LMFDB - Embedded newform 572.2.j.a.463.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(463,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("572.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.8
Character	$\chi$	$=$	572.463
Dual form			572.2.j.a.551.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34567 + 0.434926i) q^{2} +0.845393i q^{3} +(1.62168 - 1.17054i) q^{4} +(1.03191 + 1.03191i) q^{5} +(-0.367683 - 1.13762i) q^{6} +(-2.79241 - 2.79241i) q^{7} +(-1.67316 + 2.28047i) q^{8} +2.28531 q^{9} +O(q^{10})$	\(q+(-1.34567 + 0.434926i) q^{2} +0.845393i q^{3} +(1.62168 - 1.17054i) q^{4} +(1.03191 + 1.03191i) q^{5} +(-0.367683 - 1.13762i) q^{6} +(-2.79241 - 2.79241i) q^{7} +(-1.67316 + 2.28047i) q^{8} +2.28531 q^{9} +(-1.83742 - 0.939812i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(0.989563 + 1.37096i) q^{12} +(3.09604 - 1.84784i) q^{13} +(4.97217 + 2.54319i) q^{14} +(-0.872370 + 0.872370i) q^{15} +(1.25969 - 3.79647i) q^{16} +0.392917i q^{17} +(-3.07529 + 0.993940i) q^{18} +(2.19446 - 2.19446i) q^{19} +(2.88132 + 0.465540i) q^{20} +(2.36069 - 2.36069i) q^{21} +(1.25907 + 0.643997i) q^{22} +1.55405 q^{23} +(-1.92789 - 1.41447i) q^{24} -2.87032i q^{25} +(-3.36259 + 3.83314i) q^{26} +4.46816i q^{27} +(-7.79702 - 1.25978i) q^{28} +4.02495 q^{29} +(0.794510 - 1.55334i) q^{30} +(3.20923 - 3.20923i) q^{31} +(-0.0439501 + 5.65668i) q^{32} +(0.597783 - 0.597783i) q^{33} +(-0.170890 - 0.528738i) q^{34} -5.76304i q^{35} +(3.70604 - 2.67504i) q^{36} +(-3.83921 + 3.83921i) q^{37} +(-1.99860 + 3.90746i) q^{38} +(1.56215 + 2.61737i) q^{39} +(-4.07979 + 0.626694i) q^{40} +(-7.36842 - 7.36842i) q^{41} +(-2.14999 + 4.20344i) q^{42} +0.971508 q^{43} +(-1.97439 - 0.319006i) q^{44} +(2.35824 + 2.35824i) q^{45} +(-2.09125 + 0.675897i) q^{46} +(9.08741 + 9.08741i) q^{47} +(3.20951 + 1.06493i) q^{48} +8.59514i q^{49} +(1.24838 + 3.86252i) q^{50} -0.332169 q^{51} +(2.85783 - 6.62064i) q^{52} +9.45347 q^{53} +(-1.94332 - 6.01269i) q^{54} -1.45934i q^{55} +(11.0402 - 1.69587i) q^{56} +(1.85518 + 1.85518i) q^{57} +(-5.41627 + 1.75055i) q^{58} +(0.622308 + 0.622308i) q^{59} +(-0.393564 + 2.43584i) q^{60} +11.5221 q^{61} +(-2.92280 + 5.71436i) q^{62} +(-6.38153 - 6.38153i) q^{63} +(-2.40109 - 7.63117i) q^{64} +(5.10165 + 1.28803i) q^{65} +(-0.544430 + 1.06441i) q^{66} +(3.32915 - 3.32915i) q^{67} +(0.459923 + 0.637185i) q^{68} +1.31378i q^{69} +(2.50649 + 7.75518i) q^{70} +(5.20583 - 5.20583i) q^{71} +(-3.82368 + 5.21159i) q^{72} +(-3.20539 + 3.20539i) q^{73} +(3.49656 - 6.83611i) q^{74} +2.42655 q^{75} +(0.990017 - 6.12741i) q^{76} +3.94907i q^{77} +(-3.24051 - 2.84271i) q^{78} +11.0952i q^{79} +(5.21751 - 2.61773i) q^{80} +3.07858 q^{81} +(13.1202 + 6.71078i) q^{82} +(-0.757106 + 0.757106i) q^{83} +(1.06501 - 6.59154i) q^{84} +(-0.405455 + 0.405455i) q^{85} +(-1.30733 + 0.422534i) q^{86} +3.40266i q^{87} +(2.79564 - 0.429436i) q^{88} +(0.0982661 - 0.0982661i) q^{89} +(-4.19908 - 2.14776i) q^{90} +(-13.8054 - 3.48550i) q^{91} +(2.52017 - 1.81907i) q^{92} +(2.71306 + 2.71306i) q^{93} +(-16.1810 - 8.27635i) q^{94} +4.52898 q^{95} +(-4.78212 - 0.0371551i) q^{96} +(-0.535687 - 0.535687i) q^{97} +(-3.73825 - 11.5663i) q^{98} +(-1.61596 - 1.61596i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.34567	+	0.434926i	−0.951536	+	0.307539i
$2$	−1.34567	+	0.434926i	−0.951536	+	0.307539i
$3$			0.845393i			0.488088i	0.969764	+	0.244044i	$0.0784741\pi$
$3$			0.845393i			0.488088i	−0.969764	+	0.244044i	$0.921526\pi$
$4$	1.62168	−	1.17054i	0.810840	−	0.585268i
$5$	1.03191	+	1.03191i	0.461485	+	0.461485i	0.899142	−	0.437657i	$-0.144192\pi$
$5$	1.03191	+	1.03191i	0.461485	+	0.461485i	−0.437657	+	0.899142i	$0.644192\pi$
$6$	−0.367683	−	1.13762i	−0.150106	−	0.464433i
$7$	−2.79241	−	2.79241i	−1.05543	−	1.05543i	−0.998371	−	0.0570622i	$-0.981827\pi$
$7$	−2.79241	−	2.79241i	−1.05543	−	1.05543i	−0.0570622	−	0.998371i	$-0.518173\pi$
$8$	−1.67316	+	2.28047i	−0.591550	+	0.806268i
$9$	2.28531			0.761770
$10$	−1.83742	−	0.939812i	−0.581043	−	0.297195i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	0.989563	+	1.37096i	0.285662	+	0.395761i
$13$	3.09604	−	1.84784i	0.858688	−	0.512499i
$13$	3.09604	−	1.84784i	0.858688	−	0.512499i
$14$	4.97217	+	2.54319i	1.32887	+	0.679695i
$15$	−0.872370	+	0.872370i	−0.225245	+	0.225245i
$16$	1.25969	−	3.79647i	0.314922	−	0.949117i
$17$			0.392917i			0.0952963i	0.998864	+	0.0476482i	$0.0151726\pi$
$17$			0.392917i			0.0952963i	−0.998864	+	0.0476482i	$0.984827\pi$
$18$	−3.07529	+	0.993940i	−0.724852	+	0.234274i
$19$	2.19446	−	2.19446i	0.503444	−	0.503444i	−0.409062	−	0.912506i	$-0.634144\pi$
$19$	2.19446	−	2.19446i	0.503444	−	0.503444i	0.912506	+	0.409062i	$0.134144\pi$
$20$	2.88132	+	0.465540i	0.644282	+	0.104098i
$21$	2.36069	−	2.36069i	0.515144	−	0.515144i
$22$	1.25907	+	0.643997i	0.268436	+	0.137301i
$23$	1.55405			0.324042			0.162021	−	0.986787i	$-0.448199\pi$
$23$	1.55405			0.324042			0.162021	+	0.986787i	$0.448199\pi$
$24$	−1.92789	−	1.41447i	−0.393530	−	0.288728i
$25$		−	2.87032i		−	0.574064i
$26$	−3.36259	+	3.83314i	−0.659459	+	0.751741i
$27$			4.46816i			0.859898i
$28$	−7.79702	−	1.25978i	−1.47350	−	0.238076i
$29$	4.02495			0.747414			0.373707	−	0.927547i	$-0.378087\pi$
$29$	4.02495			0.747414			0.373707	+	0.927547i	$0.378087\pi$
$30$	0.794510	−	1.55334i	0.145057	−	0.283600i
$31$	3.20923	−	3.20923i	0.576395	−	0.576395i	−0.357513	−	0.933908i	$-0.616375\pi$
$31$	3.20923	−	3.20923i	0.576395	−	0.576395i	0.933908	+	0.357513i	$0.116375\pi$
$32$	−0.0439501	+	5.65668i	−0.00776935	+	0.999970i
$33$	0.597783	−	0.597783i	0.104061	−	0.104061i
$34$	−0.170890	−	0.528738i	−0.0293073	−	0.0906779i
$35$		−	5.76304i		−	0.974132i
$36$	3.70604	−	2.67504i	0.617674	−	0.445840i
$37$	−3.83921	+	3.83921i	−0.631163	+	0.631163i	−0.948360	−	0.317197i	$-0.897258\pi$
$37$	−3.83921	+	3.83921i	−0.631163	+	0.631163i	0.317197	+	0.948360i	$0.397258\pi$
$38$	−1.99860	+	3.90746i	−0.324216	+	0.633873i
$39$	1.56215	+	2.61737i	0.250144	+	0.419115i
$40$	−4.07979	+	0.626694i	−0.645072	+	0.0990890i
$41$	−7.36842	−	7.36842i	−1.15075	−	1.15075i	−0.986402	−	0.164352i	$-0.947447\pi$
$41$	−7.36842	−	7.36842i	−1.15075	−	1.15075i	−0.164352	−	0.986402i	$-0.552553\pi$
$42$	−2.14999	+	4.20344i	−0.331751	+	0.648604i
$43$	0.971508			0.148154			0.0740768	−	0.997253i	$-0.476399\pi$
$43$	0.971508			0.148154			0.0740768	+	0.997253i	$0.476399\pi$
$44$	−1.97439	−	0.319006i	−0.297651	−	0.0480920i
$45$	2.35824	+	2.35824i	0.351545	+	0.351545i
$46$	−2.09125	+	0.675897i	−0.308338	+	0.0996555i
$47$	9.08741	+	9.08741i	1.32553	+	1.32553i	0.909221	+	0.416313i	$0.136678\pi$
$47$	9.08741	+	9.08741i	1.32553	+	1.32553i	0.416313	+	0.909221i	$0.363322\pi$
$48$	3.20951	+	1.06493i	0.463252	+	0.153710i
$49$			8.59514i			1.22788i
$50$	1.24838	+	3.86252i	0.176547	+	0.546242i
$51$	−0.332169			−0.0465130
$52$	2.85783	−	6.62064i	0.396309	−	0.918117i
$53$	9.45347			1.29853			0.649267	−	0.760561i	$-0.275076\pi$
$53$	9.45347			1.29853			0.649267	+	0.760561i	$0.275076\pi$
$54$	−1.94332	−	6.01269i	−0.264452	−	0.818224i
$55$		−	1.45934i		−	0.196778i
$56$	11.0402	−	1.69587i	1.47530	−	0.226620i
$57$	1.85518	+	1.85518i	0.245725	+	0.245725i
$58$	−5.41627	+	1.75055i	−0.711191	+	0.229859i
$59$	0.622308	+	0.622308i	0.0810176	+	0.0810176i	0.746454	−	0.665437i	$-0.231755\pi$
$59$	0.622308	+	0.622308i	0.0810176	+	0.0810176i	−0.665437	+	0.746454i	$0.731755\pi$
$60$	−0.393564	+	2.43584i	−0.0508089	+	0.314466i
$61$	11.5221			1.47525			0.737626	−	0.675209i	$-0.235947\pi$
$61$	11.5221			1.47525			0.737626	+	0.675209i	$0.235947\pi$
$62$	−2.92280	+	5.71436i	−0.371196	+	0.725724i
$63$	−6.38153	−	6.38153i	−0.803998	−	0.803998i
$64$	−2.40109	−	7.63117i	−0.300137	−	0.953896i
$65$	5.10165	+	1.28803i	0.632781	+	0.159761i
$66$	−0.544430	+	1.06441i	−0.0670147	+	0.131020i
$67$	3.32915	−	3.32915i	0.406720	−	0.406720i	−0.473873	−	0.880593i	$-0.657144\pi$
$67$	3.32915	−	3.32915i	0.406720	−	0.406720i	0.880593	+	0.473873i	$0.157144\pi$
$68$	0.459923	+	0.637185i	0.0557739	+	0.0772701i
$69$			1.31378i			0.158161i
$70$	2.50649	+	7.75518i	0.299583	+	0.926921i
$71$	5.20583	−	5.20583i	0.617819	−	0.617819i	−0.327153	−	0.944971i	$-0.606089\pi$
$71$	5.20583	−	5.20583i	0.617819	−	0.617819i	0.944971	+	0.327153i	$0.106089\pi$
$72$	−3.82368	+	5.21159i	−0.450625	+	0.614191i
$73$	−3.20539	+	3.20539i	−0.375162	+	0.375162i	−0.869353	−	0.494191i	$-0.835464\pi$
$73$	−3.20539	+	3.20539i	−0.375162	+	0.375162i	0.494191	+	0.869353i	$0.335464\pi$
$74$	3.49656	−	6.83611i	0.406467	−	0.794681i
$75$	2.42655			0.280194
$76$	0.990017	−	6.12741i	0.113563	−	0.702862i
$77$			3.94907i			0.450038i
$78$	−3.24051	−	2.84271i	−0.366915	−	0.321874i
$79$			11.0952i			1.24831i	0.781302	+	0.624153i	$0.214556\pi$
$79$			11.0952i			1.24831i	−0.781302	+	0.624153i	$0.785444\pi$
$80$	5.21751	−	2.61773i	0.583335	−	0.292671i
$81$	3.07858			0.342065
$82$	13.1202	+	6.71078i	1.44888	+	0.741082i
$83$	−0.757106	+	0.757106i	−0.0831032	+	0.0831032i	−0.747436	−	0.664333i	$-0.768716\pi$
$83$	−0.757106	+	0.757106i	−0.0831032	+	0.0831032i	0.664333	+	0.747436i	$0.268716\pi$
$84$	1.06501	−	6.59154i	0.116202	−	0.719196i
$85$	−0.405455	+	0.405455i	−0.0439778	+	0.0439778i
$86$	−1.30733	+	0.422534i	−0.140973	+	0.0455630i
$87$			3.40266i			0.364804i
$88$	2.79564	−	0.429436i	0.298016	−	0.0457780i
$89$	0.0982661	−	0.0982661i	0.0104162	−	0.0104162i	−0.701880	−	0.712296i	$-0.747656\pi$
$89$	0.0982661	−	0.0982661i	0.0104162	−	0.0104162i	0.712296	+	0.701880i	$0.247656\pi$
$90$	−4.19908	−	2.14776i	−0.442622	−	0.226394i
$91$	−13.8054	−	3.48550i	−1.44720	−	0.365380i
$92$	2.52017	−	1.81907i	0.262746	−	0.189652i
$93$	2.71306	+	2.71306i	0.281331	+	0.281331i
$94$	−16.1810	−	8.27635i	−1.66895	−	0.853640i
$95$	4.52898			0.464663
$96$	−4.78212	−	0.0371551i	−0.488073	−	0.00379212i
$97$	−0.535687	−	0.535687i	−0.0543908	−	0.0543908i	0.679388	−	0.733779i	$-0.262245\pi$
$97$	−0.535687	−	0.535687i	−0.0543908	−	0.0543908i	−0.733779	+	0.679388i	$0.762245\pi$
$98$	−3.73825	−	11.5663i	−0.377620	−	1.16837i
$99$	−1.61596	−	1.61596i	−0.162410	−	0.162410i
$100$	−3.35981	−	4.65474i	−0.335981	−	0.465474i
$101$			4.05762i			0.403748i	0.979411	+	0.201874i	$0.0647032\pi$
$101$			4.05762i			0.403748i	−0.979411	+	0.201874i	$0.935297\pi$
$102$	0.446991	−	0.144469i	0.0442587	−	0.0143045i
$103$	−19.9787			−1.96856			−0.984278	−	0.176627i	$-0.943481\pi$
$103$	−19.9787			−1.96856			−0.984278	+	0.176627i	$0.943481\pi$
$104$	−0.966220	+	10.1522i	−0.0947457	+	0.995502i
$105$	4.87203			0.475462
$106$	−12.7213	+	4.11155i	−1.23560	+	0.399350i
$107$		−	7.57360i		−	0.732167i	−0.930582	−	0.366084i	$-0.880698\pi$
$107$		−	7.57360i		−	0.732167i	0.930582	−	0.366084i	$-0.119302\pi$
$108$	5.23015	+	7.24593i	0.503271	+	0.697240i
$109$	−9.29273	−	9.29273i	−0.890082	−	0.890082i	0.104448	−	0.994530i	$-0.466692\pi$
$109$	−9.29273	−	9.29273i	−0.890082	−	0.890082i	−0.994530	+	0.104448i	$0.966692\pi$
$110$	0.634705	+	1.96380i	0.0605168	+	0.187241i
$111$	−3.24564	−	3.24564i	−0.308063	−	0.308063i
$112$	−14.1189	+	7.08374i	−1.33411	+	0.669350i
$113$	−19.4955			−1.83398			−0.916992	−	0.398906i	$-0.869390\pi$
$113$	−19.4955			−1.83398			−0.916992	+	0.398906i	$0.869390\pi$
$114$	−3.30334	−	1.68960i	−0.309386	−	0.158246i
$115$	1.60364	+	1.60364i	0.149540	+	0.149540i
$116$	6.52718	−	4.71135i	0.606033	−	0.437438i
$117$	7.07542	−	4.22289i	0.654123	−	0.390406i
$118$	−1.10808	−	0.566767i	−0.102007	−	0.0521751i
$119$	1.09719	−	1.09719i	0.100579	−	0.100579i
$120$	−0.529802	−	3.44903i	−0.0483641	−	0.314851i
$121$			1.00000i			0.0909091i
$122$	−15.5050	+	5.01125i	−1.40376	+	0.453697i
$123$	6.22921	−	6.22921i	0.561669	−	0.561669i
$124$	1.44782	−	8.96087i	0.130018	−	0.804710i
$125$	8.12147	−	8.12147i	0.726406	−	0.726406i
$126$	11.3630	+	5.81197i	1.01229	+	0.517772i
$127$	3.10242			0.275295			0.137648	−	0.990481i	$-0.456046\pi$
$127$	3.10242			0.275295			0.137648	+	0.990481i	$0.456046\pi$
$128$	6.55008	+	9.22477i	0.578951	+	0.815362i
$129$			0.821306i			0.0723119i
$130$	−7.42536	+	0.485561i	−0.651247	+	0.0425866i
$131$			3.26599i			0.285351i	0.989770	+	0.142676i	$0.0455705\pi$
$131$			3.26599i			0.285351i	−0.989770	+	0.142676i	$0.954429\pi$
$132$	0.269686	−	1.66914i	0.0234731	−	0.145280i
$133$	−12.2557			−1.06270
$134$	−3.03202	+	5.92788i	−0.261926	+	0.512091i
$135$	−4.61075	+	4.61075i	−0.396830	+	0.396830i
$136$	−0.896035	−	0.657411i	−0.0768344	−	0.0563726i
$137$	−7.71695	+	7.71695i	−0.659303	+	0.659303i	−0.955215	−	0.295912i	$-0.904376\pi$
$137$	−7.71695	+	7.71695i	−0.659303	+	0.659303i	0.295912	+	0.955215i	$0.404376\pi$
$138$	−0.571398	−	1.76792i	−0.0486406	−	0.150496i
$139$		−	13.7391i		−	1.16533i	−0.812712	−	0.582666i	$-0.802009\pi$
$139$		−	13.7391i		−	1.16533i	0.812712	−	0.582666i	$-0.197991\pi$
$140$	−6.74585	−	9.34581i	−0.570128	−	0.789865i
$141$	−7.68243	+	7.68243i	−0.646977	+	0.646977i
$142$	−4.74121	+	9.26950i	−0.397873	+	0.777879i
$143$	−3.49585	−	0.882613i	−0.292338	−	0.0738078i
$144$	2.87878	−	8.67612i	0.239899	−	0.723010i
$145$	4.15339	+	4.15339i	0.344920	+	0.344920i
$146$	2.91930	−	5.70751i	0.241603	−	0.472357i
$147$	−7.26627			−0.599312
$148$	−1.73204	+	10.7199i	−0.142372	+	0.881172i
$149$	−3.14307	−	3.14307i	−0.257491	−	0.257491i	0.566542	−	0.824033i	$-0.308281\pi$
$149$	−3.14307	−	3.14307i	−0.257491	−	0.257491i	−0.824033	+	0.566542i	$0.808281\pi$
$150$	−3.26534	+	1.05537i	−0.266614	+	0.0861704i
$151$	−3.66000	−	3.66000i	−0.297846	−	0.297846i	0.542324	−	0.840170i	$-0.317545\pi$
$151$	−3.66000	−	3.66000i	−0.297846	−	0.297846i	−0.840170	+	0.542324i	$0.817545\pi$
$152$	1.33273	+	8.67608i	0.108098	+	0.703723i
$153$			0.897937i			0.0725939i
$154$	−1.71755	−	5.31416i	−0.138404	−	0.428227i
$155$	6.62328			0.531995
$156$	5.59704	+	2.41599i	0.448122	+	0.193434i
$157$	−12.8634			−1.02661			−0.513304	−	0.858207i	$-0.671579\pi$
$157$	−12.8634			−1.02661			−0.513304	+	0.858207i	$0.671579\pi$
$158$	−4.82558	−	14.9305i	−0.383902	−	1.18781i
$159$			7.99189i			0.633798i
$160$	−5.88255	+	5.79184i	−0.465056	+	0.457885i
$161$	−4.33955	−	4.33955i	−0.342005	−	0.342005i
$162$	−4.14277	+	1.33895i	−0.325487	+	0.105198i
$163$	−13.9597	−	13.9597i	−1.09341	−	1.09341i	−0.995162	−	0.0982464i	$-0.968677\pi$
$163$	−13.9597	−	13.9597i	−1.09341	−	1.09341i	−0.0982464	−	0.995162i	$-0.531323\pi$
$164$	−20.5742	−	3.32421i	−1.60658	−	0.259577i
$165$	1.23372			0.0960448
$166$	0.689533	−	1.34810i	0.0535182	−	0.104633i
$167$	12.9701	+	12.9701i	1.00366	+	1.00366i	0.999993	+	0.00366268i	$0.00116587\pi$
$167$	12.9701	+	12.9701i	1.00366	+	1.00366i	0.00366268	+	0.999993i	$0.498834\pi$
$168$	1.43368	+	9.33327i	0.110611	+	0.720077i
$169$	6.17097	−	11.4420i	0.474690	−	0.880153i
$170$	0.369268	−	0.721954i	0.0283216	−	0.0553713i
$171$	5.01503	−	5.01503i	0.383509	−	0.383509i
$172$	1.57547	−	1.13719i	0.120129	−	0.0867096i
$173$		−	18.8954i		−	1.43659i	−0.695739	−	0.718294i	$-0.744923\pi$
$173$		−	18.8954i		−	1.43659i	0.695739	−	0.718294i	$-0.255077\pi$
$174$	−1.47990	−	4.57888i	−0.112191	−	0.347124i
$175$	−8.01512	+	8.01512i	−0.605886	+	0.605886i
$176$	−3.57524	+	1.79377i	−0.269494	+	0.135211i
$177$	−0.526095	+	0.526095i	−0.0395437	+	0.0395437i
$178$	−0.0894958	+	0.174973i	−0.00670799	+	0.0131148i
$179$	13.6784			1.02237			0.511185	−	0.859471i	$-0.329207\pi$
$179$	13.6784			1.02237			0.511185	+	0.859471i	$0.329207\pi$
$180$	6.58471	+	1.06390i	0.490795	+	0.0792986i
$181$			17.4204i			1.29485i	0.762131	+	0.647423i	$0.224153\pi$
$181$			17.4204i			1.29485i	−0.762131	+	0.647423i	$0.775847\pi$
$182$	20.0935	−	1.31396i	1.48943	−	0.0973971i
$183$			9.74069i			0.720053i
$184$	−2.60017	+	3.54397i	−0.191687	+	0.261265i
$185$	−7.92345			−0.582544
$186$	−4.83087	−	2.47092i	−0.354217	−	0.181176i
$187$	0.277834	−	0.277834i	0.0203172	−	0.0203172i
$188$	25.3740	+	4.09972i	1.85059	+	0.299003i
$189$	12.4770	−	12.4770i	0.907565	−	0.907565i
$190$	−6.09453	+	1.96977i	−0.442144	+	0.142902i
$191$		−	10.0522i		−	0.727352i	−0.931526	−	0.363676i	$-0.881522\pi$
$191$		−	10.0522i		−	0.727352i	0.931526	−	0.363676i	$-0.118478\pi$
$192$	6.45133	−	2.02987i	0.465585	−	0.146493i
$193$	−12.7503	+	12.7503i	−0.917787	+	0.917787i	−0.996868	−	0.0790809i	$-0.974801\pi$
$193$	−12.7503	+	12.7503i	−0.917787	+	0.917787i	0.0790809	+	0.996868i	$0.474801\pi$
$194$	0.953845	+	0.487877i	0.0684821	+	0.0350275i
$195$	−1.08889	+	4.31289i	−0.0779774	+	0.308853i
$196$	10.0609	+	13.9386i	0.718637	+	0.995612i
$197$	3.05224	+	3.05224i	0.217463	+	0.217463i	0.807429	−	0.589965i	$-0.200859\pi$
$197$	3.05224	+	3.05224i	0.217463	+	0.217463i	−0.589965	+	0.807429i	$0.700859\pi$
$198$	2.87738	+	1.47173i	0.204486	+	0.104592i
$199$	13.9868			0.991498			0.495749	−	0.868466i	$-0.334894\pi$
$199$	13.9868			0.991498			0.495749	+	0.868466i	$0.334894\pi$
$200$	6.54568	+	4.80249i	0.462850	+	0.339588i
$201$	2.81444	+	2.81444i	0.198515	+	0.198515i
$202$	−1.76476	−	5.46023i	−0.124168	−	0.384181i
$203$	−11.2393	−	11.2393i	−0.788846	−	0.788846i
$204$	−0.538672	+	0.388816i	−0.0377146	+	0.0272226i
$205$		−	15.2071i		−	1.06211i
$206$	26.8848	−	8.68923i	1.87315	−	0.605407i
$207$	3.55149			0.246846
$208$	−3.11522	−	14.0817i	−0.216001	−	0.976393i
$209$	−3.10344			−0.214669
$210$	−6.55617	+	2.11897i	−0.452419	+	0.146223i
$211$			9.17173i			0.631408i	0.948858	+	0.315704i	$0.102241\pi$
$211$			9.17173i			0.631408i	−0.948858	+	0.315704i	$0.897759\pi$
$212$	15.3305	−	11.0656i	1.05290	−	0.759990i
$213$	4.40097	+	4.40097i	0.301550	+	0.301550i
$214$	3.29395	+	10.1916i	0.225170	+	0.696683i
$215$	1.00251	+	1.00251i	0.0683706	+	0.0683706i
$216$	−10.1895	−	7.47594i	−0.693309	−	0.508673i
$217$	−17.9230			−1.21669
$218$	16.5466	+	8.46334i	1.12068	+	0.573210i
$219$	−2.70981	−	2.70981i	−0.183112	−	0.183112i
$220$	−1.70821	−	2.36659i	−0.115168	−	0.159555i
$221$	0.726048	+	1.21649i	0.0488392	+	0.0818298i
$222$	5.77919	+	2.95597i	0.387874	+	0.198391i
$223$	14.3597	−	14.3597i	0.961596	−	0.961596i	−0.0376932	−	0.999289i	$-0.512001\pi$
$223$	14.3597	−	14.3597i	0.961596	−	0.961596i	0.999289	+	0.0376932i	$0.0120010\pi$
$224$	15.9185	−	15.6731i	1.06360	−	1.04720i
$225$		−	6.55957i		−	0.437305i
$226$	26.2346	−	8.47910i	1.74510	−	0.564021i
$227$	−13.3407	+	13.3407i	−0.885450	+	0.885450i	−0.994082	−	0.108632i	$-0.965353\pi$
$227$	−13.3407	+	13.3407i	−0.885450	+	0.885450i	0.108632	+	0.994082i	$0.465353\pi$
$228$	5.18007	+	0.836953i	0.343058	+	0.0554285i
$229$	−16.5520	+	16.5520i	−1.09379	+	1.09379i	−0.0986678	+	0.995120i	$0.531458\pi$
$229$	−16.5520	+	16.5520i	−1.09379	+	1.09379i	−0.995120	+	0.0986678i	$0.968542\pi$
$230$	−2.85545	−	1.46052i	−0.188283	−	0.0963035i
$231$	−3.33851			−0.219658
$232$	−6.73437	+	9.17878i	−0.442133	+	0.602616i
$233$			5.44861i			0.356950i	0.983944	+	0.178475i	$0.0571164\pi$
$233$			5.44861i			0.356950i	−0.983944	+	0.178475i	$0.942884\pi$
$234$	−7.68457	+	8.75992i	−0.502356	+	0.572654i
$235$			18.7548i			1.22343i
$236$	1.73762	+	0.280750i	0.113109	+	0.0182753i
$237$	−9.37978			−0.609282
$238$	−0.999261	+	1.95365i	−0.0647725	+	0.126636i
$239$	−8.16008	+	8.16008i	−0.527832	+	0.527832i	−0.919925	−	0.392093i	$-0.871751\pi$
$239$	−8.16008	+	8.16008i	−0.527832	+	0.527832i	0.392093	+	0.919925i	$0.371751\pi$
$240$	2.21301	+	4.41084i	0.142849	+	0.284719i
$241$	1.12200	−	1.12200i	0.0722741	−	0.0722741i	−0.670046	−	0.742320i	$-0.733726\pi$
$241$	1.12200	−	1.12200i	0.0722741	−	0.0722741i	0.742320	+	0.670046i	$0.233726\pi$
$242$	−0.434926	−	1.34567i	−0.0279581	−	0.0865032i
$243$			16.0071i			1.02686i
$244$	18.6851	−	13.4870i	1.19619	−	0.863418i
$245$	−8.86942	+	8.86942i	−0.566646	+	0.566646i
$246$	−5.67324	+	11.0917i	−0.361713	+	0.707183i
$247$	2.73913	−	10.8492i	0.174287	−	0.690316i
$248$	1.94901	+	12.6881i	0.123762	+	0.805695i
$249$	−0.640052	−	0.640052i	−0.0405616	−	0.0405616i
$250$	−7.39662	+	14.4611i	−0.467803	+	0.914599i
$251$	−9.98001			−0.629933			−0.314966	−	0.949103i	$-0.601993\pi$
$251$	−9.98001			−0.629933			−0.314966	+	0.949103i	$0.601993\pi$
$252$	−17.8186	−	2.87899i	−1.12247	−	0.181359i
$253$	−1.09888	−	1.09888i	−0.0690860	−	0.0690860i
$254$	−4.17485	+	1.34932i	−0.261953	+	0.0846640i
$255$	−0.342769	−	0.342769i	−0.0214650	−	0.0214650i
$256$	−12.8264	−	9.56474i	−0.801648	−	0.597797i
$257$		−	9.55083i		−	0.595765i	−0.954603	−	0.297882i	$-0.903720\pi$
$257$		−	9.55083i		−	0.595765i	0.954603	−	0.297882i	$-0.0962803\pi$
$258$	−0.357207	−	1.10521i	−0.0222387	−	0.0688074i
$259$	21.4413			1.33230
$260$	9.78093	−	3.88288i	0.606587	−	0.240806i
$261$	9.19826			0.569358
$262$	−1.42046	−	4.39496i	−0.0877565	−	0.271522i
$263$			18.1748i			1.12071i	0.828254	+	0.560353i	$0.189334\pi$
$263$			18.1748i			1.12071i	−0.828254	+	0.560353i	$0.810666\pi$
$264$	0.363042	+	2.36341i	0.0223437	+	0.145458i
$265$	9.75514	+	9.75514i	0.599253	+	0.599253i
$266$	16.4922	−	5.33031i	1.01120	−	0.326822i
$267$	0.0830734	+	0.0830734i	0.00508401	+	0.00508401i
$268$	1.50192	−	9.29569i	0.0917445	−	0.567825i
$269$	−17.9003			−1.09140			−0.545700	−	0.837980i	$-0.683736\pi$
$269$	−17.9003			−1.09140			−0.545700	+	0.837980i	$0.683736\pi$
$270$	4.19923	−	8.20989i	0.255557	−	0.499638i
$271$	10.9003	+	10.9003i	0.662146	+	0.662146i	0.955885	−	0.293740i	$-0.0948998\pi$
$271$	10.9003	+	10.9003i	0.662146	+	0.662146i	−0.293740	+	0.955885i	$0.594900\pi$
$272$	1.49170	+	0.494953i	0.0904474	+	0.0300109i
$273$	2.94662	−	11.6710i	0.178337	−	0.706358i
$274$	7.02820	−	13.7408i	0.424589	−	0.830112i
$275$	−2.02962	+	2.02962i	−0.122391	+	0.122391i
$276$	1.53783	+	2.13054i	0.0925666	+	0.128243i
$277$			1.99867i			0.120089i	0.998196	+	0.0600443i	$0.0191242\pi$
$277$			1.99867i			0.120089i	−0.998196	+	0.0600443i	$0.980876\pi$
$278$	5.97547	+	18.4883i	0.358385	+	1.10886i
$279$	7.33409	−	7.33409i	0.439081	−	0.439081i
$280$	13.1424	+	9.64247i	0.785412	+	0.576248i
$281$	0.505041	−	0.505041i	0.0301282	−	0.0301282i	−0.691882	−	0.722010i	$-0.743218\pi$
$281$	0.505041	−	0.505041i	0.0301282	−	0.0301282i	0.722010	+	0.691882i	$0.243218\pi$
$282$	6.99676	−	13.6793i	0.416651	−	0.814592i
$283$	−18.0066			−1.07038			−0.535190	−	0.844731i	$-0.679760\pi$
$283$	−18.0066			−1.07038			−0.535190	+	0.844731i	$0.679760\pi$
$284$	2.34858	−	14.5358i	0.139362	−	0.862541i
$285$			3.82876i			0.226796i
$286$	5.08815	−	0.332726i	0.300869	−	0.0196745i
$287$			41.1513i			2.42909i
$288$	−0.100440	+	12.9273i	−0.00591846	+	0.761747i
$289$	16.8456			0.990919
$290$	−7.39552	−	3.78269i	−0.434280	−	0.222127i
$291$	0.452866	−	0.452866i	0.0265475	−	0.0265475i
$292$	−1.44609	+	8.95013i	−0.0846259	+	0.523767i
$293$	4.81196	−	4.81196i	0.281118	−	0.281118i	−0.552437	−	0.833555i	$-0.686302\pi$
$293$	4.81196	−	4.81196i	0.281118	−	0.281118i	0.833555	+	0.552437i	$0.186302\pi$
$294$	9.77803	−	3.16028i	0.570266	−	0.184312i
$295$			1.28433i			0.0747768i
$296$	−2.33161	−	15.1788i	−0.135522	−	0.882251i
$297$	3.15947	−	3.15947i	0.183331	−	0.183331i
$298$	5.59655	+	2.86255i	0.324200	+	0.165823i
$299$	4.81141	−	2.87164i	0.278251	−	0.166071i
$300$	3.93508	−	2.84036i	0.227192	−	0.163988i
$301$	−2.71285	−	2.71285i	−0.156366	−	0.156366i
$302$	6.51699	+	3.33334i	0.375011	+	0.191812i
$303$	−3.43028			−0.197064
$304$	−5.56687	−	11.0955i	−0.319282	−	0.636373i
$305$	11.8898	+	11.8898i	0.680806	+	0.680806i
$306$	−0.390536	−	1.20833i	−0.0223255	−	0.0690757i
$307$	−7.97697	−	7.97697i	−0.455270	−	0.455270i	0.441829	−	0.897099i	$-0.354330\pi$
$307$	−7.97697	−	7.97697i	−0.455270	−	0.455270i	−0.897099	+	0.441829i	$0.854330\pi$
$308$	4.62253	+	6.40412i	0.263393	+	0.364909i
$309$		−	16.8898i		−	0.960828i
$310$	−8.91278	+	2.88063i	−0.506212	+	0.163609i
$311$	9.35290			0.530354			0.265177	−	0.964200i	$-0.414570\pi$
$311$	9.35290			0.530354			0.265177	+	0.964200i	$0.414570\pi$
$312$	−8.58256	−	0.816836i	−0.485892	−	0.0462442i
$313$	30.5023			1.72409			0.862046	−	0.506829i	$-0.169183\pi$
$313$	30.5023			1.72409			0.862046	+	0.506829i	$0.169183\pi$
$314$	17.3099	−	5.59460i	0.976854	−	0.315722i
$315$		−	13.1703i		−	0.742065i
$316$	12.9873	+	17.9928i	0.730593	+	1.01218i
$317$	−24.2811	−	24.2811i	−1.36376	−	1.36376i	−0.869069	−	0.494691i	$-0.835281\pi$
$317$	−24.2811	−	24.2811i	−1.36376	−	1.36376i	−0.494691	−	0.869069i	$-0.664719\pi$
$318$	−3.47588	−	10.7545i	−0.194918	−	0.603082i
$319$	−2.84607	−	2.84607i	−0.159349	−	0.159349i
$320$	5.39697	−	10.3524i	0.301700	−	0.578717i
$321$	6.40266			0.357362
$322$	7.72701	+	3.95224i	0.430609	+	0.220250i
$323$	0.862241	+	0.862241i	0.0479764	+	0.0479764i
$324$	4.99247	−	3.60359i	0.277360	−	0.200200i
$325$	−5.30389	−	8.88664i	−0.294207	−	0.492942i
$326$	24.8567	+	12.7138i	1.37668	+	0.704152i
$327$	7.85600	−	7.85600i	0.434438	−	0.434438i
$328$	29.1320	−	4.47495i	1.60854	−	0.247088i
$329$		−	50.7516i		−	2.79803i
$330$	−1.66018	+	0.536575i	−0.0913900	+	0.0295375i
$331$	4.96516	−	4.96516i	0.272910	−	0.272910i	−0.557361	−	0.830270i	$-0.688186\pi$
$331$	4.96516	−	4.96516i	0.272910	−	0.272910i	0.830270	+	0.557361i	$0.188186\pi$
$332$	−0.341563	+	2.11400i	−0.0187457	+	0.116021i
$333$	−8.77380	+	8.77380i	−0.480801	+	0.480801i
$334$	−23.0945	−	11.8125i	−1.26368	−	0.646351i
$335$	6.87076			0.375390
$336$	−5.98854	−	11.9360i	−0.326702	−	0.651162i
$337$			2.53533i			0.138108i	0.997613	+	0.0690542i	$0.0219981\pi$
$337$			2.53533i			0.138108i	−0.997613	+	0.0690542i	$0.978002\pi$
$338$	−3.32771	+	18.0811i	−0.181003	+	0.983482i
$339$		−	16.4814i		−	0.895145i
$340$	−0.182918	+	1.13212i	−0.00992014	+	0.0613977i
$341$	−4.53854			−0.245776
$342$	−4.56743	+	8.92976i	−0.246978	+	0.482866i
$343$	4.45429	−	4.45429i	0.240509	−	0.240509i
$344$	−1.62548	+	2.21550i	−0.0876403	+	0.119451i
$345$	−1.35571	+	1.35571i	−0.0729888	+	0.0729888i
$346$	8.21808	+	25.4270i	0.441807	+	1.36697i
$347$			34.7035i			1.86298i	0.363764	+	0.931491i	$0.381491\pi$
$347$			34.7035i			1.86298i	−0.363764	+	0.931491i	$0.618509\pi$
$348$	3.98294	+	5.51803i	0.213508	+	0.295797i
$349$	0.133334	−	0.133334i	0.00713719	−	0.00713719i	−0.703529	−	0.710666i	$-0.748394\pi$
$349$	0.133334	−	0.133334i	0.00713719	−	0.00713719i	0.710666	+	0.703529i	$0.248394\pi$
$350$	7.29976	−	14.2717i	0.390189	−	0.762856i
$351$	8.25645	+	13.8336i	0.440697	+	0.738384i
$352$	4.03096	−	3.96880i	0.214851	−	0.211538i
$353$	6.33905	+	6.33905i	0.337394	+	0.337394i	0.855385	−	0.517992i	$-0.173320\pi$
$353$	6.33905	+	6.33905i	0.337394	+	0.337394i	−0.517992	+	0.855385i	$0.673320\pi$
$354$	0.479140	−	0.936764i	0.0254660	−	0.0497885i
$355$	10.7439			0.570227
$356$	0.0443321	−	0.274380i	0.00234960	−	0.0145421i
$357$	0.927553	+	0.927553i	0.0490913	+	0.0490913i
$358$	−18.4066	+	5.94908i	−0.972822	+	0.314418i
$359$	2.19656	+	2.19656i	0.115930	+	0.115930i	0.762692	−	0.646762i	$-0.223877\pi$
$359$	2.19656	+	2.19656i	0.115930	+	0.115930i	−0.646762	+	0.762692i	$0.723877\pi$
$360$	−9.32359	+	1.43219i	−0.491396	+	0.0754831i
$361$			9.36868i			0.493088i
$362$	−7.57656	−	23.4421i	−0.398215	−	1.23209i
$363$	−0.845393			−0.0443716
$364$	−26.4678	+	10.5073i	−1.38729	+	0.550733i
$365$	−6.61534			−0.346263
$366$	−4.23647	−	13.1078i	−0.221444	−	0.685156i
$367$		−	5.90517i		−	0.308248i	−0.988052	−	0.154124i	$-0.950745\pi$
$367$		−	5.90517i		−	0.308248i	0.988052	−	0.154124i	$-0.0492555\pi$
$368$	1.95762	−	5.89991i	0.102048	−	0.307554i
$369$	−16.8391	−	16.8391i	−0.876610	−	0.876610i
$370$	10.6624	−	3.44611i	0.554311	−	0.179155i
$371$	−26.3980	−	26.3980i	−1.37052	−	1.37052i
$372$	7.57545	+	1.22398i	0.392769	+	0.0634603i
$373$	5.31520			0.275211			0.137605	−	0.990487i	$-0.456059\pi$
$373$	5.31520			0.275211			0.137605	+	0.990487i	$0.456059\pi$
$374$	−0.253037	+	0.494712i	−0.0130842	+	0.0255809i
$375$	6.86583	+	6.86583i	0.354550	+	0.354550i
$376$	−35.9282	+	5.51891i	−1.85286	+	0.284616i
$377$	12.4614	−	7.43746i	0.641796	−	0.383049i
$378$	−11.3634	+	22.2165i	−0.584469	+	1.14269i
$379$	13.2339	−	13.2339i	0.679782	−	0.679782i	−0.280169	−	0.959951i	$-0.590390\pi$
$379$	13.2339	−	13.2339i	0.679782	−	0.679782i	0.959951	+	0.280169i	$0.0903904\pi$
$380$	7.34455	−	5.30133i	0.376768	−	0.271953i
$381$			2.62277i			0.134368i
$382$	4.37196	+	13.5270i	0.223689	+	0.692101i
$383$	−14.9150	+	14.9150i	−0.762122	+	0.762122i	−0.976706	−	0.214584i	$-0.931161\pi$
$383$	−14.9150	+	14.9150i	−0.762122	+	0.762122i	0.214584	+	0.976706i	$0.431161\pi$
$384$	−7.79855	+	5.53739i	−0.397968	+	0.282579i
$385$	−4.07509	+	4.07509i	−0.207686	+	0.207686i
$386$	11.6123	−	22.7032i	0.591052	−	1.15556i
$387$	2.22020			0.112859
$388$	−1.49575	−	0.241672i	−0.0759354	−	0.0122690i
$389$			34.1611i			1.73203i	0.500015	+	0.866017i	$0.333328\pi$
$389$			34.1611i			1.73203i	−0.500015	+	0.866017i	$0.666672\pi$
$390$	−0.410490	−	6.27734i	−0.0207860	−	0.317866i
$391$			0.610613i			0.0308800i
$392$	−19.6010	−	14.3810i	−0.989998	−	0.726351i
$393$	−2.76105			−0.139276
$394$	−5.43482	−	2.77982i	−0.273802	−	0.140046i
$395$	−11.4492	+	11.4492i	−0.576074	+	0.576074i
$396$	−4.51211	−	0.729029i	−0.226742	−	0.0366351i
$397$	17.7953	−	17.7953i	0.893122	−	0.893122i	−0.101694	−	0.994816i	$-0.532426\pi$
$397$	17.7953	−	17.7953i	0.893122	−	0.893122i	0.994816	+	0.101694i	$0.0324262\pi$
$398$	−18.8217	+	6.08321i	−0.943445	+	0.304924i
$399$		−	10.3609i		−	0.518692i
$400$	−10.8971	−	3.61571i	−0.544854	−	0.180786i
$401$	−16.8446	+	16.8446i	−0.841179	+	0.841179i	−0.989012	−	0.147833i	$-0.952770\pi$
$401$	−16.8446	+	16.8446i	−0.841179	+	0.841179i	0.147833	+	0.989012i	$0.452770\pi$
$402$	−5.01138	−	2.56324i	−0.249945	−	0.127843i
$403$	4.00577	−	15.8661i	0.199542	−	0.790345i
$404$	4.74959	+	6.58016i	0.236301	+	0.327375i
$405$	3.17682	+	3.17682i	0.157858	+	0.157858i
$406$	20.0127	+	10.2362i	0.993215	+	0.508014i
$407$	5.42947			0.269129
$408$	0.555771	−	0.757502i	0.0275148	−	0.0375019i
$409$	4.64165	+	4.64165i	0.229515	+	0.229515i	0.812490	−	0.582975i	$-0.198111\pi$
$409$	4.64165	+	4.64165i	0.229515	+	0.229515i	−0.582975	+	0.812490i	$0.698111\pi$
$410$	6.61396	+	20.4638i	0.326640	+	1.01064i
$411$	−6.52385	−	6.52385i	−0.321798	−	0.321798i
$412$	−32.3990	+	23.3857i	−1.59618	+	1.15213i
$413$		−	3.47548i		−	0.171017i
$414$	−4.77915	+	1.54463i	−0.234882	+	0.0759146i
$415$	−1.56253			−0.0767017
$416$	10.3166	+	17.5946i	0.505812	+	0.862644i
$417$	11.6149			0.568784
$418$	4.17622	−	1.34976i	0.204265	−	0.0660191i
$419$			14.9302i			0.729387i	0.931128	+	0.364694i	$0.118826\pi$
$419$			14.9302i			0.729387i	−0.931128	+	0.364694i	$0.881174\pi$
$420$	7.90088	−	5.70289i	0.385523	−	0.278273i
$421$	18.7300	+	18.7300i	0.912847	+	0.912847i	0.996495	−	0.0836486i	$-0.0266573\pi$
$421$	18.7300	+	18.7300i	0.912847	+	0.912847i	−0.0836486	+	0.996495i	$0.526657\pi$
$422$	−3.98902	−	12.3422i	−0.194182	−	0.600807i
$423$	20.7676	+	20.7676i	1.00975	+	1.00975i
$424$	−15.8171	+	21.5584i	−0.768148	+	1.04697i
$425$	1.12780			0.0547062
$426$	−7.83637	−	4.00818i	−0.379673	−	0.194197i
$427$	−32.1744	−	32.1744i	−1.55703	−	1.55703i
$428$	−8.86517	−	12.2819i	−0.428514	−	0.593670i
$429$	0.746155	−	2.95537i	0.0360247	−	0.142687i
$430$	−1.78507	−	0.913034i	−0.0860836	−	0.0440304i
$431$	−25.5889	+	25.5889i	−1.23257	+	1.23257i	−0.269600	+	0.962972i	$0.586892\pi$
$431$	−25.5889	+	25.5889i	−1.23257	+	1.23257i	−0.962972	+	0.269600i	$0.913108\pi$
$432$	16.9632	+	5.62850i	0.816145	+	0.270801i
$433$		−	27.3244i		−	1.31313i	−0.754272	−	0.656563i	$-0.772010\pi$
$433$		−	27.3244i		−	1.31313i	0.754272	−	0.656563i	$-0.227990\pi$
$434$	24.1185	−	7.79517i	1.15773	−	0.374180i
$435$	−3.51124	+	3.51124i	−0.168351	+	0.168351i
$436$	−25.9473	−	4.19235i	−1.24265	−	0.200777i
$437$	3.41031	−	3.41031i	0.163137	−	0.163137i
$438$	4.82509	+	2.46796i	0.230552	+	0.117923i
$439$	7.36871			0.351689			0.175845	−	0.984418i	$-0.443734\pi$
$439$	7.36871			0.351689			0.175845	+	0.984418i	$0.443734\pi$
$440$	3.32799	+	2.44171i	0.158656	+	0.116404i
$441$			19.6426i			0.935360i
$442$	−1.50611	−	1.32122i	−0.0716381	−	0.0628440i
$443$		−	7.60809i		−	0.361471i	−0.983532	−	0.180736i	$-0.942152\pi$
$443$		−	7.60809i		−	0.361471i	0.983532	−	0.180736i	$-0.0578479\pi$
$444$	−9.06254	−	1.46425i	−0.430089	−	0.0694902i
$445$	0.202804			0.00961382
$446$	−13.0781	+	25.5689i	−0.619265	+	1.21072i
$447$	2.65713	−	2.65713i	0.125678	−	0.125678i
$448$	−14.6045	+	28.0142i	−0.689999	+	1.32355i
$449$	−24.3883	+	24.3883i	−1.15095	+	1.15095i	−0.164592	+	0.986362i	$0.552631\pi$
$449$	−24.3883	+	24.3883i	−1.15095	+	1.15095i	−0.986362	+	0.164592i	$0.947369\pi$
$450$	2.85293	+	8.82705i	0.134488	+	0.416111i
$451$			10.4205i			0.490683i
$452$	−31.6155	+	22.8202i	−1.48707	+	1.07337i
$453$	3.09413	−	3.09413i	0.145375	−	0.145375i
$454$	12.1500	−	23.7544i	0.570227	−	1.11485i
$455$	−10.6492	−	17.8426i	−0.499241	−	0.836475i
$456$	−7.33470	+	1.12668i	−0.343479	+	0.0527615i
$457$	25.8599	+	25.8599i	1.20967	+	1.20967i	0.971132	+	0.238541i	$0.0766692\pi$
$457$	25.8599	+	25.8599i	1.20967	+	1.20967i	0.238541	+	0.971132i	$0.423331\pi$
$458$	15.0747	−	29.4725i	0.704396	−	1.37716i
$459$	−1.75562			−0.0819452
$460$	4.47772	+	0.723472i	0.208775	+	0.0337321i
$461$	9.42982	+	9.42982i	0.439191	+	0.439191i	0.891740	−	0.452549i	$-0.149485\pi$
$461$	9.42982	+	9.42982i	0.439191	+	0.439191i	−0.452549	+	0.891740i	$0.649485\pi$
$462$	4.49255	−	1.45200i	0.209012	−	0.0675534i
$463$	2.42552	+	2.42552i	0.112724	+	0.112724i	0.761219	−	0.648495i	$-0.224601\pi$
$463$	2.42552	+	2.42552i	0.112724	+	0.112724i	−0.648495	+	0.761219i	$0.724601\pi$
$464$	5.07019	−	15.2806i	0.235377	−	0.709384i
$465$			5.59927i			0.259660i
$466$	−2.36974	−	7.33205i	−0.109776	−	0.339651i
$467$	−16.4605			−0.761699			−0.380850	−	0.924637i	$-0.624368\pi$
$467$	−16.4605			−0.761699			−0.380850	+	0.924637i	$0.624368\pi$
$468$	6.53102	−	15.1302i	0.301897	−	0.699394i
$469$	−18.5927			−0.858531
$470$	−8.15694	−	25.2378i	−0.376251	−	1.16413i
$471$		−	10.8746i		−	0.501074i
$472$	−2.46038	+	0.377937i	−0.113248	+	0.0173959i
$473$	−0.686960	−	0.686960i	−0.0315864	−	0.0315864i
$474$	12.6221	−	4.07951i	0.579754	−	0.187378i
$475$	−6.29881	−	6.29881i	−0.289009	−	0.289009i
$476$	0.494988	−	3.06358i	0.0226877	−	0.140419i
$477$	21.6041			0.989185
$478$	7.43179	−	14.5298i	0.339922	−	0.664580i
$479$	18.0855	+	18.0855i	0.826347	+	0.826347i	0.987009	−	0.160662i	$-0.0513630\pi$
$479$	18.0855	+	18.0855i	0.826347	+	0.826347i	−0.160662	+	0.987009i	$0.551363\pi$
$480$	−4.89638	−	4.97306i	−0.223488	−	0.226988i
$481$	−4.79212	+	18.9806i	−0.218502	+	0.865442i
$482$	−1.02186	+	1.99783i	−0.0465443	+	0.0909985i
$483$	3.66863	−	3.66863i	0.166928	−	0.166928i
$484$	1.17054	+	1.62168i	0.0532062	+	0.0737127i
$485$		−	1.10556i		−	0.0502010i
$486$	−6.96190	−	21.5403i	−0.315798	−	0.977090i
$487$	−21.1320	+	21.1320i	−0.957583	+	0.957583i	−0.999136	−	0.0415537i	$-0.986769\pi$
$487$	−21.1320	+	21.1320i	−0.957583	+	0.957583i	0.0415537	+	0.999136i	$0.486769\pi$
$488$	−19.2783	+	26.2758i	−0.872686	+	1.18945i
$489$	11.8014	−	11.8014i	0.533679	−	0.533679i
$490$	8.07781	−	15.7929i	0.364918	−	0.713450i
$491$	−27.2859			−1.23139			−0.615697	−	0.787983i	$-0.711126\pi$
$491$	−27.2859			−1.23139			−0.615697	+	0.787983i	$0.711126\pi$
$492$	2.81026	−	17.3933i	0.126697	−	0.784150i
$493$			1.58147i			0.0712258i
$494$	1.03259	+	15.7908i	0.0464586	+	0.710460i
$495$		−	3.33505i		−	0.149899i
$496$	−8.14111	−	16.2264i	−0.365547	−	0.728586i
$497$	−29.0737			−1.30413
$498$	1.13968	+	0.582926i	0.0510701	+	0.0261216i
$499$	15.2067	−	15.2067i	0.680747	−	0.680747i	−0.279421	−	0.960169i	$-0.590143\pi$
$499$	15.2067	−	15.2067i	0.680747	−	0.680747i	0.960169	+	0.279421i	$0.0901426\pi$
$500$	3.66395	−	22.6769i	0.163857	−	1.01414i
$501$	−10.9648	+	10.9648i	−0.489872	+	0.489872i
$502$	13.4298	−	4.34056i	0.599403	−	0.193729i
$503$		−	28.9377i		−	1.29027i	−0.764070	−	0.645133i	$-0.776802\pi$
$503$		−	28.9377i		−	1.29027i	0.764070	−	0.645133i	$-0.223198\pi$
$504$	25.2302	−	3.87559i	1.12384	−	0.172633i
$505$	−4.18710	+	4.18710i	−0.186323	+	0.186323i
$506$	1.95667	+	1.00080i	0.0869844	+	0.0444912i
$507$	9.67297	+	5.21689i	0.429592	+	0.231690i
$508$	5.03114	−	3.63150i	0.223221	−	0.161122i
$509$	10.2390	+	10.2390i	0.453836	+	0.453836i	0.896626	−	0.442790i	$-0.146011\pi$
$509$	10.2390	+	10.2390i	0.453836	+	0.453836i	−0.442790	+	0.896626i	$0.646011\pi$
$510$	0.610334	+	0.312176i	0.0270261	+	0.0138234i
$511$	17.9015			0.791916
$512$	21.4201	+	7.29252i	0.946642	+	0.322287i
$513$	9.80521	+	9.80521i	0.432911	+	0.432911i
$514$	4.15390	+	12.8523i	0.183221	+	0.566891i
$515$	−20.6162	−	20.6162i	−0.908458	−	0.908458i
$516$	0.961368	+	1.33189i	0.0423219	+	0.0586334i
$517$		−	12.8515i		−	0.565210i
$518$	−28.8531	+	9.32539i	−1.26773	+	0.409734i
$519$	15.9740			0.701181
$520$	−11.4732	+	9.47907i	−0.503132	+	0.415685i
$521$	−22.8339			−1.00037			−0.500185	−	0.865918i	$-0.666735\pi$
$521$	−22.8339			−1.00037			−0.500185	+	0.865918i	$0.666735\pi$
$522$	−12.3779	+	4.00056i	−0.541765	+	0.175100i
$523$			5.09237i			0.222674i	0.993783	+	0.111337i	$0.0355133\pi$
$523$			5.09237i			0.222674i	−0.993783	+	0.111337i	$0.964487\pi$
$524$	3.82296	+	5.29639i	0.167007	+	0.231374i
$525$	−6.77592	−	6.77592i	−0.295725	−	0.295725i
$526$	−7.90468	−	24.4574i	−0.344660	−	1.06639i
$527$	1.26096	+	1.26096i	0.0549283	+	0.0549283i
$528$	−1.51644	−	3.02249i	−0.0659947	−	0.131537i
$529$	−20.5849			−0.894997
$530$	−17.3700	−	8.88448i	−0.754504	−	0.385917i
$531$	1.42217	+	1.42217i	0.0617168	+	0.0617168i
$532$	−19.8748	+	14.3457i	−0.861682	+	0.621966i
$533$	−36.4286	−	9.19729i	−1.57790	−	0.398379i
$534$	−0.147921	−	0.0756590i	−0.00640115	−	0.00327409i
$535$	7.81528	−	7.81528i	0.337884	−	0.337884i
$536$	2.02184	+	13.1622i	0.0873301	+	0.568521i
$537$			11.5636i			0.499006i
$538$	24.0880	−	7.78530i	1.03851	−	0.335648i
$539$	6.07768	−	6.07768i	0.261784	−	0.261784i
$540$	−2.08011	+	12.8742i	−0.0895135	+	0.554017i
$541$	5.06201	−	5.06201i	0.217633	−	0.217633i	−0.589867	−	0.807500i	$-0.700820\pi$
$541$	5.06201	−	5.06201i	0.217633	−	0.217633i	0.807500	+	0.589867i	$0.200820\pi$
$542$	−19.4091	−	9.92743i	−0.833691	−	0.426420i
$543$	−14.7270			−0.631998
$544$	−2.22261	−	0.0172687i	−0.0952935	−	0.000740390i
$545$		−	19.1785i		−	0.821518i
$546$	1.11081	+	16.9869i	0.0475383	+	0.726971i
$547$		−	31.1904i		−	1.33361i	−0.745234	−	0.666803i	$-0.767662\pi$
$547$		−	31.1904i		−	1.33361i	0.745234	−	0.666803i	$-0.232338\pi$
$548$	−3.48145	+	21.5474i	−0.148720	+	0.920458i
$549$	26.3316			1.12380
$550$	1.84848	−	3.61395i	0.0788193	−	0.154099i
$551$	8.83260	−	8.83260i	0.376281	−	0.376281i
$552$	−2.99604	−	2.19817i	−0.127520	−	0.0935601i
$553$	30.9823	−	30.9823i	1.31750	−	1.31750i
$554$	−0.869273	−	2.68956i	−0.0369319	−	0.114269i
$555$		−	6.69843i		−	0.284332i
$556$	−16.0821	−	22.2804i	−0.682032	−	0.944898i
$557$	−6.87709	+	6.87709i	−0.291392	+	0.291392i	−0.837630	−	0.546238i	$-0.816059\pi$
$557$	−6.87709	+	6.87709i	−0.291392	+	0.291392i	0.546238	+	0.837630i	$0.316059\pi$
$558$	−6.67952	+	13.0591i	−0.282766	+	0.552835i
$559$	3.00783	−	1.79519i	0.127218	−	0.0759285i
$560$	−21.8792	−	7.25964i	−0.924566	−	0.306776i
$561$	0.234879	+	0.234879i	0.00991660	+	0.00991660i
$562$	−0.459966	+	0.899276i	−0.0194025	+	0.0379337i
$563$	−7.27962			−0.306799			−0.153400	−	0.988164i	$-0.549022\pi$
$563$	−7.27962			−0.306799			−0.153400	+	0.988164i	$0.549022\pi$
$564$	−3.46587	+	21.4510i	−0.145940	+	0.903250i
$565$	−20.1176	−	20.1176i	−0.846355	−	0.846355i
$566$	24.2310	−	7.83153i	1.01851	−	0.329184i
$567$	−8.59667	−	8.59667i	−0.361026	−	0.361026i
$568$	3.16157	+	20.5819i	0.132657	+	0.863598i
$569$			12.8180i			0.537357i	0.963230	+	0.268678i	$0.0865869\pi$
$569$			12.8180i			0.537357i	−0.963230	+	0.268678i	$0.913413\pi$
$570$	−1.66523	−	5.15227i	−0.0697487	−	0.215805i
$571$	−14.4102			−0.603049			−0.301525	−	0.953458i	$-0.597496\pi$
$571$	−14.4102			−0.603049			−0.301525	+	0.953458i	$0.597496\pi$
$572$	−6.70229	+	2.66071i	−0.280237	+	0.111250i
$573$	8.49806			0.355011
$574$	−17.8978	−	55.3763i	−0.747038	−	2.31136i
$575$		−	4.46062i		−	0.186021i
$576$	−5.48725	−	17.4396i	−0.228635	−	0.726650i
$577$	12.3974	+	12.3974i	0.516110	+	0.516110i	0.916392	−	0.400282i	$-0.131088\pi$
$577$	12.3974	+	12.3974i	0.516110	+	0.516110i	−0.400282	+	0.916392i	$0.631088\pi$
$578$	−22.6687	+	7.32659i	−0.942894	+	0.304746i
$579$	−10.7790	−	10.7790i	−0.447961	−	0.447961i
$580$	11.5972	+	1.87377i	0.481546	+	0.0778042i
$581$	4.22830			0.175420
$582$	−0.412447	+	0.806373i	−0.0170965	+	0.0334253i
$583$	−6.68461	−	6.68461i	−0.276848	−	0.276848i
$584$	−1.94668	−	12.6729i	−0.0805540	−	0.524408i
$585$	11.6589	+	2.94356i	0.482034	+	0.121701i
$586$	−4.38249	+	8.56818i	−0.181039	+	0.353948i
$587$	9.84943	−	9.84943i	0.406530	−	0.406530i	−0.473997	−	0.880527i	$-0.657189\pi$
$587$	9.84943	−	9.84943i	0.406530	−	0.406530i	0.880527	+	0.473997i	$0.157189\pi$
$588$	−11.7836	+	8.50543i	−0.485946	+	0.350758i
$589$		−	14.0851i		−	0.580365i
$590$	−0.558589	−	1.72829i	−0.0229968	−	0.0711528i
$591$	−2.58034	+	2.58034i	−0.106141	+	0.106141i
$592$	9.73924	+	19.4117i	0.400280	+	0.797815i
$593$	19.5287	−	19.5287i	0.801948	−	0.801948i	−0.181452	−	0.983400i	$-0.558080\pi$
$593$	19.5287	−	19.5287i	0.801948	−	0.801948i	0.983400	+	0.181452i	$0.0580798\pi$
$594$	−2.87748	+	5.62575i	−0.118065	+	0.230827i
$595$	2.26440			0.0928312
$596$	−8.77614	−	1.41798i	−0.359485	−	0.0580826i
$597$			11.8243i			0.483938i
$598$	−5.22564	+	5.95690i	−0.213692	+	0.243596i
$599$		−	20.9565i		−	0.856260i	−0.903717	−	0.428130i	$-0.859173\pi$
$599$		−	20.9565i		−	0.856260i	0.903717	−	0.428130i	$-0.140827\pi$
$600$	−4.05999	+	5.53367i	−0.165749	+	0.225911i
$601$	−37.0785			−1.51246			−0.756232	−	0.654304i	$-0.772962\pi$
$601$	−37.0785			−1.51246			−0.756232	+	0.654304i	$0.772962\pi$
$602$	4.83050	+	2.47073i	0.196877	+	0.100699i
$603$	7.60814	−	7.60814i	0.309827	−	0.309827i
$604$	−10.2195	−	1.65118i	−0.415825	−	0.0671856i
$605$	−1.03191	+	1.03191i	−0.0419531	+	0.0419531i
$606$	4.61604	−	1.49192i	0.187514	−	0.0606050i
$607$			42.2576i			1.71518i	0.514332	+	0.857591i	$0.328040\pi$
$607$			42.2576i			1.71518i	−0.514332	+	0.857591i	$0.671960\pi$
$608$	12.3169	+	12.5098i	0.499517	+	0.507340i
$609$	9.50164	−	9.50164i	0.385026	−	0.385026i
$610$	−21.1709	−	10.8286i	−0.857186	−	0.438437i
$611$	44.9271	+	11.3429i	1.81756	+	0.458886i
$612$	1.05107	+	1.45617i	0.0424869	+	0.0588621i
$613$	21.6921	+	21.6921i	0.876136	+	0.876136i	0.993132	−	0.116996i	$-0.0373265\pi$
$613$	21.6921	+	21.6921i	0.876136	+	0.876136i	−0.116996	+	0.993132i	$0.537327\pi$
$614$	14.2038	+	7.26502i	0.573219	+	0.293192i
$615$	12.8560			0.518403
$616$	−9.00573	−	6.60741i	−0.362851	−	0.266220i
$617$	16.5746	+	16.5746i	0.667268	+	0.667268i	0.957083	−	0.289815i	$-0.0935937\pi$
$617$	16.5746	+	16.5746i	0.667268	+	0.667268i	−0.289815	+	0.957083i	$0.593594\pi$
$618$	7.34581	+	22.7282i	0.295492	+	0.914262i
$619$	−4.06469	−	4.06469i	−0.163374	−	0.163374i	0.620686	−	0.784059i	$-0.286854\pi$
$619$	−4.06469	−	4.06469i	−0.163374	−	0.163374i	−0.784059	+	0.620686i	$0.786854\pi$
$620$	10.7408	−	7.75279i	0.431362	−	0.311360i
$621$			6.94375i			0.278643i
$622$	−12.5860	+	4.06781i	−0.504651	+	0.163105i
$623$	−0.548799			−0.0219872
$624$	11.9046	−	2.63358i	0.476565	−	0.105428i
$625$	2.40966			0.0963865
$626$	−41.0462	+	13.2662i	−1.64054	+	0.530225i
$627$		−	2.62362i		−	0.104777i
$628$	−20.8602	+	15.0570i	−0.832414	+	0.600841i
$629$	−1.50849	−	1.50849i	−0.0601475	−	0.0601475i
$630$	5.72812	+	17.7230i	0.228214	+	0.706101i
$631$	34.6609	+	34.6609i	1.37983	+	1.37983i	0.844896	+	0.534931i	$0.179662\pi$
$631$	34.6609	+	34.6609i	1.37983	+	1.37983i	0.534931	+	0.844896i	$0.320338\pi$
$632$	−25.3022	−	18.5640i	−1.00647	−	0.738435i
$633$	−7.75371			−0.308182
$634$	43.2348	+	22.1139i	1.71708	+	0.878257i
$635$	3.20142	+	3.20142i	0.127045	+	0.127045i
$636$	9.35480	+	12.9603i	0.370942	+	0.513909i
$637$	15.8824	+	26.6109i	0.629285	+	1.05436i
$638$	5.06771	+	2.59205i	0.200633	+	0.102620i
$639$	11.8969	−	11.8969i	0.470636	−	0.470636i
$640$	−2.76004	+	16.2782i	−0.109100	+	0.643454i
$641$		−	3.34234i		−	0.132014i	−0.997819	−	0.0660072i	$-0.978974\pi$
$641$		−	3.34234i		−	0.132014i	0.997819	−	0.0660072i	$-0.0210260\pi$
$642$	−8.61590	+	2.78468i	−0.340042	+	0.109903i
$643$	2.03169	−	2.03169i	0.0801219	−	0.0801219i	−0.665910	−	0.746032i	$-0.731957\pi$
$643$	2.03169	−	2.03169i	0.0801219	−	0.0801219i	0.746032	+	0.665910i	$0.231957\pi$
$644$	−12.1170	−	1.95776i	−0.477475	−	0.0771465i
$645$	−0.847514	+	0.847514i	−0.0333708	+	0.0333708i
$646$	−1.53531	−	0.785285i	−0.0604058	−	0.0308966i
$647$	37.5867			1.47769			0.738843	−	0.673877i	$-0.235372\pi$
$647$	37.5867			1.47769			0.738843	+	0.673877i	$0.235372\pi$
$648$	−5.15095	+	7.02062i	−0.202348	+	0.275796i
$649$		−	0.880077i		−	0.0345460i
$650$	11.0023	+	9.65172i	0.431547	+	0.378572i
$651$		−	15.1520i		−	0.593852i
$652$	−38.9785	−	6.29783i	−1.52652	−	0.246642i
$653$	14.6707			0.574109			0.287054	−	0.957914i	$-0.407324\pi$
$653$	14.6707			0.574109			0.287054	+	0.957914i	$0.407324\pi$
$654$	−7.15485	+	13.9884i	−0.279777	+	0.546990i
$655$	−3.37021	+	3.37021i	−0.131685	+	0.131685i
$656$	−37.2559	+	18.6921i	−1.45460	+	0.729803i
$657$	−7.32530	+	7.32530i	−0.285787	+	0.285787i
$658$	22.0732	+	68.2951i	0.860501	+	2.66242i
$659$		−	22.4382i		−	0.874068i	−0.899445	−	0.437034i	$-0.856029\pi$
$659$		−	22.4382i		−	0.874068i	0.899445	−	0.437034i	$-0.143971\pi$
$660$	2.00069	−	1.44411i	0.0778769	−	0.0562119i
$661$	2.63053	−	2.63053i	0.102316	−	0.102316i	−0.654096	−	0.756412i	$-0.726951\pi$
$661$	2.63053	−	2.63053i	0.102316	−	0.102316i	0.756412	+	0.654096i	$0.226951\pi$
$662$	−4.52201	+	8.84096i	−0.175753	+	0.343614i
$663$	−1.02841	+	0.613795i	−0.0399401	+	0.0238378i
$664$	−0.459801	−	2.99331i	−0.0178437	−	0.116163i
$665$	−12.6468	−	12.6468i	−0.490421	−	0.490421i
$666$	7.99073	−	15.6226i	0.309634	−	0.605365i
$667$	6.25498			0.242194
$668$	36.2153	+	5.85137i	1.40121	+	0.226396i
$669$	12.1396	+	12.1396i	0.469343	+	0.469343i
$670$	−9.24581	+	2.98827i	−0.357197	+	0.115447i
$671$	−8.14735	−	8.14735i	−0.314525	−	0.314525i
$672$	13.2499	+	13.4574i	0.511126	+	0.519131i
$673$		−	27.2076i		−	1.04878i	−0.851479	−	0.524388i	$-0.824294\pi$
$673$		−	27.2076i		−	1.04878i	0.851479	−	0.524388i	$-0.175706\pi$
$674$	−1.10268	−	3.41173i	−0.0424737	−	0.131415i
$675$	12.8251			0.493637
$676$	−3.38592	−	25.7786i	−0.130228	−	0.991484i
$677$	38.1773			1.46727			0.733636	−	0.679543i	$-0.237822\pi$
$677$	38.1773			1.46727			0.733636	+	0.679543i	$0.237822\pi$
$678$	7.16817	+	22.1786i	0.275292	+	0.851762i
$679$			2.99172i			0.114812i
$680$	−0.246239	−	1.60302i	−0.00944282	−	0.0614730i
$681$	−11.2781	−	11.2781i	−0.432177	−	0.432177i
$682$	6.10739	−	1.97393i	0.233864	−	0.0755855i
$683$	−17.1104	−	17.1104i	−0.654712	−	0.654712i	0.299412	−	0.954124i	$-0.403209\pi$
$683$	−17.1104	−	17.1104i	−0.654712	−	0.654712i	−0.954124	+	0.299412i	$0.903209\pi$
$684$	2.26250	−	14.0030i	0.0865087	−	0.535420i
$685$	−15.9264			−0.608516
$686$	−4.05674	+	7.93130i	−0.154887	+	0.302819i
$687$	−13.9930	−	13.9930i	−0.533865	−	0.533865i
$688$	1.22380	−	3.68830i	0.0466569	−	0.140615i
$689$	29.2684	−	17.4685i	1.11504	−	0.665497i
$690$	1.23471	−	2.41397i	0.0470046	−	0.0918984i
$691$	22.4549	−	22.4549i	0.854225	−	0.854225i	−0.136426	−	0.990650i	$-0.543561\pi$
$691$	22.4549	−	22.4549i	0.854225	−	0.854225i	0.990650	+	0.136426i	$0.0435615\pi$
$692$	−22.1177	−	30.6422i	−0.840790	−	1.16484i
$693$			9.02485i			0.342826i
$694$	−15.0934	−	46.6996i	−0.572939	−	1.77269i
$695$	14.1775	−	14.1775i	0.537783	−	0.537783i
$696$	−7.75967	−	5.69319i	−0.294130	−	0.215800i
$697$	2.89518	−	2.89518i	0.109663	−	0.109663i
$698$	−0.121434	+	0.237414i	−0.00459633	+	0.00898626i
$699$	−4.60621			−0.174223
$700$	−3.61597	+	22.3799i	−0.136671	+	0.845882i
$701$			44.3652i			1.67565i	0.545940	+	0.837824i	$0.316173\pi$
$701$			44.3652i			1.67565i	−0.545940	+	0.837824i	$0.683827\pi$
$702$	−17.1271	−	15.0246i	−0.646421	−	0.567068i
$703$			16.8500i			0.635510i
$704$	−3.69822	+	7.09388i	−0.139382	+	0.267361i
$705$	−15.8552			−0.597140
$706$	−11.2873	−	5.77328i	−0.424804	−	0.217280i
$707$	11.3305	−	11.3305i	0.426129	−	0.426129i
$708$	−0.237344	+	1.46897i	−0.00891994	+	0.0552073i
$709$	27.6426	−	27.6426i	1.03814	−	1.03814i	0.0388971	−	0.999243i	$-0.487616\pi$
$709$	27.6426	−	27.6426i	1.03814	−	1.03814i	0.999243	−	0.0388971i	$-0.0123845\pi$
$710$	−14.4578	+	4.67280i	−0.542592	+	0.175367i
$711$			25.3559i			0.950922i
$712$	0.0596784	+	0.388508i	0.00223654	+	0.0145599i
$713$	4.98731	−	4.98731i	0.186776	−	0.186776i
$714$	−1.65160	−	0.844768i	−0.0618096	−	0.0316146i
$715$	−2.69663	−	4.51819i	−0.100848	−	0.168971i
$716$	22.1819	−	16.0110i	0.828978	−	0.598361i
$717$	−6.89848	−	6.89848i	−0.257628	−	0.257628i
$718$	−3.91119	−	2.00051i	−0.145964	−	0.0746584i
$719$	−34.4219			−1.28372			−0.641860	−	0.766822i	$-0.721837\pi$
$719$	−34.4219			−1.28372			−0.641860	+	0.766822i	$0.721837\pi$
$720$	11.9236	−	5.98233i	0.444367	−	0.222948i
$721$	55.7887	+	55.7887i	2.07768	+	2.07768i
$722$	−4.07468	−	12.6072i	−0.151644	−	0.469191i
$723$	0.948527	+	0.948527i	0.0352761	+	0.0352761i
$724$	20.3912	+	28.2502i	0.757832	+	1.04991i
$725$		−	11.5529i		−	0.429064i
$726$	1.13762	−	0.367683i	0.0422212	−	0.0136460i
$727$	4.97292			0.184435			0.0922177	−	0.995739i	$-0.470604\pi$
$727$	4.97292			0.184435			0.0922177	+	0.995739i	$0.470604\pi$
$728$	31.0471	−	25.6509i	1.15068	−	0.950687i
$729$	−4.29654			−0.159131
$730$	8.90210	−	2.87718i	0.329481	−	0.106489i
$731$			0.381722i			0.0141185i
$732$	11.4018	+	15.7963i	0.421424	+	0.583847i
$733$	33.2125	+	33.2125i	1.22673	+	1.22673i	0.965193	+	0.261540i	$0.0842305\pi$
$733$	33.2125	+	33.2125i	1.22673	+	1.22673i	0.261540	+	0.965193i	$0.415770\pi$
$734$	2.56831	+	7.94644i	0.0947981	+	0.293309i
$735$	−7.49814	−	7.49814i	−0.276573	−	0.276573i
$736$	−0.0683006	+	8.79078i	−0.00251759	+	0.324032i
$737$	−4.70812			−0.173426
$738$	29.9838	+	15.3362i	1.10372	+	0.564534i
$739$	−14.7581	−	14.7581i	−0.542886	−	0.542886i	0.381488	−	0.924374i	$-0.375412\pi$
$739$	−14.7581	−	14.7581i	−0.542886	−	0.542886i	−0.924374	+	0.381488i	$0.875412\pi$
$740$	−12.8493	+	9.27469i	−0.472350	+	0.340944i
$741$	9.17180	+	2.31564i	0.336935	+	0.0850673i
$742$	47.0043	+	24.0419i	1.72558	+	0.882607i
$743$	−8.70184	+	8.70184i	−0.319240	+	0.319240i	−0.848475	−	0.529235i	$-0.822479\pi$
$743$	−8.70184	+	8.70184i	−0.319240	+	0.319240i	0.529235	+	0.848475i	$0.322479\pi$
$744$	−10.7264	+	1.64768i	−0.393250	+	0.0604069i
$745$		−	6.48674i		−	0.237656i
$746$	−7.15253	+	2.31172i	−0.261873	+	0.0846380i
$747$	−1.73022	+	1.73022i	−0.0633055	+	0.0633055i
$748$	0.125343	−	0.775773i	0.00458299	−	0.0283651i
$749$	−21.1486	+	21.1486i	−0.772753	+	0.772753i
$750$	−12.2253	−	6.25305i	−0.446405	−	0.228329i
$751$	−42.5669			−1.55329			−0.776643	−	0.629940i	$-0.783079\pi$
$751$	−42.5669			−1.55329			−0.776643	+	0.629940i	$0.783079\pi$
$752$	45.9474	−	23.0528i	1.67553	−	0.840648i
$753$		−	8.43703i		−	0.307462i
$754$	−13.5343	+	15.4282i	−0.492889	+	0.561862i
$755$		−	7.55358i		−	0.274903i
$756$	5.62889	−	34.8384i	0.204721	−	1.26706i
$757$	−23.4376			−0.851856			−0.425928	−	0.904757i	$-0.640052\pi$
$757$	−23.4376			−0.851856			−0.425928	+	0.904757i	$0.640052\pi$
$758$	−12.0528	+	23.5644i	−0.437777	+	0.855896i
$759$	0.928985	−	0.928985i	0.0337200	−	0.0337200i
$760$	−7.57769	+	10.3282i	−0.274872	+	0.374643i
$761$	−10.3741	+	10.3741i	−0.376059	+	0.376059i	−0.869678	−	0.493619i	$-0.835674\pi$
$761$	−10.3741	+	10.3741i	−0.376059	+	0.376059i	0.493619	+	0.869678i	$0.335674\pi$
$762$	−1.14071	−	3.52939i	−0.0413235	−	0.127856i
$763$			51.8983i			1.87884i
$764$	−11.7665	−	16.3015i	−0.425696	−	0.589766i
$765$	−0.926591	+	0.926591i	−0.0335010	+	0.0335010i
$766$	13.5838	−	26.5577i	0.490804	−	0.959568i
$767$	3.07662	+	0.776767i	0.111090	+	0.0280474i
$768$	8.08596	−	10.8433i	0.291777	−	0.391274i
$769$	−26.8075	−	26.8075i	−0.966703	−	0.966703i	0.0327601	−	0.999463i	$-0.489570\pi$
$769$	−26.8075	−	26.8075i	−0.966703	−	0.966703i	−0.999463	+	0.0327601i	$0.989570\pi$
$770$	3.71138	−	7.25610i	0.133749	−	0.261492i
$771$	8.07420			0.290785
$772$	−5.75222	+	35.6016i	−0.207027	+	1.28133i
$773$	−8.79625	−	8.79625i	−0.316379	−	0.316379i	0.530995	−	0.847375i	$-0.321818\pi$
$773$	−8.79625	−	8.79625i	−0.316379	−	0.316379i	−0.847375	+	0.530995i	$0.821818\pi$
$774$	−2.98766	+	0.965621i	−0.107389	+	0.0347085i
$775$	−9.21152	−	9.21152i	−0.330888	−	0.330888i
$776$	2.11791	−	0.325330i	0.0760285	−	0.0116787i
$777$			18.1264i			0.650279i
$778$	−14.8575	−	45.9697i	−0.532668	−	1.64809i
$779$	−32.3394			−1.15868
$780$	3.28256	+	8.26872i	0.117535	+	0.296068i
$781$	−7.36216			−0.263439
$782$	−0.265571	−	0.821686i	−0.00949681	−	0.0293834i
$783$			17.9841i			0.642700i
$784$	32.6312	+	10.8272i	1.16540	+	0.386686i
$785$	−13.2738	−	13.2738i	−0.473764	−	0.473764i
$786$	3.71547	−	1.20085i	0.132526	−	0.0428329i
$787$	22.8947	+	22.8947i	0.816108	+	0.816108i	0.985542	−	0.169434i	$-0.0541939\pi$
$787$	22.8947	+	22.8947i	0.816108	+	0.816108i	−0.169434	+	0.985542i	$0.554194\pi$
$788$	8.52251	+	1.37700i	0.303602	+	0.0490535i
$789$	−15.3648			−0.547003
$790$	10.4274	−	20.3865i	0.370990	−	0.725319i
$791$	54.4395	+	54.4395i	1.93565	+	1.93565i
$792$	6.38890	−	0.981395i	0.227020	−	0.0348723i
$793$	35.6729	−	21.2910i	1.26678	−	0.756065i
$794$	−16.2071	+	31.6864i	−0.575168	+	1.12451i
$795$	−8.24692	+	8.24692i	−0.292488	+	0.292488i
$796$	22.6821	−	16.3721i	0.803946	−	0.580292i
$797$		−	38.9339i		−	1.37911i	−0.724233	−	0.689555i	$-0.757806\pi$
$797$		−	38.9339i		−	1.37911i	0.724233	−	0.689555i	$-0.242194\pi$
$798$	4.50621	+	13.9424i	0.159518	+	0.493554i
$799$	−3.57060	+	3.57060i	−0.126319	+	0.126319i
$800$	16.2365	+	0.126151i	0.574047	+	0.00446010i
$801$	0.224569	−	0.224569i	0.00793474	−	0.00793474i
$802$	15.3412	−	29.9935i	0.541717	−	1.05911i
$803$	4.53310			0.159970
$804$	7.85851	+	1.26971i	0.277148	+	0.0447793i
$805$		−	8.95606i		−	0.315660i
$806$	1.51009	+	23.0928i	0.0531907	+	0.813408i
$807$		−	15.1328i		−	0.532699i
$808$	−9.25328	−	6.78903i	−0.325529	−	0.238837i
$809$	−10.3223			−0.362913			−0.181457	−	0.983399i	$-0.558081\pi$
$809$	−10.3223			−0.362913			−0.181457	+	0.983399i	$0.558081\pi$
$810$	−5.65665	−	2.89329i	−0.198754	−	0.101660i
$811$	−25.7141	+	25.7141i	−0.902944	+	0.902944i	−0.995690	−	0.0927458i	$-0.970436\pi$
$811$	−25.7141	+	25.7141i	−0.902944	+	0.902944i	0.0927458	+	0.995690i	$0.470436\pi$
$812$	−31.3826	−	5.07054i	−1.10131	−	0.177941i
$813$	−9.21503	+	9.21503i	−0.323185	+	0.323185i
$814$	−7.30630	+	2.36141i	−0.256086	+	0.0827675i
$815$		−	28.8103i		−	1.00918i
$816$	−0.418430	+	1.26107i	−0.0146480	+	0.0441463i
$817$	2.13194	−	2.13194i	0.0745870	−	0.0745870i
$818$	−8.26492	−	4.22738i	−0.288976	−	0.147807i
$819$	−31.5496	−	7.96545i	−1.10243	−	0.278335i
$820$	−17.8005	−	24.6611i	−0.621619	−	0.861201i
$821$	13.2590	+	13.2590i	0.462742	+	0.462742i	0.899553	−	0.436811i	$-0.143892\pi$
$821$	13.2590	+	13.2590i	0.462742	+	0.462742i	−0.436811	+	0.899553i	$0.643892\pi$
$822$	11.6164	+	5.94159i	0.405167	+	0.207237i
$823$	−46.8538			−1.63322			−0.816610	−	0.577190i	$-0.804149\pi$
$823$	−46.8538			−1.63322			−0.816610	+	0.577190i	$0.804149\pi$
$824$	33.4274	−	45.5607i	1.16450	−	1.58718i
$825$	−1.71583	−	1.71583i	−0.0597375	−	0.0597375i
$826$	1.51158	+	4.67687i	0.0525945	+	0.162729i
$827$	21.2272	+	21.2272i	0.738141	+	0.738141i	0.972218	−	0.234077i	$-0.0752068\pi$
$827$	21.2272	+	21.2272i	0.738141	+	0.738141i	−0.234077	+	0.972218i	$0.575207\pi$
$828$	5.75938	−	4.15715i	0.200152	−	0.144471i
$829$			18.9373i			0.657718i	0.944379	+	0.328859i	$0.106664\pi$
$829$			18.9373i			0.657718i	−0.944379	+	0.328859i	$0.893336\pi$
$830$	2.10266	−	0.679585i	0.0729843	−	0.0235887i
$831$	−1.68966			−0.0586137
$832$	−21.5351	−	19.1896i	−0.746594	−	0.665280i
$833$	−3.37718			−0.117012
$834$	−15.6299	+	5.05162i	−0.541219	+	0.174923i
$835$			26.7680i			0.926343i
$836$	−5.03278	+	3.63269i	−0.174062	+	0.125639i
$837$	14.3394	+	14.3394i	0.495641	+	0.495641i
$838$	−6.49352	−	20.0912i	−0.224315	−	0.694038i
$839$	7.75605	+	7.75605i	0.267769	+	0.267769i	0.828201	−	0.560432i	$-0.189365\pi$
$839$	7.75605	+	7.75605i	0.267769	+	0.267769i	−0.560432	+	0.828201i	$0.689365\pi$
$840$	−8.15167	+	11.1105i	−0.281260	+	0.383350i
$841$	−12.7998			−0.441372
$842$	−33.3507	−	17.0584i	−1.14934	−	0.587870i
$843$	0.426958	+	0.426958i	0.0147052	+	0.0147052i
$844$	10.7358	+	14.8736i	0.369543	+	0.511970i
$845$	18.1750	−	5.43922i	0.625239	−	0.187115i
$846$	−36.9787	−	18.9140i	−1.27135	−	0.650278i
$847$	2.79241	−	2.79241i	0.0959484	−	0.0959484i
$848$	11.9084	−	35.8898i	0.408937	−	1.23246i
$849$		−	15.2226i		−	0.522440i
$850$	−1.51765	+	0.490508i	−0.0520549	+	0.0168243i
$851$	−5.96634	+	5.96634i	−0.204523	+	0.204523i
$852$	12.2885	+	1.98547i	0.420996	+	0.0680210i
$853$	39.8357	−	39.8357i	1.36395	−	1.36395i	0.495129	−	0.868819i	$-0.335121\pi$
$853$	39.8357	−	39.8357i	1.36395	−	1.36395i	0.868819	−	0.495129i	$-0.164879\pi$
$854$	57.2898	+	29.3028i	1.96042	+	1.00272i
$855$	10.3501			0.353967
$856$	17.2714	+	12.6718i	0.590323	+	0.433114i
$857$			33.5151i			1.14485i	0.819956	+	0.572427i	$0.193998\pi$
$857$			33.5151i			1.14485i	−0.819956	+	0.572427i	$0.806002\pi$
$858$	0.281284	+	4.30149i	0.00960289	+	0.146850i
$859$			33.4028i			1.13969i	0.821753	+	0.569844i	$0.192996\pi$
$859$			33.4028i			1.13969i	−0.821753	+	0.569844i	$0.807004\pi$
$860$	2.79922	+	0.452275i	0.0954527	+	0.0154225i
$861$	−34.7890			−1.18561
$862$	23.3050	−	45.5635i	0.793773	−	1.55190i
$863$	−33.2690	+	33.2690i	−1.13249	+	1.13249i	−0.142727	+	0.989762i	$0.545587\pi$
$863$	−33.2690	+	33.2690i	−1.13249	+	1.13249i	−0.989762	+	0.142727i	$0.954413\pi$
$864$	−25.2750	−	0.196376i	−0.859872	−	0.00668085i
$865$	19.4983	−	19.4983i	0.662964	−	0.662964i
$866$	11.8841	+	36.7697i	0.403837	+	1.24949i
$867$			14.2412i			0.483655i
$868$	−29.0654	+	20.9795i	−0.986542	+	0.712091i
$869$	7.84548	−	7.84548i	0.266140	−	0.266140i
$870$	3.19786	−	6.25212i	0.108418	−	0.211967i
$871$	4.15545	−	16.4589i	0.140802	−	0.557689i
$872$	36.7400	−	5.64360i	1.24417	−	0.191117i
$873$	−1.22421	−	1.22421i	−0.0414333	−	0.0414333i
$874$	−3.10593	+	6.07239i	−0.105060	+	0.205402i
$875$	−45.3570			−1.53335
$876$	−7.56637	−	1.22251i	−0.255644	−	0.0413048i
$877$	−32.2035	−	32.2035i	−1.08744	−	1.08744i	−0.995792	−	0.0916437i	$-0.970788\pi$
$877$	−32.2035	−	32.2035i	−1.08744	−	1.08744i	−0.0916437	−	0.995792i	$-0.529212\pi$
$878$	−9.91589	+	3.20484i	−0.334645	+	0.108158i
$879$	4.06800	+	4.06800i	0.137210	+	0.137210i
$880$	−5.54035	−	1.83832i	−0.186765	−	0.0619697i
$881$		−	54.8136i		−	1.84672i	−0.383938	−	0.923359i	$-0.625432\pi$
$881$		−	54.8136i		−	1.84672i	0.383938	−	0.923359i	$-0.374568\pi$
$882$	−8.54305	−	26.4325i	−0.287660	−	0.890029i
$883$	11.4708			0.386022			0.193011	−	0.981197i	$-0.438175\pi$
$883$	11.4708			0.386022			0.193011	+	0.981197i	$0.438175\pi$
$884$	2.60136	+	1.12289i	0.0874932	+	0.0377668i
$885$	−1.08577			−0.0364976
$886$	3.30895	+	10.2380i	0.111166	+	0.343953i
$887$			30.4002i			1.02074i	0.859955	+	0.510370i	$0.170491\pi$
$887$			30.4002i			1.02074i	−0.859955	+	0.510370i	$0.829509\pi$
$888$	12.8321	−	1.97112i	0.430616	−	0.0661466i
$889$	−8.66324	−	8.66324i	−0.290556	−	0.290556i
$890$	−0.272908	+	0.0882045i	−0.00914789	+	0.00295662i
$891$	−2.17689	−	2.17689i	−0.0729284	−	0.0729284i
$892$	6.47828	−	40.0954i	0.216909	−	1.34249i
$893$	39.8839			1.33466
$894$	−2.41998	+	4.73129i	−0.0809362	+	0.158238i
$895$	14.1149	+	14.1149i	0.471808	+	0.471808i
$896$	7.46885	−	44.0499i	0.249517	−	1.47160i
$897$	2.42766	+	4.06753i	0.0810573	+	0.135811i
$898$	22.2116	−	43.4258i	0.741210	−	1.44914i
$899$	12.9170	−	12.9170i	0.430806	−	0.430806i
$900$	−7.67822	−	10.6375i	−0.255941	−	0.354584i
$901$			3.71443i			0.123746i
$902$	−4.53215	−	14.0226i	−0.150904	−	0.466902i
$903$	2.29342	−	2.29342i	0.0763204	−	0.0763204i
$904$	32.6191	−	44.4590i	1.08489	−	1.47868i
$905$	−17.9763	+	17.9763i	−0.597551	+	0.597551i
$906$	−2.81798	+	5.50941i	−0.0936211	+	0.183038i
$907$	40.1620			1.33356			0.666779	−	0.745256i	$-0.267673\pi$
$907$	40.1620			1.33356			0.666779	+	0.745256i	$0.267673\pi$
$908$	−6.01855	+	37.2500i	−0.199732	+	1.23618i
$909$			9.27292i			0.307563i
$910$	22.0905	+	19.3788i	0.732295	+	0.642400i
$911$		−	1.74294i		−	0.0577461i	−0.999583	−	0.0288731i	$-0.990808\pi$
$911$		−	1.74294i		−	0.0577461i	0.999583	−	0.0288731i	$-0.00919186\pi$
$912$	9.38009	−	4.70619i	0.310606	−	0.155837i
$913$	1.07071			0.0354353
$914$	−46.0461	−	23.5518i	−1.52307	−	0.779026i
$915$	−10.0515	+	10.0515i	−0.332293	+	0.332293i
$916$	−7.46733	+	46.2168i	−0.246728	+	1.52705i
$917$	9.12000	−	9.12000i	0.301169	−	0.301169i
$918$	2.36249	−	0.763563i	0.0779737	−	0.0252013i
$919$		−	49.0989i		−	1.61962i	−0.586690	−	0.809812i	$-0.699569\pi$
$919$		−	49.0989i		−	1.61962i	0.586690	−	0.809812i	$-0.300431\pi$
$920$	−6.34020	+	0.973915i	−0.209030	+	0.0321090i
$921$	6.74367	−	6.74367i	0.222212	−	0.222212i
$922$	−16.7907	−	8.58820i	−0.552974	−	0.282837i
$923$	6.49794	−	25.7370i	0.213882	−	0.847145i
$924$	−5.41400	+	3.90785i	−0.178107	+	0.128559i
$925$	11.0198	+	11.0198i	0.362328	+	0.362328i
$926$	−4.31888	−	2.20904i	−0.141927	−	0.0725936i
$927$	−45.6575			−1.49959
$928$	−0.176897	+	22.7679i	−0.00580692	+	0.747392i
$929$	−23.9636	−	23.9636i	−0.786221	−	0.786221i	0.194652	−	0.980872i	$-0.437642\pi$
$929$	−23.9636	−	23.9636i	−0.786221	−	0.786221i	−0.980872	+	0.194652i	$0.937642\pi$
$930$	−2.43527	−	7.53480i	−0.0798555	−	0.247076i
$931$	18.8617	+	18.8617i	0.618167	+	0.618167i
$932$	6.37780	+	8.83590i	0.208912	+	0.289429i
$933$			7.90687i			0.258859i
$934$	22.1504	−	7.15908i	0.724784	−	0.234252i
$935$	0.573400			0.0187522
$936$	−2.20811	+	23.2009i	−0.0721745	+	0.758344i
$937$	7.49974			0.245006			0.122503	−	0.992468i	$-0.460908\pi$
$937$	7.49974			0.245006			0.122503	+	0.992468i	$0.460908\pi$
$938$	25.0197	−	8.08644i	0.816923	−	0.264032i
$939$			25.7864i			0.841508i
$940$	21.9532	+	30.4143i	0.716033	+	0.992004i
$941$	−22.9465	−	22.9465i	−0.748035	−	0.748035i	0.226075	−	0.974110i	$-0.427411\pi$
$941$	−22.9465	−	22.9465i	−0.748035	−	0.748035i	−0.974110	+	0.226075i	$0.927411\pi$
$942$	4.72964	+	14.6337i	0.154100	+	0.476790i
$943$	−11.4509	−	11.4509i	−0.372893	−	0.372893i
$944$	3.14649	−	1.57866i	0.102410	−	0.0513810i
$945$	25.7502			0.837654
$946$	1.22320	+	0.625648i	0.0397697	+	0.0203416i
$947$	−16.4883	−	16.4883i	−0.535796	−	0.535796i	0.386495	−	0.922291i	$-0.373686\pi$
$947$	−16.4883	−	16.4883i	−0.535796	−	0.535796i	−0.922291	+	0.386495i	$0.873686\pi$
$948$	−15.2110	+	10.9794i	−0.494030	+	0.356594i
$949$	−4.00097	+	15.8471i	−0.129877	+	0.514417i
$950$	11.2157	+	5.73663i	0.363884	+	0.186121i
$951$	20.5270	−	20.5270i	0.665634	−	0.665634i
$952$	0.666337	+	4.33787i	0.0215961	+	0.140591i
$953$			35.3199i			1.14413i	0.820210	+	0.572063i	$0.193857\pi$
$953$			35.3199i			1.14413i	−0.820210	+	0.572063i	$0.806143\pi$
$954$	−29.0721	+	9.39618i	−0.941244	+	0.304213i
$955$	10.3730	−	10.3730i	0.335662	−	0.335662i
$956$	−3.68137	+	22.7847i	−0.119064	+	0.736910i
$957$	2.40605	−	2.40605i	0.0777764	−	0.0777764i
$958$	−32.2030	−	16.4713i	−1.04043	−	0.532165i
$959$	43.0978			1.39170
$960$	8.75184	+	4.56256i	0.282465	+	0.147256i
$961$			10.4017i			0.335538i
$962$	−1.80653	−	27.6260i	−0.0582448	−	0.890697i
$963$		−	17.3080i		−	0.557743i
$964$	0.506181	−	3.13286i	0.0163030	−	0.100903i
$965$	−26.3144			−0.847089
$966$	−3.34120	+	6.53235i	−0.107501	+	0.210175i
$967$	5.83435	−	5.83435i	0.187620	−	0.187620i	−0.607046	−	0.794666i	$-0.707646\pi$
$967$	5.83435	−	5.83435i	0.187620	−	0.187620i	0.794666	+	0.607046i	$0.207646\pi$
$968$	−2.28047	−	1.67316i	−0.0732971	−	0.0537773i
$969$	−0.728932	+	0.728932i	−0.0234167	+	0.0234167i
$970$	0.480838	+	1.48773i	0.0154388	+	0.0477681i
$971$		−	25.3095i		−	0.812219i	−0.913824	−	0.406110i	$-0.866885\pi$
$971$		−	25.3095i		−	0.812219i	0.913824	−	0.406110i	$-0.133115\pi$
$972$	18.7369	+	25.9584i	0.600986	+	0.832616i
$973$	−38.3652	+	38.3652i	−1.22993	+	1.22993i
$974$	19.2460	−	37.6276i	0.616680	−	1.20567i
$975$	7.51270	−	4.48387i	0.240599	−	0.143599i
$976$	14.5143	−	43.7433i	0.464590	−	1.40019i
$977$	19.2565	+	19.2565i	0.616070	+	0.616070i	0.944521	−	0.328451i	$-0.106527\pi$
$977$	19.2565	+	19.2565i	0.616070	+	0.616070i	−0.328451	+	0.944521i	$0.606527\pi$
$978$	−10.7481	+	21.0136i	−0.343688	+	0.671942i
$979$	−0.138969			−0.00444148
$980$	−4.00138	+	24.7653i	−0.127819	+	0.791099i
$981$	−21.2368	−	21.2368i	−0.678038	−	0.678038i
$982$	36.7179	−	11.8673i	1.17172	−	0.378702i
$983$	1.09953	+	1.09953i	0.0350697	+	0.0350697i	0.724424	−	0.689354i	$-0.242106\pi$
$983$	1.09953	+	1.09953i	0.0350697	+	0.0350697i	−0.689354	+	0.724424i	$0.742106\pi$
$984$	3.78309	+	24.6280i	0.120600	+	0.785111i
$985$			6.29928i			0.200712i
$986$	−0.687822	−	2.12814i	−0.0219047	−	0.0677739i
$987$	42.9050			1.36568
$988$	−8.25734	−	20.8001i	−0.262701	−	0.661740i
$989$	1.50977			0.0480080
$990$	1.45050	+	4.48789i	0.0460999	+	0.142635i
$991$			2.76339i			0.0877818i	0.999036	+	0.0438909i	$0.0139754\pi$
$991$			2.76339i			0.0877818i	−0.999036	+	0.0438909i	$0.986025\pi$
$992$	18.0126	+	18.2947i	0.571899	+	0.580856i
$993$	4.19751	+	4.19751i	0.133204	+	0.133204i
$994$	39.1237	−	12.6449i	1.24093	−	0.401071i
$995$	14.4331	+	14.4331i	0.457561	+	0.457561i
$996$	−1.78716	−	0.288755i	−0.0566284	−	0.00914955i
$997$	−29.7880			−0.943394			−0.471697	−	0.881761i	$-0.656358\pi$
$997$	−29.7880			−0.943394			−0.471697	+	0.881761i	$0.656358\pi$
$998$	−13.8495	+	27.0771i	−0.438399	+	0.857111i
$999$	−17.1542	−	17.1542i	−0.542736	−	0.542736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.j.a.463.8	✓	140
4.3	odd	2	inner	572.2.j.a.463.44	yes	140
13.5	odd	4	inner	572.2.j.a.551.44	yes	140
52.31	even	4	inner	572.2.j.a.551.8	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.j.a.463.8	✓	140	1.1	even	1	trivial
572.2.j.a.463.44	yes	140	4.3	odd	2	inner
572.2.j.a.551.8	yes	140	52.31	even	4	inner
572.2.j.a.551.44	yes	140	13.5	odd	4	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34567 + 0.434926i) q^{2} +0.845393i q^{3} +(1.62168 - 1.17054i) q^{4} +(1.03191 + 1.03191i) q^{5} +(-0.367683 - 1.13762i) q^{6} +(-2.79241 - 2.79241i) q^{7} +(-1.67316 + 2.28047i) q^{8} +2.28531 q^{9} +O(q^{10})\)	\(q+(-1.34567 + 0.434926i) q^{2} +0.845393i q^{3} +(1.62168 - 1.17054i) q^{4} +(1.03191 + 1.03191i) q^{5} +(-0.367683 - 1.13762i) q^{6} +(-2.79241 - 2.79241i) q^{7} +(-1.67316 + 2.28047i) q^{8} +2.28531 q^{9} +(-1.83742 - 0.939812i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(0.989563 + 1.37096i) q^{12} +(3.09604 - 1.84784i) q^{13} +(4.97217 + 2.54319i) q^{14} +(-0.872370 + 0.872370i) q^{15} +(1.25969 - 3.79647i) q^{16} +0.392917i q^{17} +(-3.07529 + 0.993940i) q^{18} +(2.19446 - 2.19446i) q^{19} +(2.88132 + 0.465540i) q^{20} +(2.36069 - 2.36069i) q^{21} +(1.25907 + 0.643997i) q^{22} +1.55405 q^{23} +(-1.92789 - 1.41447i) q^{24} -2.87032i q^{25} +(-3.36259 + 3.83314i) q^{26} +4.46816i q^{27} +(-7.79702 - 1.25978i) q^{28} +4.02495 q^{29} +(0.794510 - 1.55334i) q^{30} +(3.20923 - 3.20923i) q^{31} +(-0.0439501 + 5.65668i) q^{32} +(0.597783 - 0.597783i) q^{33} +(-0.170890 - 0.528738i) q^{34} -5.76304i q^{35} +(3.70604 - 2.67504i) q^{36} +(-3.83921 + 3.83921i) q^{37} +(-1.99860 + 3.90746i) q^{38} +(1.56215 + 2.61737i) q^{39} +(-4.07979 + 0.626694i) q^{40} +(-7.36842 - 7.36842i) q^{41} +(-2.14999 + 4.20344i) q^{42} +0.971508 q^{43} +(-1.97439 - 0.319006i) q^{44} +(2.35824 + 2.35824i) q^{45} +(-2.09125 + 0.675897i) q^{46} +(9.08741 + 9.08741i) q^{47} +(3.20951 + 1.06493i) q^{48} +8.59514i q^{49} +(1.24838 + 3.86252i) q^{50} -0.332169 q^{51} +(2.85783 - 6.62064i) q^{52} +9.45347 q^{53} +(-1.94332 - 6.01269i) q^{54} -1.45934i q^{55} +(11.0402 - 1.69587i) q^{56} +(1.85518 + 1.85518i) q^{57} +(-5.41627 + 1.75055i) q^{58} +(0.622308 + 0.622308i) q^{59} +(-0.393564 + 2.43584i) q^{60} +11.5221 q^{61} +(-2.92280 + 5.71436i) q^{62} +(-6.38153 - 6.38153i) q^{63} +(-2.40109 - 7.63117i) q^{64} +(5.10165 + 1.28803i) q^{65} +(-0.544430 + 1.06441i) q^{66} +(3.32915 - 3.32915i) q^{67} +(0.459923 + 0.637185i) q^{68} +1.31378i q^{69} +(2.50649 + 7.75518i) q^{70} +(5.20583 - 5.20583i) q^{71} +(-3.82368 + 5.21159i) q^{72} +(-3.20539 + 3.20539i) q^{73} +(3.49656 - 6.83611i) q^{74} +2.42655 q^{75} +(0.990017 - 6.12741i) q^{76} +3.94907i q^{77} +(-3.24051 - 2.84271i) q^{78} +11.0952i q^{79} +(5.21751 - 2.61773i) q^{80} +3.07858 q^{81} +(13.1202 + 6.71078i) q^{82} +(-0.757106 + 0.757106i) q^{83} +(1.06501 - 6.59154i) q^{84} +(-0.405455 + 0.405455i) q^{85} +(-1.30733 + 0.422534i) q^{86} +3.40266i q^{87} +(2.79564 - 0.429436i) q^{88} +(0.0982661 - 0.0982661i) q^{89} +(-4.19908 - 2.14776i) q^{90} +(-13.8054 - 3.48550i) q^{91} +(2.52017 - 1.81907i) q^{92} +(2.71306 + 2.71306i) q^{93} +(-16.1810 - 8.27635i) q^{94} +4.52898 q^{95} +(-4.78212 - 0.0371551i) q^{96} +(-0.535687 - 0.535687i) q^{97} +(-3.73825 - 11.5663i) q^{98} +(-1.61596 - 1.61596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

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