+	0.163421i
$136$	3.73722	+	2.15768i	0.320464	+	0.185020i
$137$	−2.74503	+	10.2446i	−0.234524	+	0.875256i	0.743839	+	0.668359i	$0.233003\pi$
$137$	−2.74503	+	10.2446i	−0.234524	+	0.875256i	−0.978363	+	0.206897i	$0.933664\pi$
$138$	−0.916939	−	3.42206i	−0.0780550	−	0.291305i
$139$	3.66655	−	2.11689i	0.310993	−	0.179552i	−0.336378	−	0.941727i	$-0.609202\pi$
$139$	3.66655	−	2.11689i	0.310993	−	0.179552i	0.647371	+	0.762175i	$0.275869\pi$
$140$	−8.06995	−	0.264810i	−0.682035	−	0.0223805i
$141$			6.75448i			0.568830i
$142$	−0.132345	+	0.493918i	−0.0111061	+	0.0414487i
$143$	0.189390	−	0.706812i	0.0158376	−	0.0591066i
$144$		−	1.00000i		−	0.0833333i
$145$	−0.626748	−	0.669276i	−0.0520486	−	0.0555804i
$146$	−4.95431	+	2.86037i	−0.410022	+	0.236726i
$147$	1.56297	+	5.83307i	0.128911	+	0.481104i
$148$	1.32199	−	4.93372i	0.108667	−	0.405549i
$149$	−11.0405	−	6.37423i	−0.904473	−	0.522197i	−0.0258240	−	0.999667i	$-0.508221\pi$
$149$	−11.0405	−	6.37423i	−0.904473	−	0.522197i	−0.878649	+	0.477469i	$0.841554\pi$
$150$	4.15692	+	2.77850i	0.339411	+	0.226863i
$151$		−	3.11702i		−	0.253660i	−0.991924	−	0.126830i	$-0.959520\pi$
$151$		−	3.11702i		−	0.253660i	0.991924	−	0.126830i	$-0.0404802\pi$
$152$	1.72450	+	4.00326i	0.139875	+	0.324707i
$153$	−3.05143	+	3.05143i	−0.246693	+	0.246693i
$154$	−3.79274	+	6.56921i	−0.305627	+	0.529362i
$155$	4.69116	+	20.1264i	0.376803	+	1.61659i
$156$	−0.174167	−	0.301667i	−0.0139445	−	0.0241527i
$157$	−13.0106	+	3.48618i	−1.03836	+	0.278228i	−0.737433	−	0.675420i	$-0.763962\pi$
$157$	−13.0106	+	3.48618i	−1.03836	+	0.278228i	−0.300926	+	0.953647i	$0.597296\pi$
$158$	9.64378	+	2.58404i	0.767218	+	0.205576i
$159$		−	12.9018i		−	1.02318i
$160$	−2.23487	−	0.0733356i	−0.176682	−	0.00579769i
$161$	6.39637	+	11.0788i	0.504105	+	0.873135i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−11.9295	+	11.9295i	−0.934394	+	0.934394i	−0.997977	−	0.0635829i	$-0.979747\pi$
$163$	−11.9295	+	11.9295i	−0.934394	+	0.934394i	0.0635829	+	0.997977i	$0.479747\pi$
$164$	−8.02616			−0.626738
$165$	4.14282	−	2.21397i	0.322518	−	0.172357i
$166$	−5.74667	−	3.31784i	−0.446028	−	0.257515i
$167$	−14.1297	−	3.78603i	−1.09339	−	0.292972i	−0.333318	−	0.942815i	$-0.608168\pi$
$167$	−14.1297	−	3.78603i	−1.09339	−	0.292972i	−0.760069	+	0.649843i	$0.774835\pi$
$168$	0.934578	+	3.48789i	0.0721043	+	0.269097i
$169$	11.1532	+	6.43933i	0.857942	+	0.495333i
$170$	6.59575	+	7.04330i	0.505871	+	0.540197i
$171$	−4.31319	+	0.629617i	−0.329838	+	0.0481480i
$172$	−1.64392	−	1.64392i	−0.125348	−	0.125348i
$173$	3.71861	−	0.996399i	0.282721	−	0.0757548i	−0.114672	−	0.993403i	$-0.536582\pi$
$173$	3.71861	−	0.996399i	0.282721	−	0.0757548i	0.397393	+	0.917649i	$0.369915\pi$
$174$	−0.205030	+	0.355122i	−0.0155433	+	0.0269217i
$175$	−17.0956	−	5.80614i	−1.29231	−	0.438903i
$176$	−1.05035	+	1.81926i	−0.0791730	+	0.137132i
$177$	−3.39272	+	12.6618i	−0.255012	+	0.951718i
$178$	−11.6591	+	11.6591i	−0.873890	+	0.873890i
$179$	16.9895			1.26985			0.634926	−	0.772573i	$-0.281031\pi$
$179$	16.9895			1.26985			0.634926	+	0.772573i	$0.281031\pi$
$180$	0.649262	−	2.13973i	0.0483932	−	0.159486i
$181$	3.80982	−	2.19960i	0.283182	−	0.163495i	−0.351681	−	0.936120i	$-0.614390\pi$
$181$	3.80982	−	2.19960i	0.283182	−	0.163495i	0.634863	+	0.772625i	$0.281057\pi$
$182$	0.889408	+	0.889408i	0.0659273	+	0.0659273i
$183$	0.242373	+	0.242373i	0.0179167	+	0.0179167i
$184$	1.77139	+	3.06814i	0.130589	+	0.226186i
$185$	6.03197	−	9.69853i	0.443480	−	0.713050i
$186$	8.00385	−	4.62103i	0.586871	−	0.338830i
$187$	8.75639	−	2.34627i	0.640330	−	0.171576i
$188$	−1.74819	−	6.52433i	−0.127500	−	0.475836i
$189$	−3.61093			−0.262657
$190$	1.09080	+	9.68556i	0.0791349	+	0.702665i
$191$	−0.439783			−0.0318216			−0.0159108	−	0.999873i	$-0.505065\pi$
$191$	−0.439783			−0.0318216			−0.0159108	+	0.999873i	$0.505065\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	10.6452	−	2.85237i	0.766258	−	0.205318i	0.145540	−	0.989352i	$-0.453508\pi$
$193$	10.6452	−	2.85237i	0.766258	−	0.205318i	0.620718	+	0.784034i	$0.286841\pi$
$194$	11.2315	−	6.48449i	0.806372	−	0.465559i
$195$	−0.176811	−	0.758566i	−0.0126617	−	0.0543221i
$196$	−3.01942	−	5.22979i	−0.215673	−	0.373556i
$197$	1.81311	+	1.81311i	0.129179	+	0.129179i	0.768740	−	0.639561i	$-0.220884\pi$
$197$	1.81311	+	1.81311i	0.129179	+	0.129179i	−0.639561	+	0.768740i	$0.720884\pi$
$198$	−1.48542	−	1.48542i	−0.105564	−	0.105564i
$199$	16.7198	−	9.65315i	1.18523	−	0.684294i	0.228013	−	0.973658i	$-0.426777\pi$
$199$	16.7198	−	9.65315i	1.18523	−	0.684294i	0.957219	+	0.289364i	$0.0934439\pi$
$200$	−4.73440	−	1.60793i	−0.334773	−	0.113698i
$201$	−5.96862			−0.420994
$202$	−2.89190	+	2.89190i	−0.203474	+	0.203474i
$203$	0.383233	−	1.43024i	0.0268977	−	0.100383i
$204$	2.15768	−	3.73722i	0.151068	−	0.261658i
$205$	−17.1738	−	5.21108i	−1.19947	−	0.363958i
$206$	6.93219	−	12.0069i	0.482989	−	0.836561i
$207$	−3.42206	+	0.916939i	−0.237850	+	0.0637317i
$208$	0.246310	+	0.246310i	0.0170785	+	0.0170785i
$209$	8.50811	+	3.38491i	0.588518	+	0.234139i
$210$	−0.264810	+	8.06995i	−0.0182736	+	0.556879i
$211$	−22.0409	−	12.7253i	−1.51736	−	0.876047i	−0.999792	−	0.0204046i	$-0.993505\pi$
$211$	−22.0409	−	12.7253i	−1.51736	−	0.876047i	−0.517567	−	0.855643i	$-0.673162\pi$
$212$	3.33923	+	12.4622i	0.229339	+	0.855906i
$213$	0.493918	+	0.132345i	0.0338427	+	0.00906813i
$214$	3.60223	+	2.07975i	0.246244	+	0.142169i
$215$	−2.45022	−	4.58490i	−0.167104	−	0.312688i
$216$	−1.00000			−0.0680414
$217$	−23.5979	+	23.5979i	−1.60193	+	1.60193i
$218$	−3.02979	−	0.811829i	−0.205203	−	0.0549840i
$219$	2.86037	+	4.95431i	0.193286	+	0.334781i
$220$	−3.42864	+	3.21077i	−0.231159	+	0.216470i
$221$		−	1.50319i		−	0.101116i
$222$	−4.93372	−	1.32199i	−0.331129	−	0.0887259i
$223$	19.0032	−	5.09189i	1.27255	−	0.340978i	0.441541	−	0.897241i	$-0.354432\pi$
$223$	19.0032	−	5.09189i	1.27255	−	0.340978i	0.831006	+	0.556263i	$0.187765\pi$
$224$	−1.80547	−	3.12716i	−0.120633	−	0.208942i
$225$	2.77850	−	4.15692i	0.185233	−	0.277128i
$226$	9.01047	−	15.6066i	0.599368	−	1.03814i
$227$	1.15211	−	1.15211i	0.0764685	−	0.0764685i	−0.667838	−	0.744307i	$-0.732780\pi$
$227$	1.15211	−	1.15211i	0.0764685	−	0.0764685i	0.744307	+	0.667838i	$0.232780\pi$
$228$	4.00326	−	1.72450i	0.265122	−	0.114208i
$229$			16.4589i			1.08763i	0.839204	+	0.543816i	$0.183021\pi$
$229$			16.4589i			1.08763i	−0.839204	+	0.543816i	$0.816979\pi$
$230$	1.79828	+	7.71509i	0.118575	+	0.508718i
$231$	6.56921	+	3.79274i	0.432223	+	0.249544i
$232$	0.106131	−	0.396087i	0.00696785	−	0.0260044i
$233$	0.203326	+	0.758821i	0.0133203	+	0.0497120i	0.972266	−	0.233877i	$-0.0751414\pi$
$233$	0.203326	+	0.758821i	0.0133203	+	0.0497120i	−0.958946	+	0.283589i	$0.908475\pi$
$234$	−0.301667	+	0.174167i	−0.0197206	+	0.0113857i
$235$	0.495344	−	15.0954i	0.0323127	−	0.984712i
$236$		−	13.1084i		−	0.853287i
$237$	2.58404	−	9.64378i	0.167852	−	0.626431i
$238$	−4.03305	+	15.0515i	−0.261424	+	0.975647i
$239$		−	29.1615i		−	1.88630i	−0.332363	−	0.943152i	$-0.607846\pi$
$239$		−	29.1615i		−	1.88630i	0.332363	−	0.943152i	$-0.392154\pi$
$240$	−0.0733356	+	2.23487i	−0.00473379	+	0.144260i
$241$	9.82040	−	5.66981i	0.632588	−	0.365225i	−0.149166	−	0.988812i	$-0.547659\pi$
$241$	9.82040	−	5.66981i	0.632588	−	0.365225i	0.781753	+	0.623588i	$0.214326\pi$
$242$	−1.70486	−	6.36263i	−0.109593	−	0.409005i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−0.296845	−	0.171384i	−0.0190036	−	0.0109717i
$245$	−3.06525	−	13.1507i	−0.195832	−	0.840170i
$246$			8.02616i			0.511729i
$247$	0.907299	−	1.21746i	0.0577301	−	0.0774652i
$248$	−6.53512	+	6.53512i	−0.414980	+	0.414980i
$249$	−3.31784	+	5.74667i	−0.210260	+	0.364181i
$250$	−9.08638	−	6.51442i	−0.574673	−	0.412008i
$251$	1.79991	+	3.11753i	0.113609	+	0.196777i	0.917223	−	0.398374i	$-0.130425\pi$
$251$	1.79991	+	3.11753i	0.113609	+	0.196777i	−0.803614	+	0.595151i	$0.797092\pi$
$252$	3.48789	−	0.934578i	0.219717	−	0.0588729i
$253$	7.18871	+	1.92621i	0.451951	+	0.121100i
$254$			3.69809i			0.232039i
$255$	7.04330	−	6.59575i	0.441069	−	0.413042i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−16.5971	−	4.44719i	−1.03530	−	0.277408i	−0.299136	−	0.954211i	$-0.596698\pi$
$257$	−16.5971	−	4.44719i	−1.03530	−	0.277408i	−0.736164	+	0.676803i	$0.763365\pi$
$258$	−1.64392	+	1.64392i	−0.102346	+	0.102346i
$259$	18.4438			1.14604
$260$	0.367118	+	0.686957i	0.0227677	+	0.0426033i
$261$	0.355122	+	0.205030i	0.0219815	+	0.0126910i
$262$	13.4732	+	3.61013i	0.832376	+	0.223034i
$263$	−7.75319	−	28.9353i	−0.478082	−	1.78423i	−0.609375	−	0.792882i	$-0.708579\pi$
$263$	−7.75319	−	28.9353i	−0.478082	−	1.78423i	0.131293	−	0.991344i	$-0.458087\pi$
$264$	1.81926	+	1.05035i	0.111967	+	0.0646445i
$265$	−0.946161	+	28.8338i	−0.0581222	+	1.77124i
$266$	−12.3513	+	9.75623i	−0.757305	+	0.598193i
$267$	11.6591	+	11.6591i	0.713528	+	0.713528i
$268$	5.76524	−	1.54479i	0.352168	−	0.0943632i
$269$	−0.746279	+	1.29259i	−0.0455015	+	0.0788108i	−0.887879	−	0.460077i	$-0.847822\pi$
$269$	−0.746279	+	1.29259i	−0.0455015	+	0.0788108i	0.842378	+	0.538888i	$0.181155\pi$
$270$	−2.13973	−	0.649262i	−0.130220	−	0.0395129i
$271$	9.57368	−	16.5821i	0.581560	−	1.00729i	−0.413735	−	0.910397i	$-0.635776\pi$
$271$	9.57368	−	16.5821i	0.581560	−	1.00729i	0.995295	−	0.0968935i	$-0.0308906\pi$
$272$	−1.11690	+	4.16833i	−0.0677220	+	0.252742i
$273$	0.889408	−	0.889408i	0.0538294	−	0.0538294i
$274$	−10.6060			−0.640732
$275$	−9.42101	+	4.64411i	−0.568108	+	0.280050i
$276$	3.06814	−	1.77139i	0.184680	−	0.106625i
$277$	−8.61938	−	8.61938i	−0.517888	−	0.517888i	0.399044	−	0.916932i	$-0.369342\pi$
$277$	−8.61938	−	8.61938i	−0.517888	−	0.517888i	−0.916932	+	0.399044i	$0.869342\pi$
$278$	2.99373	+	2.99373i	0.179552	+	0.179552i
$279$	−4.62103	−	8.00385i	−0.276654	−	0.479178i
$280$	−1.83287	−	7.86351i	−0.109535	−	0.469935i
$281$	10.3774	−	5.99142i	0.619066	−	0.357418i	−0.157439	−	0.987529i	$-0.550324\pi$
$281$	10.3774	−	5.99142i	0.619066	−	0.357418i	0.776505	+	0.630111i	$0.216990\pi$
$282$	−6.52433	+	1.74819i	−0.388518	+	0.104103i
$283$	−5.74805	−	21.4520i	−0.341686	−	1.27519i	−0.896436	−	0.443173i	$-0.853853\pi$
$283$	−5.74805	−	21.4520i	−0.341686	−	1.27519i	0.554750	−	0.832017i	$-0.312814\pi$
$284$	−0.511342			−0.0303425
$285$	9.68556	−	1.09080i	0.573723	−	0.0646134i
$286$	0.731745			0.0432690
$287$	−7.50107	−	27.9944i	−0.442774	−	1.65246i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	1.40504	−	0.811201i	0.0826495	−	0.0477177i
$290$	0.484257	−	0.778613i	0.0284365	−	0.0457218i
$291$	−6.48449	−	11.2315i	−0.380127	−	0.658400i
$292$	−4.04518	−	4.04518i	−0.236726	−	0.236726i
$293$	−8.79369	−	8.79369i	−0.513733	−	0.513733i	0.401935	−	0.915668i	$-0.368338\pi$
$293$	−8.79369	−	8.79369i	−0.513733	−	0.513733i	−0.915668	+	0.401935i	$0.868338\pi$
$294$	−5.22979	+	3.01942i	−0.305007	+	0.176096i
$295$	8.51082	−	28.0486i	0.495519	−	1.63305i
$296$	5.10776			0.296883
$297$	−1.48542	+	1.48542i	−0.0861926	+	0.0861926i
$298$	3.29955	−	12.3141i	0.191138	−	0.713335i
$299$	0.617036	−	1.06874i	0.0356841	−	0.0618067i
$300$	−1.60793	+	4.73440i	−0.0928340	+	0.273341i
$301$	4.19746	−	7.27021i	0.241938	−	0.419048i
$302$	3.01081	−	0.806745i	0.173253	−	0.0464230i
$303$	2.89190	+	2.89190i	0.166136	+	0.166136i
$304$	−3.42052	+	2.70186i	−0.196180	+	0.154962i
$305$	−0.523896	−	0.559445i	−0.0299982	−	0.0320338i
$306$	−3.73722	−	2.15768i	−0.213643	−	0.123347i
$307$	−0.650298	−	2.42695i	−0.0371145	−	0.138513i	0.944883	−	0.327409i	$-0.106176\pi$
$307$	−0.650298	−	2.42695i	−0.0371145	−	0.138513i	−0.981997	+	0.188896i	$0.939509\pi$
$308$	−7.32701	−	1.96327i	−0.417495	−	0.111867i
$309$	−12.0069	−	6.93219i	−0.683049	−	0.394359i
$310$	−18.2264	+	9.74040i	−1.03519	+	0.553218i
$311$	−25.2295			−1.43064			−0.715318	−	0.698799i	$-0.753718\pi$
$311$	−25.2295			−1.43064			−0.715318	+	0.698799i	$0.753718\pi$
$312$	0.246310	−	0.246310i	0.0139445	−	0.0139445i
$313$	14.0466	+	3.76378i	0.793962	+	0.212742i	0.632931	−	0.774208i	$-0.281851\pi$
$313$	14.0466	+	3.76378i	0.793962	+	0.212742i	0.161031	+	0.986949i	$0.448518\pi$
$314$	−6.73479	−	11.6650i	−0.380066	−	0.658293i
$315$	8.06995	+	0.264810i	0.454690	+	0.0149204i
$316$			9.98398i			0.561643i
$317$	−26.5772	−	7.12134i	−1.49272	−	0.399974i	−0.582069	−	0.813140i	$-0.697756\pi$
$317$	−26.5772	−	7.12134i	−1.49272	−	0.399974i	−0.910656	+	0.413165i	$0.864423\pi$
$318$	12.4622	−	3.33923i	0.698844	−	0.187255i
$319$	−0.430705	−	0.746003i	−0.0241149	−	0.0417682i
$320$	−0.507589	−	2.17769i	−0.0283751	−	0.121737i
$321$	2.07975	−	3.60223i	0.116080	−	0.201057i
$322$	−9.04583	+	9.04583i	−0.504105	+	0.504105i
$323$	18.6820	+	2.19295i	1.03949	+	0.122019i
$324$			1.00000i			0.0555556i
$325$	0.339518	+	1.70826i	0.0188331	+	0.0947572i
$326$	−14.6106	−	8.43546i	−0.809209	−	0.467197i
$327$	−0.811829	+	3.02979i	−0.0448943	+	0.167548i
$328$	−2.07732	−	7.75267i	−0.114701	−	0.428070i
$329$	21.1223	−	12.1950i	1.16451	−	0.672332i
$330$	3.21077	+	3.42864i	0.176747	+	0.188740i
$331$			11.2451i			0.618089i	0.951048	+	0.309044i	$0.100009\pi$
$331$			11.2451i			0.618089i	−0.951048	+	0.309044i	$0.899991\pi$
$332$	1.71744	−	6.40958i	0.0942569	−	0.351771i
$333$	−1.32199	+	4.93372i	−0.0724444	+	0.270366i
$334$		−	14.6281i		−	0.800415i
$335$	13.3391	+	0.437712i	0.728790	+	0.0239148i
$336$	−3.12716	+	1.80547i	−0.170601	+	0.0984963i
$337$	5.45473	+	20.3573i	0.297138	+	1.10893i	0.939504	+	0.342537i	$0.111286\pi$
$337$	5.45473	+	20.3573i	0.297138	+	1.10893i	−0.642366	+	0.766398i	$0.722047\pi$
$338$	−3.33324	+	12.4398i	−0.181305	+	0.676638i
$339$	−15.6066	−	9.01047i	−0.847634	−	0.489382i
$340$	−5.09620	+	8.19394i	−0.276380	+	0.444379i
$341$			19.4147i			1.05137i
$342$	−1.72450	−	4.00326i	−0.0932502	−	0.216472i
$343$	−2.45415	+	2.45415i	−0.132511	+	0.132511i
$344$	1.16243	−	2.01339i	0.0626741	−	0.108555i
$345$	7.71509	−	1.79828i	0.415367	−	0.0968159i
$346$	1.92490	+	3.33402i	0.103483	+	0.179238i
$347$	18.7106	−	5.01349i	1.00444	−	0.269138i	0.281134	−	0.959669i	$-0.409290\pi$
$347$	18.7106	−	5.01349i	1.00444	−	0.269138i	0.723303	+	0.690531i	$0.242623\pi$
$348$	−0.396087	−	0.106131i	−0.0212325	−	0.00568923i
$349$			14.9066i			0.797930i	0.916966	+	0.398965i	$0.130631\pi$
$349$			14.9066i			0.797930i	−0.916966	+	0.398965i	$0.869369\pi$
$350$	1.18363	−	18.0158i	0.0632677	−	0.962986i
$351$	0.174167	+	0.301667i	0.00929636	+	0.0161018i
$352$	−2.02912	−	0.543700i	−0.108152	−	0.0289793i
$353$	−7.95535	+	7.95535i	−0.423421	+	0.423421i	−0.886380	−	0.462959i	$-0.846788\pi$
$353$	−7.95535	+	7.95535i	−0.423421	+	0.423421i	0.462959	+	0.886380i	$0.346788\pi$
$354$	−13.1084			−0.696706
$355$	−1.09413	−	0.331995i	−0.0580706	−	0.0176205i
$356$	−14.2795	−	8.24426i	−0.756811	−	0.436945i
$357$	15.0515	+	4.03305i	0.796612	+	0.213452i
$358$	4.39719	+	16.4106i	0.232399	+	0.867325i
$359$	−17.9192	−	10.3457i	−0.945740	−	0.546023i	−0.0539852	−	0.998542i	$-0.517192\pi$
$359$	−17.9192	−	10.3457i	−0.945740	−	0.546023i	−0.891755	+	0.452518i	$0.850526\pi$
$360$	2.23487	+	0.0733356i	0.117788	+	0.00386513i
$361$	13.8072	+	13.0522i	0.726697	+	0.686958i
$362$	3.11071	+	3.11071i	0.163495	+	0.163495i
$363$	−6.36263	+	1.70486i	−0.333951	+	0.0894820i
$364$	−0.628907	+	1.08930i	−0.0329637	+	0.0570947i
$365$	−6.02922	−	11.2820i	−0.315584	−	0.590526i
$366$	−0.171384	+	0.296845i	−0.00895836	+	0.0155163i
$367$	−2.85326	+	10.6485i	−0.148939	+	0.555847i	0.850610	+	0.525798i	$0.176233\pi$
$367$	−2.85326	+	10.6485i	−0.148939	+	0.555847i	−0.999548	+	0.0300493i	$0.990434\pi$
$368$	−2.50512	+	2.50512i	−0.130589	+	0.130589i
$369$	8.02616			0.417825
$370$	10.9292	+	3.31628i	0.568184	+	0.172405i
$371$	−40.3460	+	23.2938i	−2.09466	+	1.20935i
$372$	6.53512	+	6.53512i	0.338830	+	0.338830i
$373$	−7.47821	−	7.47821i	−0.387207	−	0.387207i	0.486483	−	0.873690i	$-0.338279\pi$
$373$	−7.47821	−	7.47821i	−0.387207	−	0.387207i	−0.873690	+	0.486483i	$0.838279\pi$
$374$	4.53264	+	7.85076i	0.234377	+	0.405953i
$375$	−6.51442	+	9.08638i	−0.336403	+	0.469219i
$376$	5.84955	−	3.37724i	0.301668	−	0.174168i
$377$	−0.137971	+	0.0369692i	−0.00710586	+	0.00190401i
$378$	−0.934578	−	3.48789i	−0.0480695	−	0.179398i
$379$	30.7818			1.58116			0.790578	−	0.612362i	$-0.209780\pi$
$379$	30.7818			1.58116			0.790578	+	0.612362i	$0.209780\pi$
$380$	−9.07322	+	3.56044i	−0.465446	+	0.182647i
$381$	3.69809			0.189459
$382$	−0.113824	−	0.424798i	−0.00582376	−	0.0217346i
$383$	2.34284	−	0.627763i	0.119714	−	0.0320772i	−0.198465	−	0.980108i	$-0.563596\pi$
$383$	2.34284	−	0.627763i	0.119714	−	0.0320772i	0.318178	+	0.948031i	$0.396929\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	−14.4032	−	8.95801i	−0.734053	−	0.456543i
$386$	5.51036	+	9.54423i	0.280470	+	0.485788i
$387$	1.64392	+	1.64392i	0.0835654	+	0.0835654i
$388$	9.17045	+	9.17045i	0.465559	+	0.465559i
$389$	−22.5537	+	13.0214i	−1.14352	+	0.660211i	−0.947300	−	0.320349i	$-0.896200\pi$
$389$	−22.5537	+	13.0214i	−1.14352	+	0.660211i	−0.196220	+	0.980560i	$0.562867\pi$
$390$	0.686957	−	0.367118i	0.0347854	−	0.0185897i
$391$	15.2884			0.773167
$392$	4.27010	−	4.27010i	0.215673	−	0.215673i
$393$	3.61013	−	13.4732i	0.182107	−	0.679632i
$394$	−1.28206	+	2.22059i	−0.0645893	+	0.111872i
$395$	−6.48222	+	21.3631i	−0.326156	+	1.07489i
$396$	1.05035	−	1.81926i	0.0527820	−	0.0914211i
$397$	28.1496	−	7.54265i	1.41279	−	0.378555i	0.529867	−	0.848081i	$-0.322242\pi$
$397$	28.1496	−	7.54265i	1.41279	−	0.378555i	0.882919	+	0.469526i	$0.155575\pi$
$398$	13.6516	+	13.6516i	0.684294	+	0.684294i
$399$	9.75623	+	12.3513i	0.488422	+	0.618337i
$400$	0.327790	−	4.98924i	0.0163895	−	0.249462i
$401$	−25.6507	−	14.8094i	−1.28094	−	0.739548i	−0.303916	−	0.952699i	$-0.598294\pi$
$401$	−25.6507	−	14.8094i	−1.28094	−	0.739548i	−0.977019	+	0.213151i	$0.931627\pi$
$402$	−1.54479	−	5.76524i	−0.0770472	−	0.287544i
$403$	3.10963	+	0.833223i	0.154902	+	0.0415058i
$404$	−3.54184	−	2.04489i	−0.176213	−	0.101737i
$405$	−0.649262	+	2.13973i	−0.0322621	+	0.106324i
$406$	1.48070			0.0734858
$407$	7.58715	−	7.58715i	0.376081	−	0.376081i
$408$	4.16833	+	1.11690i	0.206363	+	0.0552948i
$409$	−13.1467	−	22.7708i	−0.650062	−	1.12594i	−0.983107	−	0.183030i	$-0.941409\pi$
$409$	−13.1467	−	22.7708i	−0.650062	−	1.12594i	0.333045	−	0.942911i	$-0.391924\pi$
$410$	0.588603	−	17.9374i	0.0290690	−	0.885864i
$411$			10.6060i			0.523155i
$412$	13.3920	+	3.58837i	0.659775	+	0.176786i
$413$	45.7209	−	12.2509i	2.24978	−	0.602826i
$414$	−1.77139	−	3.06814i	−0.0870591	−	0.150791i
$415$	7.83637	−	12.5997i	0.384672	−	0.618496i
$416$	−0.174167	+	0.301667i	−0.00853926	+	0.0147904i
$417$	2.99373	−	2.99373i	0.146604	−	0.146604i
$418$	−1.06751	+	9.09428i	−0.0522138	+	0.444816i
$419$			17.8031i			0.869740i	0.900493	+	0.434870i	$0.143206\pi$
$419$			17.8031i			0.869740i	−0.900493	+	0.434870i	$0.856794\pi$
$420$	−7.86351	+	1.83287i	−0.383700	+	0.0894349i
$421$	30.6780	+	17.7119i	1.49515	+	0.863226i	0.999984	−	0.00557118i	$-0.00177337\pi$
$421$	30.6780	+	17.7119i	1.49515	+	0.863226i	0.495167	+	0.868798i	$0.335107\pi$
$422$	6.58711	−	24.5834i	0.320656	−	1.19670i
$423$	1.74819	+	6.52433i	0.0849998	+	0.317224i
$424$	−11.1733	+	6.45090i	−0.542622	+	0.313283i
$425$	−16.2245	+	14.2241i	−0.787006	+	0.689969i
$426$			0.511342i			0.0247746i
$427$	0.320343	−	1.19554i	0.0155025	−	0.0578560i
$428$	−1.07656	+	4.01777i	−0.0520374	+	0.194206i
$429$		−	0.731745i		−	0.0353290i
$430$	3.79451	−	3.55339i	0.182987	−	0.171360i
$431$	−13.0045	+	7.50814i	−0.626404	+	0.361655i	−0.779358	−	0.626579i	$-0.784455\pi$
$431$	−13.0045	+	7.50814i	−0.626404	+	0.361655i	0.152954	+	0.988233i	$0.451121\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	−7.32676	+	27.3438i	−0.352101	+	1.31406i	0.531992	+	0.846750i	$0.321444\pi$
$433$	−7.32676	+	27.3438i	−0.352101	+	1.31406i	−0.884093	+	0.467311i	$0.845223\pi$
$434$	−28.9014	−	16.6862i	−1.38731	−	0.800964i
$435$	−0.778613	−	0.484257i	−0.0373317	−	0.0232183i
$436$		−	3.13667i		−	0.150219i
$437$	12.3823	+	9.22780i	0.592327	+	0.441425i
$438$	−4.04518	+	4.04518i	−0.193286	+	0.193286i
$439$	−15.4901	+	26.8296i	−0.739301	+	1.28051i	0.213510	+	0.976941i	$0.431511\pi$
$439$	−15.4901	+	26.8296i	−0.739301	+	1.28051i	−0.952811	+	0.303566i	$0.901823\pi$
$440$	−3.98876	−	2.48080i	−0.190157	−	0.118268i
$441$	3.01942	+	5.22979i	0.143782	+	0.249038i
$442$	1.45197	−	0.389055i	0.0690633	−	0.0185054i
$443$	−4.05091	−	1.08544i	−0.192464	−	0.0515707i	0.161299	−	0.986906i	$-0.448432\pi$
$443$	−4.05091	−	1.08544i	−0.192464	−	0.0515707i	−0.353764	+	0.935335i	$0.615098\pi$
$444$		−	5.10776i		−	0.242404i
$445$	−25.2016	−	26.9116i	−1.19467	−	1.27573i
$446$	9.83677	+	17.0378i	0.465785	+	0.806763i
$447$	−12.3141	−	3.29955i	−0.582436	−	0.156063i
$448$	2.55332	−	2.55332i	0.120633	−	0.120633i
$449$	1.06168			0.0501037			0.0250519	−	0.999686i	$-0.492025\pi$
$449$	1.06168			0.0501037			0.0250519	+	0.999686i	$0.492025\pi$
$450$	4.73440	+	1.60793i	0.223182	+	0.0757987i
$451$	−14.6016	−	8.43026i	−0.687564	−	0.396965i
$452$	17.4069	+	4.66416i	0.818752	+	0.219384i
$453$	−0.806745	−	3.01081i	−0.0379042	−	0.141460i
$454$	1.41105	+	0.814668i	0.0662237	+	0.0382343i
$455$	−2.05293	+	1.92248i	−0.0962430	+	0.0901274i
$456$	2.70186	+	3.42052i	0.126526	+	0.160181i
$457$	−27.1293	−	27.1293i	−1.26905	−	1.26905i	−0.946577	−	0.322477i	$-0.895485\pi$
$457$	−27.1293	−	27.1293i	−1.26905	−	1.26905i	−0.322477	−	0.946577i	$-0.604515\pi$
$458$	−15.8980	+	4.25987i	−0.742867	+	0.199051i
$459$	−2.15768	+	3.73722i	−0.100712	+	0.174438i
$460$	−6.98678	+	3.73381i	−0.325760	+	0.174090i
$461$	−2.05885	+	3.56603i	−0.0958900	+	0.166086i	−0.909980	−	0.414653i	$-0.863903\pi$
$461$	−2.05885	+	3.56603i	−0.0958900	+	0.166086i	0.814090	+	0.580739i	$0.197236\pi$
$462$	−1.96327	+	7.32701i	−0.0913394	+	0.340883i
$463$	1.64021	−	1.64021i	0.0762270	−	0.0762270i	−0.667965	−	0.744192i	$-0.732835\pi$
$463$	1.64021	−	1.64021i	0.0762270	−	0.0762270i	0.744192	+	0.667965i	$0.232835\pi$
$464$	0.410059			0.0190365
$465$	9.74040	+	18.2264i	0.451700	+	0.845230i
$466$	−0.680341	+	0.392795i	−0.0315162	+	0.0181959i
$467$	−26.3268	−	26.3268i	−1.21826	−	1.21826i	−0.968241	−	0.250020i	$-0.919563\pi$
$467$	−26.3268	−	26.3268i	−1.21826	−	1.21826i	−0.250020	−	0.968241i	$-0.580437\pi$
$468$	−0.246310	−	0.246310i	−0.0113857	−	0.0113857i
$469$	10.7761	+	18.6648i	0.497596	+	0.861861i
$470$	14.7092	−	3.42850i	0.678485	−	0.158145i
$471$	−11.6650	+	6.73479i	−0.537494	+	0.310323i
$472$	12.6618	−	3.39272i	0.582806	−	0.156162i
$473$	−1.26403	−	4.71741i	−0.0581200	−	0.216907i
$474$	9.98398			0.458579
$475$	−21.7259	+	1.72749i	−0.996854	+	0.0792628i
$476$	−15.5825			−0.714223
$477$	−3.33923	−	12.4622i	−0.152893	−	0.570604i
$478$	28.1679	−	7.54756i	1.28837	−	0.345217i
$479$	−12.1166	+	6.99550i	−0.553620	+	0.319633i	−0.750581	−	0.660779i	$-0.770226\pi$
$479$	−12.1166	+	6.99550i	−0.553620	+	0.319633i	0.196961	+	0.980411i	$0.436893\pi$
$480$	−2.17769	+	0.507589i	−0.0993977	+	0.0231682i
$481$	−0.889605	−	1.54084i	−0.0405625	−	0.0702563i
$482$	8.01832	+	8.01832i	0.365225	+	0.365225i
$483$	9.04583	+	9.04583i	0.411600	+	0.411600i
$484$	5.70457	−	3.29354i	0.259299	−	0.149706i
$485$	13.6683	+	25.5764i	0.620645	+	1.16136i
$486$	1.00000			0.0453609
$487$	−4.19344	+	4.19344i	−0.190023	+	0.190023i	−0.795706	−	0.605683i	$-0.792900\pi$
$487$	−4.19344	+	4.19344i	−0.190023	+	0.190023i	0.605683	+	0.795706i	$0.292900\pi$
$488$	0.0887147	−	0.331088i	0.00401592	−	0.0149876i
$489$	−8.43546	+	14.6106i	−0.381465	+	0.660716i
$490$	11.9093	−	6.36447i	0.538007	−	0.287517i
$491$	7.03900	−	12.1919i	0.317666	−	0.550213i	−0.662335	−	0.749208i	$-0.730434\pi$
$491$	7.03900	−	12.1919i	0.317666	−	0.550213i	0.980001	+	0.198995i	$0.0637677\pi$
$492$	−7.75267	+	2.07732i	−0.349517	+	0.0936529i
$493$	−1.25127	−	1.25127i	−0.0563542	−	0.0563542i
$494$	1.41080	+	0.561282i	0.0634750	+	0.0252533i
$495$	3.42864	−	3.21077i	0.154106	−	0.144313i
$496$	−8.00385	−	4.62103i	−0.359384	−	0.207490i
$497$	−0.477889	−	1.78351i	−0.0214362	−	0.0800012i
$498$	−6.40958	−	1.71744i	−0.287220	−	0.0769604i
$499$	−4.70862	−	2.71852i	−0.210787	−	0.121698i	0.390890	−	0.920437i	$-0.372167\pi$
$499$	−4.70862	−	2.71852i	−0.210787	−	0.121698i	−0.601677	+	0.798739i	$0.705501\pi$
$500$	3.94071	−	10.4628i	0.176234	−	0.467912i
$501$	−14.6281			−0.653536
$502$	−2.54545	+	2.54545i	−0.113609	+	0.113609i
$503$	−14.3750	−	3.85177i	−0.640950	−	0.171742i	−0.0763163	−	0.997084i	$-0.524316\pi$
$503$	−14.3750	−	3.85177i	−0.640950	−	0.171742i	−0.564634	+	0.825342i	$0.690983\pi$
$504$	1.80547	+	3.12716i	0.0804219	+	0.139295i
$505$	−6.25094	−	6.67510i	−0.278163	−	0.297038i
$506$			7.44230i			0.330851i
$507$	12.4398	+	3.33324i	0.552472	+	0.148035i
$508$	−3.57208	+	0.957135i	−0.158485	+	0.0424660i
$509$	8.43101	+	14.6029i	0.373698	+	0.647264i	0.990131	−	0.140143i	$-0.0447564\pi$
$509$	8.43101	+	14.6029i	0.373698	+	0.647264i	−0.616433	+	0.787407i	$0.711423\pi$
$510$	8.19394	+	5.09620i	0.362834	+	0.225664i
$511$	10.3286	−	17.8897i	0.456911	−	0.791393i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.00326	+	1.72450i	−0.176748	+	0.0761385i
$514$		−	17.1826i		−	0.757892i
$515$	26.3254	+	16.3730i	1.16004	+	0.721483i
$516$	−2.01339	−	1.16243i	−0.0886345	−	0.0511731i
$517$	3.67241	−	13.7056i	0.161513	−	0.602773i
$518$	4.77360	+	17.8153i	0.209740	+	0.782761i
$519$	3.33402	−	1.92490i	0.146347	−	0.0844935i
$520$	−0.568532	+	0.532406i	−0.0249318	+	0.0233475i
$521$		−	4.21584i		−	0.184699i	−0.995727	−	0.0923497i	$-0.970562\pi$
$521$		−	4.21584i		−	0.184699i	0.995727	−	0.0923497i	$-0.0294378\pi$
$522$	−0.106131	+	0.396087i	−0.00464524	+	0.0173363i
$523$	−6.45819	+	24.1023i	−0.282397	+	1.05392i	0.668324	+	0.743871i	$0.267012\pi$
$523$	−6.45819	+	24.1023i	−0.282397	+	1.05392i	−0.950721	+	0.310049i	$0.899654\pi$
$524$			13.9485i			0.609341i
$525$	−18.0158	−	1.18363i	−0.786275	−	0.0516578i
$526$	25.9427	−	14.9780i	1.13115	−	0.653072i
$527$	10.3224	+	38.5239i	0.449653	+	1.67813i
$528$	−0.543700	+	2.02912i	−0.0236615	+	0.0883060i
$529$	−9.04885	−	5.22436i	−0.393428	−	0.227146i
$530$	−28.0962	+	6.54881i	−1.22042	+	0.284462i
$531$			13.1084i			0.568858i
$532$	−12.6205	−	9.40532i	−0.547170	−	0.407772i
$533$	−1.97692	+	1.97692i	−0.0856300	+	0.0856300i
$534$	−8.24426	+	14.2795i	−0.356764	+	0.617933i
$535$	−4.91214	+	7.89799i	−0.212370	+	0.341460i
$536$	2.98431	+	5.16897i	0.128902	+	0.223266i
$537$	16.4106	−	4.39719i	0.708168	−	0.189753i
$538$	−1.44170	−	0.386303i	−0.0621561	−	0.0166547i
$539$		−	12.6858i		−	0.546415i
$540$	0.0733356	−	2.23487i	0.00315586	−	0.0961733i
$541$	−9.74261	−	16.8747i	−0.418868	−	0.725500i	0.576958	−	0.816774i	$-0.304240\pi$
$541$	−9.74261	−	16.8747i	−0.418868	−	0.725500i	−0.995826	+	0.0912737i	$0.970906\pi$
$542$	18.4949	+	4.95570i	0.794425	+	0.212866i
$543$	3.11071	−	3.11071i	0.133493	−	0.133493i
$544$	−4.31537			−0.185020
$545$	2.03652	−	6.71163i	0.0872349	−	0.287495i
$546$	1.08930	+	0.628907i	0.0466177	+	0.0269147i
$547$	31.9212	+	8.55327i	1.36485	+	0.365711i	0.865596	−	0.500742i	$-0.166940\pi$
$547$	31.9212	+	8.55327i	1.36485	+	0.365711i	0.499257	+	0.866454i	$0.333606\pi$
$548$	−2.74503	−	10.2446i	−0.117262	−	0.437628i
$549$	0.296845	+	0.171384i	0.0126690	+	0.00731447i
$550$	−6.92420	−	7.89801i	−0.295249	−	0.336772i
$551$	−0.258180	−	1.76866i	−0.0109989	−	0.0753476i
$552$	2.50512	+	2.50512i	0.106625	+	0.106625i
$553$	−34.8231	+	9.33081i	−1.48083	+	0.396786i
$554$	6.09482	−	10.5565i	0.258944	−	0.448505i
$555$	3.31628	−	10.9292i	0.140768	−	0.463921i
$556$	−2.11689	+	3.66655i	−0.0897759	+	0.155496i
$557$	1.31990	−	4.92592i	0.0559258	−	0.208718i	−0.932309	−	0.361663i	$-0.882209\pi$
$557$	1.31990	−	4.92592i	0.0559258	−	0.208718i	0.988235	+	0.152945i	$0.0488758\pi$
$558$	6.53512	−	6.53512i	0.276654	−	0.276654i
$559$	−0.809830			−0.0342521
$560$	7.12119	−	3.80564i	0.300925	−	0.160818i
$561$	7.85076	−	4.53264i	0.331459	−	0.191368i
$562$	8.47315	+	8.47315i	0.357418	+	0.357418i
$563$	26.6625	+	26.6625i	1.12369	+	1.12369i	0.991182	+	0.132508i	$0.0423031\pi$
$563$	26.6625	+	26.6625i	1.12369	+	1.12369i	0.132508	+	0.991182i	$0.457697\pi$
$564$	−3.37724	−	5.84955i	−0.142207	−	0.246311i
$565$	34.2179	+	21.2817i	1.43956	+	0.895328i
$566$	19.2334	−	11.1044i	0.808438	−	0.466752i
$567$	−3.48789	+	0.934578i	−0.146478	+	0.0392486i
$568$	−0.132345	−	0.493918i	−0.00555307	−	0.0207243i
$569$	−15.1158			−0.633686			−0.316843	−	0.948478i	$-0.602623\pi$
$569$	−15.1158			−0.633686			−0.316843	+	0.948478i	$0.602623\pi$
$570$	3.56044	+	9.07322i	0.149130	+	0.380035i
$571$	33.9088			1.41904			0.709519	−	0.704686i	$-0.248912\pi$
$571$	33.9088			1.41904			0.709519	+	0.704686i	$0.248912\pi$
$572$	0.189390	+	0.706812i	0.00791878	+	0.0295533i
$573$	−0.424798	+	0.113824i	−0.0177462	+	0.00475508i
$574$	25.0991	−	14.4910i	1.04762	−	0.604841i
$575$	−17.3741	+	3.45311i	−0.724549	+	0.144005i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	27.6664	+	27.6664i	1.15177	+	1.15177i	0.986198	+	0.165569i	$0.0529460\pi$
$577$	27.6664	+	27.6664i	1.15177	+	1.15177i	0.165569	+	0.986198i	$0.447054\pi$
$578$	1.14721	+	1.14721i	0.0477177	+	0.0477177i
$579$	9.54423	−	5.51036i	0.396644	−	0.229003i
$580$	0.877418	+	0.266236i	0.0364328	+	0.0110549i
$581$	23.9610			0.994071
$582$	9.17045	−	9.17045i	0.380127	−	0.380127i
$583$	−7.01471	+	26.1792i	−0.290520	+	1.08423i
$584$	2.86037	−	4.95431i	0.118363	−	0.205011i
$585$	−0.367118	−	0.686957i	−0.0151784	−	0.0284022i
$586$	6.21808	−	10.7700i	0.256866	−	0.444906i
$587$	23.9111	−	6.40696i	0.986916	−	0.264443i	0.270962	−	0.962590i	$-0.412658\pi$
$587$	23.9111	−	6.40696i	0.986916	−	0.264443i	0.715955	+	0.698147i	$0.245992\pi$
$588$	−4.27010	−	4.27010i	−0.176096	−	0.176096i
$589$	−14.8920	+	37.4316i	−0.613614	+	1.54234i
$590$	29.2956	+	0.961316i	1.20608	+	0.0395768i
$591$	2.22059	+	1.28206i	0.0913430	+	0.0527369i
$592$	1.32199	+	4.93372i	0.0543333	+	0.202775i
$593$	−31.4008	−	8.41381i	−1.28947	−	0.345514i	−0.452014	−	0.892011i	$-0.649294\pi$
$593$	−31.4008	−	8.41381i	−1.28947	−	0.345514i	−0.837461	+	0.546497i	$0.815961\pi$
$594$	−1.81926	−	1.05035i	−0.0746450	−	0.0430963i
$595$	−33.3424	−	10.1171i	−1.36691	−	0.414762i
$596$	12.7485			0.522197
$597$	13.6516	−	13.6516i	0.558724	−	0.558724i
$598$	1.19202	+	0.319402i	0.0487454	+	0.0130613i
$599$	12.8343	+	22.2297i	0.524396	+	0.908281i	0.999597	+	0.0284033i	$0.00904227\pi$
$599$	12.8343	+	22.2297i	0.524396	+	0.908281i	−0.475200	+	0.879878i	$0.657624\pi$
$600$	−4.98924	−	0.327790i	−0.203685	−	0.0133820i
$601$			19.9085i			0.812087i	0.913854	+	0.406043i	$0.133092\pi$
$601$			19.9085i			0.812087i	−0.913854	+	0.406043i	$0.866908\pi$
$602$	8.10887	+	2.17276i	0.330493	+	0.0885553i
$603$	−5.76524	+	1.54479i	−0.234779	+	0.0629088i
$604$	1.55851	+	2.69942i	0.0634149	+	0.109838i
$605$	14.3446	−	3.34353i	0.583192	−	0.135934i
$606$	−2.04489	+	3.54184i	−0.0830678	+	0.143878i
$607$	−9.82532	+	9.82532i	−0.398797	+	0.398797i	−0.877809	−	0.479011i	$-0.840995\pi$
$607$	−9.82532	+	9.82532i	−0.398797	+	0.398797i	0.479011	+	0.877809i	$0.340995\pi$
$608$	−3.49509	−	2.60468i	−0.141745	−	0.105634i
$609$		−	1.48070i		−	0.0600009i
$610$	0.404788	−	0.650840i	0.0163894	−	0.0263517i
$611$	−2.03760	−	1.17641i	−0.0824325	−	0.0475925i
$612$	1.11690	−	4.16833i	0.0451480	−	0.168495i
$613$	5.52370	+	20.6147i	0.223100	+	0.832621i	0.983157	+	0.182764i	$0.0585045\pi$
$613$	5.52370	+	20.6147i	0.223100	+	0.832621i	−0.760057	+	0.649857i	$0.774829\pi$
$614$	2.17594	−	1.25628i	0.0878138	−	0.0506993i
$615$	−17.9374	−	0.588603i	−0.723305	−	0.0237348i
$616$		−	7.58547i		−	0.305627i
$617$	6.28265	−	23.4472i	0.252930	−	0.943947i	−0.716301	−	0.697792i	$-0.754166\pi$
$617$	6.28265	−	23.4472i	0.252930	−	0.943947i	0.969230	−	0.246155i	$-0.0791673\pi$
$618$	3.58837	−	13.3920i	0.144345	−	0.538704i
$619$			16.3404i			0.656777i	0.944543	+	0.328389i	$0.106506\pi$
$619$			16.3404i			0.656777i	−0.944543	+	0.328389i	$0.893494\pi$
$620$	−14.1258	−	15.0844i	−0.567308	−	0.605803i
$621$	−3.06814	+	1.77139i	−0.123120	+	0.0710834i
$622$	−6.52988	−	24.3699i	−0.261824	−	0.977142i
$623$	15.4098	−	57.5102i	0.617381	−	2.30410i
$624$	0.301667	+	0.174167i	0.0120763	+	0.00697227i
$625$	15.2252	−	19.8291i	0.609008	−	0.793164i
$626$			14.5421i			0.581221i
$627$	9.09428	+	1.06751i	0.363191	+	0.0426324i
$628$	9.52442	−	9.52442i	0.380066	−	0.380066i
$629$	11.0209	−	19.0888i	0.439433	−	0.761121i
$630$	1.83287	+	7.86351i	0.0730233	+	0.313290i
$631$	2.68120	+	4.64397i	0.106737	+	0.184874i	0.914446	−	0.404707i	$-0.132626\pi$
$631$	2.68120	+	4.64397i	0.106737	+	0.184874i	−0.807710	+	0.589580i	$0.799293\pi$
$632$	−9.64378	+	2.58404i	−0.383609	+	0.102788i
$633$	−24.5834	−	6.58711i	−0.977104	−	0.261814i
$634$		−	27.5147i		−	1.09275i
$635$	−8.26472	−	0.271201i	−0.327976	−	0.0107623i
$636$	6.45090	+	11.1733i	0.255795	+	0.443049i
$637$	−2.03186	−	0.544435i	−0.0805053	−	0.0215713i
$638$	0.609109	−	0.609109i	0.0241149	−	0.0241149i
$639$	0.511342			0.0202284
$640$	1.97212	−	1.05392i	0.0779548	−	0.0416599i
$641$	0.239266	+	0.138140i	0.00945043	+	0.00545621i	0.504718	−	0.863284i	$-0.331597\pi$
$641$	0.239266	+	0.138140i	0.00945043	+	0.00545621i	−0.495267	+	0.868741i	$0.664930\pi$
$642$	4.01777	+	1.07656i	0.158569	+	0.0424884i
$643$	7.19249	+	26.8427i	0.283644	+	1.05857i	0.949824	+	0.312784i	$0.101261\pi$
$643$	7.19249	+	26.8427i	0.283644	+	1.05857i	−0.666180	+	0.745791i	$0.732072\pi$
$644$	−11.0788	−	6.39637i	−0.436567	−	0.252052i
$645$	−3.55339	−	3.79451i	−0.139915	−	0.149409i
$646$	2.71703	+	18.6130i	0.106900	+	0.732318i
$647$	11.9653	+	11.9653i	0.470405	+	0.470405i	0.902046	−	0.431641i	$-0.142065\pi$
$647$	11.9653	+	11.9653i	0.470405	+	0.470405i	−0.431641	+	0.902046i	$0.642065\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	13.7684	−	23.8476i	0.540458	−	0.936101i
$650$	−1.56218	+	0.770080i	−0.0612737	+	0.0302050i
$651$	−16.6862	+	28.9014i	−0.653984	+	1.13273i
$652$	4.36651	−	16.2961i	0.171006	−	0.638203i
$653$	−25.9411	+	25.9411i	−1.01515	+	1.01515i	−0.0152712	+	0.999883i	$0.504861\pi$
$653$	−25.9411	+	25.9411i	−1.01515	+	1.01515i	−0.999883	+	0.0152712i	$0.995139\pi$
$654$	−3.13667			−0.122653
$655$	−9.05621	+	29.8460i	−0.353856	+	1.16618i
$656$	6.95086	−	4.01308i	0.271385	−	0.156684i
$657$	4.04518	+	4.04518i	0.157817	+	0.157817i
$658$	17.2463	+	17.2463i	0.672332	+	0.672332i
$659$	7.67096	+	13.2865i	0.298818	+	0.517568i	0.975866	−	0.218371i	$-0.0700743\pi$
$659$	7.67096	+	13.2865i	0.298818	+	0.517568i	−0.677048	+	0.735939i	$0.736741\pi$
$660$	−2.48080	+	3.98876i	−0.0965651	+	0.155262i
$661$	−9.50421	+	5.48726i	−0.369671	+	0.213430i	−0.673315	−	0.739356i	$-0.735130\pi$
$661$	−9.50421	+	5.48726i	−0.369671	+	0.213430i	0.303644	+	0.952786i	$0.401797\pi$
$662$	−10.8620	+	2.91046i	−0.422162	+	0.113118i
$663$	−0.389055	−	1.45197i	−0.0151096	−	0.0563899i
$664$	6.63569			0.257515
$665$	−20.8981	−	28.3189i	−0.810392	−	1.09816i
$666$	−5.10776			−0.197922
$667$	−0.375999	−	1.40325i	−0.0145588	−	0.0543340i
$668$	14.1297	−	3.78603i	0.546693	−	0.146486i
$669$	17.0378	−	9.83677i	0.658719	−	0.380312i
$670$	3.02960	+	12.9978i	0.117044	+	0.502150i
$671$	−0.360025	−	0.623581i	−0.0138986	−	0.0240731i
$672$	−2.55332	−	2.55332i	−0.0984963	−	0.0984963i
$673$	−21.9694	−	21.9694i	−0.846858	−	0.846858i	0.142881	−	0.989740i	$-0.454363\pi$
$673$	−21.9694	−	21.9694i	−0.846858	−	0.846858i	−0.989740	+	0.142881i	$0.954363\pi$
$674$	−18.2519	+	10.5377i	−0.703036	+	0.405898i
$675$	1.60793	−	4.73440i	0.0618894	−	0.182227i
$676$	−12.8787			−0.495333
$677$	23.8620	−	23.8620i	0.917091	−	0.917091i	−0.0797259	−	0.996817i	$-0.525405\pi$
$677$	23.8620	−	23.8620i	0.917091	−	0.917091i	0.996817	+	0.0797259i	$0.0254045\pi$
$678$	4.66416	−	17.4069i	0.179126	−	0.668508i
$679$	−23.4151	+	40.5561i	−0.898587	+	1.55640i
$680$	−9.23374	−	2.80181i	−0.354098	−	0.107444i
$681$	0.814668	−	1.41105i	0.0312181	−	0.0540714i
$682$	−18.7532	+	5.02491i	−0.718097	+	0.192414i
$683$	23.3602	+	23.3602i	0.893855	+	0.893855i	0.994884	−	0.101028i	$-0.0322133\pi$
$683$	23.3602	+	23.3602i	0.893855	+	0.893855i	−0.101028	+	0.994884i	$0.532213\pi$
$684$	3.42052	−	2.70186i	0.130787	−	0.103308i
$685$	0.777797	−	23.7030i	0.0297181	−	0.905644i
$686$	−3.00570	−	1.73534i	−0.114758	−	0.0662557i
$687$	4.25987	+	15.8980i	0.162524	+	0.606548i
$688$	2.24564	+	0.601718i	0.0856143	+	0.0229403i
$689$	3.89204	+	2.24707i	0.148275	+	0.0856066i
$690$	3.73381	+	6.98678i	0.142144	+	0.265982i
$691$	−48.2999			−1.83742			−0.918708	−	0.394938i	$-0.870766\pi$
$691$	−48.2999			−1.83742			−0.918708	+	0.394938i	$0.870766\pi$
$692$	−2.72221	+	2.72221i	−0.103483	+	0.103483i
$693$	7.32701	+	1.96327i	0.278330	+	0.0745783i
$694$	9.68531	+	16.7754i	0.367649	+	0.636787i
$695$	−6.91013	+	6.47103i	−0.262116	+	0.245460i
$696$		−	0.410059i		−	0.0155433i
$697$	−33.4556	−	8.96441i	−1.26722	−	0.339551i
$698$	−14.3986	+	3.85810i	−0.544997	+	0.146031i
$699$	0.392795	+	0.680341i	0.0148569	+	0.0257328i
$700$	17.7083	−	3.51954i	0.669311	−	0.133026i
$701$	7.03494	−	12.1849i	0.265706	−	0.460216i	−0.702042	−	0.712135i	$-0.747728\pi$
$701$	7.03494	−	12.1849i	0.265706	−	0.460216i	0.967748	+	0.251919i	$0.0810616\pi$
$702$	−0.246310	+	0.246310i	−0.00929636	+	0.00929636i
$703$	20.4477	−	8.80833i	0.771200	−	0.332212i
$704$		−	2.10070i		−	0.0791730i
$705$	−3.42850	−	14.7092i	−0.129125	−	0.553980i
$706$	−9.74327	−	5.62528i	−0.366693	−	0.211710i
$707$	3.82221	−	14.2647i	0.143749	−	0.536479i
$708$	−3.39272	−	12.6618i	−0.127506	−	0.475859i
$709$	34.5593	−	19.9528i	1.29790	−	0.749343i	0.317860	−	0.948138i	$-0.397036\pi$
$709$	34.5593	−	19.9528i	1.29790	−	0.749343i	0.980041	+	0.198794i	$0.0637026\pi$
$710$	0.0374996	−	1.14278i	0.00140733	−	0.0428878i
$711$		−	9.98398i		−	0.374429i
$712$	4.26754	−	15.9267i	0.159933	−	0.596878i
$713$	−8.47440	+	31.6269i	−0.317369	+	1.18444i
$714$			15.5825i			0.583161i
$715$	−0.0536630	+	1.63535i	−0.00200688	+	0.0611587i
$716$	−14.7133	+	8.49473i	−0.549862	+	0.317463i
$717$	−7.54756	−	28.1679i	−0.281869	−	1.05195i
$718$	5.35531	−	19.9863i	0.199858	−	0.745882i
$719$	−36.1835	−	20.8905i	−1.34942	−	0.779085i	−0.361249	−	0.932470i	$-0.617649\pi$
$719$	−36.1835	−	20.8905i	−1.34942	−	0.779085i	−0.988167	+	0.153384i	$0.950983\pi$
$720$	0.507589	+	2.17769i	0.0189167	+	0.0811579i
$721$			50.0634i			1.86446i
$722$	−9.03389	+	16.7149i	−0.336207	+	0.622065i
$723$	8.01832	−	8.01832i	0.298205	−	0.298205i
$724$	−2.19960	+	3.80982i	−0.0817475	+	0.141591i
$725$	1.70458	+	1.13935i	0.0633066	+	0.0423143i
$726$	−3.29354	−	5.70457i	−0.122235	−	0.211717i
$727$	32.9643	−	8.83275i	1.22258	−	0.327589i	0.410893	−	0.911684i	$-0.365217\pi$
$727$	32.9643	−	8.83275i	1.22258	−	0.327589i	0.811685	+	0.584095i	$0.198550\pi$
$728$	−1.21495	−	0.325546i	−0.0450292	−	0.0120655i
$729$		−	1.00000i		−	0.0370370i
$730$	9.33708	−	8.74377i	0.345581	−	0.323621i
$731$	−5.01632	−	8.68851i	−0.185535	−	0.321356i
$732$	−0.331088	−	0.0887147i	−0.0122374	−	0.00327899i
$733$	−30.1762	+	30.1762i	−1.11458	+	1.11458i	−0.122060	+	0.992523i	$0.538950\pi$
$733$	−30.1762	+	30.1762i	−1.11458	+	1.11458i	−0.992523	+	0.122060i	$0.961050\pi$
$734$	−11.0241			−0.406908
$735$	−6.36447	−	11.9093i	−0.234757	−	0.439281i
$736$	−3.06814	−	1.77139i	−0.113093	−	0.0652943i
$737$	12.1110	+	3.24514i	0.446115	+	0.119536i
$738$	2.07732	+	7.75267i	0.0764673	+	0.285380i
$739$	−40.6851	−	23.4896i	−1.49663	−	0.864077i	−0.496633	−	0.867961i	$-0.665431\pi$
$739$	−40.6851	−	23.4896i	−1.49663	−	0.864077i	−0.999992	+	0.00388331i	$0.998764\pi$
$740$	−0.374581	+	11.4152i	−0.0137699	+	0.419630i
$741$	0.561282	−	1.41080i	0.0206192	−	0.0518272i
$742$	−32.9423	−	32.9423i	−1.20935	−	1.20935i
$743$	21.7505	−	5.82804i	0.797950	−	0.213810i	0.163266	−	0.986582i	$-0.447797\pi$
$743$	21.7505	−	5.82804i	0.797950	−	0.213810i	0.634684	+	0.772772i	$0.281130\pi$
$744$	−4.62103	+	8.00385i	−0.169415	+	0.293435i
$745$	27.2783	+	8.27710i	0.999400	+	0.303249i
$746$	5.28789	−	9.15889i	0.193603	−	0.335331i
$747$	−1.71744	+	6.40958i	−0.0628379	+	0.234514i
$748$	−6.41012	+	6.41012i	−0.234377	+	0.234377i
$749$	−15.0197			−0.548807
$750$	−10.4628	−	3.94071i	−0.382048	−	0.143894i
$751$	8.67517	−	5.00861i	0.316561	−	0.182767i	−0.333297	−	0.942822i	$-0.608161\pi$
$751$	8.67517	−	5.00861i	0.316561	−	0.182767i	0.649859	+	0.760055i	$0.274828\pi$
$752$	4.77614	+	4.77614i	0.174168	+	0.174168i
$753$	2.54545	+	2.54545i	0.0927615	+	0.0927615i
$754$	−0.0714189	−	0.123701i	−0.00260092	−	0.00450493i
$755$	1.58217	+	6.78792i	0.0575809	+	0.247038i
$756$	3.12716	−	1.80547i	0.113734	−	0.0656642i
$757$	13.9652	−	3.74198i	0.507575	−	0.136004i	0.00406187	−	0.999992i	$-0.498707\pi$
$757$	13.9652	−	3.74198i	0.507575	−	0.136004i	0.503514	+	0.863987i	$0.332040\pi$
$758$	7.96692	+	29.7329i	0.289371	+	1.07995i
$759$	7.44230			0.270139
$760$	−5.78744	−	7.84255i	−0.209933	−	0.284479i
$761$	6.10595			0.221340			0.110670	−	0.993857i	$-0.464700\pi$
$761$	6.10595			0.221340			0.110670	+	0.993857i	$0.464700\pi$
$762$	0.957135	+	3.57208i	0.0346733	+	0.129403i
$763$	10.9404	−	2.93146i	0.396068	−	0.106126i
$764$	0.380863	−	0.219892i	0.0137792	−	0.00795540i
$765$	5.09620	−	8.19394i	0.184254	−	0.296253i
$766$	1.21275	+	2.10054i	0.0438183	+	0.0758955i
$767$	−3.22874	−	3.22874i	−0.116583	−	0.116583i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−5.75768	+	3.32420i	−0.207627	+	0.119874i	−0.600208	−	0.799844i	$-0.704916\pi$
$769$	−5.75768	+	3.32420i	−0.207627	+	0.119874i	0.392581	+	0.919717i	$0.371582\pi$
$770$	4.92496	−	16.2309i	0.177483	−	0.584921i
$771$	−17.1826			−0.618817
$772$	−7.79283	+	7.79283i	−0.280470	+	0.280470i
$773$	−5.31590	+	19.8392i	−0.191200	+	0.713567i	0.802018	+	0.597300i	$0.203760\pi$
$773$	−5.31590	+	19.8392i	−0.191200	+	0.713567i	−0.993218	+	0.116267i	$0.962907\pi$
$774$	−1.16243	+	2.01339i	−0.0417827	+	0.0723698i
$775$	−20.4318	−	41.4479i	−0.733933	−	1.48885i
$776$	−6.48449	+	11.2315i	−0.232780	+	0.403186i
$777$	17.8153	−	4.77360i	0.639121	−	0.171252i
$778$	−18.4150	−	18.4150i	−0.660211	−	0.660211i
$779$	−21.6855	−	27.4536i	−0.776965	−	0.983629i
$780$	0.532406	+	0.568532i	0.0190632	+	0.0203567i
$781$	−0.930262	−	0.537087i	−0.0332874	−	0.0192185i
$782$	3.95693	+	14.7675i	0.141499	+	0.528083i
$783$	0.396087	+	0.106131i	0.0141550	+	0.00379282i
$784$	5.22979	+	3.01942i	0.186778	+	0.107836i
$785$	26.5636	−	14.1959i	0.948095	−	0.506673i
$786$	13.9485			0.497525
$787$	−19.0545	+	19.0545i	−0.679221	+	0.679221i	−0.959824	−	0.280603i	$-0.909465\pi$
$787$	−19.0545	+	19.0545i	−0.679221	+	0.679221i	0.280603	+	0.959824i	$0.409465\pi$
$788$	−2.47675	−	0.663643i	−0.0882306	−	0.0236413i
$789$	−14.9780	−	25.9427i	−0.533231	−	0.923583i
$790$	−22.3128	−	0.732181i	−0.793856	−	0.0260498i
$791$			65.0724i			2.31371i
$792$	2.02912	+	0.543700i	0.0721015	+	0.0193195i
$793$	−0.115329	+	0.0309024i	−0.00409546	+	0.00109738i
$794$	14.5713	+	25.2382i	0.517115	+	0.895670i
$795$	6.54881	+	28.0962i	0.232262	+	0.996468i
$796$	−9.65315	+	16.7198i	−0.342147	+	0.592616i
$797$	1.79325	−	1.79325i	0.0635202	−	0.0635202i	−0.674633	−	0.738153i	$-0.735698\pi$
$797$	1.79325	−	1.79325i	0.0635202	−	0.0635202i	0.738153	+	0.674633i	$0.235698\pi$
$798$	−9.40532	+	12.6205i	−0.332945	+	0.446762i
$799$		−	29.1481i		−	1.03118i
$800$	4.90408	−	0.974690i	0.173385	−	0.0344605i
$801$	14.2795	+	8.24426i	0.504540	+	0.291297i
$802$	7.66593	−	28.6096i	0.270693	−	1.01024i
$803$	−3.11037	−	11.6081i	−0.109763	−	0.409639i
$804$	5.16897	−	2.98431i	0.182296	−	0.105248i
$805$	−19.5528	−	20.8796i	−0.689147	−	0.735909i
$806$			3.21933i			0.113396i
$807$	−0.386303	+	1.44170i	−0.0135985	+	0.0507503i
$808$	1.05851	−	3.95041i	0.0372383	−	0.138975i
$809$		−	16.8282i		−	0.591649i	−0.955242	−	0.295825i	$-0.904406\pi$
$809$		−	16.8282i		−	0.591649i	0.955242	−	0.295825i	$-0.0955944\pi$
$810$	−2.23487	−	0.0733356i	−0.0785252	−	0.00257675i
$811$	−28.2330	+	16.3003i	−0.991394	+	0.572381i	−0.905691	−	0.423939i	$-0.860647\pi$
$811$	−28.2330	+	16.3003i	−0.991394	+	0.572381i	−0.0857031	+	0.996321i	$0.527314\pi$
$812$	0.383233	+	1.43024i	0.0134488	+	0.0501917i
$813$	4.95570	−	18.4949i	0.173804	−	0.648645i
$814$	9.29233	+	5.36493i	0.325696	+	0.188041i
$815$	19.9236	−	32.0342i	0.697893	−	1.12211i
$816$			4.31537i			0.151068i
$817$	1.18143	−	10.0647i	0.0413329	−	0.352120i
$818$	18.5922	−	18.5922i	0.650062	−	0.650062i
$819$	0.628907	−	1.08930i	0.0219758	−	0.0380632i
$820$	17.4785	−	4.07399i	0.610376	−	0.142270i
$821$	17.9017	+	31.0067i	0.624774	+	1.08214i	0.988585	+	0.150667i	$0.0481422\pi$
$821$	17.9017	+	31.0067i	0.624774	+	1.08214i	−0.363811	+	0.931473i	$0.618524\pi$
$822$	−10.2446	+	2.74503i	−0.357322	+	0.0957440i
$823$	8.88216	+	2.37997i	0.309613	+	0.0829605i	0.410280	−	0.911960i	$-0.365431\pi$
$823$	8.88216	+	2.37997i	0.309613	+	0.0829605i	−0.100667	+	0.994920i	$0.532098\pi$
$824$			13.8644i			0.482989i
$825$	−7.89801	+	6.92420i	−0.274973	+	0.241070i
$826$	23.6669	+	40.9922i	0.823476	+	1.42630i
$827$	−16.0260	−	4.29416i	−0.557280	−	0.149323i	−0.0308234	−	0.999525i	$-0.509813\pi$
$827$	−16.0260	−	4.29416i	−0.557280	−	0.149323i	−0.526456	+	0.850202i	$0.676480\pi$
$828$	2.50512	−	2.50512i	0.0870591	−	0.0870591i
$829$	−31.8941			−1.10773			−0.553864	−	0.832607i	$-0.686847\pi$
$829$	−31.8941			−1.10773			−0.553864	+	0.832607i	$0.686847\pi$
$830$	14.1986	+	4.30830i	0.492840	+	0.149543i
$831$	−10.5565	−	6.09482i	−0.366202	−	0.211427i
$832$	−0.336465	−	0.0901556i	−0.0116648	−	0.00312558i
$833$	−6.74478	−	25.1718i	−0.233693	−	0.872153i
$834$	3.66655	+	2.11689i	0.126962	+	0.0733018i
$835$	32.6919	+	1.07276i	1.13135	+	0.0371244i
$836$	−9.06070	+	1.32263i	−0.313371	+	0.0457443i
$837$	−6.53512	−	6.53512i	−0.225887	−	0.225887i
$838$	−17.1965	+	4.60779i	−0.594044	+	0.159174i
$839$	−3.92529	+	6.79881i	−0.135516	+	0.234721i	−0.925795	−	0.378027i	$-0.876603\pi$
$839$	−3.92529	+	6.79881i	−0.135516	+	0.234721i	0.790278	+	0.612748i	$0.209936\pi$
$840$	−3.80564	−	7.12119i	−0.131307	−	0.245704i
$841$	14.4159	−	24.9691i	0.497101	−	0.861004i
$842$	−9.16837	+	34.2168i	−0.315963	+	1.17919i
$843$	8.47315	−	8.47315i	0.291831	−	0.291831i
$844$	25.4506			0.876047
$845$	−27.5569	−	8.36163i	−0.947986	−	0.287649i
$846$	−5.84955	+	3.37724i	−0.201112	+	0.116112i
$847$	16.8189	+	16.8189i	0.577904	+	0.577904i
$848$	−9.12295	−	9.12295i	−0.313283	−	0.313283i
$849$	−11.1044	−	19.2334i	−0.381101	−	0.660087i
$850$	−17.9386	−	11.9902i	−0.615290	−	0.411262i
$851$	15.6713	−	9.04784i	0.537206	−	0.310156i
$852$	−0.493918	+	0.132345i	−0.0169214	+	0.00453406i
$853$	12.5975	+	47.0145i	0.431330	+	1.60974i	0.749700	+	0.661778i	$0.230198\pi$
$853$	12.5975	+	47.0145i	0.431330	+	1.60974i	−0.318370	+	0.947967i	$0.603135\pi$
$854$	1.23771			0.0423535
$855$	9.07322	−	3.56044i	0.310297	−	0.121764i
$856$	−4.15950			−0.142169
$857$	−2.68404	−	10.0170i	−0.0916849	−	0.342173i	0.904811	−	0.425813i	$-0.140012\pi$
$857$	−2.68404	−	10.0170i	−0.0916849	−	0.342173i	−0.996496	+	0.0836405i	$0.973345\pi$
$858$	0.706812	−	0.189390i	0.0241302	−	0.00646566i
$859$	−33.6433	+	19.4240i	−1.14789	+	0.662737i	−0.948373	−	0.317157i	$-0.897272\pi$
$859$	−33.6433	+	19.4240i	−1.14789	+	0.662737i	−0.199521	+	0.979894i	$0.563939\pi$
$860$	4.41440	+	2.74553i	0.150530	+	0.0936217i
$861$	−14.4910	−	25.0991i	−0.493851	−	0.855374i
$862$	−10.6181	−	10.6181i	−0.361655	−	0.361655i
$863$	−7.55551	−	7.55551i	−0.257193	−	0.257193i	0.566719	−	0.823911i	$-0.308213\pi$
$863$	−7.55551	−	7.55551i	−0.257193	−	0.257193i	−0.823911	+	0.566719i	$0.808213\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−7.59224	+	4.05738i	−0.258144	+	0.137955i
$866$	−28.3084			−0.961959
$867$	1.14721	−	1.14721i	0.0389613	−	0.0389613i
$868$	8.63742	−	32.2353i	0.293173	−	1.09414i
$869$	−10.4867	+	18.1634i	−0.355735	+	0.616152i
$870$	0.266236	−	0.877418i	0.00902625	−	0.0297472i
$871$	1.03954	−	1.80053i	0.0352234	−	0.0610087i
$872$	3.02979	−	0.811829i	0.102602	−	0.0274920i
$873$	−9.17045	−	9.17045i	−0.310373	−	0.310373i
$874$	−5.70858	+	14.3487i	−0.193096	+	0.485354i
$875$	40.1761	+	3.96645i	1.35820	+	0.134091i
$876$	−4.95431	−	2.86037i	−0.167391	−	0.0966430i
$877$	−5.19814	−	19.3997i	−0.175529	−	0.655083i	−0.996461	−	0.0840569i	$-0.973212\pi$
$877$	−5.19814	−	19.3997i	−0.175529	−	0.655083i	0.820932	−	0.571026i	$-0.193454\pi$
$878$	−29.9245	−	8.01825i	−1.00990	−	0.270603i
$879$	−10.7700	−	6.21808i	−0.363264	−	0.209731i
$880$	1.36390	−	4.49493i	0.0459772	−	0.151524i
$881$	49.8255			1.67866			0.839332	−	0.543619i	$-0.182946\pi$
$881$	49.8255			1.67866			0.839332	+	0.543619i	$0.182946\pi$
$882$	−4.27010	+	4.27010i	−0.143782	+	0.143782i
$883$	−25.9700	−	6.95865i	−0.873962	−	0.234177i	−0.206161	−	0.978518i	$-0.566097\pi$
$883$	−25.9700	−	6.95865i	−0.873962	−	0.234177i	−0.667800	+	0.744341i	$0.732764\pi$
$884$	0.751596	+	1.30180i	0.0252789	+	0.0437844i
$885$	0.961316	−	29.2956i	0.0323143	−	0.984761i
$886$		−	4.19381i		−	0.140894i
$887$	15.9810	+	4.28209i	0.536589	+	0.143779i	0.516929	−	0.856028i	$-0.327075\pi$
$887$	15.9810	+	4.28209i	0.536589	+	0.143779i	0.0196598	+	0.999807i	$0.493742\pi$
$888$	4.93372	−	1.32199i	0.165565	−	0.0443629i
$889$	−6.67677	−	11.5645i	−0.223932	−	0.387861i
$890$	19.4720	−	31.3081i	0.652703	−	1.04945i
$891$	−1.05035	+	1.81926i	−0.0351880	+	0.0609474i
$892$	−13.9113	+	13.9113i	−0.465785	+	0.465785i
$893$	17.5932	−	23.6075i	0.588735	−	0.789996i
$894$		−	12.7485i		−	0.426372i
$895$	−36.9978	+	8.62366i	−1.23670	+	0.288257i
$896$	3.12716	+	1.80547i	0.104471	+	0.0603164i
$897$	0.319402	−	1.19202i	0.0106645	−	0.0398005i
$898$	0.274783	+	1.02550i	0.00916962	+	0.0342215i
$899$	3.28205	−	1.89490i	0.109463	−	0.0631983i
$900$	−0.327790	+	4.98924i	−0.0109263	+	0.166308i
$901$			55.6760i			1.85484i
$902$	4.36382	−	16.2860i	0.145299	−	0.542265i
$903$	2.17276	−	8.10887i	0.0723051	−	0.269846i
$904$			18.0209i			0.599368i
$905$	−7.18013	+	6.72388i	−0.238676	+	0.223509i
$906$	2.69942	−	1.55851i	0.0896823	−	0.0517781i
$907$	8.21824	+	30.6709i	0.272882	+	1.01841i	0.957247	+	0.289270i	$0.0934127\pi$
$907$	8.21824	+	30.6709i	0.272882	+	1.01841i	−0.684365	+	0.729139i	$0.739921\pi$
$908$	−0.421703	+	1.57382i	−0.0139947	+	0.0522290i
$909$	3.54184	+	2.04489i	0.117476	+	0.0678246i
$910$	−2.38831	−	1.48541i	−0.0791718	−	0.0492407i
$911$			17.5316i			0.580847i	0.956898	+	0.290424i	$0.0937962\pi$
$911$			17.5316i			0.580847i	−0.956898	+	0.290424i	$0.906204\pi$
$912$	−2.60468	+	3.49509i	−0.0862495	+	0.115734i
$913$	9.85676	−	9.85676i	0.326211	−	0.326211i
$914$	19.1833	−	33.2264i	0.634527	−	1.09903i
$915$	−0.650840	−	0.404788i	−0.0215161	−	0.0133819i
$916$	−8.22943	−	14.2538i	−0.271908	−	0.470959i
$917$	−48.6508	+	13.0359i	−1.60659	+	0.430484i
$918$	−4.16833	−	1.11690i	−0.137575	−	0.0368632i
$919$		−	53.5050i		−	1.76497i	−0.470344	−	0.882483i	$-0.655870\pi$
$919$		−	53.5050i		−	1.76497i	0.470344	−	0.882483i	$-0.344130\pi$
$920$	−5.41490	−	5.78233i	−0.178524	−	0.190638i
$921$	−1.25628	−	2.17594i	−0.0413958	−	0.0716997i
$922$	−3.97739	−	1.06574i	−0.130988	−	0.0350982i
$923$	−0.125948	+	0.125948i	−0.00414564	+	0.00414564i
$924$	−7.58547			−0.249544
$925$	−8.21294	+	24.1822i	−0.270040	+	0.795105i
$926$	2.00884	+	1.15980i	0.0660145	+	0.0381135i
$927$	−13.3920	−	3.58837i	−0.439850	−	0.117857i
$928$	0.106131	+	0.396087i	0.00348393	+	0.0130022i
$929$	−0.839101	−	0.484455i	−0.0275300	−	0.0158945i	0.486172	−	0.873863i	$-0.338393\pi$
$929$	−0.839101	−	0.484455i	−0.0275300	−	0.0158945i	−0.513702	+	0.857969i	$0.671726\pi$
$930$	−15.0844	+	14.1258i	−0.494636	+	0.463205i
$931$	9.73056	−	24.4581i	0.318906	−	0.801583i
$932$	−0.555496	−	0.555496i	−0.0181959	−	0.0181959i
$933$	−24.3699	+	6.52988i	−0.797833	+	0.213779i
$934$	18.6159	−	32.2437i	0.609130	−	1.05504i
$935$	−17.8778	+	9.55410i	−0.584666	+	0.312452i
$936$	0.174167	−	0.301667i	0.00569284	−	0.00986028i
$937$	10.2625	−	38.3002i	0.335261	−	1.25121i	−0.568325	−	0.822804i	$-0.692408\pi$
$937$	10.2625	−	38.3002i	0.335261	−	1.25121i	0.903586	−	0.428407i	$-0.140925\pi$
$938$	−15.2398	+	15.2398i	−0.497596	+	0.497596i
$939$	14.5421			0.474565
$940$	7.11870	+	13.3206i	0.232186	+	0.434471i
$941$	26.9536	−	15.5617i	0.878664	−	0.507297i	0.00844603	−	0.999964i	$-0.497312\pi$
$941$	26.9536	−	15.5617i	0.878664	−	0.507297i	0.870218	+	0.492668i	$0.163978\pi$
$942$	−9.52442	−	9.52442i	−0.310323	−	0.310323i
$943$	−20.1065	−	20.1065i	−0.654758	−	0.654758i
$944$	6.55422	+	11.3522i	0.213322	+	0.369484i
$945$	7.86351	−	1.83287i	0.255800	−	0.0596233i
$946$	4.22952	−	2.44191i	0.137514	−	0.0793935i
$947$	−35.9441	+	9.63120i	−1.16803	+	0.312972i	−0.790167	−	0.612891i	$-0.790006\pi$
$947$	−35.9441	+	9.63120i	−1.16803	+	0.312972i	−0.377859	+	0.925863i	$0.623340\pi$
$948$	2.58404	+	9.64378i	0.0839259	+	0.313216i
$949$	−1.99273			−0.0646869
$950$	−7.29171	−	20.5385i	−0.236574	−	0.666358i
$951$	−27.5147			−0.892227
$952$	−4.03305	−	15.0515i	−0.130712	−	0.487823i
$953$	30.8531	−	8.26705i	0.999428	−	0.267796i	0.278222	−	0.960517i	$-0.410255\pi$
$953$	30.8531	−	8.26705i	0.999428	−	0.267796i	0.721206	+	0.692721i	$0.243588\pi$
$954$	11.1733	−	6.45090i	0.361748	−	0.208855i
$955$	0.957714	−	0.223229i	0.0309909	−	0.00722352i
$956$	14.5808	+	25.2546i	0.471576	+	0.816793i
$957$	−0.609109	−	0.609109i	−0.0196897	−	0.0196897i
$958$	−9.89314	−	9.89314i	−0.319633	−	0.319633i
$959$	33.1666	−	19.1488i	1.07101	−	0.618346i
$960$	−1.05392	−	1.97212i	−0.0340152	−	0.0636498i
$961$	−54.4155			−1.75534
$962$	1.25809	−	1.25809i	0.0405625	−	0.0405625i
$963$	1.07656	−	4.01777i	0.0346916	−	0.129471i
$964$	−5.66981	+	9.82040i	−0.182612	+	0.316294i
$965$	−21.7342	+	11.6150i	−0.699647	+	0.373899i
$966$	−6.39637	+	11.0788i	−0.205800	+	0.356456i
$967$	15.3285	−	4.10727i	0.492933	−	0.132081i	−0.00378551	−	0.999993i	$-0.501205\pi$
$967$	15.3285	−	4.10727i	0.492933	−	0.132081i	0.496718	+	0.867912i	$0.334538\pi$
$968$	4.65777	+	4.65777i	0.149706	+	0.149706i
$969$	18.6130	−	2.71703i	0.597935	−	0.0872836i
$970$	−21.1672	+	19.8222i	−0.679639	+	0.636453i
$971$	16.5768	+	9.57063i	0.531975	+	0.307136i	0.741820	−	0.670599i	$-0.233963\pi$
$971$	16.5768	+	9.57063i	0.531975	+	0.307136i	−0.209845	+	0.977735i	$0.567296\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	−14.7669	−	3.95679i	−0.473406	−	0.126849i
$974$	−5.13589	−	2.96521i	−0.164565	−	0.0950114i
$975$	0.770080	+	1.56218i	0.0246623	+	0.0500298i
$976$	0.342767			0.0109717
$977$	4.62126	−	4.62126i	0.147847	−	0.147847i	−0.629309	−	0.777156i	$-0.716662\pi$
$977$	4.62126	−	4.62126i	0.147847	−	0.147847i	0.777156	+	0.629309i	$0.216662\pi$
$978$	−16.2961	−	4.36651i	−0.521090	−	0.139626i
$979$	−17.3187	−	29.9968i	−0.553508	−	0.958703i
$980$	9.22996	+	9.85626i	0.294840	+	0.314847i
$981$			3.13667i			0.100146i
$982$	13.5983	+	3.64366i	0.433940	+	0.116274i
$983$	24.8172	−	6.64976i	0.791547	−	0.212094i	0.159678	−	0.987169i	$-0.448955\pi$
$983$	24.8172	−	6.64976i	0.791547	−	0.212094i	0.631869	+	0.775075i	$0.282288\pi$
$984$	−4.01308	−	6.95086i	−0.127932	−	0.221585i
$985$	−4.86871	−	3.02808i	−0.155130	−	0.0964827i
$986$	0.884779	−	1.53248i	0.0281771	−	0.0488042i
$987$	17.2463	−	17.2463i	0.548956	−	0.548956i
$988$	−0.177014	+	1.50800i	−0.00563156	+	0.0479759i
$989$		−	8.23647i		−	0.261904i
$990$	3.98876	+	2.48080i	0.126771	+	0.0788451i
$991$	−13.5501	−	7.82313i	−0.430432	−	0.248510i	0.269099	−	0.963113i	$-0.413274\pi$
$991$	−13.5501	−	7.82313i	−0.430432	−	0.248510i	−0.699531	+	0.714603i	$0.746608\pi$
$992$	2.39202	−	8.92714i	0.0759467	−	0.283437i
$993$	2.91046	+	10.8620i	0.0923605	+	0.344694i
$994$	1.59905	−	0.923210i	0.0507187	−	0.0292825i
$995$	−31.5107	+	29.5084i	−0.998956	+	0.935479i
$996$		−	6.63569i		−	0.210260i
$997$	7.01143	−	26.1670i	0.222054	−	0.828718i	−0.761509	−	0.648154i	$-0.775541\pi$
$997$	7.01143	−	26.1670i	0.222054	−	0.828718i	0.983563	−	0.180563i	$-0.0577921\pi$
$998$	1.40721	−	5.25178i	0.0445445	−	0.166242i
$999$			5.10776i			0.161602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.b.217.6	yes	40
5.3	odd	4	inner	570.2.x.b.103.8	✓	40
19.12	odd	6	inner	570.2.x.b.487.8	yes	40
95.88	even	12	inner	570.2.x.b.373.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.8	✓	40	5.3	odd	4	inner
570.2.x.b.217.6	yes	40	1.1	even	1	trivial
570.2.x.b.373.6	yes	40	95.88	even	12	inner
570.2.x.b.487.8	yes	40	19.12	odd	6	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.17769 + 0.507589i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.55332 - 2.55332i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.17769 + 0.507589i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.55332 - 2.55332i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.05392 - 1.97212i) q^{10} -2.10070 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-0.0901556 + 0.336465i) q^{13} +(1.80547 - 3.12716i) q^{14} +(-1.97212 + 1.05392i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.16833 + 1.11690i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.05014 - 1.61133i) q^{19} +(1.63214 - 1.52843i) q^{20} +(-3.12716 - 1.80547i) q^{21} +(-0.543700 - 2.02912i) q^{22} +(-3.42206 - 0.916939i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(4.48471 - 2.21075i) q^{25} -0.348335 q^{26} +(0.707107 - 0.707107i) q^{27} +(3.48789 + 0.934578i) q^{28} +(0.205030 + 0.355122i) q^{29} +(-1.52843 - 1.63214i) q^{30} -9.24205i q^{31} +(0.965926 + 0.258819i) q^{32} +(-2.02912 + 0.543700i) q^{33} +(-2.15768 - 3.73722i) q^{34} +(6.85638 + 4.26431i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.61173 + 3.61173i) q^{37} +(0.508171 - 4.32918i) q^{38} +0.348335i q^{39} +(1.89878 + 1.18094i) q^{40} +(6.95086 + 4.01308i) q^{41} +(0.934578 - 3.48789i) q^{42} +(0.601718 + 2.24564i) q^{43} +(1.81926 - 1.05035i) q^{44} +(-1.63214 + 1.52843i) q^{45} -3.54278i q^{46} +(-1.74819 + 6.52433i) q^{47} +(0.258819 - 0.965926i) q^{48} +6.03884i q^{49} +(3.29615 + 3.75971i) q^{50} +(-3.73722 + 2.15768i) q^{51} +(-0.0901556 - 0.336465i) q^{52} +(3.33923 - 12.4622i) q^{53} +(0.866025 + 0.500000i) q^{54} +(4.57468 - 1.06629i) q^{55} +3.61093i q^{56} +(-4.32918 - 0.508171i) q^{57} +(-0.289956 + 0.289956i) q^{58} +(-6.55422 + 11.3522i) q^{59} +(1.18094 - 1.89878i) q^{60} +(0.171384 + 0.296845i) q^{61} +(8.92714 - 2.39202i) q^{62} +(-3.48789 - 0.934578i) q^{63} +1.00000i q^{64} +(0.0255453 - 0.778481i) q^{65} +(-1.05035 - 1.81926i) q^{66} +(-5.76524 - 1.54479i) q^{67} +(3.05143 - 3.05143i) q^{68} -3.54278 q^{69} +(-2.34444 + 7.72643i) q^{70} +(0.442835 + 0.255671i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(1.48064 + 5.52581i) q^{73} +(-4.42345 - 2.55388i) q^{74} +(3.75971 - 3.29615i) q^{75} +(4.31319 - 0.629617i) q^{76} +(5.36374 + 5.36374i) q^{77} +(-0.336465 + 0.0901556i) q^{78} +(4.99199 - 8.64638i) q^{79} +(-0.649262 + 2.13973i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.07732 + 7.75267i) q^{82} +(-4.69214 + 4.69214i) q^{83} +3.61093 q^{84} +(8.51041 - 4.54806i) q^{85} +(-2.01339 + 1.16243i) q^{86} +(0.289956 + 0.289956i) q^{87} +(1.48542 + 1.48542i) q^{88} +(8.24426 + 14.2795i) q^{89} +(-1.89878 - 1.18094i) q^{90} +(1.08930 - 0.628907i) q^{91} +(3.42206 - 0.916939i) q^{92} +(-2.39202 - 8.92714i) q^{93} -6.75448 q^{94} +(9.63786 + 1.45318i) q^{95} +1.00000 q^{96} +(-3.35662 - 12.5271i) q^{97} +(-5.83307 + 1.56297i) q^{98} +(-1.81926 + 1.05035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q + 20 * q^6 - 8 * q^7	\( 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

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