LMFDB - Embedded newform 572.2.bv.a.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(41,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 18, 5]))

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

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

chi := DirichletCharacter("572.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bv (of order $60$, degree $16$, 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:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			85.3
Character	$\chi$	$=$	572.85
Dual form			572.2.bv.a.249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.09433 - 0.445163i) q^{3} +(-0.0295100 - 0.186319i) q^{5} +(0.788511 + 0.512065i) q^{7} +(1.44740 + 0.644424i) q^{9} +O(q^{10})$	\(q+(-2.09433 - 0.445163i) q^{3} +(-0.0295100 - 0.186319i) q^{5} +(0.788511 + 0.512065i) q^{7} +(1.44740 + 0.644424i) q^{9} +(2.36624 + 2.32399i) q^{11} +(-3.60046 - 0.191547i) q^{13} +(-0.0211387 + 0.403350i) q^{15} +(0.167487 - 1.59353i) q^{17} +(0.000427686 + 0.00816073i) q^{19} +(-1.42345 - 1.42345i) q^{21} +(5.06452 + 2.92400i) q^{23} +(4.72144 - 1.53409i) q^{25} +(2.45214 + 1.78159i) q^{27} +(4.05510 - 3.65123i) q^{29} +(4.31241 + 0.683018i) q^{31} +(-3.92112 - 5.92055i) q^{33} +(0.0721385 - 0.162026i) q^{35} +(5.83831 + 0.305973i) q^{37} +(7.45527 + 2.00395i) q^{39} +(9.31660 - 6.05027i) q^{41} +(5.79926 + 10.0446i) q^{43} +(0.0773556 - 0.288695i) q^{45} +(-5.96221 - 3.03790i) q^{47} +(-2.48762 - 5.58728i) q^{49} +(-1.06015 + 3.26281i) q^{51} +(-11.1948 + 8.13352i) q^{53} +(0.363176 - 0.509456i) q^{55} +(0.00273714 - 0.0172816i) q^{57} +(-0.951072 + 1.46452i) q^{59} +(1.97824 + 0.207921i) q^{61} +(0.811303 + 1.24930i) q^{63} +(0.0705608 + 0.676487i) q^{65} +(8.32006 - 2.22935i) q^{67} +(-9.30511 - 8.37836i) q^{69} +(2.51175 - 2.03398i) q^{71} +(4.62547 - 2.35679i) q^{73} +(-10.5712 + 1.11107i) q^{75} +(0.675769 + 3.04416i) q^{77} +(4.04902 + 5.57300i) q^{79} +(-7.52296 - 8.35509i) q^{81} +(-15.9720 + 2.52972i) q^{83} +(-0.301848 + 0.0158192i) q^{85} +(-10.1181 + 5.84169i) q^{87} +(1.46565 + 5.46989i) q^{89} +(-2.74092 - 1.99471i) q^{91} +(-8.72754 - 3.35019i) q^{93} +(0.00150788 - 0.000320509i) q^{95} +(2.45427 + 6.39358i) q^{97} +(1.92725 + 4.88860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 28 q^{9}+O(q^{10}) $ 224 * q + 28 * q^9	$ 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) $ 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{10}\right)$

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
$3$	−2.09433	−	0.445163i	−1.20916	−	0.257015i	−0.441139	−	0.897439i	$-0.645425\pi$
$3$	−2.09433	−	0.445163i	−1.20916	−	0.257015i	−0.768022	+	0.640424i	$0.778759\pi$
$4$		0			0
$5$	−0.0295100	−	0.186319i	−0.0131973	−	0.0833244i	0.980211	−	0.197957i	$-0.0634308\pi$
$5$	−0.0295100	−	0.186319i	−0.0131973	−	0.0833244i	−0.993408	+	0.114633i	$0.963431\pi$
$6$		0			0
$7$	0.788511	+	0.512065i	0.298029	+	0.193542i	0.684988	−	0.728555i	$-0.259808\pi$
$7$	0.788511	+	0.512065i	0.298029	+	0.193542i	−0.386958	+	0.922097i	$0.626474\pi$
$8$		0			0
$9$	1.44740	+	0.644424i	0.482466	+	0.214808i
$10$		0			0
$11$	2.36624	+	2.32399i	0.713447	+	0.700709i
$11$	2.36624	+	2.32399i	0.713447	+	0.700709i
$12$		0			0
$13$	−3.60046	−	0.191547i	−0.998588	−	0.0531256i
$13$	−3.60046	−	0.191547i	−0.998588	−	0.0531256i
$14$		0			0
$15$	−0.0211387	+	0.403350i	−0.00545798	+	0.104144i
$16$		0			0
$17$	0.167487	−	1.59353i	0.0406215	−	0.386488i	−0.955256	−	0.295780i	$-0.904420\pi$
$17$	0.167487	−	1.59353i	0.0406215	−	0.386488i	0.995878	−	0.0907077i	$-0.0289129\pi$
$18$		0			0
$19$	0.000427686		0.00816073i	9.81178e−5		0.00187220i	0.998678	−	0.0513998i	$-0.0163683\pi$
$19$	0.000427686		0.00816073i	9.81178e−5		0.00187220i	−0.998580	+	0.0532720i	$0.983035\pi$
$20$		0			0
$21$	−1.42345	−	1.42345i	−0.310622	−	0.310622i
$22$		0			0
$23$	5.06452	+	2.92400i	1.05603	+	0.609697i	0.924330	−	0.381593i	$-0.124625\pi$
$23$	5.06452	+	2.92400i	1.05603	+	0.609697i	0.131696	+	0.991290i	$0.457958\pi$
$24$		0			0
$25$	4.72144	−	1.53409i	0.944288	−	0.306818i
$26$		0			0
$27$	2.45214	+	1.78159i	0.471915	+	0.342866i
$28$		0			0
$29$	4.05510	−	3.65123i	0.753014	−	0.678017i	−0.200389	−	0.979716i	$-0.564221\pi$
$29$	4.05510	−	3.65123i	0.753014	−	0.678017i	0.953403	+	0.301700i	$0.0975540\pi$
$30$		0			0
$31$	4.31241	+	0.683018i	0.774531	+	0.122674i	0.531174	−	0.847263i	$-0.321751\pi$
$31$	4.31241	+	0.683018i	0.774531	+	0.122674i	0.243358	+	0.969937i	$0.421751\pi$
$32$		0			0
$33$	−3.92112	−	5.92055i	−0.682579	−	1.03064i
$34$		0			0
$35$	0.0721385	−	0.162026i	0.0121936	−	0.0273873i
$36$		0			0
$37$	5.83831	+	0.305973i	0.959813	+	0.0503016i	0.525803	−	0.850606i	$-0.323765\pi$
$37$	5.83831	+	0.305973i	0.959813	+	0.0503016i	0.434010	+	0.900908i	$0.357098\pi$
$38$		0			0
$39$	7.45527	+	2.00395i	1.19380	+	0.320889i
$40$		0			0
$41$	9.31660	−	6.05027i	1.45501	−	0.944894i	0.456533	−	0.889706i	$-0.349091\pi$
$41$	9.31660	−	6.05027i	1.45501	−	0.944894i	0.998476	−	0.0551876i	$-0.0175757\pi$
$42$		0			0
$43$	5.79926	+	10.0446i	0.884378	+	1.53179i	0.846424	+	0.532509i	$0.178751\pi$
$43$	5.79926	+	10.0446i	0.884378	+	1.53179i	0.0379539	+	0.999279i	$0.487916\pi$
$44$		0			0
$45$	0.0773556	−	0.288695i	0.0115315	−	0.0430361i
$46$		0			0
$47$	−5.96221	−	3.03790i	−0.869678	−	0.443123i	−0.0385842	−	0.999255i	$-0.512285\pi$
$47$	−5.96221	−	3.03790i	−0.869678	−	0.443123i	−0.831094	+	0.556132i	$0.812285\pi$
$48$		0			0
$49$	−2.48762	−	5.58728i	−0.355374	−	0.798183i
$50$		0			0
$51$	−1.06015	+	3.26281i	−0.148451	+	0.456885i
$52$		0			0
$53$	−11.1948	+	8.13352i	−1.53773	+	1.11722i	−0.585987	+	0.810320i	$0.699293\pi$
$53$	−11.1948	+	8.13352i	−1.53773	+	1.11722i	−0.951740	+	0.306904i	$0.900707\pi$
$54$		0			0
$55$	0.363176	−	0.509456i	0.0489706	−	0.0686950i
$56$		0			0
$57$	0.00273714	−	0.0172816i	0.000362543	−	0.00228901i
$58$		0			0
$59$	−0.951072	+	1.46452i	−0.123819	+	0.190665i	−0.895144	−	0.445777i	$-0.852928\pi$
$59$	−0.951072	+	1.46452i	−0.123819	+	0.190665i	0.771325	+	0.636441i	$0.219594\pi$
$60$		0			0
$61$	1.97824	+	0.207921i	0.253287	+	0.0266216i	0.230321	−	0.973115i	$-0.426022\pi$
$61$	1.97824	+	0.207921i	0.253287	+	0.0266216i	0.0229662	+	0.999736i	$0.492689\pi$
$62$		0			0
$63$	0.811303	+	1.24930i	0.102215	+	0.157397i
$64$		0			0
$65$	0.0705608	+	0.676487i	0.00875199	+	0.0839079i
$66$		0			0
$67$	8.32006	−	2.22935i	1.01646	−	0.272359i	0.288132	−	0.957591i	$-0.406966\pi$
$67$	8.32006	−	2.22935i	1.01646	−	0.272359i	0.728325	+	0.685232i	$0.240299\pi$
$68$		0			0
$69$	−9.30511	−	8.37836i	−1.12020	−	1.00864i
$70$		0			0
$71$	2.51175	−	2.03398i	0.298090	−	0.241389i	−0.468593	−	0.883414i	$-0.655239\pi$
$71$	2.51175	−	2.03398i	0.298090	−	0.241389i	0.766683	+	0.642025i	$0.221906\pi$
$72$		0			0
$73$	4.62547	−	2.35679i	0.541370	−	0.275842i	−0.161849	−	0.986816i	$-0.551746\pi$
$73$	4.62547	−	2.35679i	0.541370	−	0.275842i	0.703218	+	0.710974i	$0.251746\pi$
$74$		0			0
$75$	−10.5712	+	1.11107i	−1.22065	+	0.128296i
$76$		0			0
$77$	0.675769	+	3.04416i	0.0770111	+	0.346914i
$78$		0			0
$79$	4.04902	+	5.57300i	0.455550	+	0.627011i	0.973579	−	0.228352i	$-0.0733338\pi$
$79$	4.04902	+	5.57300i	0.455550	+	0.627011i	−0.518028	+	0.855363i	$0.673334\pi$
$80$		0			0
$81$	−7.52296	−	8.35509i	−0.835884	−	0.928343i
$82$		0			0
$83$	−15.9720	+	2.52972i	−1.75316	+	0.277673i	−0.948663	−	0.316289i	$-0.897563\pi$
$83$	−15.9720	+	2.52972i	−1.75316	+	0.277673i	−0.804493	+	0.593962i	$0.797563\pi$
$84$		0			0
$85$	−0.301848	+	0.0158192i	−0.0327400	+	0.00171583i
$86$		0			0
$87$	−10.1181	+	5.84169i	−1.08477	+	0.626295i
$88$		0			0
$89$	1.46565	+	5.46989i	0.155359	+	0.579808i	0.999074	+	0.0430168i	$0.0136969\pi$
$89$	1.46565	+	5.46989i	0.155359	+	0.579808i	−0.843715	+	0.536791i	$0.819636\pi$
$90$		0			0
$91$	−2.74092	−	1.99471i	−0.287326	−	0.209102i
$92$		0			0
$93$	−8.72754	−	3.35019i	−0.905003	−	0.347398i
$94$		0			0
$95$	0.00150788		0.000320509i	0.000154705		3.28836e-5i
$96$		0			0
$97$	2.45427	+	6.39358i	0.249193	+	0.649170i	0.999935	−	0.0114258i	$-0.00363703\pi$
$97$	2.45427	+	6.39358i	0.249193	+	0.649170i	−0.750742	+	0.660596i	$0.770304\pi$
$98$		0			0
$99$	1.92725	+	4.88860i	0.193696	+	0.491323i
$100$		0			0
$101$	−0.734906	−	6.99216i	−0.0731259	−	0.695746i	−0.968259	−	0.249948i	$-0.919586\pi$
$101$	−0.734906	−	6.99216i	−0.0731259	−	0.695746i	0.895133	−	0.445798i	$-0.147080\pi$
$102$		0			0
$103$	7.32386	+	2.37967i	0.721641	+	0.234475i	0.646735	−	0.762715i	$-0.276134\pi$
$103$	7.32386	+	2.37967i	0.721641	+	0.234475i	0.0749066	+	0.997191i	$0.476134\pi$
$104$		0			0
$105$	−0.223209	+	0.307222i	−0.0217830	+	0.0299817i
$106$		0			0
$107$	3.44190	−	16.1929i	0.332741	−	1.56542i	−0.420260	−	0.907404i	$-0.638061\pi$
$107$	3.44190	−	16.1929i	0.332741	−	1.56542i	0.753001	−	0.658019i	$-0.228605\pi$
$108$		0			0
$109$	−4.10271	+	4.10271i	−0.392968	+	0.392968i	−0.875744	−	0.482776i	$-0.839629\pi$
$109$	−4.10271	+	4.10271i	−0.392968	+	0.392968i	0.482776	+	0.875744i	$0.339629\pi$
$110$		0			0
$111$	−12.0911	−	3.23981i	−1.14764	−	0.307509i
$112$		0			0
$113$	−9.86452	+	10.9557i	−0.927976	+	1.03062i	0.0714735	+	0.997442i	$0.477230\pi$
$113$	−9.86452	+	10.9557i	−0.927976	+	1.03062i	−0.999449	+	0.0331791i	$0.989437\pi$
$114$		0			0
$115$	0.395343	−	1.02990i	0.0368660	−	0.0960391i
$116$		0			0
$117$	−5.08786	−	2.59747i	−0.470373	−	0.240136i
$118$		0			0
$119$	0.948056	−	1.17075i	0.0869082	−	0.107323i
$120$		0			0
$121$	0.198145	+	10.9982i	0.0180131	+	0.999838i
$122$		0			0
$123$	−22.2054	+	8.52384i	−2.00219	+	0.768569i
$124$		0			0
$125$	−0.853367	−	1.67483i	−0.0763275	−	0.149801i
$126$		0			0
$127$	−2.73808	+	1.21907i	−0.242965	+	0.108175i	−0.524607	−	0.851345i	$-0.675788\pi$
$127$	−2.73808	+	1.21907i	−0.242965	+	0.108175i	0.281642	+	0.959520i	$0.409121\pi$
$128$		0			0
$129$	−7.67405	−	23.6183i	−0.675663	−	2.07948i
$130$		0			0
$131$			8.36775i			0.731094i	0.930793	+	0.365547i	$0.119118\pi$
$131$			8.36775i			0.731094i	−0.930793	+	0.365547i	$0.880882\pi$
$132$		0			0
$133$	−0.00384159	+	0.00665383i	−0.000333108	+	0.000576960i
$134$		0			0
$135$	0.259581	−	0.509456i	0.0223411	−	0.0438470i
$136$		0			0
$137$	−4.36905	−	5.39532i	−0.373273	−	0.460953i	0.555547	−	0.831485i	$-0.312509\pi$
$137$	−4.36905	−	5.39532i	−0.373273	−	0.460953i	−0.928820	+	0.370532i	$0.879176\pi$
$138$		0			0
$139$	0.551322	+	2.59376i	0.0467625	+	0.220000i	0.995324	−	0.0965927i	$-0.0307944\pi$
$139$	0.551322	+	2.59376i	0.0467625	+	0.220000i	−0.948562	+	0.316593i	$0.897461\pi$
$140$		0			0
$141$	11.1345	+	9.01651i	0.937691	+	0.759327i
$142$		0			0
$143$	−8.07438	−	8.82068i	−0.675214	−	0.737622i
$144$		0			0
$145$	−0.799960	−	0.647795i	−0.0664331	−	0.0537965i
$146$		0			0
$147$	2.72263	+	12.8090i	0.224559	+	1.05647i
$148$		0			0
$149$	0.103445	+	0.127744i	0.00847457	+	0.0104652i	0.781366	−	0.624074i	$-0.214523\pi$
$149$	0.103445	+	0.127744i	0.00847457	+	0.0104652i	−0.772891	+	0.634539i	$0.781190\pi$
$150$		0			0
$151$	4.97993	−	9.77366i	0.405261	−	0.795369i	−0.594702	−	0.803946i	$-0.702730\pi$
$151$	4.97993	−	9.77366i	0.405261	−	0.795369i	0.999963	+	0.00857688i	$0.00273014\pi$
$152$		0			0
$153$	1.26933	−	2.19854i	0.102619	−	0.177742i
$154$		0			0
$155$		−	0.823640i		−	0.0661563i
$156$		0			0
$157$	−0.512800	−	1.57824i	−0.0409259	−	0.125957i	0.928506	−	0.371317i	$-0.121094\pi$
$157$	−0.512800	−	1.57824i	−0.0409259	−	0.125957i	−0.969432	+	0.245360i	$0.921094\pi$
$158$		0			0
$159$	27.0664	−	12.0507i	2.14650	−	0.955685i
$160$		0			0
$161$	2.49615	+	4.89897i	0.196724	+	0.386093i
$162$		0			0
$163$	−20.3915	+	7.82758i	−1.59719	+	0.613103i	−0.984211	−	0.176998i	$-0.943362\pi$
$163$	−20.3915	+	7.82758i	−1.59719	+	0.613103i	−0.612977	+	0.790101i	$0.710028\pi$
$164$		0			0
$165$	−0.987400	+	0.905295i	−0.0768690	+	0.0704771i
$166$		0			0
$167$	0.702346	−	0.867326i	0.0543492	−	0.0671157i	−0.749246	−	0.662291i	$-0.769584\pi$
$167$	0.702346	−	0.867326i	0.0543492	−	0.0671157i	0.803596	+	0.595176i	$0.202917\pi$
$168$		0			0
$169$	12.9266	+	1.37932i	0.994355	+	0.106101i
$170$		0			0
$171$	−0.00463993	+	0.0120874i	−0.000354825	+	0.000924350i
$172$		0			0
$173$	−0.874303	+	0.971012i	−0.0664720	+	0.0738246i	−0.775464	−	0.631392i	$-0.782484\pi$
$173$	−0.874303	+	0.971012i	−0.0664720	+	0.0738246i	0.708992	+	0.705217i	$0.249150\pi$
$174$		0			0
$175$	4.50846	+	1.20804i	0.340808	+	0.0913191i
$176$		0			0
$177$	2.64381	−	2.64381i	0.198721	−	0.198721i
$178$		0			0
$179$	−1.14363	+	5.38034i	−0.0854787	+	0.402145i	−0.999997	−	0.00239869i	$-0.999236\pi$
$179$	−1.14363	+	5.38034i	−0.0854787	+	0.402145i	0.914518	+	0.404544i	$0.132570\pi$
$180$		0			0
$181$	6.08403	−	8.37395i	0.452222	−	0.622431i	−0.520651	−	0.853770i	$-0.674311\pi$
$181$	6.08403	−	8.37395i	0.452222	−	0.622431i	0.972873	+	0.231339i	$0.0743106\pi$
$182$		0			0
$183$	−4.05052	−	1.31609i	−0.299423	−	0.0972884i
$184$		0			0
$185$	−0.115280	−	1.09682i	−0.00847557	−	0.0806397i
$186$		0			0
$187$	4.09966	−	3.38143i	0.299797	−	0.247275i
$188$		0			0
$189$	1.02125	+	2.66046i	0.0742853	+	0.193520i
$190$		0			0
$191$	9.18977	−	1.95335i	0.664948	−	0.141339i	0.136941	−	0.990579i	$-0.456273\pi$
$191$	9.18977	−	1.95335i	0.664948	−	0.141339i	0.528007	+	0.849240i	$0.322939\pi$
$192$		0			0
$193$	12.3467	+	4.73946i	0.888736	+	0.341154i	0.759536	−	0.650465i	$-0.225426\pi$
$193$	12.3467	+	4.73946i	0.888736	+	0.341154i	0.129200	+	0.991619i	$0.458759\pi$
$194$		0			0
$195$	0.153369	−	1.44820i	0.0109830	−	0.103707i
$196$		0			0
$197$	−0.243861	−	0.910100i	−0.0173743	−	0.0648419i	0.956694	−	0.291094i	$-0.0940193\pi$
$197$	−0.243861	−	0.910100i	−0.0173743	−	0.0648419i	−0.974069	+	0.226252i	$0.927353\pi$
$198$		0			0
$199$	2.60690	−	1.50509i	0.184798	−	0.106693i	−0.404747	−	0.914429i	$-0.632640\pi$
$199$	2.60690	−	1.50509i	0.184798	−	0.106693i	0.589545	+	0.807735i	$0.299307\pi$
$200$		0			0
$201$	−18.4174	+	0.965213i	−1.29906	+	0.0680809i
$202$		0			0
$203$	5.06716	−	0.802560i	0.355645	−	0.0563286i
$204$		0			0
$205$	−1.40221	−	1.55732i	−0.0979349	−	0.108768i
$206$		0			0
$207$	5.44609	+	7.49590i	0.378529	+	0.521001i
$208$		0			0
$209$	−0.0179534	+	0.0203041i	−0.00124187	+	0.00140447i
$210$		0			0
$211$	7.40704	−	0.778511i	0.509922	−	0.0535949i	0.153926	−	0.988082i	$-0.450808\pi$
$211$	7.40704	−	0.778511i	0.509922	−	0.0535949i	0.355996	+	0.934488i	$0.384142\pi$
$212$		0			0
$213$	−6.16589	+	3.14168i	−0.422480	+	0.215264i
$214$		0			0
$215$	1.70037	−	1.37693i	0.115964	−	0.0939058i
$216$		0			0
$217$	3.05063	+	2.74680i	0.207090	+	0.186465i
$218$		0			0
$219$	−10.7364	+	2.87681i	−0.725498	+	0.194397i
$220$		0			0
$221$	−0.908265	+	5.70536i	−0.0610965	+	0.383784i
$222$		0			0
$223$	−9.28132	−	14.2920i	−0.621523	−	0.957062i	−0.999512	−	0.0312515i	$-0.990051\pi$
$223$	−9.28132	−	14.2920i	−0.621523	−	0.957062i	0.377988	−	0.925810i	$-0.376616\pi$
$224$		0			0
$225$	7.82241	+	0.822168i	0.521494	+	0.0548112i
$226$		0			0
$227$	−1.08752	+	1.67464i	−0.0721816	+	0.111150i	−0.872918	−	0.487867i	$-0.837775\pi$
$227$	−1.08752	+	1.67464i	−0.0721816	+	0.111150i	0.800736	+	0.599017i	$0.204442\pi$
$228$		0			0
$229$	−3.21965	+	20.3281i	−0.212760	+	1.34332i	0.617777	+	0.786353i	$0.288033\pi$
$229$	−3.21965	+	20.3281i	−0.212760	+	1.34332i	−0.830537	+	0.556963i	$0.811967\pi$
$230$		0			0
$231$	−0.0601353	−	6.67629i	−0.00395662	−	0.439268i
$232$		0			0
$233$	0.763464	−	0.554689i	0.0500162	−	0.0363389i	−0.562496	−	0.826800i	$-0.690159\pi$
$233$	0.763464	−	0.554689i	0.0500162	−	0.0363389i	0.612512	+	0.790461i	$0.290159\pi$
$234$		0			0
$235$	−0.390073	+	1.20052i	−0.0254456	+	0.0783135i
$236$		0			0
$237$	−5.99908	−	13.4741i	−0.389682	−	0.875240i
$238$		0			0
$239$	−3.71908	−	1.89496i	−0.240567	−	0.122575i	0.329551	−	0.944138i	$-0.393103\pi$
$239$	−3.71908	−	1.89496i	−0.240567	−	0.122575i	−0.570118	+	0.821563i	$0.693103\pi$
$240$		0			0
$241$	5.80718	−	21.6727i	0.374073	−	1.39606i	−0.480621	−	0.876929i	$-0.659589\pi$
$241$	5.80718	−	21.6727i	0.374073	−	1.39606i	0.854694	−	0.519132i	$-0.173745\pi$
$242$		0			0
$243$	7.48963	+	12.9724i	0.480460	+	0.832181i
$244$		0			0
$245$	−0.967607	+	0.628372i	−0.0618182	+	0.0401452i
$246$		0			0
$247$	2.33000e−5	−	0.0294643i	1.48255e−6	−	0.00187477i
$248$		0			0
$249$	34.5767	+	1.81209i	2.19121	+	0.114837i
$250$		0			0
$251$	7.01754	−	15.7616i	0.442943	−	0.994866i	−0.544770	−	0.838586i	$-0.683383\pi$
$251$	7.01754	−	15.7616i	0.442943	−	0.994866i	0.987713	−	0.156281i	$-0.0499504\pi$
$252$		0			0
$253$	5.18850	+	18.6888i	0.326198	+	1.17495i
$254$		0			0
$255$	0.639210	+	0.101241i	0.0400289	+	0.00633995i
$256$		0			0
$257$	1.57540	−	1.41850i	0.0982708	−	0.0884835i	−0.618531	−	0.785760i	$-0.712272\pi$
$257$	1.57540	−	1.41850i	0.0982708	−	0.0884835i	0.716802	+	0.697277i	$0.245605\pi$
$258$		0			0
$259$	4.44690	+	3.23086i	0.276317	+	0.200756i
$260$		0			0
$261$	8.22229	−	2.67158i	0.508947	−	0.165367i
$262$		0			0
$263$	−15.2307	−	8.79347i	−0.939168	−	0.542229i	−0.0494684	−	0.998776i	$-0.515753\pi$
$263$	−15.2307	−	8.79347i	−0.939168	−	0.542229i	−0.889699	+	0.456547i	$0.849086\pi$
$264$		0			0
$265$	1.84579	+	1.84579i	0.113386	+	0.113386i
$266$		0			0
$267$	−0.634564	−	12.1082i	−0.0388347	−	0.741010i
$268$		0			0
$269$	−1.47990	+	14.0803i	−0.0902312	+	0.858493i	0.852003	+	0.523537i	$0.175388\pi$
$269$	−1.47990	+	14.0803i	−0.0902312	+	0.858493i	−0.942234	+	0.334955i	$0.891279\pi$
$270$		0			0
$271$	−1.25422	+	23.9319i	−0.0761882	+	1.45376i	0.646675	+	0.762766i	$0.276159\pi$
$271$	−1.25422	+	23.9319i	−0.0761882	+	1.45376i	−0.722863	+	0.690991i	$0.757174\pi$
$272$		0			0
$273$	4.85241	+	5.39772i	0.293681	+	0.326685i
$274$		0			0
$275$	14.7372	+	7.34256i	0.888689	+	0.442773i
$276$		0			0
$277$	−21.5239	−	9.58305i	−1.29324	−	0.575790i	−0.359305	−	0.933220i	$-0.616986\pi$
$277$	−21.5239	−	9.58305i	−1.29324	−	0.575790i	−0.933940	+	0.357431i	$0.883653\pi$
$278$		0			0
$279$	5.80162	+	3.76762i	0.347334	+	0.225561i
$280$		0			0
$281$	−3.25541	−	20.5539i	−0.194202	−	1.22614i	−0.871486	−	0.490420i	$-0.836844\pi$
$281$	−3.25541	−	20.5539i	−0.194202	−	1.22614i	0.677285	−	0.735721i	$-0.263156\pi$
$282$		0			0
$283$	0.125581	+	0.0266932i	0.00746504	+	0.00158674i	0.211643	−	0.977347i	$-0.432119\pi$
$283$	0.125581	+	0.0266932i	0.00746504	+	0.00158674i	−0.204178	+	0.978934i	$0.565452\pi$
$284$		0			0
$285$	−0.00330067			−0.000195515
$286$		0			0
$287$	10.4444			0.616512
$288$		0			0
$289$	14.1172	+	3.00071i	0.830425	+	0.176512i
$290$		0			0
$291$	−2.29385	−	14.4828i	−0.134468	−	0.848997i
$292$		0			0
$293$	−20.8452	−	13.5371i	−1.21779	−	0.790843i	−0.234365	−	0.972149i	$-0.575301\pi$
$293$	−20.8452	−	13.5371i	−1.21779	−	0.790843i	−0.983427	+	0.181306i	$0.941968\pi$
$294$		0			0
$295$	0.300935	+	0.133985i	0.0175211	+	0.00780089i
$296$		0			0
$297$	1.66196	+	9.91441i	0.0964368	+	0.575292i
$298$		0			0
$299$	−17.6745	−	11.4979i	−1.02214	−	0.664938i
$300$		0			0
$301$	−0.570715	+	10.8899i	−0.0328954	+	0.627682i
$302$		0			0
$303$	−1.57352	+	14.9710i	−0.0903963	+	0.860063i
$304$		0			0
$305$	−0.0196382	−	0.374719i	−0.00112448	−	0.0214564i
$306$		0			0
$307$	−8.77640	−	8.77640i	−0.500895	−	0.500895i	0.410821	−	0.911716i	$-0.365242\pi$
$307$	−8.77640	−	8.77640i	−0.500895	−	0.500895i	−0.911716	+	0.410821i	$0.865242\pi$
$308$		0			0
$309$	−14.2792	−	8.24411i	−0.812316	−	0.468991i
$310$		0			0
$311$	−14.9120	+	4.84520i	−0.845581	+	0.274746i	−0.699594	−	0.714540i	$-0.746636\pi$
$311$	−14.9120	+	4.84520i	−0.845581	+	0.274746i	−0.145987	+	0.989286i	$0.546636\pi$
$312$		0			0
$313$	25.7614	+	18.7167i	1.45612	+	1.05793i	0.984353	+	0.176209i	$0.0563834\pi$
$313$	25.7614	+	18.7167i	1.45612	+	1.05793i	0.471766	+	0.881724i	$0.343617\pi$
$314$		0			0
$315$	0.208826	−	0.188028i	0.0117660	−	0.0105942i
$316$		0			0
$317$	22.3296	+	3.53666i	1.25415	+	0.198639i	0.747939	−	0.663768i	$-0.231044\pi$
$317$	22.3296	+	3.53666i	1.25415	+	0.198639i	0.506216	+	0.862407i	$0.331044\pi$
$318$		0			0
$319$	18.0808	+	0.784343i	1.01233	+	0.0439148i
$320$		0			0
$321$	−14.4169	+	32.3809i	−0.804674	+	1.80733i
$322$		0			0
$323$	0.0130760		0.000685284i	0.000727568		3.81302e-5i
$324$		0			0
$325$	−17.2932	+	4.61904i	−0.959254	+	0.256219i
$326$		0			0
$327$	10.4188	−	6.76604i	0.576160	−	0.374163i
$328$		0			0
$329$	−3.14567	−	5.44846i	−0.173426	−	0.300383i
$330$		0			0
$331$	−7.46987	+	27.8779i	−0.410581	+	1.53231i	0.382944	+	0.923772i	$0.374910\pi$
$331$	−7.46987	+	27.8779i	−0.410581	+	1.53231i	−0.793525	+	0.608538i	$0.791756\pi$
$332$		0			0
$333$	8.25319	+	4.20521i	0.452272	+	0.230444i
$334$		0			0
$335$	−0.660897	−	1.48440i	−0.0361086	−	0.0811013i
$336$		0			0
$337$	8.73216	−	26.8748i	0.475671	−	1.46396i	−0.369380	−	0.929278i	$-0.620430\pi$
$337$	8.73216	−	26.8748i	0.475671	−	1.46396i	0.845051	−	0.534686i	$-0.179570\pi$
$338$		0			0
$339$	25.5366	−	18.5534i	1.38696	−	1.00768i
$340$		0			0
$341$	8.61685	+	11.6382i	0.466628	+	0.630242i
$342$		0			0
$343$	1.92909	−	12.1798i	0.104161	−	0.657646i
$344$		0			0
$345$	−1.28645	+	1.98096i	−0.0692603	+	0.106652i
$346$		0			0
$347$	23.3689	+	2.45617i	1.25451	+	0.131854i	0.708369	−	0.705842i	$-0.249431\pi$
$347$	23.3689	+	2.45617i	1.25451	+	0.131854i	0.546137	+	0.837696i	$0.316098\pi$
$348$		0			0
$349$	−16.2938	−	25.0903i	−0.872189	−	1.34305i	−0.938509	−	0.345255i	$-0.887792\pi$
$349$	−16.2938	−	25.0903i	−0.872189	−	1.34305i	0.0663193	−	0.997798i	$-0.478874\pi$
$350$		0			0
$351$	−8.48758	−	6.88423i	−0.453034	−	0.367453i
$352$		0			0
$353$	−17.5442	+	4.70095i	−0.933782	+	0.250206i	−0.693467	−	0.720489i	$-0.743918\pi$
$353$	−17.5442	+	4.70095i	−0.933782	+	0.250206i	−0.240315	+	0.970695i	$0.577251\pi$
$354$		0			0
$355$	−0.453091	−	0.407965i	−0.0240476	−	0.0216525i
$356$		0			0
$357$	−2.50672	+	2.02990i	−0.132669	+	0.107434i
$358$		0			0
$359$	−19.4392	+	9.90477i	−1.02596	+	0.522754i	−0.884181	−	0.467145i	$-0.845283\pi$
$359$	−19.4392	+	9.90477i	−1.02596	+	0.522754i	−0.141781	+	0.989898i	$0.545283\pi$
$360$		0			0
$361$	18.8958	−	1.98603i	0.994518	−	0.104528i
$362$		0			0
$363$	4.48102	−	23.1221i	0.235192	−	1.21359i
$364$		0			0
$365$	−0.575613	−	0.792263i	−0.0301290	−	0.0414690i
$366$		0			0
$367$	21.1092	+	23.4442i	1.10189	+	1.22378i	0.972678	+	0.232159i	$0.0745790\pi$
$367$	21.1092	+	23.4442i	1.10189	+	1.22378i	0.129215	+	0.991617i	$0.458754\pi$
$368$		0			0
$369$	17.3838	−	2.75332i	0.904964	−	0.143332i
$370$		0			0
$371$	−12.9921	+	0.680889i	−0.674518	+	0.0353500i
$372$		0			0
$373$	17.7076	−	10.2235i	0.916863	−	0.529351i	0.0342303	−	0.999414i	$-0.489102\pi$
$373$	17.7076	−	10.2235i	0.916863	−	0.529351i	0.882633	+	0.470063i	$0.155769\pi$
$374$		0			0
$375$	1.04166	+	3.88752i	0.0537910	+	0.200751i
$376$		0			0
$377$	−15.2996	+	12.3694i	−0.787970	+	0.637055i
$378$		0			0
$379$	18.1341	+	6.96101i	0.931484	+	0.357563i	0.776330	−	0.630327i	$-0.217079\pi$
$379$	18.1341	+	6.96101i	0.931484	+	0.357563i	0.155154	+	0.987890i	$0.450412\pi$
$380$		0			0
$381$	6.27711	−	1.33424i	0.321586	−	0.0683552i
$382$		0			0
$383$	0.595125	+	1.55035i	0.0304095	+	0.0792194i	0.947945	−	0.318436i	$-0.103157\pi$
$383$	0.595125	+	1.55035i	0.0304095	+	0.0792194i	−0.917535	+	0.397655i	$0.869824\pi$
$384$		0			0
$385$	0.547243	−	0.215742i	0.0278901	−	0.0109952i
$386$		0			0
$387$	1.92086	+	18.2757i	0.0976427	+	0.929008i
$388$		0			0
$389$	5.36014	+	1.74162i	0.271770	+	0.0883034i	0.441732	−	0.897147i	$-0.354364\pi$
$389$	5.36014	+	1.74162i	0.271770	+	0.0883034i	−0.169962	+	0.985451i	$0.554364\pi$
$390$		0			0
$391$	5.50773	−	7.58074i	0.278538	−	0.383374i
$392$		0			0
$393$	3.72501	−	17.5248i	0.187902	−	0.884010i
$394$		0			0
$395$	0.918869	−	0.918869i	0.0462333	−	0.0462333i
$396$		0			0
$397$	−20.2433	−	5.42418i	−1.01598	−	0.272232i	−0.287855	−	0.957674i	$-0.592942\pi$
$397$	−20.2433	−	5.42418i	−1.01598	−	0.272232i	−0.728127	+	0.685442i	$0.759609\pi$
$398$		0			0
$399$	0.0110076	−	0.0122252i	0.000551068	−	0.000612023i
$400$		0			0
$401$	8.18298	−	21.3174i	0.408639	−	1.06454i	−0.562663	−	0.826687i	$-0.690223\pi$
$401$	8.18298	−	21.3174i	0.408639	−	1.06454i	0.971301	−	0.237853i	$-0.0764437\pi$
$402$		0			0
$403$	−15.3958	−	3.28521i	−0.766920	−	0.163648i
$404$		0			0
$405$	−1.33471	+	1.64823i	−0.0663223	+	0.0819012i
$406$		0			0
$407$	13.1037	+	14.2922i	0.649529	+	0.708437i
$408$		0			0
$409$	27.7371	−	10.6473i	1.37151	−	0.526475i	0.442582	−	0.896728i	$-0.354062\pi$
$409$	27.7371	−	10.6473i	1.37151	−	0.526475i	0.928931	+	0.370253i	$0.120729\pi$
$410$		0			0
$411$	6.74841	+	13.2445i	0.332875	+	0.653303i
$412$		0			0
$413$	−1.49986	+	0.667781i	−0.0738033	+	0.0328594i
$414$		0			0
$415$	0.942670	+	2.90124i	0.0462738	+	0.142416i
$416$		0			0
$417$		−	5.67762i		−	0.278034i
$418$		0			0
$419$	9.47878	−	16.4177i	0.463069	−	0.802058i	−0.536043	−	0.844190i	$-0.680082\pi$
$419$	9.47878	−	16.4177i	0.463069	−	0.802058i	0.999112	+	0.0421321i	$0.0134150\pi$
$420$		0			0
$421$	−5.37336	+	10.5458i	−0.261882	+	0.513972i	−0.984083	−	0.177712i	$-0.943131\pi$
$421$	−5.37336	+	10.5458i	−0.261882	+	0.513972i	0.722201	+	0.691683i	$0.243131\pi$
$422$		0			0
$423$	−6.67201	−	8.23924i	−0.324404	−	0.400606i
$424$		0			0
$425$	−1.65384	−	7.78069i	−0.0802229	−	0.377419i
$426$		0			0
$427$	1.45339	+	1.17693i	0.0703346	+	0.0569559i
$428$		0			0
$429$	12.9838	+	22.0678i	0.626862	+	1.06544i
$430$		0			0
$431$	−3.76047	−	3.04517i	−0.181136	−	0.146681i	0.534464	−	0.845191i	$-0.320513\pi$
$431$	−3.76047	−	3.04517i	−0.181136	−	0.146681i	−0.715600	+	0.698510i	$0.753847\pi$
$432$		0			0
$433$	−7.02291	−	33.0402i	−0.337500	−	1.58781i	−0.740140	−	0.672453i	$-0.765241\pi$
$433$	−7.02291	−	33.0402i	−0.337500	−	1.58781i	0.402641	−	0.915358i	$-0.368092\pi$
$434$		0			0
$435$	1.38700	+	1.71281i	0.0665018	+	0.0821228i
$436$		0			0
$437$	−0.0216960	+	0.0425807i	−0.00103786	+	0.00203691i
$438$		0			0
$439$	5.20052	−	9.00756i	0.248207	−	0.429907i	−0.714821	−	0.699307i	$-0.753492\pi$
$439$	5.20052	−	9.00756i	0.248207	−	0.429907i	0.963028	+	0.269400i	$0.0868253\pi$
$440$		0			0
$441$		−	9.69010i		−	0.461434i
$442$		0			0
$443$	−4.30285	−	13.2428i	−0.204435	−	0.629185i	−0.999736	−	0.0229710i	$-0.992687\pi$
$443$	−4.30285	−	13.2428i	−0.204435	−	0.629185i	0.795302	−	0.606214i	$-0.207313\pi$
$444$		0			0
$445$	0.975894	−	0.434496i	0.0462618	−	0.0205971i
$446$		0			0
$447$	−0.159781	−	0.313589i	−0.00755740	−	0.0148322i
$448$		0			0
$449$	−24.5090	+	9.40811i	−1.15665	+	0.443996i	−0.859651	−	0.510882i	$-0.829319\pi$
$449$	−24.5090	+	9.40811i	−1.15665	+	0.443996i	−0.296998	+	0.954878i	$0.595986\pi$
$450$		0			0
$451$	36.1061	+	7.33532i	1.70017	+	0.345407i
$452$		0			0
$453$	−14.7805	+	18.2524i	−0.694447	+	0.857571i
$454$		0			0
$455$	−0.290767	+	0.569549i	−0.0136314	+	0.0267009i
$456$		0			0
$457$	−11.1853	+	29.1386i	−0.523225	+	1.36305i	0.376429	+	0.926445i	$0.377152\pi$
$457$	−11.1853	+	29.1386i	−0.523225	+	1.36305i	−0.899654	+	0.436603i	$0.856181\pi$
$458$		0			0
$459$	3.24971	−	3.60917i	0.151684	−	0.168462i
$460$		0			0
$461$	−21.5571	−	5.77620i	−1.00401	−	0.269024i	−0.280887	−	0.959741i	$-0.590629\pi$
$461$	−21.5571	−	5.77620i	−1.00401	−	0.269024i	−0.723125	+	0.690717i	$0.757295\pi$
$462$		0			0
$463$	−24.8262	+	24.8262i	−1.15377	+	1.15377i	−0.167980	+	0.985790i	$0.553724\pi$
$463$	−24.8262	+	24.8262i	−1.15377	+	1.15377i	−0.985790	+	0.167980i	$0.946276\pi$
$464$		0			0
$465$	−0.366654	+	1.72497i	−0.0170032	+	0.0799936i
$466$		0			0
$467$	4.62639	−	6.36768i	0.214084	−	0.294661i	−0.688447	−	0.725287i	$-0.741707\pi$
$467$	4.62639	−	6.36768i	0.214084	−	0.294661i	0.902531	+	0.430626i	$0.141707\pi$
$468$		0			0
$469$	7.70204	+	2.50254i	0.355647	+	0.115557i
$470$		0			0
$471$	0.371399	+	3.53362i	0.0171132	+	0.162821i
$472$		0			0
$473$	−9.62115	+	37.2453i	−0.442381	+	1.71254i
$474$		0			0
$475$	0.0145386	+	0.0378743i	0.000667075	+	0.00173779i
$476$		0			0
$477$	−21.4448	+	4.55824i	−0.981891	+	0.208707i
$478$		0			0
$479$	−37.1886	−	14.2754i	−1.69919	−	0.652259i	−0.701045	−	0.713117i	$-0.747283\pi$
$479$	−37.1886	−	14.2754i	−1.69919	−	0.652259i	−0.998146	+	0.0608584i	$0.980616\pi$
$480$		0			0
$481$	−20.9620	−	2.21996i	−0.955785	−	0.101221i
$482$		0			0
$483$	−3.04692	−	11.3712i	−0.138640	−	0.517410i
$484$		0			0
$485$	1.11882	−	0.645952i	0.0508031	−	0.0293312i
$486$		0			0
$487$	−25.0349	+	1.31202i	−1.13444	+	0.0594534i	−0.610294	−	0.792175i	$-0.708949\pi$
$487$	−25.0349	+	1.31202i	−1.13444	+	0.0594534i	−0.524146	+	0.851629i	$0.675615\pi$
$488$		0			0
$489$	46.1911	−	7.31595i	2.08883	−	0.330839i
$490$		0			0
$491$	−24.0154	−	26.6718i	−1.08380	−	1.20368i	−0.977849	−	0.209311i	$-0.932878\pi$
$491$	−24.0154	−	26.6718i	−1.08380	−	1.20368i	−0.105952	−	0.994371i	$-0.533789\pi$
$492$		0			0
$493$	−5.13917	−	7.07346i	−0.231457	−	0.318573i
$494$		0			0
$495$	0.853966	−	0.503347i	0.0383829	−	0.0226238i
$496$		0			0
$497$	3.02208	−	0.317633i	0.135559	−	0.0142478i
$498$		0			0
$499$	9.11911	−	4.64642i	0.408227	−	0.208002i	−0.237804	−	0.971313i	$-0.576428\pi$
$499$	9.11911	−	4.64642i	0.408227	−	0.208002i	0.646031	+	0.763311i	$0.276428\pi$
$500$		0			0
$501$	−1.85704	+	1.50380i	−0.0829666	+	0.0671851i
$502$		0			0
$503$	−1.41403	−	1.27319i	−0.0630483	−	0.0567690i	0.637004	−	0.770860i	$-0.280173\pi$
$503$	−1.41403	−	1.27319i	−0.0630483	−	0.0567690i	−0.700052	+	0.714091i	$0.746840\pi$
$504$		0			0
$505$	−1.28109	+	0.343266i	−0.0570076	+	0.0152751i
$506$		0			0
$507$	−26.4585	−	8.64319i	−1.17507	−	0.383858i
$508$		0			0
$509$	19.9922	+	30.7852i	0.886137	+	1.36453i	0.930800	+	0.365530i	$0.119112\pi$
$509$	19.9922	+	30.7852i	0.886137	+	1.36453i	−0.0446624	+	0.999002i	$0.514221\pi$
$510$		0			0
$511$	4.85406	+	0.510182i	0.214731	+	0.0225691i
$512$		0			0
$513$	−0.0134903	+	0.0207732i	−0.000595611	+	0.000917160i
$514$		0			0
$515$	0.227250	−	1.43480i	0.0100138	−	0.0632248i
$516$		0			0
$517$	−7.04796	−	21.0445i	−0.309969	−	0.925536i
$518$		0			0
$519$	2.26333	−	1.64441i	0.0993493	−	0.0721815i
$520$		0			0
$521$	−2.94005	+	9.04855i	−0.128806	+	0.396424i	−0.994575	−	0.104019i	$-0.966830\pi$
$521$	−2.94005	+	9.04855i	−0.128806	+	0.396424i	0.865769	+	0.500443i	$0.166830\pi$
$522$		0			0
$523$	2.62025	+	5.88517i	0.114575	+	0.257341i	0.961726	−	0.274012i	$-0.0883507\pi$
$523$	2.62025	+	5.88517i	0.114575	+	0.257341i	−0.847151	+	0.531352i	$0.821684\pi$
$524$		0			0
$525$	−8.90442	−	4.53703i	−0.388621	−	0.198012i
$526$		0			0
$527$	1.81068	−	6.75755i	0.0788745	−	0.294364i
$528$		0			0
$529$	5.59959	+	9.69877i	0.243460	+	0.421686i
$530$		0			0
$531$	−2.32035	+	1.50685i	−0.100695	+	0.0653919i
$532$		0			0
$533$	−34.7030	+	19.9992i	−1.50315	+	0.866261i
$534$		0			0
$535$	−3.11861	−	0.163439i	−0.134829	−	0.00706610i
$536$		0			0
$537$	4.79026	−	10.7591i	0.206715	−	0.464289i
$538$		0			0
$539$	7.09849	−	19.0020i	0.305754	−	0.818475i
$540$		0			0
$541$	−3.72518	−	0.590010i	−0.160158	−	0.0253665i	0.0758406	−	0.997120i	$-0.475836\pi$
$541$	−3.72518	−	0.590010i	−0.160158	−	0.0253665i	−0.235998	+	0.971753i	$0.575836\pi$
$542$		0			0
$543$	−16.4697	+	14.8294i	−0.706783	+	0.636391i
$544$		0			0
$545$	0.885484	+	0.643342i	0.0379300	+	0.0275577i
$546$		0			0
$547$	−2.78066	+	0.903490i	−0.118892	+	0.0386305i	−0.367859	−	0.929882i	$-0.619909\pi$
$547$	−2.78066	+	0.903490i	−0.118892	+	0.0386305i	0.248967	+	0.968512i	$0.419909\pi$
$548$		0			0
$549$	2.72931	+	1.57577i	0.116484	+	0.0672521i
$550$		0			0
$551$	0.0315310	+	0.0315310i	0.00134327	+	0.00134327i
$552$		0			0
$553$	0.338959	+	6.46773i	0.0144140	+	0.275036i
$554$		0			0
$555$	−0.246828	+	2.34841i	−0.0104773	+	0.0996847i
$556$		0			0
$557$	−2.17394	+	41.4812i	−0.0921127	+	1.75761i	0.428242	+	0.903664i	$0.359133\pi$
$557$	−2.17394	+	41.4812i	−0.0921127	+	1.75761i	−0.520354	+	0.853951i	$0.674200\pi$
$558$		0			0
$559$	−18.9560	−	37.2760i	−0.801752	−	1.57661i
$560$		0			0
$561$	−10.0913	+	5.25680i	−0.426056	+	0.221942i
$562$		0			0
$563$	−22.2454	−	9.90429i	−0.937531	−	0.417416i	−0.119659	−	0.992815i	$-0.538180\pi$
$563$	−22.2454	−	9.90429i	−0.937531	−	0.417416i	−0.817873	+	0.575399i	$0.804847\pi$
$564$		0			0
$565$	2.33235	+	1.51465i	0.0981227	+	0.0637216i
$566$		0			0
$567$	−1.65358	−	10.4403i	−0.0694440	−	0.438452i
$568$		0			0
$569$	13.0592	+	2.77581i	0.547468	+	0.116368i	0.473339	−	0.880881i	$-0.343049\pi$
$569$	13.0592	+	2.77581i	0.547468	+	0.116368i	0.0741299	+	0.997249i	$0.476382\pi$
$570$		0			0
$571$	−39.3734			−1.64772			−0.823862	−	0.566791i	$-0.808185\pi$
$571$	−39.3734			−1.64772			−0.823862	+	0.566791i	$0.808185\pi$
$572$		0			0
$573$	−20.1159			−0.840355
$574$		0			0
$575$	28.3975	+	6.03608i	1.18426	+	0.251722i
$576$		0			0
$577$	0.336835	+	2.12669i	0.0140226	+	0.0885353i	0.993707	−	0.112010i	$-0.0357287\pi$
$577$	0.336835	+	2.12669i	0.0140226	+	0.0885353i	−0.979685	+	0.200545i	$0.935729\pi$
$578$		0			0
$579$	−23.7482	−	15.4223i	−0.986943	−	0.640928i
$580$		0			0
$581$	−13.8895	−	6.18400i	−0.576233	−	0.256555i
$582$		0			0
$583$	−45.3918	−	6.77084i	−1.87994	−	0.280420i
$584$		0			0
$585$	−0.333815	+	1.02462i	−0.0138015	+	0.0423627i
$586$		0			0
$587$	0.604747	−	11.5393i	0.0249606	−	0.476276i	−0.957340	−	0.288964i	$-0.906689\pi$
$587$	0.604747	−	11.5393i	0.0249606	−	0.476276i	0.982300	−	0.187312i	$-0.0599776\pi$
$588$		0			0
$589$	−0.00372957	+	0.0354845i	−0.000153674	+	0.00146211i
$590$		0			0
$591$	0.105581	+	2.01460i	0.00434302	+	0.0828698i
$592$		0			0
$593$	13.4004	+	13.4004i	0.550288	+	0.550288i	0.926524	−	0.376236i	$-0.122782\pi$
$593$	13.4004	+	13.4004i	0.550288	+	0.550288i	−0.376236	+	0.926524i	$0.622782\pi$
$594$		0			0
$595$	−0.246111	−	0.142092i	−0.0100896	−	0.00582521i
$596$		0			0
$597$	−6.12971	+	1.99167i	−0.250873	+	0.0815134i
$598$		0			0
$599$	−2.92583	−	2.12574i	−0.119546	−	0.0868554i	0.526406	−	0.850234i	$-0.323539\pi$
$599$	−2.92583	−	2.12574i	−0.119546	−	0.0868554i	−0.645952	+	0.763378i	$0.723539\pi$
$600$		0			0
$601$	3.22963	−	2.90797i	0.131739	−	0.118619i	−0.600627	−	0.799529i	$-0.705082\pi$
$601$	3.22963	−	2.90797i	0.131739	−	0.118619i	0.732367	+	0.680910i	$0.238416\pi$
$602$		0			0
$603$	13.4791	+	2.13488i	0.548911	+	0.0869390i
$604$		0			0
$605$	2.04333	−	0.361476i	0.0830732	−	0.0146961i
$606$		0			0
$607$	−6.01439	+	13.5085i	−0.244117	+	0.548295i	−0.993499	−	0.113843i	$-0.963684\pi$
$607$	−6.01439	+	13.5085i	−0.244117	+	0.548295i	0.749382	+	0.662138i	$0.230351\pi$
$608$		0			0
$609$	−10.9696	−	0.574890i	−0.444509	−	0.0232957i
$610$		0			0
$611$	20.8848	+	12.0799i	0.844909	+	0.488700i
$612$		0			0
$613$	−26.8190	+	17.4165i	−1.08321	+	0.703444i	−0.957445	−	0.288616i	$-0.906805\pi$
$613$	−26.8190	+	17.4165i	−1.08321	+	0.703444i	−0.125764	+	0.992060i	$0.540138\pi$
$614$		0			0
$615$	2.24344	+	3.88575i	0.0904641	+	0.156688i
$616$		0			0
$617$	−1.72038	+	6.42054i	−0.0692598	+	0.258481i	−0.991871	−	0.127251i	$-0.959385\pi$
$617$	−1.72038	+	6.42054i	−0.0692598	+	0.258481i	0.922611	+	0.385732i	$0.126051\pi$
$618$		0			0
$619$	−13.9525	−	7.10914i	−0.560797	−	0.285740i	0.150526	−	0.988606i	$-0.451903\pi$
$619$	−13.9525	−	7.10914i	−0.560797	−	0.285740i	−0.711322	+	0.702866i	$0.751903\pi$
$620$		0			0
$621$	7.20957	+	16.1930i	0.289310	+	0.649801i
$622$		0			0
$623$	−1.64526	+	5.06358i	−0.0659159	+	0.202868i
$624$		0			0
$625$	19.7946	−	14.3816i	0.791784	−	0.575265i
$626$		0			0
$627$	0.0466390	−	0.0345313i	0.00186258	−	0.00137905i
$628$		0			0
$629$	1.46542	−	9.25228i	0.0584300	−	0.368912i
$630$		0			0
$631$	−5.09152	+	7.84026i	−0.202690	+	0.312116i	−0.925368	−	0.379069i	$-0.876244\pi$
$631$	−5.09152	+	7.84026i	−0.202690	+	0.312116i	0.722678	+	0.691185i	$0.242911\pi$
$632$		0			0
$633$	−15.8593	−	1.66688i	−0.630352	−	0.0662526i
$634$		0			0
$635$	0.307937	+	0.474181i	0.0122201	+	0.0188173i
$636$		0			0
$637$	7.88634	+	20.5933i	0.312468	+	0.815935i
$638$		0			0
$639$	4.94626	−	1.32535i	0.195671	−	0.0524298i
$640$		0			0
$641$	−11.3160	−	10.1889i	−0.446954	−	0.402439i	0.414682	−	0.909967i	$-0.363893\pi$
$641$	−11.3160	−	10.1889i	−0.446954	−	0.402439i	−0.861636	+	0.507527i	$0.830560\pi$
$642$		0			0
$643$	−15.5727	+	12.6105i	−0.614127	+	0.497311i	−0.885177	−	0.465255i	$-0.845963\pi$
$643$	−15.5727	+	12.6105i	−0.614127	+	0.497311i	0.271049	+	0.962565i	$0.412629\pi$
$644$		0			0
$645$	−4.17408	+	2.12680i	−0.164354	+	0.0837427i
$646$		0			0
$647$	−35.3093	+	3.71116i	−1.38815	+	0.145901i	−0.768940	−	0.639321i	$-0.779215\pi$
$647$	−35.3093	+	3.71116i	−1.38815	+	0.145901i	−0.619214	+	0.785222i	$0.712549\pi$
$648$		0			0
$649$	−5.65399	+	1.25512i	−0.221939	+	0.0492679i
$650$		0			0
$651$	−5.16625	−	7.11073i	−0.202481	−	0.278691i
$652$		0			0
$653$	9.83640	+	10.9244i	0.384928	+	0.427506i	0.904204	−	0.427101i	$-0.140465\pi$
$653$	9.83640	+	10.9244i	0.384928	+	0.427506i	−0.519276	+	0.854607i	$0.673798\pi$
$654$		0			0
$655$	1.55907	−	0.246933i	0.0609180	−	0.00964846i
$656$		0			0
$657$	8.21367	−	0.430460i	0.320446	−	0.0167938i
$658$		0			0
$659$	26.4838	−	15.2904i	1.03166	−	0.595631i	0.114203	−	0.993457i	$-0.463569\pi$
$659$	26.4838	−	15.2904i	1.03166	−	0.595631i	0.917461	+	0.397826i	$0.130235\pi$
$660$		0			0
$661$	−8.11588	−	30.2889i	−0.315671	−	1.17810i	−0.923363	−	0.383928i	$-0.874571\pi$
$661$	−8.11588	−	30.2889i	−0.315671	−	1.17810i	0.607692	−	0.794173i	$-0.292096\pi$
$662$		0			0
$663$	4.44202	−	11.5446i	0.172514	−	0.448354i
$664$		0			0
$665$	0.00135310		0.000519407i	5.24710e−5		2.01417e-5i
$666$		0			0
$667$	31.2134	−	6.63461i	1.20859	−	0.256893i
$668$		0			0
$669$	13.0759	+	34.0638i	0.505542	+	1.31698i
$670$		0			0
$671$	4.19777	+	5.08939i	0.162053	+	0.196474i
$672$		0			0
$673$	−0.0592848	−	0.564057i	−0.00228526	−	0.0217428i	0.993320	−	0.115394i	$-0.0368129\pi$
$673$	−0.0592848	−	0.564057i	−0.00228526	−	0.0217428i	−0.995605	+	0.0936508i	$0.970146\pi$
$674$		0			0
$675$	14.3108	+	4.64985i	0.550821	+	0.178973i
$676$		0			0
$677$	18.3723	−	25.2874i	0.706106	−	0.971872i	−0.293766	−	0.955877i	$-0.594909\pi$
$677$	18.3723	−	25.2874i	0.706106	−	0.971872i	0.999872	−	0.0159945i	$-0.00509143\pi$
$678$		0			0
$679$	−1.33871	+	6.29816i	−0.0513751	+	0.241701i
$680$		0			0
$681$	3.02312	−	3.02312i	0.115846	−	0.115846i
$682$		0			0
$683$	30.9097	+	8.28222i	1.18273	+	0.316910i	0.796007	−	0.605288i	$-0.206942\pi$
$683$	30.9097	+	8.28222i	1.18273	+	0.316910i	0.386718	+	0.922198i	$0.373609\pi$
$684$		0			0
$685$	−0.876321	+	0.973253i	−0.0334825	+	0.0371861i
$686$		0			0
$687$	15.7923	−	41.1403i	0.602514	−	1.56960i
$688$		0			0
$689$	41.8645	−	27.1401i	1.59491	−	1.03395i
$690$		0			0
$691$	5.43856	−	6.71607i	0.206893	−	0.255491i	−0.663128	−	0.748506i	$-0.730772\pi$
$691$	5.43856	−	6.71607i	0.206893	−	0.255491i	0.870021	+	0.493014i	$0.164105\pi$
$692$		0			0
$693$	−0.983620	+	4.84159i	−0.0373646	+	0.183917i
$694$		0			0
$695$	0.466998	−	0.179264i	0.0177143	−	0.00679986i
$696$		0			0
$697$	−8.08088	−	15.8596i	−0.306085	−	0.600726i
$698$		0			0
$699$	−1.84587	+	0.821834i	−0.0698172	+	0.0310846i
$700$		0			0
$701$	−8.78963	−	27.0517i	−0.331980	−	1.02173i	−0.968191	−	0.250213i	$-0.919499\pi$
$701$	−8.78963	−	27.0517i	−0.331980	−	1.02173i	0.636211	−	0.771515i	$-0.280501\pi$
$702$		0			0
$703$			0.0477757i			0.00180190i
$704$		0			0
$705$	1.35137	−	2.34064i	0.0508955	−	0.0881536i
$706$		0			0
$707$	3.00096	−	5.88972i	0.112863	−	0.221506i
$708$		0			0
$709$	−4.62987	−	5.71741i	−0.173878	−	0.214722i	0.682755	−	0.730647i	$-0.260782\pi$
$709$	−4.62987	−	5.71741i	−0.173878	−	0.214722i	−0.856634	+	0.515925i	$0.827448\pi$
$710$		0			0
$711$	2.26918	+	10.6756i	0.0851007	+	0.400367i
$712$		0			0
$713$	19.8431	+	16.0687i	0.743131	+	0.601776i
$714$		0			0
$715$	−1.40519	+	1.76471i	−0.0525509	+	0.0659964i
$716$		0			0
$717$	6.94540	+	5.62427i	0.259381	+	0.210042i
$718$		0			0
$719$	5.14052	+	24.1842i	0.191709	+	0.901919i	0.963845	+	0.266463i	$0.0858549\pi$
$719$	5.14052	+	24.1842i	0.191709	+	0.901919i	−0.772136	+	0.635457i	$0.780812\pi$
$720$		0			0
$721$	4.55640	+	5.62669i	0.169689	+	0.209549i
$722$		0			0
$723$	−21.8100	+	42.8046i	−0.811123	+	1.59192i
$724$		0			0
$725$	13.5446	−	23.4599i	0.503034	−	0.871281i
$726$		0			0
$727$		−	4.95510i		−	0.183774i	−0.995769	−	0.0918872i	$-0.970710\pi$
$727$		−	4.95510i		−	0.183774i	0.995769	−	0.0918872i	$-0.0292899\pi$
$728$		0			0
$729$	0.511830	+	1.57525i	0.0189567	+	0.0583426i
$730$		0			0
$731$	16.9777	−	7.55895i	0.627942	−	0.279578i
$732$		0			0
$733$	13.7849	+	27.0544i	0.509157	+	0.999276i	0.992314	+	0.123743i	$0.0394897\pi$
$733$	13.7849	+	27.0544i	0.509157	+	0.999276i	−0.483158	+	0.875533i	$0.660510\pi$
$734$		0			0
$735$	2.30621	−	0.885273i	0.0850660	−	0.0326538i
$736$		0			0
$737$	24.8682	+	14.0606i	0.916033	+	0.517927i
$738$		0			0
$739$	27.7531	−	34.2722i	1.02091	−	1.26072i	0.0559236	−	0.998435i	$-0.482190\pi$
$739$	27.7531	−	34.2722i	1.02091	−	1.26072i	0.964990	−	0.262288i	$-0.0844770\pi$
$740$		0			0
$741$	−0.0131652	+	0.0616975i	−0.000483636	+	0.00226651i
$742$		0			0
$743$	11.2867	−	29.4027i	0.414067	−	1.07868i	−0.554992	−	0.831855i	$-0.687279\pi$
$743$	11.2867	−	29.4027i	0.414067	−	1.07868i	0.969060	−	0.246827i	$-0.0793878\pi$
$744$		0			0
$745$	0.0207485	−	0.0230436i	0.000760168	−	0.000844252i
$746$		0			0
$747$	−24.7481	−	6.63123i	−0.905485	−	0.242624i
$748$		0			0
$749$	11.0058	−	11.0058i	0.402142	−	0.402142i
$750$		0			0
$751$	−3.69728	+	17.3943i	−0.134916	+	0.634728i	0.857773	+	0.514028i	$0.171847\pi$
$751$	−3.69728	+	17.3943i	−0.134916	+	0.634728i	−0.992689	+	0.120700i	$0.961486\pi$
$752$		0			0
$753$	−21.7135	+	29.8861i	−0.791285	+	1.08911i
$754$		0			0
$755$	−1.96798	−	0.639434i	−0.0716220	−	0.0232714i
$756$		0			0
$757$	3.75057	+	35.6843i	0.136317	+	1.29697i	0.822176	+	0.569233i	$0.192760\pi$
$757$	3.75057	+	35.6843i	0.136317	+	1.29697i	−0.685860	+	0.727734i	$0.740574\pi$
$758$		0			0
$759$	−2.54687	−	41.4501i	−0.0924454	−	1.50454i
$760$		0			0
$761$	8.26964	+	21.5431i	0.299774	+	0.780938i	0.997888	+	0.0649518i	$0.0206894\pi$
$761$	8.26964	+	21.5431i	0.299774	+	0.780938i	−0.698114	+	0.715986i	$0.745977\pi$
$762$		0			0
$763$	−5.33588	+	1.13418i	−0.193172	+	0.0410600i
$764$		0			0
$765$	−0.447088	−	0.171621i	−0.0161645	−	0.00620497i
$766$		0			0
$767$	3.70482	−	5.09078i	0.133773	−	0.183817i
$768$		0			0
$769$	1.46373	+	5.46272i	0.0527835	+	0.196991i	0.987283	−	0.158975i	$-0.0508188\pi$
$769$	1.46373	+	5.46272i	0.0527835	+	0.196991i	−0.934499	+	0.355965i	$0.884152\pi$
$770$		0			0
$771$	−3.93087	+	2.26949i	−0.141567	+	0.0817336i
$772$		0			0
$773$	33.7384	−	1.76815i	1.21349	−	0.0635961i	0.565175	−	0.824971i	$-0.308809\pi$
$773$	33.7384	−	1.76815i	1.21349	−	0.0635961i	0.648311	+	0.761375i	$0.275475\pi$
$774$		0			0
$775$	21.4086	−	3.39079i	0.769019	−	0.121801i
$776$		0			0
$777$	−7.87500	−	8.74607i	−0.282514	−	0.313763i
$778$		0			0
$779$	0.0533592	+	0.0734427i	0.00191179	+	0.00263136i
$780$		0			0
$781$	10.6703	+	1.02442i	0.381815	+	0.0366566i
$782$		0			0
$783$	16.4487	−	1.72883i	0.587828	−	0.0617832i
$784$		0			0
$785$	−0.278923	+	0.142118i	−0.00995519	+	0.00507242i
$786$		0			0
$787$	−29.1481	+	23.6037i	−1.03902	+	0.841381i	−0.987552	−	0.157294i	$-0.949723\pi$
$787$	−29.1481	+	23.6037i	−1.03902	+	0.841381i	−0.0514672	+	0.998675i	$0.516390\pi$
$788$		0			0
$789$	27.9836	+	25.1966i	0.996243	+	0.897022i
$790$		0			0
$791$	−13.3883	+	3.58738i	−0.476033	+	0.127553i
$792$		0			0
$793$	−7.08274	−	1.12754i	−0.251515	−	0.0400400i
$794$		0			0
$795$	−3.04401	−	4.68736i	−0.107960	−	0.166244i
$796$		0			0
$797$	−30.4017	−	3.19534i	−1.07688	−	0.113185i	−0.450558	−	0.892747i	$-0.648775\pi$
$797$	−30.4017	−	3.19534i	−1.07688	−	0.113185i	−0.626325	+	0.779562i	$0.715442\pi$
$798$		0			0
$799$	−5.83957	+	8.99216i	−0.206589	+	0.318120i
$800$		0			0
$801$	−1.40354	+	8.86162i	−0.0495918	+	0.313110i
$802$		0			0
$803$	16.4221	+	5.17281i	0.579523	+	0.182544i
$804$		0			0
$805$	0.839111	−	0.609650i	0.0295748	−	0.0214873i
$806$		0			0
$807$	9.36744	−	28.8300i	0.329749	−	1.01486i
$808$		0			0
$809$	1.28367	+	2.88317i	0.0451314	+	0.101367i	0.934704	−	0.355427i	$-0.115664\pi$
$809$	1.28367	+	2.88317i	0.0451314	+	0.101367i	−0.889573	+	0.456794i	$0.848998\pi$
$810$		0			0
$811$	16.4035	+	8.35801i	0.576006	+	0.293489i	0.717623	−	0.696432i	$-0.245230\pi$
$811$	16.4035	+	8.35801i	0.576006	+	0.293489i	−0.141617	+	0.989921i	$0.545230\pi$
$812$		0			0
$813$	13.2803	−	49.5628i	0.465761	−	1.73824i
$814$		0			0
$815$	2.06018	+	3.56834i	0.0721650	+	0.124994i
$816$		0			0
$817$	−0.0794910	+	0.0516221i	−0.00278104	+	0.00180603i
$818$		0			0
$819$	−2.68177	−	4.65345i	−0.0937085	−	0.162605i
$820$		0			0
$821$	−11.8842	−	0.622823i	−0.414760	−	0.0217367i	−0.156185	−	0.987728i	$-0.549920\pi$
$821$	−11.8842	−	0.622823i	−0.414760	−	0.0217367i	−0.258575	+	0.965991i	$0.583253\pi$
$822$		0			0
$823$	21.3356	−	47.9205i	0.743712	−	1.67041i	0.00171837	−	0.999999i	$-0.499453\pi$
$823$	21.3356	−	47.9205i	0.743712	−	1.67041i	0.741994	−	0.670407i	$-0.233880\pi$
$824$		0			0
$825$	−27.5960	−	21.9382i	−0.960768	−	0.763790i
$826$		0			0
$827$	19.5787	+	3.10096i	0.680817	+	0.107831i	0.487258	−	0.873258i	$-0.337997\pi$
$827$	19.5787	+	3.10096i	0.680817	+	0.107831i	0.193559	+	0.981089i	$0.437997\pi$
$828$		0			0
$829$	28.3430	−	25.5201i	0.984393	−	0.886351i	−0.00913282	−	0.999958i	$-0.502907\pi$
$829$	28.3430	−	25.5201i	0.984393	−	0.886351i	0.993526	+	0.113607i	$0.0362404\pi$
$830$		0			0
$831$	40.8120	+	29.6517i	1.41575	+	1.02861i
$832$		0			0
$833$	−9.32014	+	3.02830i	−0.322924	+	0.104924i
$834$		0			0
$835$	−0.182326	−	0.105266i	−0.00630964	−	0.00364287i
$836$		0			0
$837$	9.35778	+	9.35778i	0.323452	+	0.323452i
$838$		0			0
$839$	0.463803	+	8.84989i	0.0160123	+	0.305532i	0.994882	+	0.101046i	$0.0322190\pi$
$839$	0.463803	+	8.84989i	0.0160123	+	0.305532i	−0.978869	+	0.204486i	$0.934448\pi$
$840$		0			0
$841$	0.0810455	−	0.771097i	0.00279467	−	0.0265895i
$842$		0			0
$843$	−2.33192	+	44.4957i	−0.0803156	+	1.53251i
$844$		0			0
$845$	−0.124472	−	2.44918i	−0.00428197	−	0.0842543i
$846$		0			0
$847$	−5.47556	+	8.77368i	−0.188143	+	0.301467i
$848$		0			0
$849$	−0.251126	−	0.111808i	−0.00861861	−	0.00383725i
$850$		0			0
$851$	28.6736	+	18.6208i	0.982918	+	0.638315i
$852$		0			0
$853$	−5.91420	−	37.3408i	−0.202498	−	1.27852i	−0.854158	−	0.520013i	$-0.825927\pi$
$853$	−5.91420	−	37.3408i	−0.202498	−	1.27852i	0.651660	−	0.758512i	$-0.274073\pi$
$854$		0			0
$855$	0.00238905		0.000507807i	8.17036e−5		1.73666e-5i
$856$		0			0
$857$	8.83344			0.301745			0.150872	−	0.988553i	$-0.451792\pi$
$857$	8.83344			0.301745			0.150872	+	0.988553i	$0.451792\pi$
$858$		0			0
$859$	34.2215			1.16762			0.583811	−	0.811889i	$-0.301561\pi$
$859$	34.2215			1.16762			0.583811	+	0.811889i	$0.301561\pi$
$860$		0			0
$861$	−21.8739	−	4.64945i	−0.745462	−	0.158453i
$862$		0			0
$863$	0.253616	+	1.60127i	0.00863320	+	0.0545079i	0.991629	−	0.129121i	$-0.0412156\pi$
$863$	0.253616	+	1.60127i	0.00863320	+	0.0545079i	−0.982996	+	0.183629i	$0.941216\pi$
$864$		0			0
$865$	0.206719	+	0.134245i	0.00702865	+	0.00456446i
$866$		0			0
$867$	−28.2303	−	12.5689i	−0.958751	−	0.426863i
$868$		0			0
$869$	−3.37065	+	22.5969i	−0.114342	+	0.766547i
$870$		0			0
$871$	−30.3831	+	6.43301i	−1.02949	+	0.217974i
$872$		0			0
$873$	−0.567873	+	10.8357i	−0.0192196	+	0.366731i
$874$		0			0
$875$	0.184731	−	1.75760i	0.00624505	−	0.0594177i
$876$		0			0
$877$	−1.94643	−	37.1401i	−0.0657262	−	1.25413i	−0.810070	−	0.586334i	$-0.800571\pi$
$877$	−1.94643	−	37.1401i	−0.0657262	−	1.25413i	0.744343	−	0.667797i	$-0.232763\pi$
$878$		0			0
$879$	37.6305	+	37.6305i	1.26925	+	1.26925i
$880$		0			0
$881$	22.8226	+	13.1766i	0.768912	+	0.443932i	0.832487	−	0.554045i	$-0.186917\pi$
$881$	22.8226	+	13.1766i	0.768912	+	0.443932i	−0.0635741	+	0.997977i	$0.520250\pi$
$882$		0			0
$883$	28.9078	−	9.39273i	0.972826	−	0.316090i	0.220870	−	0.975303i	$-0.429110\pi$
$883$	28.9078	−	9.39273i	0.972826	−	0.316090i	0.751956	+	0.659213i	$0.229110\pi$
$884$		0			0
$885$	−0.570610	−	0.414573i	−0.0191809	−	0.0139357i
$886$		0			0
$887$	−22.6390	+	20.3843i	−0.760144	+	0.684437i	−0.955070	−	0.296381i	$-0.904220\pi$
$887$	−22.6390	+	20.3843i	−0.760144	+	0.684437i	0.194925	+	0.980818i	$0.437554\pi$
$888$		0			0
$889$	−2.78325	−	0.440823i	−0.0933471	−	0.0147847i
$890$		0			0
$891$	1.61605	−	37.2534i	0.0541398	−	1.24804i
$892$		0			0
$893$	0.0222415	−	0.0499553i	0.000744284	−	0.00167169i
$894$		0			0
$895$	1.03621	+	0.0543054i	0.0346366	+	0.00181523i
$896$		0			0
$897$	31.8978	+	31.9483i	1.06504	+	1.06672i
$898$		0			0
$899$	19.9811	−	12.9759i	0.666407	−	0.432770i
$900$		0			0
$901$	11.0860	+	19.2015i	0.369329	+	0.639696i
$902$		0			0
$903$	6.04303	−	22.5529i	0.201100	−	0.750514i
$904$		0			0
$905$	−1.73977	−	0.886455i	−0.0578318	−	0.0294668i
$906$		0			0
$907$	4.98757	+	11.2023i	0.165610	+	0.371965i	0.977218	−	0.212236i	$-0.0680745\pi$
$907$	4.98757	+	11.2023i	0.165610	+	0.371965i	−0.811609	+	0.584201i	$0.801408\pi$
$908$		0			0
$909$	3.44221	−	10.5940i	0.114171	−	0.351382i
$910$		0			0
$911$	−40.3741	+	29.3335i	−1.33765	+	0.971863i	−0.338128	+	0.941100i	$0.609794\pi$
$911$	−40.3741	+	29.3335i	−1.33765	+	0.971863i	−0.999527	+	0.0307625i	$0.990206\pi$
$912$		0			0
$913$	−43.6726	−	31.1329i	−1.44535	−	1.03035i
$914$		0			0
$915$	−0.125682	+	0.793527i	−0.00415493	+	0.0262332i
$916$		0			0
$917$	−4.28483	+	6.59807i	−0.141498	+	0.217887i
$918$		0			0
$919$	−28.1373	−	2.95735i	−0.928163	−	0.0975538i	−0.371631	−	0.928380i	$-0.621201\pi$
$919$	−28.1373	−	2.95735i	−0.928163	−	0.0975538i	−0.556531	+	0.830827i	$0.687868\pi$
$920$		0			0
$921$	14.4737	+	22.2876i	0.476925	+	0.734400i
$922$		0			0
$923$	−9.43307	+	6.84214i	−0.310493	+	0.225212i
$924$		0			0
$925$	28.0346	−	7.51185i	0.921773	−	0.246988i
$926$		0			0
$927$	9.06703	+	8.16399i	0.297800	+	0.268141i
$928$		0			0
$929$	−17.2746	+	13.9887i	−0.566762	+	0.458955i	−0.869371	−	0.494160i	$-0.835476\pi$
$929$	−17.2746	+	13.9887i	−0.566762	+	0.458955i	0.302609	+	0.953115i	$0.402142\pi$
$930$		0			0
$931$	0.0445323	−	0.0226904i	0.00145949	−	0.000743647i
$932$		0			0
$933$	33.3875	−	3.50917i	1.09306	−	0.114885i
$934$		0			0
$935$	−0.751006	−	0.664059i	−0.0245605	−	0.0217170i
$936$		0			0
$937$	−9.89376	−	13.6176i	−0.323215	−	0.444867i	0.616230	−	0.787566i	$-0.288659\pi$
$937$	−9.89376	−	13.6176i	−0.323215	−	0.444867i	−0.939445	+	0.342699i	$0.888659\pi$
$938$		0			0
$939$	−45.6208	−	50.6670i	−1.48878	−	1.65345i
$940$		0			0
$941$	−7.66712	+	1.21435i	−0.249941	+	0.0395868i	−0.280148	−	0.959957i	$-0.590383\pi$
$941$	−7.66712	+	1.21435i	−0.249941	+	0.0395868i	0.0302067	+	0.999544i	$0.490383\pi$
$942$		0			0
$943$	64.8752	−	3.39996i	2.11263	−	0.110718i
$944$		0			0
$945$	0.465557	−	0.268789i	0.0151446	−	0.00874372i
$946$		0			0
$947$	10.7296	+	40.0435i	0.348666	+	1.30124i	0.888271	+	0.459320i	$0.151907\pi$
$947$	10.7296	+	40.0435i	0.348666	+	1.30124i	−0.539605	+	0.841918i	$0.681427\pi$
$948$		0			0
$949$	−17.1052	+	7.59954i	−0.555260	+	0.246692i
$950$		0			0
$951$	−45.1911	−	17.3472i	−1.46542	−	0.562522i
$952$		0			0
$953$	19.9342	−	4.23714i	0.645731	−	0.137254i	0.126606	−	0.991953i	$-0.459591\pi$
$953$	19.9342	−	4.23714i	0.645731	−	0.137254i	0.519124	+	0.854699i	$0.326258\pi$
$954$		0			0
$955$	−0.635136	−	1.65459i	−0.0205525	−	0.0535411i
$956$		0			0
$957$	−37.5178	−	9.69155i	−1.21278	−	0.313283i
$958$		0			0
$959$	−0.682285	−	6.49151i	−0.0220321	−	0.209622i
$960$		0			0
$961$	−11.3524	−	3.68862i	−0.366207	−	0.118988i
$962$		0			0
$963$	15.4169	−	21.2195i	0.496801	−	0.683789i
$964$		0			0
$965$	0.518700	−	2.44029i	0.0166975	−	0.0785557i
$966$		0			0
$967$	−37.6779	+	37.6779i	−1.21164	+	1.21164i	−0.241154	+	0.970487i	$0.577526\pi$
$967$	−37.6779	+	37.6779i	−1.21164	+	1.21164i	−0.970487	+	0.241154i	$0.922474\pi$
$968$		0			0
$969$	−0.0270803	−	0.00725616i	−0.000869946	−	0.000233101i
$970$		0			0
$971$	13.9522	−	15.4955i	0.447749	−	0.497275i	−0.476442	−	0.879206i	$-0.658074\pi$
$971$	13.9522	−	15.4955i	0.447749	−	0.497275i	0.924191	+	0.381930i	$0.124741\pi$
$972$		0			0
$973$	−0.893453	+	2.32752i	−0.0286428	+	0.0746170i
$974$		0			0
$975$	38.2738	−	1.97550i	1.22574	−	0.0632666i
$976$		0			0
$977$	0.921601	−	1.13808i	0.0294846	−	0.0364105i	−0.762190	−	0.647353i	$-0.775876\pi$
$977$	0.921601	−	1.13808i	0.0294846	−	0.0364105i	0.791675	+	0.610942i	$0.209209\pi$
$978$		0			0
$979$	−9.24390	+	16.3492i	−0.295436	+	0.522524i
$980$		0			0
$981$	−8.58214	+	3.29437i	−0.274006	+	0.105181i
$982$		0			0
$983$	−24.1604	−	47.4174i	−0.770596	−	1.51238i	−0.856540	−	0.516080i	$-0.827391\pi$
$983$	−24.1604	−	47.4174i	−0.770596	−	1.51238i	0.0859441	−	0.996300i	$-0.472609\pi$
$984$		0			0
$985$	−0.162373	+	0.0722930i	−0.00517362	+	0.00230345i
$986$		0			0
$987$	4.16261	+	12.8112i	0.132497	+	0.407785i
$988$		0			0
$989$			67.8282i			2.15681i
$990$		0			0
$991$	−24.1012	+	41.7445i	−0.765601	+	1.32606i	0.174328	+	0.984688i	$0.444225\pi$
$991$	−24.1012	+	41.7445i	−0.765601	+	1.32606i	−0.939928	+	0.341372i	$0.889109\pi$
$992$		0			0
$993$	28.0546	−	55.0602i	0.890285	−	1.74728i
$994$		0			0
$995$	−0.357358	−	0.441300i	−0.0113290	−	0.0139901i
$996$		0			0
$997$	−8.82987	−	41.5413i	−0.279645	−	1.31562i	−0.863739	−	0.503939i	$-0.831884\pi$
$997$	−8.82987	−	41.5413i	−0.279645	−	1.31562i	0.584095	−	0.811686i	$-0.301450\pi$
$998$		0			0
$999$	13.7713	+	11.1517i	0.435703	+	0.352826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bv.a.85.3	yes	224
11.7	odd	10	inner	572.2.bv.a.293.12	yes	224
13.2	odd	12	inner	572.2.bv.a.41.12	✓	224
143.106	even	60	inner	572.2.bv.a.249.3	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bv.a.41.12	✓	224	13.2	odd	12	inner
572.2.bv.a.85.3	yes	224	1.1	even	1	trivial
572.2.bv.a.249.3	yes	224	143.106	even	60	inner
572.2.bv.a.293.12	yes	224	11.7	odd	10	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.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.09433 - 0.445163i) q^{3} +(-0.0295100 - 0.186319i) q^{5} +(0.788511 + 0.512065i) q^{7} +(1.44740 + 0.644424i) q^{9} +O(q^{10})\)	\(q+(-2.09433 - 0.445163i) q^{3} +(-0.0295100 - 0.186319i) q^{5} +(0.788511 + 0.512065i) q^{7} +(1.44740 + 0.644424i) q^{9} +(2.36624 + 2.32399i) q^{11} +(-3.60046 - 0.191547i) q^{13} +(-0.0211387 + 0.403350i) q^{15} +(0.167487 - 1.59353i) q^{17} +(0.000427686 + 0.00816073i) q^{19} +(-1.42345 - 1.42345i) q^{21} +(5.06452 + 2.92400i) q^{23} +(4.72144 - 1.53409i) q^{25} +(2.45214 + 1.78159i) q^{27} +(4.05510 - 3.65123i) q^{29} +(4.31241 + 0.683018i) q^{31} +(-3.92112 - 5.92055i) q^{33} +(0.0721385 - 0.162026i) q^{35} +(5.83831 + 0.305973i) q^{37} +(7.45527 + 2.00395i) q^{39} +(9.31660 - 6.05027i) q^{41} +(5.79926 + 10.0446i) q^{43} +(0.0773556 - 0.288695i) q^{45} +(-5.96221 - 3.03790i) q^{47} +(-2.48762 - 5.58728i) q^{49} +(-1.06015 + 3.26281i) q^{51} +(-11.1948 + 8.13352i) q^{53} +(0.363176 - 0.509456i) q^{55} +(0.00273714 - 0.0172816i) q^{57} +(-0.951072 + 1.46452i) q^{59} +(1.97824 + 0.207921i) q^{61} +(0.811303 + 1.24930i) q^{63} +(0.0705608 + 0.676487i) q^{65} +(8.32006 - 2.22935i) q^{67} +(-9.30511 - 8.37836i) q^{69} +(2.51175 - 2.03398i) q^{71} +(4.62547 - 2.35679i) q^{73} +(-10.5712 + 1.11107i) q^{75} +(0.675769 + 3.04416i) q^{77} +(4.04902 + 5.57300i) q^{79} +(-7.52296 - 8.35509i) q^{81} +(-15.9720 + 2.52972i) q^{83} +(-0.301848 + 0.0158192i) q^{85} +(-10.1181 + 5.84169i) q^{87} +(1.46565 + 5.46989i) q^{89} +(-2.74092 - 1.99471i) q^{91} +(-8.72754 - 3.35019i) q^{93} +(0.00150788 - 0.000320509i) q^{95} +(2.45427 + 6.39358i) q^{97} +(1.92725 + 4.88860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 28 q^{9}+O(q^{10}) \) 224 * q + 28 * q^9	\( 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) \) 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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