LMFDB - Embedded newform 588.2.q.a.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(85,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("588.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.q (of order $7$, degree $6$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			169.2
Character	$\chi$	$=$	588.169
Dual form			588.2.q.a.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{3} +(-0.797815 + 3.49545i) q^{5} +(2.64014 - 0.172213i) q^{7} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{3} +(-0.797815 + 3.49545i) q^{5} +(2.64014 - 0.172213i) q^{7} +(-0.900969 - 0.433884i) q^{9} +(4.83228 - 2.32710i) q^{11} +(-1.75869 + 0.846942i) q^{13} +(-3.23029 - 1.55562i) q^{15} +(4.48573 + 5.62493i) q^{17} -1.92942 q^{19} +(-0.419591 + 2.61227i) q^{21} +(-5.00173 + 6.27197i) q^{23} +(-7.07685 - 3.40803i) q^{25} +(0.623490 - 0.781831i) q^{27} +(-3.37941 - 4.23765i) q^{29} -5.12955 q^{31} +(1.19347 + 5.22895i) q^{33} +(-1.50438 + 9.36589i) q^{35} +(-4.02413 - 5.04610i) q^{37} +(-0.434361 - 1.90306i) q^{39} +(-1.73269 + 7.59143i) q^{41} +(1.27907 + 5.60396i) q^{43} +(2.23543 - 2.80314i) q^{45} +(10.5368 - 5.07424i) q^{47} +(6.94069 - 0.909333i) q^{49} +(-6.48207 + 3.12160i) q^{51} +(4.38761 - 5.50189i) q^{53} +(4.27902 + 18.7476i) q^{55} +(0.429337 - 1.88105i) q^{57} +(0.402864 + 1.76506i) q^{59} +(-8.60858 - 10.7948i) q^{61} +(-2.45340 - 0.990355i) q^{63} +(-1.55734 - 6.82314i) q^{65} +12.6160 q^{67} +(-5.00173 - 6.27197i) q^{69} +(-2.53994 + 3.18498i) q^{71} +(-1.28539 - 0.619013i) q^{73} +(4.89733 - 6.14106i) q^{75} +(12.3571 - 6.97606i) q^{77} +11.2720 q^{79} +(0.623490 + 0.781831i) q^{81} +(1.89533 + 0.912741i) q^{83} +(-23.2405 + 11.1920i) q^{85} +(4.88339 - 2.35172i) q^{87} +(4.98584 + 2.40105i) q^{89} +(-4.49734 + 2.53892i) q^{91} +(1.14143 - 5.00094i) q^{93} +(1.53932 - 6.74421i) q^{95} -0.407966 q^{97} -5.36342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 5 q^{3} - q^{7} - 5 q^{9}+O(q^{10}) $ 30 * q - 5 * q^3 - q^7 - 5 * q^9	$ 30 q - 5 q^{3} - q^{7} - 5 q^{9} + 13 q^{11} - 2 q^{13} - 7 q^{15} + 5 q^{17} - 12 q^{19} - 8 q^{21} + 8 q^{23} - 27 q^{25} - 5 q^{27} - 4 q^{29} - 10 q^{31} - 8 q^{33} + 7 q^{35} + 3 q^{37} + 12 q^{39} + 23 q^{41} + 4 q^{43} + 7 q^{45} + 21 q^{47} + 13 q^{49} - 2 q^{51} + 14 q^{53} + 21 q^{55} - 12 q^{57} + 35 q^{59} + 21 q^{61} + 6 q^{63} + 33 q^{65} - 48 q^{67} + 8 q^{69} - 20 q^{71} + 3 q^{73} - 6 q^{75} + 55 q^{77} - 40 q^{79} - 5 q^{81} - 4 q^{83} - 8 q^{85} + 3 q^{87} + 4 q^{89} - 44 q^{91} - 17 q^{93} - 2 q^{95} - 102 q^{97} - 8 q^{99}+O(q^{100}) $ 30 * q - 5 * q^3 - q^7 - 5 * q^9 + 13 * q^11 - 2 * q^13 - 7 * q^15 + 5 * q^17 - 12 * q^19 - 8 * q^21 + 8 * q^23 - 27 * q^25 - 5 * q^27 - 4 * q^29 - 10 * q^31 - 8 * q^33 + 7 * q^35 + 3 * q^37 + 12 * q^39 + 23 * q^41 + 4 * q^43 + 7 * q^45 + 21 * q^47 + 13 * q^49 - 2 * q^51 + 14 * q^53 + 21 * q^55 - 12 * q^57 + 35 * q^59 + 21 * q^61 + 6 * q^63 + 33 * q^65 - 48 * q^67 + 8 * q^69 - 20 * q^71 + 3 * q^73 - 6 * q^75 + 55 * q^77 - 40 * q^79 - 5 * q^81 - 4 * q^83 - 8 * q^85 + 3 * q^87 + 4 * q^89 - 44 * q^91 - 17 * q^93 - 2 * q^95 - 102 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{7}\right)$

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			0
$2$		0			0
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$4$		0			0
$5$	−0.797815	+	3.49545i	−0.356794	+	1.56321i	0.404333	+	0.914612i	$0.367504\pi$
$5$	−0.797815	+	3.49545i	−0.356794	+	1.56321i	−0.761127	+	0.648603i	$0.775354\pi$
$6$		0			0
$7$	2.64014	−	0.172213i	0.997879	−	0.0650904i
$7$	2.64014	−	0.172213i	0.997879	−	0.0650904i
$8$		0			0
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$		0			0
$11$	4.83228	−	2.32710i	1.45699	−	0.701648i	0.473194	−	0.880958i	$-0.343101\pi$
$11$	4.83228	−	2.32710i	1.45699	−	0.701648i	0.983792	+	0.179311i	$0.0573868\pi$
$12$		0			0
$13$	−1.75869	+	0.846942i	−0.487774	+	0.234900i	−0.661572	−	0.749882i	$-0.730110\pi$
$13$	−1.75869	+	0.846942i	−0.487774	+	0.234900i	0.173798	+	0.984781i	$0.444396\pi$
$14$		0			0
$15$	−3.23029	−	1.55562i	−0.834056	−	0.401660i
$16$		0			0
$17$	4.48573	+	5.62493i	1.08795	+	1.36424i	0.926034	+	0.377440i	$0.123196\pi$
$17$	4.48573	+	5.62493i	1.08795	+	1.36424i	0.161915	+	0.986805i	$0.448233\pi$
$18$		0			0
$19$	−1.92942			−0.442640			−0.221320	−	0.975201i	$-0.571036\pi$
$19$	−1.92942			−0.442640			−0.221320	+	0.975201i	$0.571036\pi$
$20$		0			0
$21$	−0.419591	+	2.61227i	−0.0915623	+	0.570044i
$22$		0			0
$23$	−5.00173	+	6.27197i	−1.04293	+	1.30780i	−0.0928904	+	0.995676i	$0.529611\pi$
$23$	−5.00173	+	6.27197i	−1.04293	+	1.30780i	−0.950043	+	0.312120i	$0.898961\pi$
$24$		0			0
$25$	−7.07685	−	3.40803i	−1.41537	−	0.681606i
$26$		0			0
$27$	0.623490	−	0.781831i	0.119991	−	0.150464i
$28$		0			0
$29$	−3.37941	−	4.23765i	−0.627541	−	0.786912i	0.361842	−	0.932239i	$-0.382148\pi$
$29$	−3.37941	−	4.23765i	−0.627541	−	0.786912i	−0.989384	+	0.145327i	$0.953576\pi$
$30$		0			0
$31$	−5.12955			−0.921295			−0.460647	−	0.887583i	$-0.652383\pi$
$31$	−5.12955			−0.921295			−0.460647	+	0.887583i	$0.652383\pi$
$32$		0			0
$33$	1.19347	+	5.22895i	0.207757	+	0.910243i
$34$		0			0
$35$	−1.50438	+	9.36589i	−0.254287	+	1.58312i
$36$		0			0
$37$	−4.02413	−	5.04610i	−0.661563	−	0.829574i	0.331949	−	0.943297i	$-0.392294\pi$
$37$	−4.02413	−	5.04610i	−0.661563	−	0.829574i	−0.993512	+	0.113723i	$0.963722\pi$
$38$		0			0
$39$	−0.434361	−	1.90306i	−0.0695535	−	0.304734i
$40$		0			0
$41$	−1.73269	+	7.59143i	−0.270601	+	1.18558i	0.638704	+	0.769452i	$0.279471\pi$
$41$	−1.73269	+	7.59143i	−0.270601	+	1.18558i	−0.909305	+	0.416129i	$0.863386\pi$
$42$		0			0
$43$	1.27907	+	5.60396i	0.195056	+	0.854596i	0.973827	+	0.227288i	$0.0729860\pi$
$43$	1.27907	+	5.60396i	0.195056	+	0.854596i	−0.778771	+	0.627308i	$0.784157\pi$
$44$		0			0
$45$	2.23543	−	2.80314i	0.333238	−	0.417867i
$46$		0			0
$47$	10.5368	−	5.07424i	1.53695	−	0.740154i	0.541982	−	0.840390i	$-0.317674\pi$
$47$	10.5368	−	5.07424i	1.53695	−	0.740154i	0.994964	+	0.100236i	$0.0319597\pi$
$48$		0			0
$49$	6.94069	−	0.909333i	0.991526	−	0.129905i
$50$		0			0
$51$	−6.48207	+	3.12160i	−0.907671	+	0.437111i
$52$		0			0
$53$	4.38761	−	5.50189i	0.602685	−	0.755743i	−0.383109	−	0.923703i	$-0.625147\pi$
$53$	4.38761	−	5.50189i	0.602685	−	0.755743i	0.985794	+	0.167960i	$0.0537180\pi$
$54$		0			0
$55$	4.27902	+	18.7476i	0.576983	+	2.52793i
$56$		0			0
$57$	0.429337	−	1.88105i	0.0568670	−	0.249151i
$58$		0			0
$59$	0.402864	+	1.76506i	0.0524485	+	0.229792i	0.994358	−	0.106074i	$-0.0338282\pi$
$59$	0.402864	+	1.76506i	0.0524485	+	0.229792i	−0.941910	+	0.335866i	$0.890971\pi$
$60$		0			0
$61$	−8.60858	−	10.7948i	−1.10222	−	1.38213i	−0.916740	−	0.399485i	$-0.869189\pi$
$61$	−8.60858	−	10.7948i	−1.10222	−	1.38213i	−0.185476	−	0.982649i	$-0.559383\pi$
$62$		0			0
$63$	−2.45340	−	0.990355i	−0.309100	−	0.124773i
$64$		0			0
$65$	−1.55734	−	6.82314i	−0.193164	−	0.846306i
$66$		0			0
$67$	12.6160			1.54129			0.770645	−	0.637265i	$-0.219934\pi$
$67$	12.6160			1.54129			0.770645	+	0.637265i	$0.219934\pi$
$68$		0			0
$69$	−5.00173	−	6.27197i	−0.602138	−	0.755057i
$70$		0			0
$71$	−2.53994	+	3.18498i	−0.301435	+	0.377988i	−0.909362	−	0.416005i	$-0.863430\pi$
$71$	−2.53994	+	3.18498i	−0.301435	+	0.377988i	0.607927	+	0.793993i	$0.292001\pi$
$72$		0			0
$73$	−1.28539	−	0.619013i	−0.150444	−	0.0724500i	0.357147	−	0.934048i	$-0.383750\pi$
$73$	−1.28539	−	0.619013i	−0.150444	−	0.0724500i	−0.507591	+	0.861598i	$0.669464\pi$
$74$		0			0
$75$	4.89733	−	6.14106i	0.565495	−	0.709109i
$76$		0			0
$77$	12.3571	−	6.97606i	1.40823	−	0.794996i
$78$		0			0
$79$	11.2720			1.26820			0.634099	−	0.773252i	$-0.281371\pi$
$79$	11.2720			1.26820			0.634099	+	0.773252i	$0.281371\pi$
$80$		0			0
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$		0			0
$83$	1.89533	+	0.912741i	0.208039	+	0.100186i	0.535002	−	0.844851i	$-0.320311\pi$
$83$	1.89533	+	0.912741i	0.208039	+	0.100186i	−0.326963	+	0.945037i	$0.606025\pi$
$84$		0			0
$85$	−23.2405	+	11.1920i	−2.52078	+	1.21394i
$86$		0			0
$87$	4.88339	−	2.35172i	0.523555	−	0.252131i
$88$		0			0
$89$	4.98584	+	2.40105i	0.528498	+	0.254511i	0.679051	−	0.734091i	$-0.262391\pi$
$89$	4.98584	+	2.40105i	0.528498	+	0.254511i	−0.150554	+	0.988602i	$0.548106\pi$
$90$		0			0
$91$	−4.49734	+	2.53892i	−0.471450	+	0.266151i
$92$		0			0
$93$	1.14143	−	5.00094i	0.118361	−	0.518574i
$94$		0			0
$95$	1.53932	−	6.74421i	0.157931	−	0.691941i
$96$		0			0
$97$	−0.407966			−0.0414227			−0.0207113	−	0.999785i	$-0.506593\pi$
$97$	−0.407966			−0.0414227			−0.0207113	+	0.999785i	$0.506593\pi$
$98$		0			0
$99$	−5.36342			−0.539044
$100$		0			0
$101$	2.43460	−	10.6667i	0.242251	−	1.06137i	−0.696711	−	0.717352i	$-0.745354\pi$
$101$	2.43460	−	10.6667i	0.242251	−	1.06137i	0.938962	−	0.344020i	$-0.111789\pi$
$102$		0			0
$103$	−2.55576	+	11.1975i	−0.251826	+	1.10332i	0.677924	+	0.735132i	$0.262880\pi$
$103$	−2.55576	+	11.1975i	−0.251826	+	1.10332i	−0.929750	+	0.368191i	$0.879977\pi$
$104$		0			0
$105$	−8.79631	−	3.55077i	−0.858432	−	0.346519i
$106$		0			0
$107$	−8.70842	−	4.19375i	−0.841875	−	0.405426i	−0.0373196	−	0.999303i	$-0.511882\pi$
$107$	−8.70842	−	4.19375i	−0.841875	−	0.405426i	−0.804555	+	0.593878i	$0.797596\pi$
$108$		0			0
$109$	8.07801	−	3.89016i	0.773733	−	0.372610i	−0.00498256	−	0.999988i	$-0.501586\pi$
$109$	8.07801	−	3.89016i	0.773733	−	0.372610i	0.778715	+	0.627378i	$0.215872\pi$
$110$		0			0
$111$	5.81504	−	2.80038i	0.551939	−	0.265800i
$112$		0			0
$113$	8.99155	+	4.33010i	0.845854	+	0.407342i	0.806037	−	0.591865i	$-0.201608\pi$
$113$	8.99155	+	4.33010i	0.845854	+	0.407342i	0.0398169	+	0.999207i	$0.487323\pi$
$114$		0			0
$115$	−17.9329	−	22.4872i	−1.67226	−	2.09694i
$116$		0			0
$117$	1.95200			0.180463
$118$		0			0
$119$	12.8116	+	14.0781i	1.17444	+	1.29054i
$120$		0			0
$121$	11.0771	−	13.8903i	1.00701	−	1.26275i
$122$		0			0
$123$	−7.01553	−	3.37850i	−0.632569	−	0.304629i
$124$		0			0
$125$	6.38150	−	8.00215i	0.570779	−	0.715734i
$126$		0			0
$127$	−8.46163	−	10.6106i	−0.750849	−	0.941534i	0.248786	−	0.968558i	$-0.419968\pi$
$127$	−8.46163	−	10.6106i	−0.750849	−	0.941534i	−0.999635	+	0.0270240i	$0.991397\pi$
$128$		0			0
$129$	−5.74808			−0.506090
$130$		0			0
$131$	2.37330	+	10.3981i	0.207356	+	0.908486i	0.966318	+	0.257351i	$0.0828497\pi$
$131$	2.37330	+	10.3981i	0.207356	+	0.908486i	−0.758962	+	0.651135i	$0.774293\pi$
$132$		0			0
$133$	−5.09394	+	0.332272i	−0.441701	+	0.0288116i
$134$		0			0
$135$	2.23543	+	2.80314i	0.192395	+	0.241256i
$136$		0			0
$137$	1.07459	+	4.70807i	0.0918081	+	0.402237i	0.999862	−	0.0166160i	$-0.00528927\pi$
$137$	1.07459	+	4.70807i	0.0918081	+	0.402237i	−0.908054	+	0.418853i	$0.862432\pi$
$138$		0			0
$139$	3.24643	−	14.2235i	0.275359	−	1.20643i	−0.628231	−	0.778027i	$-0.716221\pi$
$139$	3.24643	−	14.2235i	0.275359	−	1.20643i	0.903590	−	0.428399i	$-0.140922\pi$
$140$		0			0
$141$	2.60237	+	11.4017i	0.219159	+	0.960198i
$142$		0			0
$143$	−6.52757	+	8.18532i	−0.545863	+	0.684491i
$144$		0			0
$145$	17.5087	−	8.43173i	1.45402	−	0.700217i
$146$		0			0
$147$	−0.657913	+	6.96901i	−0.0542638	+	0.574795i
$148$		0			0
$149$	−5.48525	+	2.64156i	−0.449369	+	0.216405i	−0.644860	−	0.764301i	$-0.723084\pi$
$149$	−5.48525	+	2.64156i	−0.449369	+	0.216405i	0.195491	+	0.980706i	$0.437370\pi$
$150$		0			0
$151$	2.02539	−	2.53976i	0.164824	−	0.206683i	−0.692560	−	0.721361i	$-0.743517\pi$
$151$	2.02539	−	2.53976i	0.164824	−	0.206683i	0.857384	+	0.514678i	$0.172088\pi$
$152$		0			0
$153$	−1.60094	−	7.01417i	−0.129428	−	0.567062i
$154$		0			0
$155$	4.09243	−	17.9301i	0.328712	−	1.44018i
$156$		0			0
$157$	0.0227028	+	0.0994675i	0.00181188	+	0.00793837i	0.975826	−	0.218550i	$-0.0701326\pi$
$157$	0.0227028	+	0.0994675i	0.00181188	+	0.00793837i	−0.974014	+	0.226488i	$0.927276\pi$
$158$		0			0
$159$	4.38761	+	5.50189i	0.347960	+	0.436328i
$160$		0			0
$161$	−12.1252	+	17.4203i	−0.955596	+	1.37291i
$162$		0			0
$163$	−0.471534	−	2.06592i	−0.0369334	−	0.161816i	0.953098	−	0.302661i	$-0.0978751\pi$
$163$	−0.471534	−	2.06592i	−0.0369334	−	0.161816i	−0.990032	+	0.140845i	$0.955018\pi$
$164$		0			0
$165$	−19.2297			−1.49703
$166$		0			0
$167$	7.77790	+	9.75318i	0.601872	+	0.754724i	0.985668	−	0.168694i	$-0.0539549\pi$
$167$	7.77790	+	9.75318i	0.601872	+	0.754724i	−0.383796	+	0.923418i	$0.625383\pi$
$168$		0			0
$169$	−5.72967	+	7.18478i	−0.440744	+	0.552676i
$170$		0			0
$171$	1.73835	+	0.837145i	0.132935	+	0.0640181i
$172$		0			0
$173$	14.1429	−	17.7346i	1.07526	−	1.34834i	0.141706	−	0.989909i	$-0.454741\pi$
$173$	14.1429	−	17.7346i	1.07526	−	1.34834i	0.933557	−	0.358429i	$-0.116687\pi$
$174$		0			0
$175$	−19.2708	−	7.77896i	−1.45673	−	0.588034i
$176$		0			0
$177$	−1.81046			−0.136082
$178$		0			0
$179$	−0.508058	−	0.637084i	−0.0379740	−	0.0476179i	0.762482	−	0.647010i	$-0.223981\pi$
$179$	−0.508058	−	0.637084i	−0.0379740	−	0.0476179i	−0.800456	+	0.599392i	$0.795409\pi$
$180$		0			0
$181$	8.77590	+	4.22625i	0.652307	+	0.314135i	0.730610	−	0.682795i	$-0.239236\pi$
$181$	8.77590	+	4.22625i	0.652307	+	0.314135i	−0.0783028	+	0.996930i	$0.524950\pi$
$182$		0			0
$183$	12.4398	−	5.99067i	0.919573	−	0.442843i
$184$		0			0
$185$	20.8489	−	10.0403i	1.53284	−	0.738179i
$186$		0			0
$187$	34.7661	+	16.7425i	2.54235	+	1.22433i
$188$		0			0
$189$	1.51146	−	2.17152i	0.109942	−	0.157955i
$190$		0			0
$191$	−0.0506724	+	0.222010i	−0.00366653	+	0.0160641i	−0.976728	−	0.214481i	$-0.931194\pi$
$191$	−0.0506724	+	0.222010i	−0.00366653	+	0.0160641i	0.973062	+	0.230545i	$0.0740510\pi$
$192$		0			0
$193$	3.30929	−	14.4989i	0.238208	−	1.04366i	−0.704413	−	0.709790i	$-0.748790\pi$
$193$	3.30929	−	14.4989i	0.238208	−	1.04366i	0.942621	−	0.333866i	$-0.108353\pi$
$194$		0			0
$195$	6.99861			0.501181
$196$		0			0
$197$	−11.5161			−0.820490			−0.410245	−	0.911975i	$-0.634557\pi$
$197$	−11.5161			−0.820490			−0.410245	+	0.911975i	$0.634557\pi$
$198$		0			0
$199$	4.38806	−	19.2253i	0.311061	−	1.36285i	−0.541711	−	0.840565i	$-0.682223\pi$
$199$	4.38806	−	19.2253i	0.311061	−	1.36285i	0.852772	−	0.522283i	$-0.174919\pi$
$200$		0			0
$201$	−2.80732	+	12.2997i	−0.198013	+	0.867553i
$202$		0			0
$203$	−9.65191	−	10.6060i	−0.677431	−	0.744396i
$204$		0			0
$205$	−25.1531	−	12.1131i	−1.75677	−	0.846016i
$206$		0			0
$207$	7.22771	−	3.48068i	0.502361	−	0.241924i
$208$		0			0
$209$	−9.32350	+	4.48996i	−0.644920	+	0.310577i
$210$		0			0
$211$	15.0779	+	7.26113i	1.03801	+	0.499877i	0.873666	−	0.486527i	$-0.161736\pi$
$211$	15.0779	+	7.26113i	1.03801	+	0.499877i	0.164340	+	0.986404i	$0.447451\pi$
$212$		0			0
$213$	−2.53994	−	3.18498i	−0.174034	−	0.218231i
$214$		0			0
$215$	−20.6089			−1.40551
$216$		0			0
$217$	−13.5427	+	0.883376i	−0.919341	+	0.0599675i
$218$		0			0
$219$	0.889520	−	1.11542i	0.0601082	−	0.0753733i
$220$		0			0
$221$	−12.6530	−	6.09337i	−0.851134	−	0.409884i
$222$		0			0
$223$	3.82857	−	4.80088i	0.256380	−	0.321491i	−0.636938	−	0.770915i	$-0.719799\pi$
$223$	3.82857	−	4.80088i	0.256380	−	0.321491i	0.893318	+	0.449424i	$0.148371\pi$
$224$		0			0
$225$	4.89733	+	6.14106i	0.326489	+	0.409404i
$226$		0			0
$227$	−6.90501			−0.458302			−0.229151	−	0.973391i	$-0.573595\pi$
$227$	−6.90501			−0.458302			−0.229151	+	0.973391i	$0.573595\pi$
$228$		0			0
$229$	−2.37359	−	10.3994i	−0.156851	−	0.687211i	−0.990796	−	0.135363i	$-0.956780\pi$
$229$	−2.37359	−	10.3994i	−0.156851	−	0.687211i	0.833945	−	0.551848i	$-0.186077\pi$
$230$		0			0
$231$	4.05143	+	13.5996i	0.266565	+	0.894790i
$232$		0			0
$233$	−4.57841	−	5.74114i	−0.299942	−	0.376115i	0.608907	−	0.793242i	$-0.291608\pi$
$233$	−4.57841	−	5.74114i	−0.299942	−	0.376115i	−0.908848	+	0.417127i	$0.863037\pi$
$234$		0			0
$235$	9.33039	+	40.8791i	0.608648	+	2.66666i
$236$		0			0
$237$	−2.50825	+	10.9894i	−0.162929	+	0.713837i
$238$		0			0
$239$	2.38416	+	10.4457i	0.154219	+	0.675676i	0.991631	+	0.129104i	$0.0412102\pi$
$239$	2.38416	+	10.4457i	0.154219	+	0.675676i	−0.837412	+	0.546571i	$0.815933\pi$
$240$		0			0
$241$	−4.64690	+	5.82703i	−0.299333	+	0.375352i	−0.908638	−	0.417584i	$-0.862877\pi$
$241$	−4.64690	+	5.82703i	−0.299333	+	0.375352i	0.609305	+	0.792936i	$0.291448\pi$
$242$		0			0
$243$	−0.900969	+	0.433884i	−0.0577972	+	0.0278337i
$244$		0			0
$245$	−2.35885	+	24.9863i	−0.150701	+	1.59632i
$246$		0			0
$247$	3.39326	−	1.63411i	0.215908	−	0.103976i
$248$		0			0
$249$	−1.31161	+	1.64470i	−0.0831197	+	0.104229i
$250$		0			0
$251$	−0.0353279	−	0.154782i	−0.00222988	−	0.00976973i	0.973801	−	0.227403i	$-0.0730235\pi$
$251$	−0.0353279	−	0.154782i	−0.00222988	−	0.00976973i	−0.976031	+	0.217633i	$0.930166\pi$
$252$		0			0
$253$	−9.57423	+	41.9474i	−0.601927	+	2.63721i
$254$		0			0
$255$	−5.73992	−	25.1482i	−0.359448	−	1.57484i
$256$		0			0
$257$	−1.85853	−	2.33052i	−0.115932	−	0.145374i	0.720479	−	0.693476i	$-0.243922\pi$
$257$	−1.85853	−	2.33052i	−0.115932	−	0.145374i	−0.836411	+	0.548103i	$0.815350\pi$
$258$		0			0
$259$	−11.4933	−	12.6294i	−0.714158	−	0.784754i
$260$		0			0
$261$	1.20610	+	5.28426i	0.0746556	+	0.327088i
$262$		0			0
$263$	8.15214			0.502683			0.251341	−	0.967899i	$-0.419128\pi$
$263$	8.15214			0.502683			0.251341	+	0.967899i	$0.419128\pi$
$264$		0			0
$265$	15.7311	+	19.7262i	0.966355	+	1.21177i
$266$		0			0
$267$	−3.45031	+	4.32655i	−0.211155	+	0.264780i
$268$		0			0
$269$	−7.97738	−	3.84170i	−0.486389	−	0.234233i	0.174584	−	0.984642i	$-0.444142\pi$
$269$	−7.97738	−	3.84170i	−0.486389	−	0.234233i	−0.660973	+	0.750410i	$0.729856\pi$
$270$		0			0
$271$	0.621328	−	0.779121i	0.0377430	−	0.0473282i	−0.762602	−	0.646868i	$-0.776078\pi$
$271$	0.621328	−	0.779121i	0.0377430	−	0.0473282i	0.800345	+	0.599540i	$0.204650\pi$
$272$		0			0
$273$	−1.47451	−	4.94955i	−0.0892413	−	0.299560i
$274$		0			0
$275$	−42.1281			−2.54042
$276$		0			0
$277$	3.42040	+	4.28905i	0.205512	+	0.257704i	0.873896	−	0.486112i	$-0.161585\pi$
$277$	3.42040	+	4.28905i	0.205512	+	0.257704i	−0.668384	+	0.743816i	$0.733014\pi$
$278$		0			0
$279$	4.62157	+	2.22563i	0.276686	+	0.133245i
$280$		0			0
$281$	0.650722	−	0.313371i	0.0388188	−	0.0186941i	−0.414374	−	0.910107i	$-0.635999\pi$
$281$	0.650722	−	0.313371i	0.0388188	−	0.0186941i	0.453192	+	0.891413i	$0.350285\pi$
$282$		0			0
$283$	−6.02090	+	2.89951i	−0.357905	+	0.172358i	−0.604192	−	0.796839i	$-0.706504\pi$
$283$	−6.02090	+	2.89951i	−0.357905	+	0.172358i	0.246286	+	0.969197i	$0.420790\pi$
$284$		0			0
$285$	6.23258	+	3.00145i	0.369186	+	0.177791i
$286$		0			0
$287$	−3.26721	+	20.3408i	−0.192857	+	1.20068i
$288$		0			0
$289$	−7.73517	+	33.8900i	−0.455010	+	1.99353i
$290$		0			0
$291$	0.0907810	−	0.397738i	0.00532168	−	0.0233158i
$292$		0			0
$293$	−16.2259			−0.947925			−0.473962	−	0.880545i	$-0.657177\pi$
$293$	−16.2259			−0.947925			−0.473962	+	0.880545i	$0.657177\pi$
$294$		0			0
$295$	−6.49111			−0.377927
$296$		0			0
$297$	1.19347	−	5.22895i	0.0692524	−	0.303414i
$298$		0			0
$299$	3.48451	−	15.2667i	0.201515	−	0.882894i
$300$		0			0
$301$	4.34199	+	14.5750i	0.250268	+	0.840088i
$302$		0			0
$303$	9.85748	+	4.74711i	0.566297	+	0.272714i
$304$		0			0
$305$	44.6008	−	21.4786i	2.55384	−	1.22986i
$306$		0			0
$307$	23.1512	−	11.1490i	1.32131	−	0.636309i	0.365641	−	0.930756i	$-0.380850\pi$
$307$	23.1512	−	11.1490i	1.32131	−	0.636309i	0.955668	+	0.294447i	$0.0951355\pi$
$308$		0			0
$309$	−10.3481	−	4.98336i	−0.588680	−	0.283493i
$310$		0			0
$311$	−10.0067	−	12.5480i	−0.567430	−	0.711534i	0.412482	−	0.910966i	$-0.364662\pi$
$311$	−10.0067	−	12.5480i	−0.567430	−	0.711534i	−0.979912	+	0.199431i	$0.936091\pi$
$312$		0			0
$313$	10.6404			0.601430			0.300715	−	0.953714i	$-0.402775\pi$
$313$	10.6404			0.601430			0.300715	+	0.953714i	$0.402775\pi$
$314$		0			0
$315$	5.41911	−	7.78565i	0.305332	−	0.438671i
$316$		0			0
$317$	7.06628	−	8.86084i	0.396882	−	0.497674i	−0.542734	−	0.839905i	$-0.682611\pi$
$317$	7.06628	−	8.86084i	0.396882	−	0.497674i	0.939616	+	0.342230i	$0.111182\pi$
$318$		0			0
$319$	−26.1917	−	12.6133i	−1.46645	−	0.706207i
$320$		0			0
$321$	6.02641	−	7.55688i	0.336362	−	0.421784i
$322$		0			0
$323$	−8.65486	−	10.8529i	−0.481569	−	0.603869i
$324$		0			0
$325$	15.3324			0.850490
$326$		0			0
$327$	1.99510	+	8.74112i	0.110329	+	0.483385i
$328$		0			0
$329$	26.9447	−	15.2113i	1.48551	−	0.838625i
$330$		0			0
$331$	16.2666	+	20.3977i	0.894094	+	1.12116i	0.992035	+	0.125966i	$0.0402029\pi$
$331$	16.2666	+	20.3977i	0.894094	+	1.12116i	−0.0979410	+	0.995192i	$0.531226\pi$
$332$		0			0
$333$	1.43620	+	6.29239i	0.0787031	+	0.344821i
$334$		0			0
$335$	−10.0652	+	44.0986i	−0.549922	+	2.40937i
$336$		0			0
$337$	−6.30530	−	27.6253i	−0.343472	−	1.50485i	−0.791690	−	0.610923i	$-0.790798\pi$
$337$	−6.30530	−	27.6253i	−0.343472	−	1.50485i	0.448218	−	0.893924i	$-0.352059\pi$
$338$		0			0
$339$	−6.22235	+	7.80257i	−0.337951	+	0.423778i
$340$		0			0
$341$	−24.7874	+	11.9370i	−1.34231	+	0.646424i
$342$		0			0
$343$	18.1678	−	3.59605i	0.980968	−	0.194168i
$344$		0			0
$345$	25.9139	−	12.4795i	1.39515	−	0.671871i
$346$		0			0
$347$	14.0107	−	17.5688i	0.752132	−	0.943143i	−0.247537	−	0.968878i	$-0.579621\pi$
$347$	14.0107	−	17.5688i	0.752132	−	0.943143i	0.999669	+	0.0257350i	$0.00819261\pi$
$348$		0			0
$349$	2.63294	+	11.5357i	0.140938	+	0.617490i	0.995218	+	0.0976771i	$0.0311413\pi$
$349$	2.63294	+	11.5357i	0.140938	+	0.617490i	−0.854280	+	0.519813i	$0.826002\pi$
$350$		0			0
$351$	−0.434361	+	1.90306i	−0.0231845	+	0.101578i
$352$		0			0
$353$	3.49449	+	15.3103i	0.185993	+	0.814888i	0.978702	+	0.205287i	$0.0658129\pi$
$353$	3.49449	+	15.3103i	0.185993	+	0.814888i	−0.792709	+	0.609600i	$0.791330\pi$
$354$		0			0
$355$	−9.10656	−	11.4193i	−0.483326	−	0.606071i
$356$		0			0
$357$	−16.5760	+	9.35776i	−0.877294	+	0.495265i
$358$		0			0
$359$	3.46529	+	15.1824i	0.182891	+	0.801298i	0.980245	+	0.197786i	$0.0633752\pi$
$359$	3.46529	+	15.1824i	0.182891	+	0.801298i	−0.797354	+	0.603512i	$0.793768\pi$
$360$		0			0
$361$	−15.2773			−0.804070
$362$		0			0
$363$	11.0771	+	13.8903i	0.581397	+	0.729049i
$364$		0			0
$365$	3.18924	−	3.99918i	0.166932	−	0.209327i
$366$		0			0
$367$	16.2175	+	7.80993i	0.846546	+	0.407675i	0.806295	−	0.591514i	$-0.201470\pi$
$367$	16.2175	+	7.80993i	0.846546	+	0.407675i	0.0402519	+	0.999190i	$0.487184\pi$
$368$		0			0
$369$	4.85490	−	6.08785i	0.252736	−	0.316921i
$370$		0			0
$371$	10.6364	−	15.2814i	0.552215	−	0.793369i
$372$		0			0
$373$	−8.56553			−0.443506			−0.221753	−	0.975103i	$-0.571178\pi$
$373$	−8.56553			−0.443506			−0.221753	+	0.975103i	$0.571178\pi$
$374$		0			0
$375$	6.38150	+	8.00215i	0.329539	+	0.413229i
$376$		0			0
$377$	9.53240	+	4.59056i	0.490943	+	0.236426i
$378$		0			0
$379$	16.3357	−	7.86688i	0.839111	−	0.404095i	0.0355867	−	0.999367i	$-0.488670\pi$
$379$	16.3357	−	7.86688i	0.839111	−	0.404095i	0.803524	+	0.595272i	$0.202956\pi$
$380$		0			0
$381$	12.2274	−	5.88841i	0.626430	−	0.301673i
$382$		0			0
$383$	−10.0361	−	4.83313i	−0.512821	−	0.246961i	0.159531	−	0.987193i	$-0.449002\pi$
$383$	−10.0361	−	4.83313i	−0.512821	−	0.246961i	−0.672352	+	0.740231i	$0.734716\pi$
$384$		0			0
$385$	14.5258	+	48.7594i	0.740303	+	2.48501i
$386$		0			0
$387$	1.27907	−	5.60396i	0.0650187	−	0.284865i
$388$		0			0
$389$	−6.26741	+	27.4593i	−0.317771	+	1.39224i	0.523683	+	0.851913i	$0.324558\pi$
$389$	−6.26741	+	27.4593i	−0.317771	+	1.39224i	−0.841453	+	0.540330i	$0.818299\pi$
$390$		0			0
$391$	−57.7158			−2.91881
$392$		0			0
$393$	−10.6655			−0.538004
$394$		0			0
$395$	−8.99296	+	39.4007i	−0.452485	+	1.98247i
$396$		0			0
$397$	−4.36025	+	19.1035i	−0.218835	+	0.958778i	0.739506	+	0.673150i	$0.235059\pi$
$397$	−4.36025	+	19.1035i	−0.218835	+	0.958778i	−0.958341	+	0.285628i	$0.907798\pi$
$398$		0			0
$399$	0.809568	−	5.04017i	0.0405291	−	0.252324i
$400$		0			0
$401$	−22.2353	−	10.7080i	−1.11038	−	0.534731i	−0.213472	−	0.976949i	$-0.568477\pi$
$401$	−22.2353	−	10.7080i	−1.11038	−	0.534731i	−0.896907	+	0.442218i	$0.854192\pi$
$402$		0			0
$403$	9.02131	−	4.34444i	0.449384	−	0.216412i
$404$		0			0
$405$	−3.23029	+	1.55562i	−0.160514	+	0.0772996i
$406$		0			0
$407$	−31.1885	−	15.0196i	−1.54596	−	0.744494i
$408$		0			0
$409$	−5.61218	−	7.03745i	−0.277504	−	0.347980i	0.623473	−	0.781845i	$-0.285721\pi$
$409$	−5.61218	−	7.03745i	−0.277504	−	0.347980i	−0.900978	+	0.433865i	$0.857150\pi$
$410$		0			0
$411$	−4.82914			−0.238204
$412$		0			0
$413$	1.36759	+	4.59064i	0.0672945	+	0.225891i
$414$		0			0
$415$	−4.70256	+	5.89683i	−0.230840	+	0.289464i
$416$		0			0
$417$	13.1445	+	6.33007i	0.643691	+	0.309985i
$418$		0			0
$419$	−7.72796	+	9.69055i	−0.377535	+	0.473414i	−0.933905	−	0.357520i	$-0.883622\pi$
$419$	−7.72796	+	9.69055i	−0.377535	+	0.473414i	0.556370	+	0.830935i	$0.312194\pi$
$420$		0			0
$421$	−4.32007	−	5.41719i	−0.210547	−	0.264018i	0.665333	−	0.746547i	$-0.268290\pi$
$421$	−4.32007	−	5.41719i	−0.210547	−	0.264018i	−0.875880	+	0.482529i	$0.839718\pi$
$422$		0			0
$423$	−11.6949			−0.568627
$424$		0			0
$425$	−12.5749	−	55.0943i	−0.609973	−	2.67246i
$426$		0			0
$427$	−24.5869	−	27.0173i	−1.18984	−	1.30746i
$428$		0			0
$429$	−6.52757	−	8.18532i	−0.315154	−	0.395191i
$430$		0			0
$431$	−5.52438	−	24.2039i	−0.266100	−	1.16586i	−0.914508	−	0.404567i	$-0.867422\pi$
$431$	−5.52438	−	24.2039i	−0.266100	−	1.16586i	0.648409	−	0.761293i	$-0.275435\pi$
$432$		0			0
$433$	6.91809	−	30.3101i	0.332462	−	1.45661i	−0.481885	−	0.876235i	$-0.660048\pi$
$433$	6.91809	−	30.3101i	0.332462	−	1.45661i	0.814347	−	0.580378i	$-0.197095\pi$
$434$		0			0
$435$	4.32428	+	18.9459i	0.207333	+	0.908387i
$436$		0			0
$437$	9.65045	−	12.1013i	0.461644	−	0.578883i
$438$		0			0
$439$	−16.4810	+	7.93681i	−0.786593	+	0.378803i	−0.783658	−	0.621192i	$-0.786649\pi$
$439$	−16.4810	+	7.93681i	−0.786593	+	0.378803i	−0.00293525	+	0.999996i	$0.500934\pi$
$440$		0			0
$441$	−6.64789	−	2.19217i	−0.316566	−	0.104389i
$442$		0			0
$443$	−2.07439	+	0.998973i	−0.0985572	+	0.0474626i	−0.482513	−	0.875889i	$-0.660276\pi$
$443$	−2.07439	+	0.998973i	−0.0985572	+	0.0474626i	0.383956	+	0.923352i	$0.374562\pi$
$444$		0			0
$445$	−12.3705	+	15.5122i	−0.586420	+	0.735347i
$446$		0			0
$447$	−1.35475	−	5.93553i	−0.0640773	−	0.280741i
$448$		0			0
$449$	8.27168	−	36.2406i	0.390365	−	1.71030i	−0.273009	−	0.962012i	$-0.588019\pi$
$449$	8.27168	−	36.2406i	0.390365	−	1.71030i	0.663374	−	0.748288i	$-0.269124\pi$
$450$		0			0
$451$	9.29317	+	40.7160i	0.437598	+	1.91724i
$452$		0			0
$453$	2.02539	+	2.53976i	0.0951611	+	0.119328i
$454$		0			0
$455$	−5.28662	−	17.7458i	−0.247841	−	0.831938i
$456$		0			0
$457$	1.07535	+	4.71140i	0.0503026	+	0.220390i	0.993832	−	0.110900i	$-0.0353733\pi$
$457$	1.07535	+	4.71140i	0.0503026	+	0.220390i	−0.943529	+	0.331290i	$0.892516\pi$
$458$		0			0
$459$	7.19455			0.335813
$460$		0			0
$461$	6.80238	+	8.52991i	0.316818	+	0.397277i	0.914586	−	0.404392i	$-0.132517\pi$
$461$	6.80238	+	8.52991i	0.316818	+	0.397277i	−0.597768	+	0.801669i	$0.703945\pi$
$462$		0			0
$463$	9.32733	−	11.6961i	0.433478	−	0.543564i	−0.516334	−	0.856388i	$-0.672704\pi$
$463$	9.32733	−	11.6961i	0.433478	−	0.543564i	0.949811	+	0.312824i	$0.101275\pi$
$464$		0			0
$465$	16.5699	+	7.97965i	0.768412	+	0.370048i
$466$		0			0
$467$	0.928166	−	1.16388i	0.0429504	−	0.0538581i	−0.759892	−	0.650049i	$-0.774748\pi$
$467$	0.928166	−	1.16388i	0.0429504	−	0.0538581i	0.802843	+	0.596191i	$0.203320\pi$
$468$		0			0
$469$	33.3080	−	2.17264i	1.53802	−	0.100323i
$470$		0			0
$471$	−0.102025			−0.00470109
$472$		0			0
$473$	19.2218	+	24.1034i	0.883819	+	1.10827i
$474$		0			0
$475$	13.6542	+	6.57553i	0.626499	+	0.301706i
$476$		0			0
$477$	−6.34028	+	3.05332i	−0.290302	+	0.139802i
$478$		0			0
$479$	−16.5054	+	7.94860i	−0.754152	+	0.363181i	−0.771132	−	0.636675i	$-0.780309\pi$
$479$	−16.5054	+	7.94860i	−0.754152	+	0.363181i	0.0169797	+	0.999856i	$0.494595\pi$
$480$		0			0
$481$	11.3510	+	5.46634i	0.517560	+	0.249244i
$482$		0			0
$483$	−14.2854	−	15.6975i	−0.650008	−	0.714262i
$484$		0			0
$485$	0.325481	−	1.42603i	0.0147793	−	0.0647525i
$486$		0			0
$487$	4.59046	−	20.1121i	0.208014	−	0.911368i	−0.757873	−	0.652402i	$-0.773761\pi$
$487$	4.59046	−	20.1121i	0.208014	−	0.911368i	0.965887	−	0.258965i	$-0.0833816\pi$
$488$		0			0
$489$	2.11905			0.0958269
$490$		0			0
$491$	−5.19186			−0.234305			−0.117153	−	0.993114i	$-0.537377\pi$
$491$	−5.19186			−0.234305			−0.117153	+	0.993114i	$0.537377\pi$
$492$		0			0
$493$	8.67734	−	38.0179i	0.390808	−	1.71224i
$494$		0			0
$495$	4.27902	−	18.7476i	0.192328	−	0.842642i
$496$		0			0
$497$	−6.15730	+	8.84621i	−0.276192	+	0.396807i
$498$		0			0
$499$	−6.66680	−	3.21056i	−0.298447	−	0.143724i	0.278668	−	0.960388i	$-0.410107\pi$
$499$	−6.66680	−	3.21056i	−0.298447	−	0.143724i	−0.577115	+	0.816663i	$0.695821\pi$
$500$		0			0
$501$	−11.2394	+	5.41261i	−0.502139	+	0.241818i
$502$		0			0
$503$	−14.1460	+	6.81236i	−0.630740	+	0.303748i	−0.721805	−	0.692097i	$-0.756687\pi$
$503$	−14.1460	+	6.81236i	−0.630740	+	0.303748i	0.0910650	+	0.995845i	$0.470973\pi$
$504$		0			0
$505$	35.3425	+	17.0200i	1.57272	+	0.757382i
$506$		0			0
$507$	−5.72967	−	7.18478i	−0.254464	−	0.319088i
$508$		0			0
$509$	−35.8785			−1.59029			−0.795143	−	0.606422i	$-0.792604\pi$
$509$	−35.8785			−1.59029			−0.795143	+	0.606422i	$0.792604\pi$
$510$		0			0
$511$	−3.50022	−	1.41292i	−0.154841	−	0.0625039i
$512$		0			0
$513$	−1.20297	+	1.50848i	−0.0531126	+	0.0666011i
$514$		0			0
$515$	−37.1014	−	17.8671i	−1.63488	−	0.787317i
$516$		0			0
$517$	39.1083	−	49.0403i	1.71998	−	2.15679i
$518$		0			0
$519$	14.1429	+	17.7346i	0.620804	+	0.778463i
$520$		0			0
$521$	−11.8891			−0.520869			−0.260435	−	0.965491i	$-0.583866\pi$
$521$	−11.8891			−0.520869			−0.260435	+	0.965491i	$0.583866\pi$
$522$		0			0
$523$	2.20509	+	9.66115i	0.0964221	+	0.422453i	0.999982	−	0.00600920i	$-0.00191280\pi$
$523$	2.20509	+	9.66115i	0.0964221	+	0.422453i	−0.903560	+	0.428462i	$0.859056\pi$
$524$		0			0
$525$	11.8721	−	17.0567i	0.518140	−	0.744413i
$526$		0			0
$527$	−23.0098	−	28.8534i	−1.00232	−	1.25687i
$528$		0			0
$529$	−9.20234	−	40.3181i	−0.400102	−	1.75296i
$530$		0			0
$531$	0.402864	−	1.76506i	0.0174828	−	0.0765972i
$532$		0			0
$533$	−3.38222	−	14.8185i	−0.146500	−	0.641860i
$534$		0			0
$535$	21.6068	−	27.0941i	0.934143	−	1.17138i
$536$		0			0
$537$	0.734165	−	0.353555i	0.0316815	−	0.0152570i
$538$		0			0
$539$	31.4232	−	20.5458i	1.35349	−	0.884972i
$540$		0			0
$541$	1.36082	−	0.655335i	0.0585061	−	0.0281750i	−0.404402	−	0.914581i	$-0.632520\pi$
$541$	1.36082	−	0.655335i	0.0585061	−	0.0281750i	0.462908	+	0.886406i	$0.346806\pi$
$542$		0			0
$543$	−6.07311	+	7.61544i	−0.260622	+	0.326810i
$544$		0			0
$545$	7.15314	+	31.3399i	0.306407	+	1.34246i
$546$		0			0
$547$	6.77020	−	29.6622i	0.289473	−	1.26826i	−0.595778	−	0.803149i	$-0.703156\pi$
$547$	6.77020	−	29.6622i	0.289473	−	1.26826i	0.885251	−	0.465114i	$-0.153987\pi$
$548$		0			0
$549$	3.07237	+	13.4609i	0.131125	+	0.574498i
$550$		0			0
$551$	6.52031	+	8.17621i	0.277775	+	0.348318i
$552$		0			0
$553$	29.7597	−	1.94118i	1.26551	−	0.0825476i
$554$		0			0
$555$	5.14926	+	22.5604i	0.218574	+	0.957635i
$556$		0			0
$557$	34.4460			1.45952			0.729762	−	0.683701i	$-0.239631\pi$
$557$	34.4460			1.45952			0.729762	+	0.683701i	$0.239631\pi$
$558$		0			0
$559$	−6.99572	−	8.77236i	−0.295887	−	0.371031i
$560$		0			0
$561$	−24.0589	+	30.1689i	−1.01577	+	1.27373i
$562$		0			0
$563$	14.7278	+	7.09252i	0.620702	+	0.298914i	0.717681	−	0.696372i	$-0.245204\pi$
$563$	14.7278	+	7.09252i	0.620702	+	0.298914i	−0.0969791	+	0.995286i	$0.530918\pi$
$564$		0			0
$565$	−22.3093	+	27.9749i	−0.938558	+	1.17691i
$566$		0			0
$567$	1.78074	+	1.95677i	0.0747842	+	0.0821767i
$568$		0			0
$569$	−20.4226			−0.856158			−0.428079	−	0.903741i	$-0.640809\pi$
$569$	−20.4226			−0.856158			−0.428079	+	0.903741i	$0.640809\pi$
$570$		0			0
$571$	0.492074	+	0.617041i	0.0205926	+	0.0258224i	0.792021	−	0.610494i	$-0.209029\pi$
$571$	0.492074	+	0.617041i	0.0205926	+	0.0258224i	−0.771429	+	0.636316i	$0.780457\pi$
$572$		0			0
$573$	−0.205168	−	0.0988039i	−0.00857103	−	0.00412759i
$574$		0			0
$575$	56.7716	−	27.3398i	2.36754	−	1.14015i
$576$		0			0
$577$	3.61779	−	1.74224i	0.150611	−	0.0725302i	−0.357060	−	0.934081i	$-0.616221\pi$
$577$	3.61779	−	1.74224i	0.150611	−	0.0725302i	0.507671	+	0.861551i	$0.330507\pi$
$578$		0			0
$579$	13.3990	+	6.45263i	0.556845	+	0.268162i
$580$		0			0
$581$	5.16111	+	2.08336i	0.214119	+	0.0864325i
$582$		0			0
$583$	8.39870	−	36.7971i	0.347838	−	1.52398i
$584$		0			0
$585$	−1.55734	+	6.82314i	−0.0643879	+	0.282102i
$586$		0			0
$587$	−32.1783			−1.32814			−0.664070	−	0.747671i	$-0.731172\pi$
$587$	−32.1783			−1.32814			−0.664070	+	0.747671i	$0.731172\pi$
$588$		0			0
$589$	9.89707			0.407802
$590$		0			0
$591$	2.56258	−	11.2274i	0.105410	−	0.461833i
$592$		0			0
$593$	1.45367	−	6.36896i	0.0596952	−	0.261542i	−0.936270	−	0.351281i	$-0.885746\pi$
$593$	1.45367	−	6.36896i	0.0596952	−	0.261542i	0.995965	+	0.0897391i	$0.0286033\pi$
$594$		0			0
$595$	−59.4307	+	33.5508i	−2.43642	+	1.37545i
$596$		0			0
$597$	17.7669	+	8.55608i	0.727150	+	0.350177i
$598$		0			0
$599$	26.9693	−	12.9877i	1.10193	−	0.530663i	0.207668	−	0.978199i	$-0.433413\pi$
$599$	26.9693	−	12.9877i	1.10193	−	0.530663i	0.894266	+	0.447536i	$0.147698\pi$
$600$		0			0
$601$	−13.0379	+	6.27872i	−0.531827	+	0.256114i	−0.680469	−	0.732777i	$-0.738224\pi$
$601$	−13.0379	+	6.27872i	−0.531827	+	0.256114i	0.148642	+	0.988891i	$0.452510\pi$
$602$		0			0
$603$	−11.3666	−	5.47388i	−0.462885	−	0.222913i
$604$		0			0
$605$	39.7153	+	49.8014i	1.61466	+	2.02471i
$606$		0			0
$607$	40.4780			1.64295			0.821475	−	0.570245i	$-0.193152\pi$
$607$	40.4780			1.64295			0.821475	+	0.570245i	$0.193152\pi$
$608$		0			0
$609$	12.4878	−	7.04985i	0.506033	−	0.285674i
$610$		0			0
$611$	−14.2334	+	17.8481i	−0.575820	+	0.722056i
$612$		0			0
$613$	−12.0726	−	5.81385i	−0.487607	−	0.234819i	0.173893	−	0.984765i	$-0.444365\pi$
$613$	−12.0726	−	5.81385i	−0.487607	−	0.234819i	−0.661500	+	0.749946i	$0.730080\pi$
$614$		0			0
$615$	17.4065	−	21.8271i	0.701898	−	0.880152i
$616$		0			0
$617$	19.5368	+	24.4983i	0.786521	+	0.986266i	0.999957	+	0.00930851i	$0.00296303\pi$
$617$	19.5368	+	24.4983i	0.786521	+	0.986266i	−0.213436	+	0.976957i	$0.568466\pi$
$618$		0			0
$619$	3.02090			0.121420			0.0607102	−	0.998155i	$-0.480663\pi$
$619$	3.02090			0.121420			0.0607102	+	0.998155i	$0.480663\pi$
$620$		0			0
$621$	1.78510	+	7.82102i	0.0716335	+	0.313847i
$622$		0			0
$623$	13.5768	+	5.48049i	0.543943	+	0.219571i
$624$		0			0
$625$	−1.60677	−	2.01482i	−0.0642707	−	0.0805929i
$626$		0			0
$627$	−2.30271	−	10.0888i	−0.0919615	−	0.402910i
$628$		0			0
$629$	10.3328	−	45.2709i	0.411995	−	1.80507i
$630$		0			0
$631$	2.13501	+	9.35408i	0.0849933	+	0.372380i	0.999480	−	0.0322353i	$-0.0102626\pi$
$631$	2.13501	+	9.35408i	0.0849933	+	0.372380i	−0.914487	+	0.404615i	$0.867405\pi$
$632$		0			0
$633$	−10.4342	+	13.0841i	−0.414723	+	0.520047i
$634$		0			0
$635$	43.8395	−	21.1120i	1.73972	−	0.837804i
$636$		0			0
$637$	−11.4364	+	7.47760i	−0.453126	+	0.296273i
$638$		0			0
$639$	3.67032	−	1.76753i	0.145195	−	0.0699224i
$640$		0			0
$641$	−17.9021	+	22.4486i	−0.707091	+	0.886665i	−0.997531	−	0.0702288i	$-0.977627\pi$
$641$	−17.9021	+	22.4486i	−0.707091	+	0.886665i	0.290440	+	0.956893i	$0.406198\pi$
$642$		0			0
$643$	−6.53112	−	28.6147i	−0.257562	−	1.12845i	−0.923849	−	0.382758i	$-0.874974\pi$
$643$	−6.53112	−	28.6147i	−0.257562	−	1.12845i	0.666286	−	0.745696i	$-0.267883\pi$
$644$		0			0
$645$	4.58590	−	20.0921i	0.180570	−	0.791128i
$646$		0			0
$647$	−3.55747	−	15.5863i	−0.139859	−	0.612760i	−0.995465	−	0.0951328i	$-0.969672\pi$
$647$	−3.55747	−	15.5863i	−0.139859	−	0.612760i	0.855606	−	0.517628i	$-0.173185\pi$
$648$		0			0
$649$	6.05424	+	7.59177i	0.237650	+	0.298003i
$650$		0			0
$651$	2.15232	−	13.3998i	0.0843559	−	0.525178i
$652$		0			0
$653$	9.18002	+	40.2203i	0.359242	+	1.57394i	0.755087	+	0.655624i	$0.227595\pi$
$653$	9.18002	+	40.2203i	0.359242	+	1.57394i	−0.395845	+	0.918317i	$0.629548\pi$
$654$		0			0
$655$	−38.2395			−1.49414
$656$		0			0
$657$	0.889520	+	1.11542i	0.0347035	+	0.0435168i
$658$		0			0
$659$	−11.5997	+	14.5456i	−0.451861	+	0.566615i	−0.954626	−	0.297808i	$-0.903745\pi$
$659$	−11.5997	+	14.5456i	−0.451861	+	0.566615i	0.502765	+	0.864423i	$0.332316\pi$
$660$		0			0
$661$	−15.9268	−	7.66994i	−0.619481	−	0.298326i	0.0976974	−	0.995216i	$-0.468852\pi$
$661$	−15.9268	−	7.66994i	−0.619481	−	0.298326i	−0.717178	+	0.696890i	$0.754567\pi$
$662$		0			0
$663$	8.75616	−	10.9799i	0.340061	−	0.426423i
$664$		0			0
$665$	2.90258	−	18.0707i	0.112557	−	0.700753i
$666$		0			0
$667$	43.4813			1.68360
$668$		0			0
$669$	3.82857	+	4.80088i	0.148021	+	0.185613i
$670$		0			0
$671$	−66.7197	−	32.1305i	−2.57568	−	1.24038i
$672$		0			0
$673$	−0.515637	+	0.248318i	−0.0198763	+	0.00957194i	−0.443796	−	0.896128i	$-0.646368\pi$
$673$	−0.515637	+	0.248318i	−0.0198763	+	0.00957194i	0.423919	+	0.905700i	$0.360654\pi$
$674$		0			0
$675$	−7.07685	+	3.40803i	−0.272388	+	0.131175i
$676$		0			0
$677$	−28.2694	−	13.6138i	−1.08648	−	0.523222i	−0.197098	−	0.980384i	$-0.563152\pi$
$677$	−28.2694	−	13.6138i	−1.08648	−	0.523222i	−0.889383	+	0.457162i	$0.848866\pi$
$678$		0			0
$679$	−1.07709	+	0.0702571i	−0.0413348	+	0.00269622i
$680$		0			0
$681$	1.53651	−	6.73189i	0.0588792	−	0.257966i
$682$		0			0
$683$	8.16222	−	35.7610i	0.312319	−	1.36836i	−0.538379	−	0.842703i	$-0.680963\pi$
$683$	8.16222	−	35.7610i	0.312319	−	1.36836i	0.850698	−	0.525655i	$-0.176180\pi$
$684$		0			0
$685$	−17.3142			−0.661540
$686$		0			0
$687$	10.6668			0.406965
$688$		0			0
$689$	−3.05668	+	13.3922i	−0.116450	+	0.510202i
$690$		0			0
$691$	−3.06082	+	13.4103i	−0.116439	+	0.510154i	0.882748	+	0.469847i	$0.155691\pi$
$691$	−3.06082	+	13.4103i	−0.116439	+	0.510154i	−0.999187	+	0.0403071i	$0.987166\pi$
$692$		0			0
$693$	−14.1602	+	0.923651i	−0.537901	+	0.0350866i
$694$		0			0
$695$	47.1277	+	22.6955i	1.78766	+	0.860890i
$696$		0			0
$697$	−50.4736	+	24.3068i	−1.91182	+	0.920686i
$698$		0			0
$699$	6.61599	−	3.18609i	0.250240	−	0.120509i
$700$		0			0
$701$	−39.4663	−	19.0060i	−1.49062	−	0.717846i	−0.501530	−	0.865140i	$-0.667229\pi$
$701$	−39.4663	−	19.0060i	−1.49062	−	0.717846i	−0.989093	+	0.147294i	$0.952944\pi$
$702$		0			0
$703$	7.76425	+	9.73606i	0.292834	+	0.367202i
$704$		0			0
$705$	−41.9304			−1.57919
$706$		0			0
$707$	4.59074	−	28.5808i	0.172652	−	1.07489i
$708$		0			0
$709$	28.4540	−	35.6801i	1.06861	−	1.34000i	0.131362	−	0.991334i	$-0.458065\pi$
$709$	28.4540	−	35.6801i	1.06861	−	1.34000i	0.937249	−	0.348661i	$-0.113364\pi$
$710$		0			0
$711$	−10.1557	−	4.89074i	−0.380869	−	0.183417i
$712$		0			0
$713$	25.6566	−	32.1724i	0.960849	−	1.20487i
$714$		0			0
$715$	−23.4036	−	29.3472i	−0.875246	−	1.09752i
$716$		0			0
$717$	−10.7143			−0.400134
$718$		0			0
$719$	4.04882	+	17.7390i	0.150995	+	0.661554i	0.992597	+	0.121455i	$0.0387561\pi$
$719$	4.04882	+	17.7390i	0.150995	+	0.661554i	−0.841601	+	0.540099i	$0.818387\pi$
$720$		0			0
$721$	−4.81920	+	30.0031i	−0.179477	+	1.11737i
$722$		0			0
$723$	−4.64690	−	5.82703i	−0.172820	−	0.216710i
$724$		0			0
$725$	9.47356	+	41.5064i	0.351839	+	1.54151i
$726$		0			0
$727$	−9.06756	+	39.7276i	−0.336297	+	1.47341i	0.470403	+	0.882452i	$0.344109\pi$
$727$	−9.06756	+	39.7276i	−0.336297	+	1.47341i	−0.806700	+	0.590962i	$0.798748\pi$
$728$		0			0
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$		0			0
$731$	−25.7843	+	32.3325i	−0.953668	+	1.19586i
$732$		0			0
$733$	−32.9636	+	15.8744i	−1.21754	+	0.586335i	−0.928624	−	0.371021i	$-0.879008\pi$
$733$	−32.9636	+	15.8744i	−1.21754	+	0.586335i	−0.288912	+	0.957356i	$0.593294\pi$
$734$		0			0
$735$	−23.8350	−	7.85969i	−0.879166	−	0.289909i
$736$		0			0
$737$	60.9640	−	29.3587i	2.24564	−	1.08144i
$738$		0			0
$739$	−14.8015	+	18.5604i	−0.544481	+	0.682757i	−0.975604	−	0.219536i	$-0.929546\pi$
$739$	−14.8015	+	18.5604i	−0.544481	+	0.682757i	0.431124	+	0.902293i	$0.358117\pi$
$740$		0			0
$741$	0.838066	+	3.67181i	0.0307871	+	0.134887i
$742$		0			0
$743$	−9.06504	+	39.7165i	−0.332564	+	1.45706i	0.481583	+	0.876400i	$0.340062\pi$
$743$	−9.06504	+	39.7165i	−0.332564	+	1.45706i	−0.814147	+	0.580658i	$0.802795\pi$
$744$		0			0
$745$	−4.85723	−	21.2809i	−0.177955	−	0.779673i
$746$		0			0
$747$	−1.31161	−	1.64470i	−0.0479892	−	0.0601765i
$748$		0			0
$749$	−23.7137	−	9.57240i	−0.866479	−	0.349768i
$750$		0			0
$751$	0.611388	+	2.67866i	0.0223099	+	0.0977459i	0.984857	−	0.173368i	$-0.0554651\pi$
$751$	0.611388	+	2.67866i	0.0223099	+	0.0977459i	−0.962547	+	0.271114i	$0.912608\pi$
$752$		0			0
$753$	0.158762			0.00578561
$754$		0			0
$755$	7.26173	+	9.10592i	0.264281	+	0.331398i
$756$		0			0
$757$	−19.9863	+	25.0620i	−0.726413	+	0.910893i	−0.998682	−	0.0513280i	$-0.983655\pi$
$757$	−19.9863	+	25.0620i	−0.726413	+	0.910893i	0.272269	+	0.962221i	$0.412226\pi$
$758$		0			0
$759$	−38.7653	−	18.6684i	−1.40709	−	0.677619i
$760$		0			0
$761$	−20.0915	+	25.1939i	−0.728315	+	0.913278i	−0.998776	−	0.0494524i	$-0.984252\pi$
$761$	−20.0915	+	25.1939i	−0.728315	+	0.913278i	0.270461	+	0.962731i	$0.412824\pi$
$762$		0			0
$763$	20.6571	−	11.6617i	0.747839	−	0.422182i
$764$		0			0
$765$	25.7950			0.932619
$766$		0			0
$767$	−2.20342	−	2.76300i	−0.0795610	−	0.0997663i
$768$		0			0
$769$	−18.7657	−	9.03709i	−0.676709	−	0.325886i	0.0637709	−	0.997965i	$-0.479687\pi$
$769$	−18.7657	−	9.03709i	−0.676709	−	0.325886i	−0.740480	+	0.672079i	$0.765402\pi$
$770$		0			0
$771$	2.68565	−	1.29334i	0.0967213	−	0.0465785i
$772$		0			0
$773$	−36.5195	+	17.5868i	−1.31351	+	0.632555i	−0.953782	−	0.300501i	$-0.902846\pi$
$773$	−36.5195	+	17.5868i	−1.31351	+	0.632555i	−0.359732	+	0.933056i	$0.617132\pi$
$774$		0			0
$775$	36.3011	+	17.4817i	1.30397	+	0.627960i
$776$		0			0
$777$	14.8703	−	8.39481i	0.533468	−	0.301162i
$778$		0			0
$779$	3.34310	−	14.6471i	0.119779	−	0.524786i
$780$		0			0
$781$	−4.86191	+	21.3014i	−0.173973	+	0.762224i
$782$		0			0
$783$	−5.42016			−0.193701
$784$		0			0
$785$	−0.365797			−0.0130558
$786$		0			0
$787$	−3.63651	+	15.9326i	−0.129628	+	0.567936i	0.867842	+	0.496840i	$0.165507\pi$
$787$	−3.63651	+	15.9326i	−0.129628	+	0.567936i	−0.997470	+	0.0710952i	$0.977351\pi$
$788$		0			0
$789$	−1.81402	+	7.94775i	−0.0645809	+	0.282947i
$790$		0			0
$791$	24.4847	+	9.88362i	0.870574	+	0.351421i
$792$		0			0
$793$	24.2824	+	11.6938i	0.862294	+	0.415259i
$794$		0			0
$795$	−22.7321	+	10.9472i	−0.806225	+	0.388258i
$796$		0			0
$797$	−16.2862	+	7.84300i	−0.576885	+	0.277813i	−0.699490	−	0.714642i	$-0.746590\pi$
$797$	−16.2862	+	7.84300i	−0.576885	+	0.277813i	0.122605	+	0.992456i	$0.460875\pi$
$798$		0			0
$799$	75.8073	+	36.5069i	2.68187	+	1.29152i
$800$		0			0
$801$	−3.45031	−	4.32655i	−0.121911	−	0.152871i
$802$		0			0
$803$	−7.65188			−0.270029
$804$		0			0
$805$	−51.2181	−	56.2811i	−1.80520	−	1.98365i
$806$		0			0
$807$	5.52052	−	6.92251i	0.194331	−	0.243684i
$808$		0			0
$809$	11.5117	+	5.54373i	0.404729	+	0.194907i	0.625162	−	0.780495i	$-0.285033\pi$
$809$	11.5117	+	5.54373i	0.404729	+	0.194907i	−0.220433	+	0.975402i	$0.570747\pi$
$810$		0			0
$811$	−1.73729	+	2.17849i	−0.0610045	+	0.0764973i	−0.811398	−	0.584495i	$-0.801293\pi$
$811$	−1.73729	+	2.17849i	−0.0610045	+	0.0764973i	0.750393	+	0.660992i	$0.229864\pi$
$812$		0			0
$813$	0.621328	+	0.779121i	0.0217909	+	0.0273250i
$814$		0			0
$815$	7.59754			0.266130
$816$		0			0
$817$	−2.46786	−	10.8124i	−0.0863395	−	0.378278i
$818$		0			0
$819$	5.15356	−	0.336160i	0.180080	−	0.0117464i
$820$		0			0
$821$	15.9207	+	19.9640i	0.555638	+	0.696748i	0.977745	−	0.209798i	$-0.0672808\pi$
$821$	15.9207	+	19.9640i	0.555638	+	0.696748i	−0.422107	+	0.906546i	$0.638709\pi$
$822$		0			0
$823$	3.12060	+	13.6722i	0.108777	+	0.476584i	0.999746	+	0.0225202i	$0.00716900\pi$
$823$	3.12060	+	13.6722i	0.108777	+	0.476584i	−0.890969	+	0.454064i	$0.849974\pi$
$824$		0			0
$825$	9.37439	−	41.0719i	0.326374	−	1.42994i
$826$		0			0
$827$	3.84959	+	16.8661i	0.133863	+	0.586493i	0.996712	+	0.0810305i	$0.0258211\pi$
$827$	3.84959	+	16.8661i	0.133863	+	0.586493i	−0.862848	+	0.505463i	$0.831322\pi$
$828$		0			0
$829$	−11.0787	+	13.8923i	−0.384781	+	0.482500i	−0.936070	−	0.351815i	$-0.885565\pi$
$829$	−11.0787	+	13.8923i	−0.384781	+	0.482500i	0.551289	+	0.834314i	$0.314136\pi$
$830$		0			0
$831$	−4.94262	+	2.38024i	−0.171458	+	0.0825697i
$832$		0			0
$833$	36.2490	+	34.9618i	1.25595	+	1.21136i
$834$		0			0
$835$	−40.2971	+	19.4061i	−1.39454	+	0.671575i
$836$		0			0
$837$	−3.19822	+	4.01045i	−0.110547	+	0.138621i
$838$		0			0
$839$	6.36277	+	27.8771i	0.219667	+	0.962425i	0.957724	+	0.287687i	$0.0928863\pi$
$839$	6.36277	+	27.8771i	0.219667	+	0.962425i	−0.738057	+	0.674738i	$0.764257\pi$
$840$		0			0
$841$	−0.0841383	+	0.368634i	−0.00290132	+	0.0127115i
$842$		0			0
$843$	0.160715	+	0.704138i	0.00553532	+	0.0242518i
$844$		0			0
$845$	−20.5429	−	25.7599i	−0.706696	−	0.886169i
$846$		0			0
$847$	26.8530	−	38.5798i	0.922681	−	1.32562i
$848$		0			0
$849$	−1.48704	−	6.51515i	−0.0510351	−	0.223599i
$850$		0			0
$851$	51.7767			1.77488
$852$		0			0
$853$	−29.7166	−	37.2634i	−1.01748	−	1.27587i	−0.960730	−	0.277485i	$-0.910499\pi$
$853$	−29.7166	−	37.2634i	−1.01748	−	1.27587i	−0.0567456	−	0.998389i	$-0.518072\pi$
$854$		0			0
$855$	−4.31308	+	5.40843i	−0.147504	+	0.184965i
$856$		0			0
$857$	30.9985	+	14.9281i	1.05889	+	0.509934i	0.880510	−	0.474028i	$-0.157200\pi$
$857$	30.9985	+	14.9281i	1.05889	+	0.509934i	0.178379	+	0.983962i	$0.442915\pi$
$858$		0			0
$859$	−29.6861	+	37.2251i	−1.01288	+	1.27011i	−0.0504021	+	0.998729i	$0.516050\pi$
$859$	−29.6861	+	37.2251i	−1.01288	+	1.27011i	−0.962473	+	0.271376i	$0.912521\pi$
$860$		0			0
$861$	−19.1038	−	7.71156i	−0.651056	−	0.262809i
$862$		0			0
$863$	36.5214			1.24320			0.621602	−	0.783333i	$-0.286482\pi$
$863$	36.5214			1.24320			0.621602	+	0.783333i	$0.286482\pi$
$864$		0			0
$865$	50.7071	+	63.5847i	1.72409	+	2.16195i
$866$		0			0
$867$	−31.3191	−	15.0825i	−1.06365	−	0.512228i
$868$		0			0
$869$	54.4694	−	26.2311i	1.84775	−	0.889828i
$870$		0			0
$871$	−22.1877	+	10.6850i	−0.751801	+	0.362048i
$872$		0			0
$873$	0.367565	+	0.177010i	0.0124402	+	0.00599088i
$874$		0			0
$875$	15.4700	−	22.2258i	0.522981	−	0.751369i
$876$		0			0
$877$	−4.45199	+	19.5054i	−0.150333	+	0.658652i	0.842455	+	0.538767i	$0.181110\pi$
$877$	−4.45199	+	19.5054i	−0.150333	+	0.658652i	−0.992788	+	0.119885i	$0.961747\pi$
$878$		0			0
$879$	3.61059	−	15.8190i	0.121782	−	0.533563i
$880$		0			0
$881$	−3.81842			−0.128646			−0.0643229	−	0.997929i	$-0.520489\pi$
$881$	−3.81842			−0.128646			−0.0643229	+	0.997929i	$0.520489\pi$
$882$		0			0
$883$	−42.2539			−1.42196			−0.710978	−	0.703214i	$-0.751747\pi$
$883$	−42.2539			−1.42196			−0.710978	+	0.703214i	$0.751747\pi$
$884$		0			0
$885$	1.44441	−	6.32837i	0.0485533	−	0.212726i
$886$		0			0
$887$	10.6092	−	46.4819i	0.356221	−	1.56071i	−0.406297	−	0.913741i	$-0.633180\pi$
$887$	10.6092	−	46.4819i	0.356221	−	1.56071i	0.762518	−	0.646967i	$-0.223963\pi$
$888$		0			0
$889$	−24.1672	−	26.5562i	−0.810541	−	0.890665i
$890$		0			0
$891$	4.83228	+	2.32710i	0.161887	+	0.0779608i
$892$		0			0
$893$	−20.3299	+	9.79035i	−0.680313	+	0.327622i
$894$		0			0
$895$	2.63224	−	1.26762i	0.0879859	−	0.0423718i
$896$		0			0
$897$	14.1085	+	6.79430i	0.471070	+	0.226855i
$898$		0			0
$899$	17.3349	+	21.7373i	0.578151	+	0.724978i
$900$		0			0
$901$	50.6294			1.68671
$902$		0			0
$903$	−15.1757	+	0.989894i	−0.505017	+	0.0329416i
$904$		0			0
$905$	−21.7742	+	27.3040i	−0.723799	+	0.907615i
$906$		0			0
$907$	−28.6306	−	13.7878i	−0.950663	−	0.457815i	−0.106745	−	0.994286i	$-0.534043\pi$
$907$	−28.6306	−	13.7878i	−0.950663	−	0.457815i	−0.843919	+	0.536471i	$0.819757\pi$
$908$		0			0
$909$	−6.82158	+	8.55400i	−0.226258	+	0.283718i
$910$		0			0
$911$	0.297056	+	0.372497i	0.00984191	+	0.0123414i	0.786728	−	0.617300i	$-0.211773\pi$
$911$	0.297056	+	0.372497i	0.00984191	+	0.0123414i	−0.776886	+	0.629641i	$0.783202\pi$
$912$		0			0
$913$	11.2828			0.373406
$914$		0			0
$915$	11.0155	+	48.2620i	0.364161	+	1.59549i
$916$		0			0
$917$	8.05653	+	27.0437i	0.266050	+	0.893063i
$918$		0			0
$919$	25.0034	+	31.3533i	0.824788	+	1.03425i	0.998774	+	0.0495029i	$0.0157637\pi$
$919$	25.0034	+	31.3533i	0.824788	+	1.03425i	−0.173986	+	0.984748i	$0.555665\pi$
$920$		0			0
$921$	5.71787	+	25.0516i	0.188410	+	0.825480i
$922$		0			0
$923$	1.76948	−	7.75259i	0.0582430	−	0.255179i
$924$		0			0
$925$	11.2809	+	49.4249i	0.370914	+	1.62508i
$926$		0			0
$927$	7.16107	−	8.97970i	0.235201	−	0.294932i
$928$		0			0
$929$	−19.2570	+	9.27370i	−0.631803	+	0.304260i	−0.722241	−	0.691642i	$-0.756888\pi$
$929$	−19.2570	+	9.27370i	−0.631803	+	0.304260i	0.0904377	+	0.995902i	$0.471173\pi$
$930$		0			0
$931$	−13.3915	+	1.75449i	−0.438889	+	0.0575010i
$932$		0			0
$933$	14.4601	−	6.96364i	0.473404	−	0.227979i
$934$		0			0
$935$	−86.2594	+	108.166i	−2.82098	+	3.53740i
$936$		0			0
$937$	0.114085	+	0.499840i	0.00372700	+	0.0163291i	0.976757	−	0.214349i	$-0.0687629\pi$
$937$	0.114085	+	0.499840i	0.00372700	+	0.0163291i	−0.973030	+	0.230678i	$0.925906\pi$
$938$		0			0
$939$	−2.36771	+	10.3736i	−0.0772672	+	0.338530i
$940$		0			0
$941$	1.56869	+	6.87289i	0.0511379	+	0.224050i	0.994039	−	0.109022i	$-0.0347719\pi$
$941$	1.56869	+	6.87289i	0.0511379	+	0.224050i	−0.942901	+	0.333072i	$0.891915\pi$
$942$		0			0
$943$	−38.9468	−	48.8377i	−1.26828	−	1.59037i
$944$		0			0
$945$	6.38458	+	7.01571i	0.207690	+	0.228221i
$946$		0			0
$947$	−11.8462	−	51.9016i	−0.384950	−	1.68658i	−0.681709	−	0.731623i	$-0.738763\pi$
$947$	−11.8462	−	51.9016i	−0.384950	−	1.68658i	0.296760	−	0.954952i	$-0.404094\pi$
$948$		0			0
$949$	2.78488			0.0904011
$950$		0			0
$951$	7.06628	+	8.86084i	0.229140	+	0.287332i
$952$		0			0
$953$	1.38647	−	1.73858i	0.0449121	−	0.0563180i	−0.758868	−	0.651244i	$-0.774247\pi$
$953$	1.38647	−	1.73858i	0.0449121	−	0.0563180i	0.803780	+	0.594926i	$0.202819\pi$
$954$		0			0
$955$	−0.735600	−	0.354246i	−0.0238035	−	0.0114631i
$956$		0			0
$957$	18.1252	−	22.7283i	0.585905	−	0.734702i
$958$		0			0
$959$	3.64785	+	12.2449i	0.117795	+	0.395409i
$960$		0			0
$961$	−4.68769			−0.151216
$962$		0			0
$963$	6.02641	+	7.55688i	0.194198	+	0.243517i
$964$		0			0
$965$	48.0402	+	23.1349i	1.54647	+	0.744740i
$966$		0			0
$967$	−14.6910	+	7.07482i	−0.472431	+	0.227511i	−0.654922	−	0.755697i	$-0.727298\pi$
$967$	−14.6910	+	7.07482i	−0.472431	+	0.227511i	0.182490	+	0.983208i	$0.441584\pi$
$968$		0			0
$969$	12.5066	−	6.02288i	0.401771	−	0.193483i
$970$		0			0
$971$	−3.69015	−	1.77708i	−0.118423	−	0.0570293i	0.373734	−	0.927536i	$-0.378077\pi$
$971$	−3.69015	−	1.77708i	−0.118423	−	0.0570293i	−0.492157	+	0.870506i	$0.663791\pi$
$972$		0			0
$973$	6.12156	−	38.1112i	0.196248	−	1.22179i
$974$		0			0
$975$	−3.41178	+	14.9480i	−0.109265	+	0.478719i
$976$		0			0
$977$	1.74761	−	7.65679i	0.0559111	−	0.244962i	−0.939248	−	0.343239i	$-0.888476\pi$
$977$	1.74761	−	7.65679i	0.0559111	−	0.244962i	0.995159	+	0.0982767i	$0.0313330\pi$
$978$		0			0
$979$	29.6804			0.948591
$980$		0			0
$981$	−8.96591			−0.286259
$982$		0			0
$983$	−5.52673	+	24.2142i	−0.176275	+	0.772312i	0.807054	+	0.590478i	$0.201061\pi$
$983$	−5.52673	+	24.2142i	−0.176275	+	0.772312i	−0.983329	+	0.181834i	$0.941797\pi$
$984$		0			0
$985$	9.18773	−	40.2541i	0.292746	−	1.28260i
$986$		0			0
$987$	8.83414	+	29.6540i	0.281194	+	0.943896i
$988$		0			0
$989$	−41.5454	−	20.0072i	−1.32107	−	0.636193i
$990$		0			0
$991$	18.0562	−	8.69539i	0.573573	−	0.276218i	−0.124530	−	0.992216i	$-0.539742\pi$
$991$	18.0562	−	8.69539i	0.573573	−	0.276218i	0.698103	+	0.715998i	$0.254028\pi$
$992$		0			0
$993$	−23.5059	+	11.3199i	−0.745938	+	0.359225i
$994$		0			0
$995$	63.7004	+	30.6765i	2.01944	+	0.972510i
$996$		0			0
$997$	15.7014	+	19.6889i	0.497267	+	0.623553i	0.965610	−	0.259993i	$-0.0837204\pi$
$997$	15.7014	+	19.6889i	0.497267	+	0.623553i	−0.468343	+	0.883547i	$0.655149\pi$
$998$		0			0
$999$	−6.45421			−0.204202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.q.a.169.2	✓	30
49.29	even	7	inner	588.2.q.a.421.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.q.a.169.2	✓	30	1.1	even	1	trivial
588.2.q.a.421.2	yes	30	49.29	even	7	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.q (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{3} +(-0.797815 + 3.49545i) q^{5} +(2.64014 - 0.172213i) q^{7} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{3} +(-0.797815 + 3.49545i) q^{5} +(2.64014 - 0.172213i) q^{7} +(-0.900969 - 0.433884i) q^{9} +(4.83228 - 2.32710i) q^{11} +(-1.75869 + 0.846942i) q^{13} +(-3.23029 - 1.55562i) q^{15} +(4.48573 + 5.62493i) q^{17} -1.92942 q^{19} +(-0.419591 + 2.61227i) q^{21} +(-5.00173 + 6.27197i) q^{23} +(-7.07685 - 3.40803i) q^{25} +(0.623490 - 0.781831i) q^{27} +(-3.37941 - 4.23765i) q^{29} -5.12955 q^{31} +(1.19347 + 5.22895i) q^{33} +(-1.50438 + 9.36589i) q^{35} +(-4.02413 - 5.04610i) q^{37} +(-0.434361 - 1.90306i) q^{39} +(-1.73269 + 7.59143i) q^{41} +(1.27907 + 5.60396i) q^{43} +(2.23543 - 2.80314i) q^{45} +(10.5368 - 5.07424i) q^{47} +(6.94069 - 0.909333i) q^{49} +(-6.48207 + 3.12160i) q^{51} +(4.38761 - 5.50189i) q^{53} +(4.27902 + 18.7476i) q^{55} +(0.429337 - 1.88105i) q^{57} +(0.402864 + 1.76506i) q^{59} +(-8.60858 - 10.7948i) q^{61} +(-2.45340 - 0.990355i) q^{63} +(-1.55734 - 6.82314i) q^{65} +12.6160 q^{67} +(-5.00173 - 6.27197i) q^{69} +(-2.53994 + 3.18498i) q^{71} +(-1.28539 - 0.619013i) q^{73} +(4.89733 - 6.14106i) q^{75} +(12.3571 - 6.97606i) q^{77} +11.2720 q^{79} +(0.623490 + 0.781831i) q^{81} +(1.89533 + 0.912741i) q^{83} +(-23.2405 + 11.1920i) q^{85} +(4.88339 - 2.35172i) q^{87} +(4.98584 + 2.40105i) q^{89} +(-4.49734 + 2.53892i) q^{91} +(1.14143 - 5.00094i) q^{93} +(1.53932 - 6.74421i) q^{95} -0.407966 q^{97} -5.36342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 5 q^{3} - q^{7} - 5 q^{9}+O(q^{10}) \) 30 * q - 5 * q^3 - q^7 - 5 * q^9	\( 30 q - 5 q^{3} - q^{7} - 5 q^{9} + 13 q^{11} - 2 q^{13} - 7 q^{15} + 5 q^{17} - 12 q^{19} - 8 q^{21} + 8 q^{23} - 27 q^{25} - 5 q^{27} - 4 q^{29} - 10 q^{31} - 8 q^{33} + 7 q^{35} + 3 q^{37} + 12 q^{39} + 23 q^{41} + 4 q^{43} + 7 q^{45} + 21 q^{47} + 13 q^{49} - 2 q^{51} + 14 q^{53} + 21 q^{55} - 12 q^{57} + 35 q^{59} + 21 q^{61} + 6 q^{63} + 33 q^{65} - 48 q^{67} + 8 q^{69} - 20 q^{71} + 3 q^{73} - 6 q^{75} + 55 q^{77} - 40 q^{79} - 5 q^{81} - 4 q^{83} - 8 q^{85} + 3 q^{87} + 4 q^{89} - 44 q^{91} - 17 q^{93} - 2 q^{95} - 102 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q - 5 * q^3 - q^7 - 5 * q^9 + 13 * q^11 - 2 * q^13 - 7 * q^15 + 5 * q^17 - 12 * q^19 - 8 * q^21 + 8 * q^23 - 27 * q^25 - 5 * q^27 - 4 * q^29 - 10 * q^31 - 8 * q^33 + 7 * q^35 + 3 * q^37 + 12 * q^39 + 23 * q^41 + 4 * q^43 + 7 * q^45 + 21 * q^47 + 13 * q^49 - 2 * q^51 + 14 * q^53 + 21 * q^55 - 12 * q^57 + 35 * q^59 + 21 * q^61 + 6 * q^63 + 33 * q^65 - 48 * q^67 + 8 * q^69 - 20 * q^71 + 3 * q^73 - 6 * q^75 + 55 * q^77 - 40 * q^79 - 5 * q^81 - 4 * q^83 - 8 * q^85 + 3 * q^87 + 4 * q^89 - 44 * q^91 - 17 * q^93 - 2 * q^95 - 102 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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