LMFDB - Embedded newform 572.2.n.b.53.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			53.6
Character	$\chi$	$=$	572.53
Dual form			572.2.n.b.313.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.12584 - 1.54451i) q^{3} +(0.674037 + 2.07447i) q^{5} +(1.61142 + 1.17077i) q^{7} +(1.20663 - 3.71362i) q^{9} +O(q^{10})$	\(q+(2.12584 - 1.54451i) q^{3} +(0.674037 + 2.07447i) q^{5} +(1.61142 + 1.17077i) q^{7} +(1.20663 - 3.71362i) q^{9} +(-0.298220 + 3.30319i) q^{11} +(-0.309017 + 0.951057i) q^{13} +(4.63695 + 3.36894i) q^{15} +(0.140846 + 0.433479i) q^{17} +(5.92410 - 4.30411i) q^{19} +5.23390 q^{21} -8.67119 q^{23} +(0.195971 - 0.142381i) q^{25} +(-0.734638 - 2.26098i) q^{27} +(-3.00169 - 2.18086i) q^{29} +(-0.417376 + 1.28455i) q^{31} +(4.46786 + 7.48266i) q^{33} +(-1.34257 + 4.13200i) q^{35} +(-8.55569 - 6.21607i) q^{37} +(0.811999 + 2.49908i) q^{39} +(9.52544 - 6.92064i) q^{41} -1.27961 q^{43} +8.51711 q^{45} +(-4.02075 + 2.92125i) q^{47} +(-0.937130 - 2.88419i) q^{49} +(0.968930 + 0.703969i) q^{51} +(1.97949 - 6.09223i) q^{53} +(-7.05339 + 1.60782i) q^{55} +(5.94594 - 18.2997i) q^{57} +(-7.82925 - 5.68828i) q^{59} +(1.75675 + 5.40671i) q^{61} +(6.29217 - 4.57153i) q^{63} -2.18123 q^{65} -1.70561 q^{67} +(-18.4336 + 13.3928i) q^{69} +(-2.40067 - 7.38850i) q^{71} +(6.33350 + 4.60156i) q^{73} +(0.196693 - 0.605360i) q^{75} +(-4.34783 + 4.97369i) q^{77} +(1.81477 - 5.58530i) q^{79} +(4.42313 + 3.21359i) q^{81} +(3.03332 + 9.33561i) q^{83} +(-0.804305 + 0.584362i) q^{85} -9.74948 q^{87} +2.62780 q^{89} +(-1.61142 + 1.17077i) q^{91} +(1.09673 + 3.37540i) q^{93} +(12.9218 + 9.38826i) q^{95} +(0.826593 - 2.54399i) q^{97} +(11.9069 + 5.09319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	2.12584	−	1.54451i	1.22736	−	0.891726i	0.230666	−	0.973033i	$-0.425909\pi$
$3$	2.12584	−	1.54451i	1.22736	−	0.891726i	0.996689	+	0.0813072i	$0.0259095\pi$
$4$		0			0
$5$	0.674037	+	2.07447i	0.301439	+	0.927733i	0.980982	+	0.194098i	$0.0621778\pi$
$5$	0.674037	+	2.07447i	0.301439	+	0.927733i	−0.679544	+	0.733635i	$0.737822\pi$
$6$		0			0
$7$	1.61142	+	1.17077i	0.609061	+	0.442509i	0.849084	−	0.528259i	$-0.177155\pi$
$7$	1.61142	+	1.17077i	0.609061	+	0.442509i	−0.240023	+	0.970767i	$0.577155\pi$
$8$		0			0
$9$	1.20663	−	3.71362i	0.402209	−	1.23787i
$10$		0			0
$11$	−0.298220	+	3.30319i	−0.0899166	+	0.995949i
$11$	−0.298220	+	3.30319i	−0.0899166	+	0.995949i
$12$		0			0
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$		0			0
$15$	4.63695	+	3.36894i	1.19726	+	0.869857i
$16$		0			0
$17$	0.140846	+	0.433479i	0.0341601	+	0.105134i	0.966683	−	0.255978i	$-0.0823973\pi$
$17$	0.140846	+	0.433479i	0.0341601	+	0.105134i	−0.932523	+	0.361112i	$0.882397\pi$
$18$		0			0
$19$	5.92410	−	4.30411i	1.35908	−	0.987431i	0.360580	−	0.932728i	$-0.382579\pi$
$19$	5.92410	−	4.30411i	1.35908	−	0.987431i	0.998503	−	0.0547030i	$-0.0174212\pi$
$20$		0			0
$21$	5.23390			1.14213
$22$		0			0
$23$	−8.67119			−1.80807			−0.904035	−	0.427459i	$-0.859409\pi$
$23$	−8.67119			−1.80807			−0.904035	+	0.427459i	$0.859409\pi$
$24$		0			0
$25$	0.195971	−	0.142381i	0.0391942	−	0.0284763i
$26$		0			0
$27$	−0.734638	−	2.26098i	−0.141381	−	0.435126i
$28$		0			0
$29$	−3.00169	−	2.18086i	−0.557400	−	0.404975i	0.273106	−	0.961984i	$-0.411949\pi$
$29$	−3.00169	−	2.18086i	−0.557400	−	0.404975i	−0.830506	+	0.557009i	$0.811949\pi$
$30$		0			0
$31$	−0.417376	+	1.28455i	−0.0749630	+	0.230712i	−0.981516	−	0.191379i	$-0.938704\pi$
$31$	−0.417376	+	1.28455i	−0.0749630	+	0.230712i	0.906553	+	0.422092i	$0.138704\pi$
$32$		0			0
$33$	4.46786	+	7.48266i	0.777754	+	1.30256i
$34$		0			0
$35$	−1.34257	+	4.13200i	−0.226935	+	0.698435i
$36$		0			0
$37$	−8.55569	−	6.21607i	−1.40655	−	1.02192i	−0.993813	−	0.111064i	$-0.964574\pi$
$37$	−8.55569	−	6.21607i	−1.40655	−	1.02192i	−0.412733	−	0.910852i	$-0.635426\pi$
$38$		0			0
$39$	0.811999	+	2.49908i	0.130024	+	0.400173i
$40$		0			0
$41$	9.52544	−	6.92064i	1.48762	−	1.08082i	0.512625	−	0.858612i	$-0.328673\pi$
$41$	9.52544	−	6.92064i	1.48762	−	1.08082i	0.974999	−	0.222210i	$-0.0713270\pi$
$42$		0			0
$43$	−1.27961			−0.195139			−0.0975694	−	0.995229i	$-0.531107\pi$
$43$	−1.27961			−0.195139			−0.0975694	+	0.995229i	$0.531107\pi$
$44$		0			0
$45$	8.51711			1.26966
$46$		0			0
$47$	−4.02075	+	2.92125i	−0.586487	+	0.426108i	−0.841057	−	0.540946i	$-0.818066\pi$
$47$	−4.02075	+	2.92125i	−0.586487	+	0.426108i	0.254570	+	0.967054i	$0.418066\pi$
$48$		0			0
$49$	−0.937130	−	2.88419i	−0.133876	−	0.412027i
$50$		0			0
$51$	0.968930	+	0.703969i	0.135677	+	0.0985754i
$52$		0			0
$53$	1.97949	−	6.09223i	0.271903	−	0.836833i	−0.718119	−	0.695921i	$-0.754997\pi$
$53$	1.97949	−	6.09223i	0.271903	−	0.836833i	0.990022	−	0.140912i	$-0.0450035\pi$
$54$		0			0
$55$	−7.05339	+	1.60782i	−0.951079	+	0.216799i
$56$		0			0
$57$	5.94594	−	18.2997i	0.787559	−	2.42386i
$58$		0			0
$59$	−7.82925	−	5.68828i	−1.01928	−	0.740552i	−0.0531462	−	0.998587i	$-0.516925\pi$
$59$	−7.82925	−	5.68828i	−1.01928	−	0.740552i	−0.966136	+	0.258035i	$0.916925\pi$
$60$		0			0
$61$	1.75675	+	5.40671i	0.224928	+	0.692258i	0.998299	+	0.0583037i	$0.0185692\pi$
$61$	1.75675	+	5.40671i	0.224928	+	0.692258i	−0.773371	+	0.633954i	$0.781431\pi$
$62$		0			0
$63$	6.29217	−	4.57153i	0.792739	−	0.575959i
$64$		0			0
$65$	−2.18123			−0.270548
$66$		0			0
$67$	−1.70561			−0.208373			−0.104186	−	0.994558i	$-0.533224\pi$
$67$	−1.70561			−0.208373			−0.104186	+	0.994558i	$0.533224\pi$
$68$		0			0
$69$	−18.4336	+	13.3928i	−2.21914	+	1.61230i
$70$		0			0
$71$	−2.40067	−	7.38850i	−0.284907	−	0.876853i	−0.986427	−	0.164203i	$-0.947495\pi$
$71$	−2.40067	−	7.38850i	−0.284907	−	0.876853i	0.701520	−	0.712650i	$-0.252505\pi$
$72$		0			0
$73$	6.33350	+	4.60156i	0.741280	+	0.538572i	0.893112	−	0.449835i	$-0.148517\pi$
$73$	6.33350	+	4.60156i	0.741280	+	0.538572i	−0.151832	+	0.988406i	$0.548517\pi$
$74$		0			0
$75$	0.196693	−	0.605360i	0.0227122	−	0.0699010i
$76$		0			0
$77$	−4.34783	+	4.97369i	−0.495481	+	0.566805i
$78$		0			0
$79$	1.81477	−	5.58530i	0.204178	−	0.628395i	−0.795568	−	0.605864i	$-0.792828\pi$
$79$	1.81477	−	5.58530i	0.204178	−	0.628395i	0.999746	−	0.0225311i	$-0.00717249\pi$
$80$		0			0
$81$	4.42313	+	3.21359i	0.491459	+	0.357066i
$82$		0			0
$83$	3.03332	+	9.33561i	0.332951	+	1.02472i	0.967723	+	0.252017i	$0.0810939\pi$
$83$	3.03332	+	9.33561i	0.332951	+	1.02472i	−0.634772	+	0.772699i	$0.718906\pi$
$84$		0			0
$85$	−0.804305	+	0.584362i	−0.0872392	+	0.0633830i
$86$		0			0
$87$	−9.74948			−1.04525
$88$		0			0
$89$	2.62780			0.278546			0.139273	−	0.990254i	$-0.455523\pi$
$89$	2.62780			0.278546			0.139273	+	0.990254i	$0.455523\pi$
$90$		0			0
$91$	−1.61142	+	1.17077i	−0.168923	+	0.122730i
$92$		0			0
$93$	1.09673	+	3.37540i	0.113726	+	0.350012i
$94$		0			0
$95$	12.9218	+	9.38826i	1.32575	+	0.963215i
$96$		0			0
$97$	0.826593	−	2.54399i	0.0839278	−	0.258303i	−0.900283	−	0.435306i	$-0.856640\pi$
$97$	0.826593	−	2.54399i	0.0839278	−	0.258303i	0.984210	+	0.177003i	$0.0566402\pi$
$98$		0			0
$99$	11.9069	+	5.09319i	1.19669	+	0.511885i
$100$		0			0
$101$	−4.71577	+	14.5137i	−0.469237	+	1.44416i	0.384338	+	0.923193i	$0.374430\pi$
$101$	−4.71577	+	14.5137i	−0.469237	+	1.44416i	−0.853575	+	0.520970i	$0.825570\pi$
$102$		0			0
$103$	8.45516	+	6.14303i	0.833112	+	0.605291i	0.920438	−	0.390889i	$-0.127832\pi$
$103$	8.45516	+	6.14303i	0.833112	+	0.605291i	−0.0873263	+	0.996180i	$0.527832\pi$
$104$		0			0
$105$	3.52784	+	10.8576i	0.344282	+	1.05959i
$106$		0			0
$107$	−0.230210	+	0.167257i	−0.0222553	+	0.0161694i	−0.598857	−	0.800856i	$-0.704378\pi$
$107$	−0.230210	+	0.167257i	−0.0222553	+	0.0161694i	0.576602	+	0.817025i	$0.304378\pi$
$108$		0			0
$109$	4.17851			0.400228			0.200114	−	0.979773i	$-0.435869\pi$
$109$	4.17851			0.400228			0.200114	+	0.979773i	$0.435869\pi$
$110$		0			0
$111$	−27.7889			−2.63760
$112$		0			0
$113$	−16.2687	+	11.8199i	−1.53043	+	1.11192i	−0.574425	+	0.818558i	$0.694774\pi$
$113$	−16.2687	+	11.8199i	−1.53043	+	1.11192i	−0.956001	+	0.293362i	$0.905226\pi$
$114$		0			0
$115$	−5.84471	−	17.9882i	−0.545022	−	1.67740i
$116$		0			0
$117$	3.15899	+	2.29514i	0.292049	+	0.212186i
$118$		0			0
$119$	−0.280541	+	0.863416i	−0.0257171	+	0.0791492i
$120$		0			0
$121$	−10.8221	−	1.97015i	−0.983830	−	0.179105i
$122$		0			0
$123$	9.56056	−	29.4244i	0.862046	−	2.65311i
$124$		0			0
$125$	9.25072	+	6.72104i	0.827410	+	0.601148i
$126$		0			0
$127$	−3.23937	−	9.96977i	−0.287448	−	0.884674i	−0.985654	−	0.168777i	$-0.946018\pi$
$127$	−3.23937	−	9.96977i	−0.287448	−	0.884674i	0.698206	−	0.715897i	$-0.253982\pi$
$128$		0			0
$129$	−2.72025	+	1.97638i	−0.239505	+	0.174010i
$130$		0			0
$131$	−10.9923			−0.960405			−0.480203	−	0.877158i	$-0.659437\pi$
$131$	−10.9923			−0.960405			−0.480203	+	0.877158i	$0.659437\pi$
$132$		0			0
$133$	14.5854			1.26471
$134$		0			0
$135$	4.19518	−	3.04797i	0.361063	−	0.262328i
$136$		0			0
$137$	2.41417	+	7.43006i	0.206257	+	0.634793i	0.999659	+	0.0260957i	$0.00830747\pi$
$137$	2.41417	+	7.43006i	0.206257	+	0.634793i	−0.793403	+	0.608697i	$0.791693\pi$
$138$		0			0
$139$	−13.4424	−	9.76645i	−1.14017	−	0.828380i	−0.153024	−	0.988222i	$-0.548901\pi$
$139$	−13.4424	−	9.76645i	−1.14017	−	0.828380i	−0.987142	+	0.159843i	$0.948901\pi$
$140$		0			0
$141$	−4.03558	+	12.4202i	−0.339857	+	1.04597i
$142$		0			0
$143$	−3.04937	−	1.30437i	−0.255001	−	0.109077i
$144$		0			0
$145$	2.50088	−	7.69691i	0.207686	−	0.639193i
$146$		0			0
$147$	−6.44686	−	4.68392i	−0.531728	−	0.386323i
$148$		0			0
$149$	0.870119	+	2.67795i	0.0712830	+	0.219386i	0.980351	−	0.197262i	$-0.0632048\pi$
$149$	0.870119	+	2.67795i	0.0712830	+	0.219386i	−0.909068	+	0.416648i	$0.863205\pi$
$150$		0			0
$151$	−16.3183	+	11.8560i	−1.32797	+	0.964824i	−0.328170	+	0.944619i	$0.606432\pi$
$151$	−16.3183	+	11.8560i	−1.32797	+	0.964824i	−0.999796	+	0.0202055i	$0.993568\pi$
$152$		0			0
$153$	1.77972			0.143882
$154$		0			0
$155$	−2.94610			−0.236636
$156$		0			0
$157$	12.8844	−	9.36107i	1.02829	−	0.747095i	0.0603224	−	0.998179i	$-0.480787\pi$
$157$	12.8844	−	9.36107i	1.02829	−	0.747095i	0.967965	+	0.251084i	$0.0807871\pi$
$158$		0			0
$159$	−5.20147	−	16.0085i	−0.412503	−	1.26955i
$160$		0			0
$161$	−13.9730	−	10.1520i	−1.10122	−	0.800086i
$162$		0			0
$163$	−3.03776	+	9.34926i	−0.237936	+	0.732290i	0.758783	+	0.651344i	$0.225794\pi$
$163$	−3.03776	+	9.34926i	−0.237936	+	0.732290i	−0.996718	+	0.0809467i	$0.974206\pi$
$164$		0			0
$165$	−12.5111	+	14.3120i	−0.973987	+	1.11419i
$166$		0			0
$167$	−0.214083	+	0.658878i	−0.0165662	+	0.0509855i	−0.958998	−	0.283413i	$-0.908533\pi$
$167$	−0.214083	+	0.658878i	−0.0165662	+	0.0509855i	0.942432	+	0.334399i	$0.108533\pi$
$168$		0			0
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$		0			0
$171$	−8.83564	−	27.1933i	−0.675678	−	2.07952i
$172$		0			0
$173$	6.93265	−	5.03687i	0.527080	−	0.382946i	−0.292184	−	0.956362i	$-0.594382\pi$
$173$	6.93265	−	5.03687i	0.527080	−	0.382946i	0.819264	+	0.573416i	$0.194382\pi$
$174$		0			0
$175$	0.482488			0.0364727
$176$		0			0
$177$	−25.4294			−1.91139
$178$		0			0
$179$	−5.56312	+	4.04184i	−0.415807	+	0.302101i	−0.775949	−	0.630796i	$-0.782728\pi$
$179$	−5.56312	+	4.04184i	−0.415807	+	0.302101i	0.360142	+	0.932898i	$0.382728\pi$
$180$		0			0
$181$	1.42899	+	4.39798i	0.106216	+	0.326899i	0.990014	−	0.140970i	$-0.0450220\pi$
$181$	1.42899	+	4.39798i	0.106216	+	0.326899i	−0.883798	+	0.467869i	$0.845022\pi$
$182$		0			0
$183$	12.0853	+	8.78048i	0.893371	+	0.649072i
$184$		0			0
$185$	7.12822	−	21.9384i	0.524077	−	1.61294i
$186$		0			0
$187$	−1.47387	+	0.335969i	−0.107780	+	0.0245685i
$188$		0			0
$189$	1.46327	−	4.50349i	0.106437	−	0.327581i
$190$		0			0
$191$	0.889686	+	0.646395i	0.0643755	+	0.0467715i	0.619508	−	0.784991i	$-0.287332\pi$
$191$	0.889686	+	0.646395i	0.0643755	+	0.0467715i	−0.555132	+	0.831762i	$0.687332\pi$
$192$		0			0
$193$	−0.521171	−	1.60400i	−0.0375147	−	0.115458i	0.930545	−	0.366176i	$-0.119333\pi$
$193$	−0.521171	−	1.60400i	−0.0375147	−	0.115458i	−0.968060	+	0.250718i	$0.919333\pi$
$194$		0			0
$195$	−4.63695	+	3.36894i	−0.332059	+	0.241255i
$196$		0			0
$197$	−2.96837			−0.211487			−0.105744	−	0.994393i	$-0.533722\pi$
$197$	−2.96837			−0.211487			−0.105744	+	0.994393i	$0.533722\pi$
$198$		0			0
$199$	9.94487			0.704973			0.352487	−	0.935817i	$-0.385336\pi$
$199$	9.94487			0.704973			0.352487	+	0.935817i	$0.385336\pi$
$200$		0			0
$201$	−3.62585	+	2.63433i	−0.255748	+	0.185812i
$202$		0			0
$203$	−2.28372	−	7.02857i	−0.160286	−	0.493309i
$204$		0			0
$205$	20.7772	+	15.0955i	1.45114	+	1.05432i
$206$		0			0
$207$	−10.4629	+	32.2015i	−0.727222	+	2.23816i
$208$		0			0
$209$	12.4506	+	20.8520i	0.861227	+	1.44236i
$210$		0			0
$211$	7.92054	−	24.3769i	0.545272	−	1.67818i	−0.175069	−	0.984556i	$-0.556015\pi$
$211$	7.92054	−	24.3769i	0.545272	−	1.67818i	0.720341	−	0.693620i	$-0.243985\pi$
$212$		0			0
$213$	−16.5151	−	11.9989i	−1.13159	−	0.822152i
$214$		0			0
$215$	−0.862505	−	2.65452i	−0.0588224	−	0.181037i
$216$		0			0
$217$	−2.17648	+	1.58131i	−0.147749	+	0.107346i
$218$		0			0
$219$	20.5712			1.39007
$220$		0			0
$221$	−0.455787			−0.0306595
$222$		0			0
$223$	−21.9708	+	15.9627i	−1.47127	+	1.06894i	−0.491028	+	0.871144i	$0.663379\pi$
$223$	−21.9708	+	15.9627i	−1.47127	+	1.06894i	−0.980243	+	0.197797i	$0.936621\pi$
$224$		0			0
$225$	−0.292286	−	0.899563i	−0.0194857	−	0.0599708i
$226$		0			0
$227$	18.9461	+	13.7652i	1.25750	+	0.913625i	0.998632	−	0.0522879i	$-0.0166513\pi$
$227$	18.9461	+	13.7652i	1.25750	+	0.913625i	0.258866	+	0.965913i	$0.416651\pi$
$228$		0			0
$229$	4.98182	−	15.3325i	0.329208	−	1.01320i	−0.640297	−	0.768127i	$-0.721189\pi$
$229$	4.98182	−	15.3325i	0.329208	−	1.01320i	0.969505	−	0.245071i	$-0.0788113\pi$
$230$		0			0
$231$	−1.56085	+	17.2886i	−0.102697	+	1.13750i
$232$		0			0
$233$	4.09171	−	12.5930i	0.268057	−	0.824995i	−0.722916	−	0.690936i	$-0.757199\pi$
$233$	4.09171	−	12.5930i	0.268057	−	0.824995i	0.990973	−	0.134059i	$-0.0428013\pi$
$234$		0			0
$235$	−8.77019	−	6.37192i	−0.572104	−	0.415658i
$236$		0			0
$237$	−4.76865	−	14.6764i	−0.309757	−	0.953335i
$238$		0			0
$239$	9.51693	−	6.91445i	0.615599	−	0.447259i	−0.235783	−	0.971806i	$-0.575765\pi$
$239$	9.51693	−	6.91445i	0.615599	−	0.447259i	0.851381	+	0.524547i	$0.175765\pi$
$240$		0			0
$241$	7.67252			0.494231			0.247115	−	0.968986i	$-0.420517\pi$
$241$	7.67252			0.494231			0.247115	+	0.968986i	$0.420517\pi$
$242$		0			0
$243$	21.4983			1.37912
$244$		0			0
$245$	5.35151	−	3.88810i	0.341896	−	0.248402i
$246$		0			0
$247$	2.26281	+	6.96420i	0.143979	+	0.443122i
$248$		0			0
$249$	20.8674	+	15.1610i	1.32241	+	0.960790i
$250$		0			0
$251$	−5.74592	+	17.6841i	−0.362680	+	1.11621i	0.588742	+	0.808321i	$0.299623\pi$
$251$	−5.74592	+	17.6841i	−0.362680	+	1.11621i	−0.951421	+	0.307892i	$0.900377\pi$
$252$		0			0
$253$	2.58592	−	28.6426i	0.162575	−	1.80075i
$254$		0			0
$255$	−0.807270	+	2.48452i	−0.0505532	+	0.155587i
$256$		0			0
$257$	−8.71761	−	6.33372i	−0.543790	−	0.395086i	0.281701	−	0.959502i	$-0.409101\pi$
$257$	−8.71761	−	6.33372i	−0.543790	−	0.395086i	−0.825491	+	0.564416i	$0.809101\pi$
$258$		0			0
$259$	−6.50926	−	20.0335i	−0.404466	−	1.24482i
$260$		0			0
$261$	−11.7208	+	8.51565i	−0.725498	+	0.527105i
$262$		0			0
$263$	−1.32405			−0.0816447			−0.0408223	−	0.999166i	$-0.512998\pi$
$263$	−1.32405			−0.0816447			−0.0408223	+	0.999166i	$0.512998\pi$
$264$		0			0
$265$	13.9724			0.858319
$266$		0			0
$267$	5.58628	−	4.05867i	0.341875	−	0.248386i
$268$		0			0
$269$	3.51813	+	10.8277i	0.214504	+	0.660176i	0.999188	+	0.0402801i	$0.0128250\pi$
$269$	3.51813	+	10.8277i	0.214504	+	0.660176i	−0.784684	+	0.619896i	$0.787175\pi$
$270$		0			0
$271$	−2.88452	−	2.09573i	−0.175222	−	0.127306i	0.496717	−	0.867912i	$-0.334539\pi$
$271$	−2.88452	−	2.09573i	−0.175222	−	0.127306i	−0.671940	+	0.740606i	$0.734539\pi$
$272$		0			0
$273$	−1.61736	+	4.97773i	−0.0978873	+	0.301266i
$274$		0			0
$275$	0.411870	+	0.689791i	0.0248367	+	0.0415959i
$276$		0			0
$277$	−8.52985	+	26.2522i	−0.512509	+	1.57734i	0.275260	+	0.961370i	$0.411236\pi$
$277$	−8.52985	+	26.2522i	−0.512509	+	1.57734i	−0.787769	+	0.615970i	$0.788764\pi$
$278$		0			0
$279$	4.26672	+	3.09995i	0.255442	+	0.185589i
$280$		0			0
$281$	1.66244	+	5.11645i	0.0991727	+	0.305222i	0.988319	−	0.152402i	$-0.0487007\pi$
$281$	1.66244	+	5.11645i	0.0991727	+	0.305222i	−0.889146	+	0.457624i	$0.848701\pi$
$282$		0			0
$283$	−6.37240	+	4.62982i	−0.378800	+	0.275214i	−0.760851	−	0.648927i	$-0.775218\pi$
$283$	−6.37240	+	4.62982i	−0.378800	+	0.275214i	0.382051	+	0.924141i	$0.375218\pi$
$284$		0			0
$285$	41.9701			2.48609
$286$		0			0
$287$	23.4520			1.38433
$288$		0			0
$289$	13.5852	−	9.87024i	0.799131	−	0.580602i
$290$		0			0
$291$	−2.17203	−	6.68481i	−0.127326	−	0.391870i
$292$		0			0
$293$	24.5301	+	17.8222i	1.43307	+	1.04118i	0.989436	+	0.144973i	$0.0463096\pi$
$293$	24.5301	+	17.8222i	1.43307	+	1.04118i	0.443630	+	0.896210i	$0.353690\pi$
$294$		0			0
$295$	6.52299	−	20.0757i	0.379783	−	1.16885i
$296$		0			0
$297$	7.68754	−	1.75238i	0.446076	−	0.101683i
$298$		0			0
$299$	2.67955	−	8.24680i	0.154962	−	0.476925i
$300$		0			0
$301$	−2.06199	−	1.49813i	−0.118851	−	0.0863506i
$302$		0			0
$303$	12.3916	+	38.1373i	0.711877	+	2.19093i
$304$		0			0
$305$	−10.0320	+	7.28864i	−0.574428	+	0.417347i
$306$		0			0
$307$	26.9294			1.53694			0.768471	−	0.639885i	$-0.221018\pi$
$307$	26.9294			1.53694			0.768471	+	0.639885i	$0.221018\pi$
$308$		0			0
$309$	27.4623			1.56228
$310$		0			0
$311$	−15.7395	+	11.4354i	−0.892505	+	0.648443i	−0.936530	−	0.350587i	$-0.885982\pi$
$311$	−15.7395	+	11.4354i	−0.892505	+	0.648443i	0.0440248	+	0.999030i	$0.485982\pi$
$312$		0			0
$313$	1.32931	+	4.09118i	0.0751368	+	0.231247i	0.981570	−	0.191101i	$-0.0612058\pi$
$313$	1.32931	+	4.09118i	0.0751368	+	0.231247i	−0.906434	+	0.422349i	$0.861206\pi$
$314$		0			0
$315$	13.7247	+	9.97156i	0.773298	+	0.561834i
$316$		0			0
$317$	2.62234	−	8.07074i	0.147285	−	0.453298i	−0.850012	−	0.526763i	$-0.823406\pi$
$317$	2.62234	−	8.07074i	0.147285	−	0.453298i	0.997298	+	0.0734649i	$0.0234057\pi$
$318$		0			0
$319$	8.09894	−	9.26478i	0.453454	−	0.518728i
$320$		0			0
$321$	−0.231059	+	0.711126i	−0.0128964	+	0.0396912i
$322$		0			0
$323$	2.70013	+	1.96176i	0.150239	+	0.109155i
$324$		0			0
$325$	0.0748543	+	0.230378i	0.00415217	+	0.0127791i
$326$		0			0
$327$	8.88284	−	6.45376i	0.491222	−	0.356894i
$328$		0			0
$329$	−9.89924			−0.545763
$330$		0			0
$331$	−14.0875			−0.774321			−0.387160	−	0.922012i	$-0.626544\pi$
$331$	−14.0875			−0.774321			−0.387160	+	0.922012i	$0.626544\pi$
$332$		0			0
$333$	−33.4076	+	24.2721i	−1.83073	+	1.33010i
$334$		0			0
$335$	−1.14964	−	3.53823i	−0.0628117	−	0.193314i
$336$		0			0
$337$	−15.3146	−	11.1267i	−0.834242	−	0.606112i	0.0865146	−	0.996251i	$-0.472427\pi$
$337$	−15.3146	−	11.1267i	−0.834242	−	0.606112i	−0.920756	+	0.390139i	$0.872427\pi$
$338$		0			0
$339$	−16.3286	+	50.2543i	−0.886849	+	2.72944i
$340$		0			0
$341$	−4.11865	−	1.76175i	−0.223037	−	0.0954042i
$342$		0			0
$343$	6.17517	−	19.0052i	0.333428	−	1.02618i
$344$		0			0
$345$	−40.2079	−	29.2128i	−2.16472	−	1.57276i
$346$		0			0
$347$	5.67334	+	17.4608i	0.304561	+	0.937342i	0.979841	+	0.199781i	$0.0640229\pi$
$347$	5.67334	+	17.4608i	0.304561	+	0.937342i	−0.675280	+	0.737562i	$0.735977\pi$
$348$		0			0
$349$	17.2552	−	12.5366i	0.923650	−	0.671071i	−0.0207800	−	0.999784i	$-0.506615\pi$
$349$	17.2552	−	12.5366i	0.923650	−	0.671071i	0.944430	+	0.328713i	$0.106615\pi$
$350$		0			0
$351$	2.37734			0.126893
$352$		0			0
$353$	13.8906			0.739323			0.369661	−	0.929167i	$-0.379474\pi$
$353$	13.8906			0.739323			0.369661	+	0.929167i	$0.379474\pi$
$354$		0			0
$355$	13.7091	−	9.96024i	0.727603	−	0.528635i
$356$		0			0
$357$	0.737173	+	2.26879i	0.0390153	+	0.120077i
$358$		0			0
$359$	−9.60006	−	6.97485i	−0.506672	−	0.368119i	0.304888	−	0.952388i	$-0.401381\pi$
$359$	−9.60006	−	6.97485i	−0.506672	−	0.368119i	−0.811560	+	0.584270i	$0.801381\pi$
$360$		0			0
$361$	10.6983	−	32.9260i	0.563068	−	1.73294i
$362$		0			0
$363$	−26.0491	+	12.5267i	−1.36722	+	0.657481i
$364$		0			0
$365$	−5.27679	+	16.2403i	−0.276200	+	0.850056i
$366$		0			0
$367$	−20.1631	−	14.6493i	−1.05250	−	0.764688i	−0.0798164	−	0.996810i	$-0.525433\pi$
$367$	−20.1631	−	14.6493i	−1.05250	−	0.764688i	−0.972687	+	0.232121i	$0.925433\pi$
$368$		0			0
$369$	−14.2069	−	43.7245i	−0.739584	−	2.27621i
$370$		0			0
$371$	10.3224	−	7.49965i	0.535911	−	0.389362i
$372$		0			0
$373$	31.2267			1.61686			0.808429	−	0.588593i	$-0.200318\pi$
$373$	31.2267			1.61686			0.808429	+	0.588593i	$0.200318\pi$
$374$		0			0
$375$	30.0463			1.55158
$376$		0			0
$377$	3.00169	−	2.18086i	0.154595	−	0.112320i
$378$		0			0
$379$	1.82534	+	5.61781i	0.0937612	+	0.288567i	0.986929	−	0.161156i	$-0.0515224\pi$
$379$	1.82534	+	5.61781i	0.0937612	+	0.288567i	−0.893168	+	0.449724i	$0.851522\pi$
$380$		0			0
$381$	−22.2848	−	16.1909i	−1.14169	−	0.829484i
$382$		0			0
$383$	5.27168	−	16.2246i	0.269370	−	0.829037i	−0.721284	−	0.692640i	$-0.756448\pi$
$383$	5.27168	−	16.2246i	0.269370	−	0.829037i	0.990654	−	0.136397i	$-0.0435524\pi$
$384$		0			0
$385$	−13.2484	−	5.66700i	−0.675201	−	0.288817i
$386$		0			0
$387$	−1.54401	+	4.75198i	−0.0784866	+	0.241557i
$388$		0			0
$389$	−3.08753	−	2.24322i	−0.156544	−	0.113736i	0.506756	−	0.862090i	$-0.330845\pi$
$389$	−3.08753	−	2.24322i	−0.156544	−	0.113736i	−0.663300	+	0.748354i	$0.730845\pi$
$390$		0			0
$391$	−1.22130	−	3.75878i	−0.0617639	−	0.190090i
$392$		0			0
$393$	−23.3680	+	16.9778i	−1.17876	+	0.856418i
$394$		0			0
$395$	12.8098			0.644530
$396$		0			0
$397$	23.4669			1.17777			0.588886	−	0.808216i	$-0.299567\pi$
$397$	23.4669			1.17777			0.588886	+	0.808216i	$0.299567\pi$
$398$		0			0
$399$	31.0062	−	22.5273i	1.55225	−	1.12778i
$400$		0			0
$401$	−8.25983	−	25.4212i	−0.412476	−	1.26947i	−0.914489	−	0.404611i	$-0.867407\pi$
$401$	−8.25983	−	25.4212i	−0.412476	−	1.26947i	0.502012	−	0.864860i	$-0.332593\pi$
$402$		0			0
$403$	−1.09271	−	0.793897i	−0.0544315	−	0.0395468i
$404$		0			0
$405$	−3.68515	+	11.3417i	−0.183117	+	0.563576i
$406$		0			0
$407$	23.0843	−	26.4073i	1.14425	−	1.30896i
$408$		0			0
$409$	−1.81747	+	5.59358i	−0.0898679	+	0.276585i	−0.985882	−	0.167440i	$-0.946450\pi$
$409$	−1.81747	+	5.59358i	−0.0898679	+	0.276585i	0.896014	+	0.444025i	$0.146450\pi$
$410$		0			0
$411$	16.6080	+	12.0664i	0.819211	+	0.595192i
$412$		0			0
$413$	−5.95658	−	18.3325i	−0.293104	−	0.902082i
$414$		0			0
$415$	−17.3219	+	12.5851i	−0.850299	+	0.617778i
$416$		0			0
$417$	−43.6608			−2.13808
$418$		0			0
$419$	−2.09664			−0.102427			−0.0512137	−	0.998688i	$-0.516309\pi$
$419$	−2.09664			−0.102427			−0.0512137	+	0.998688i	$0.516309\pi$
$420$		0			0
$421$	−0.433469	+	0.314933i	−0.0211260	+	0.0153489i	−0.598298	−	0.801274i	$-0.704156\pi$
$421$	−0.433469	+	0.314933i	−0.0211260	+	0.0153489i	0.577172	+	0.816622i	$0.304156\pi$
$422$		0			0
$423$	5.99685	+	18.4564i	0.291577	+	0.897381i
$424$		0			0
$425$	0.0893210	+	0.0648955i	0.00433271	+	0.00314790i
$426$		0			0
$427$	−3.49914	+	10.7692i	−0.169335	+	0.521160i
$428$		0			0
$429$	−8.49708	+	1.93691i	−0.410243	+	0.0935151i
$430$		0			0
$431$	−4.86423	+	14.9706i	−0.234302	+	0.721107i	0.762911	+	0.646503i	$0.223769\pi$
$431$	−4.86423	+	14.9706i	−0.234302	+	0.721107i	−0.997213	+	0.0746040i	$0.976231\pi$
$432$		0			0
$433$	−28.1351	−	20.4413i	−1.35209	−	0.982347i	−0.998905	−	0.0467922i	$-0.985100\pi$
$433$	−28.1351	−	20.4413i	−1.35209	−	0.982347i	−0.353180	−	0.935555i	$-0.614900\pi$
$434$		0			0
$435$	−6.57151	−	20.2250i	−0.315080	−	0.969717i
$436$		0			0
$437$	−51.3691	+	37.3218i	−2.45732	+	1.78534i
$438$		0			0
$439$	−23.4194			−1.11775			−0.558874	−	0.829253i	$-0.688766\pi$
$439$	−23.4194			−1.11775			−0.558874	+	0.829253i	$0.688766\pi$
$440$		0			0
$441$	−11.8415			−0.563883
$442$		0			0
$443$	−23.7573	+	17.2607i	−1.12874	+	0.820079i	−0.985511	−	0.169610i	$-0.945749\pi$
$443$	−23.7573	+	17.2607i	−1.12874	+	0.820079i	−0.143231	+	0.989689i	$0.545749\pi$
$444$		0			0
$445$	1.77123	+	5.45129i	0.0839645	+	0.258416i
$446$		0			0
$447$	5.98587	+	4.34899i	0.283122	+	0.205700i
$448$		0			0
$449$	8.11093	−	24.9629i	0.382779	−	1.17807i	−0.555300	−	0.831650i	$-0.687397\pi$
$449$	8.11093	−	24.9629i	0.382779	−	1.17807i	0.938079	−	0.346422i	$-0.112603\pi$
$450$		0			0
$451$	20.0195	+	33.5282i	0.942682	+	1.57878i
$452$		0			0
$453$	−16.3785	+	50.4078i	−0.769528	+	2.36836i
$454$		0			0
$455$	−3.51489	−	2.55371i	−0.164780	−	0.119720i
$456$		0			0
$457$	−0.626718	−	1.92884i	−0.0293166	−	0.0902273i	0.935328	−	0.353783i	$-0.115105\pi$
$457$	−0.626718	−	1.92884i	−0.0293166	−	0.0902273i	−0.964644	+	0.263555i	$0.915105\pi$
$458$		0			0
$459$	0.876618	−	0.636900i	0.0409170	−	0.0297280i
$460$		0			0
$461$	−8.06108			−0.375442			−0.187721	−	0.982222i	$-0.560110\pi$
$461$	−8.06108			−0.375442			−0.187721	+	0.982222i	$0.560110\pi$
$462$		0			0
$463$	27.4220			1.27441			0.637205	−	0.770694i	$-0.280090\pi$
$463$	27.4220			1.27441			0.637205	+	0.770694i	$0.280090\pi$
$464$		0			0
$465$	−6.26293	+	4.55029i	−0.290437	+	0.211015i
$466$		0			0
$467$	10.7877	+	33.2012i	0.499197	+	1.53637i	0.810312	+	0.585998i	$0.199297\pi$
$467$	10.7877	+	33.2012i	0.499197	+	1.53637i	−0.311116	+	0.950372i	$0.600703\pi$
$468$		0			0
$469$	−2.74845	−	1.99687i	−0.126912	−	0.0922068i
$470$		0			0
$471$	12.9319	−	39.8003i	0.595871	−	1.83390i
$472$		0			0
$473$	0.381605	−	4.22680i	0.0175462	−	0.194348i
$474$		0			0
$475$	0.548128	−	1.68696i	0.0251498	−	0.0774032i
$476$		0			0
$477$	−20.2357	−	14.7021i	−0.926530	−	0.673163i
$478$		0			0
$479$	−5.44889	−	16.7700i	−0.248966	−	0.766239i	−0.994959	−	0.100285i	$-0.968025\pi$
$479$	−5.44889	−	16.7700i	−0.248966	−	0.766239i	0.745992	−	0.665954i	$-0.231975\pi$
$480$		0			0
$481$	8.55569	−	6.21607i	0.390106	−	0.283429i
$482$		0			0
$483$	−45.3842			−2.06505
$484$		0			0
$485$	5.83460			0.264935
$486$		0			0
$487$	−16.2400	+	11.7991i	−0.735905	+	0.534666i	−0.891426	−	0.453166i	$-0.850294\pi$
$487$	−16.2400	+	11.7991i	−0.735905	+	0.534666i	0.155521	+	0.987833i	$0.450294\pi$
$488$		0			0
$489$	7.98227	+	24.5669i	0.360971	+	1.11095i
$490$		0			0
$491$	14.3519	+	10.4272i	0.647691	+	0.470575i	0.862484	−	0.506085i	$-0.168908\pi$
$491$	14.3519	+	10.4272i	0.647691	+	0.470575i	−0.214793	+	0.976660i	$0.568908\pi$
$492$		0			0
$493$	0.522579	−	1.60833i	0.0235358	−	0.0724357i
$494$		0			0
$495$	−2.53997	+	28.1336i	−0.114163	+	1.26451i
$496$		0			0
$497$	4.78172	−	14.7166i	0.214489	−	0.660131i
$498$		0			0
$499$	20.6726	+	15.0195i	0.925432	+	0.672365i	0.944870	−	0.327446i	$-0.106188\pi$
$499$	20.6726	+	15.0195i	0.925432	+	0.672365i	−0.0194384	+	0.999811i	$0.506188\pi$
$500$		0			0
$501$	0.562542	+	1.73132i	0.0251325	+	0.0773499i
$502$		0			0
$503$	7.75429	−	5.63382i	0.345747	−	0.251200i	−0.401336	−	0.915931i	$-0.631454\pi$
$503$	7.75429	−	5.63382i	0.345747	−	0.251200i	0.747083	+	0.664731i	$0.231454\pi$
$504$		0			0
$505$	−33.2868			−1.48124
$506$		0			0
$507$	−2.62768			−0.116700
$508$		0			0
$509$	18.1080	−	13.1562i	0.802622	−	0.583139i	−0.109060	−	0.994035i	$-0.534784\pi$
$509$	18.1080	−	13.1562i	0.802622	−	0.583139i	0.911682	+	0.410896i	$0.134784\pi$
$510$		0			0
$511$	4.81860	+	14.8301i	0.213162	+	0.656046i
$512$		0			0
$513$	−14.0836	−	10.2323i	−0.621806	−	0.451769i
$514$		0			0
$515$	−7.04447	+	21.6806i	−0.310416	+	0.955363i
$516$		0			0
$517$	−8.45037	−	14.1525i	−0.371647	−	0.622426i
$518$		0			0
$519$	6.95821	−	21.4152i	0.305432	−	0.940022i
$520$		0			0
$521$	−1.43164	−	1.04015i	−0.0627213	−	0.0455697i	0.555983	−	0.831194i	$-0.312342\pi$
$521$	−1.43164	−	1.04015i	−0.0627213	−	0.0455697i	−0.618704	+	0.785624i	$0.712342\pi$
$522$		0			0
$523$	−3.24092	−	9.97451i	−0.141715	−	0.436155i	0.854859	−	0.518861i	$-0.173644\pi$
$523$	−3.24092	−	9.97451i	−0.141715	−	0.436155i	−0.996574	+	0.0827060i	$0.973644\pi$
$524$		0			0
$525$	1.02569	−	0.745210i	0.0447649	−	0.0325236i
$526$		0			0
$527$	−0.615612			−0.0268165
$528$		0			0
$529$	52.1896			2.26911
$530$		0			0
$531$	−30.5711	+	22.2112i	−1.32667	+	0.963884i
$532$		0			0
$533$	3.63840	+	11.1978i	0.157596	+	0.485032i
$534$		0			0
$535$	−0.502141	−	0.364827i	−0.0217095	−	0.0157729i
$536$		0			0
$537$	−5.58362	+	17.1846i	−0.240951	+	0.741572i
$538$		0			0
$539$	9.80650	−	2.23540i	0.422396	−	0.0962853i
$540$		0			0
$541$	5.10360	−	15.7073i	0.219421	−	0.675308i	−0.779389	−	0.626540i	$-0.784470\pi$
$541$	5.10360	−	15.7073i	0.219421	−	0.675308i	0.998810	−	0.0487681i	$-0.0155295\pi$
$542$		0			0
$543$	9.83055	+	7.14231i	0.421869	+	0.306506i
$544$		0			0
$545$	2.81647	+	8.66820i	0.120644	+	0.371305i
$546$		0			0
$547$	−7.04277	+	5.11687i	−0.301127	+	0.218782i	−0.728080	−	0.685492i	$-0.759587\pi$
$547$	−7.04277	+	5.11687i	−0.301127	+	0.218782i	0.426953	+	0.904274i	$0.359587\pi$
$548$		0			0
$549$	22.1982			0.947395
$550$		0			0
$551$	−27.1690			−1.15744
$552$		0			0
$553$	9.46346	−	6.87560i	0.402427	−	0.292380i
$554$		0			0
$555$	−18.7307	−	57.6472i	−0.795075	−	2.44699i
$556$		0			0
$557$	−20.4112	−	14.8296i	−0.864852	−	0.628352i	0.0643486	−	0.997927i	$-0.479503\pi$
$557$	−20.4112	−	14.8296i	−0.864852	−	0.628352i	−0.929201	+	0.369576i	$0.879503\pi$
$558$		0			0
$559$	0.395421	−	1.21698i	0.0167245	−	0.0514728i
$560$		0			0
$561$	−2.61430	+	2.99062i	−0.110376	+	0.126264i
$562$		0			0
$563$	14.4868	−	44.5857i	0.610545	−	1.87906i	0.157661	−	0.987493i	$-0.449605\pi$
$563$	14.4868	−	44.5857i	0.610545	−	1.87906i	0.452884	−	0.891570i	$-0.350395\pi$
$564$		0			0
$565$	−35.4857	−	25.7819i	−1.49289	−	1.08465i
$566$		0			0
$567$	3.36516	+	10.3569i	0.141324	+	0.434949i
$568$		0			0
$569$	23.7676	−	17.2682i	0.996389	−	0.723919i	0.0350784	−	0.999385i	$-0.488832\pi$
$569$	23.7676	−	17.2682i	0.996389	−	0.723919i	0.961311	+	0.275465i	$0.0888319\pi$
$570$		0			0
$571$	−17.4329			−0.729545			−0.364772	−	0.931097i	$-0.618853\pi$
$571$	−17.4329			−0.729545			−0.364772	+	0.931097i	$0.618853\pi$
$572$		0			0
$573$	2.88970			0.120719
$574$		0			0
$575$	−1.69930	+	1.23462i	−0.0708659	+	0.0514871i
$576$		0			0
$577$	6.94872	+	21.3859i	0.289279	+	0.890309i	0.985083	+	0.172078i	$0.0550480\pi$
$577$	6.94872	+	21.3859i	0.289279	+	0.890309i	−0.695805	+	0.718231i	$0.744952\pi$
$578$		0			0
$579$	−3.58532	−	2.60489i	−0.149001	−	0.108256i
$580$		0			0
$581$	−6.04186	+	18.5949i	−0.250659	+	0.771448i
$582$		0			0
$583$	19.5335	+	8.35545i	0.808994	+	0.346047i
$584$		0			0
$585$	−2.63193	+	8.10025i	−0.108817	+	0.334904i
$586$		0			0
$587$	8.78354	+	6.38161i	0.362535	+	0.263397i	0.754109	−	0.656749i	$-0.228069\pi$
$587$	8.78354	+	6.38161i	0.362535	+	0.263397i	−0.391573	+	0.920147i	$0.628069\pi$
$588$		0			0
$589$	3.05628	+	9.40625i	0.125932	+	0.387578i
$590$		0			0
$591$	−6.31028	+	4.58469i	−0.259570	+	0.188589i
$592$		0			0
$593$	15.2320			0.625503			0.312751	−	0.949835i	$-0.398749\pi$
$593$	15.2320			0.625503			0.312751	+	0.949835i	$0.398749\pi$
$594$		0			0
$595$	−1.98023			−0.0811815
$596$		0			0
$597$	21.1412	−	15.3600i	0.865253	−	0.628643i
$598$		0			0
$599$	−0.0903987	−	0.278219i	−0.00369359	−	0.0113677i	0.949193	−	0.314695i	$-0.101902\pi$
$599$	−0.0903987	−	0.278219i	−0.00369359	−	0.0113677i	−0.952886	+	0.303328i	$0.901902\pi$
$600$		0			0
$601$	−10.2291	−	7.43189i	−0.417255	−	0.303153i	0.359278	−	0.933231i	$-0.383023\pi$
$601$	−10.2291	−	7.43189i	−0.417255	−	0.303153i	−0.776532	+	0.630077i	$0.783023\pi$
$602$		0			0
$603$	−2.05803	+	6.33397i	−0.0838095	+	0.257939i
$604$		0			0
$605$	−3.20749	−	23.7782i	−0.130403	−	0.966720i
$606$		0			0
$607$	−11.4083	+	35.1111i	−0.463048	+	1.42512i	0.398372	+	0.917224i	$0.369575\pi$
$607$	−11.4083	+	35.1111i	−0.463048	+	1.42512i	−0.861421	+	0.507892i	$0.830425\pi$
$608$		0			0
$609$	−15.7105	−	11.4144i	−0.636623	−	0.462534i
$610$		0			0
$611$	−1.53579	−	4.72668i	−0.0621315	−	0.191221i
$612$		0			0
$613$	−34.0079	+	24.7082i	−1.37357	+	0.997955i	−0.376119	+	0.926571i	$0.622742\pi$
$613$	−34.0079	+	24.7082i	−1.37357	+	0.997955i	−0.997449	+	0.0713838i	$0.977258\pi$
$614$		0			0
$615$	67.4842			2.72123
$616$		0			0
$617$	−24.2075			−0.974557			−0.487279	−	0.873247i	$-0.662010\pi$
$617$	−24.2075			−0.974557			−0.487279	+	0.873247i	$0.662010\pi$
$618$		0			0
$619$	−28.6813	+	20.8382i	−1.15280	+	0.837557i	−0.988850	−	0.148912i	$-0.952423\pi$
$619$	−28.6813	+	20.8382i	−1.15280	+	0.837557i	−0.163948	+	0.986469i	$0.552423\pi$
$620$		0			0
$621$	6.37019	+	19.6054i	0.255627	+	0.786739i
$622$		0			0
$623$	4.23449	+	3.07654i	0.169651	+	0.123259i
$624$		0			0
$625$	−7.33302	+	22.5687i	−0.293321	+	0.902749i
$626$		0			0
$627$	58.6743	+	25.0979i	2.34322	+	1.00231i
$628$		0			0
$629$	1.48950	−	4.58422i	0.0593904	−	0.182785i
$630$		0			0
$631$	21.8583	+	15.8810i	0.870166	+	0.632213i	0.930632	−	0.365958i	$-0.119258\pi$
$631$	21.8583	+	15.8810i	0.870166	+	0.632213i	−0.0604654	+	0.998170i	$0.519258\pi$
$632$		0			0
$633$	−20.8127	−	64.0548i	−0.827230	−	2.54595i
$634$		0			0
$635$	18.4986	−	13.4400i	0.734093	−	0.533350i
$636$		0			0
$637$	3.03262			0.120157
$638$		0			0
$639$	−30.3348			−1.20002
$640$		0			0
$641$	−32.8504	+	23.8672i	−1.29751	+	0.942698i	−0.999928	−	0.0119968i	$-0.996181\pi$
$641$	−32.8504	+	23.8672i	−1.29751	+	0.942698i	−0.297585	+	0.954695i	$0.596181\pi$
$642$		0			0
$643$	0.395523	+	1.21730i	0.0155979	+	0.0480055i	0.958553	−	0.284916i	$-0.0919657\pi$
$643$	0.395523	+	1.21730i	0.0155979	+	0.0480055i	−0.942955	+	0.332921i	$0.891966\pi$
$644$		0			0
$645$	−5.93349	−	4.31093i	−0.233631	−	0.169743i
$646$		0			0
$647$	2.79889	−	8.61410i	0.110036	−	0.338655i	−0.880844	−	0.473407i	$-0.843024\pi$
$647$	2.79889	−	8.61410i	0.110036	−	0.338655i	0.990879	+	0.134752i	$0.0430238\pi$
$648$		0			0
$649$	21.1243	−	24.1651i	0.829202	−	0.948565i
$650$		0			0
$651$	−2.18451	+	6.72322i	−0.0856175	+	0.263504i
$652$		0			0
$653$	−3.23500	−	2.35037i	−0.126595	−	0.0919769i	0.522686	−	0.852525i	$-0.324930\pi$
$653$	−3.23500	−	2.35037i	−0.126595	−	0.0919769i	−0.649281	+	0.760549i	$0.724930\pi$
$654$		0			0
$655$	−7.40925	−	22.8033i	−0.289503	−	0.891000i
$656$		0			0
$657$	24.7306	−	17.9678i	0.964832	−	0.700992i
$658$		0			0
$659$	−36.6692			−1.42843			−0.714214	−	0.699927i	$-0.753216\pi$
$659$	−36.6692			−1.42843			−0.714214	+	0.699927i	$0.753216\pi$
$660$		0			0
$661$	42.3119			1.64574			0.822871	−	0.568228i	$-0.192371\pi$
$661$	42.3119			1.64574			0.822871	+	0.568228i	$0.192371\pi$
$662$		0			0
$663$	−0.968930	+	0.703969i	−0.0376301	+	0.0273399i
$664$		0			0
$665$	9.83108	+	30.2569i	0.381233	+	1.17331i
$666$		0			0
$667$	26.0282	+	18.9106i	1.00782	+	0.732222i
$668$		0			0
$669$	−22.0517	+	67.8683i	−0.852570	+	2.62394i
$670$		0			0
$671$	−18.3833	+	4.19048i	−0.709678	+	0.161772i
$672$		0			0
$673$	−4.34115	+	13.3607i	−0.167339	+	0.515016i	−0.999201	−	0.0399662i	$-0.987275\pi$
$673$	−4.34115	+	13.3607i	−0.167339	+	0.515016i	0.831862	+	0.554982i	$0.187275\pi$
$674$		0			0
$675$	−0.465890	−	0.338489i	−0.0179321	−	0.0130284i
$676$		0			0
$677$	3.80995	+	11.7258i	0.146428	+	0.450660i	0.997192	−	0.0748884i	$-0.0238601\pi$
$677$	3.80995	+	11.7258i	0.146428	+	0.450660i	−0.850764	+	0.525549i	$0.823860\pi$
$678$		0			0
$679$	4.31042	−	3.13170i	0.165419	−	0.120184i
$680$		0			0
$681$	61.5369			2.35810
$682$		0			0
$683$	−18.5369			−0.709296			−0.354648	−	0.935000i	$-0.615399\pi$
$683$	−18.5369			−0.709296			−0.354648	+	0.935000i	$0.615399\pi$
$684$		0			0
$685$	−13.7862	+	10.0163i	−0.526744	+	0.382702i
$686$		0			0
$687$	−13.0907	−	40.2889i	−0.499440	−	1.53712i
$688$		0			0
$689$	5.18236	+	3.76521i	0.197432	+	0.143443i
$690$		0			0
$691$	−9.23129	+	28.4110i	−0.351175	+	1.08080i	0.607020	+	0.794687i	$0.292365\pi$
$691$	−9.23129	+	28.4110i	−0.351175	+	1.08080i	−0.958194	+	0.286118i	$0.907635\pi$
$692$		0			0
$693$	13.2242	+	22.1476i	0.502345	+	0.841316i
$694$		0			0
$695$	11.1996	−	34.4688i	0.424825	−	1.30748i
$696$		0			0
$697$	4.34157	+	3.15434i	0.164449	+	0.119479i
$698$		0			0
$699$	−10.7517	−	33.0904i	−0.406668	−	1.25160i
$700$		0			0
$701$	−27.8022	+	20.1994i	−1.05007	+	0.762923i	−0.972226	−	0.234043i	$-0.924804\pi$
$701$	−27.8022	+	20.1994i	−1.05007	+	0.762923i	−0.0778465	+	0.996965i	$0.524804\pi$
$702$		0			0
$703$	−77.4395			−2.92068
$704$		0			0
$705$	−28.4856			−1.07283
$706$		0			0
$707$	−24.5912	+	17.8666i	−0.924849	+	0.671942i
$708$		0			0
$709$	−6.36350	−	19.5848i	−0.238986	−	0.735524i	−0.996568	−	0.0827833i	$-0.973619\pi$
$709$	−6.36350	−	19.5848i	−0.238986	−	0.735524i	0.757581	−	0.652741i	$-0.226381\pi$
$710$		0			0
$711$	−18.5519	−	13.4787i	−0.695751	−	0.505492i
$712$		0			0
$713$	3.61915	−	11.1386i	0.135538	−	0.417144i
$714$		0			0
$715$	0.650486	−	7.20502i	0.0243268	−	0.269452i
$716$		0			0
$717$	9.55201	−	29.3981i	0.356726	−	1.09789i
$718$		0			0
$719$	−21.1384	−	15.3580i	−0.788330	−	0.572755i	0.119137	−	0.992878i	$-0.461987\pi$
$719$	−21.1384	−	15.3580i	−0.788330	−	0.572755i	−0.907467	+	0.420122i	$0.861987\pi$
$720$		0			0
$721$	6.43278	+	19.7981i	0.239569	+	0.737318i
$722$		0			0
$723$	16.3106	−	11.8503i	0.606596	−	0.440718i
$724$		0			0
$725$	−0.898758			−0.0333790
$726$		0			0
$727$	−3.88707			−0.144163			−0.0720817	−	0.997399i	$-0.522964\pi$
$727$	−3.88707			−0.144163			−0.0720817	+	0.997399i	$0.522964\pi$
$728$		0			0
$729$	32.4326	−	23.5637i	1.20121	−	0.872729i
$730$		0			0
$731$	−0.180228	−	0.554684i	−0.00666597	−	0.0205157i
$732$		0			0
$733$	12.7255	+	9.24562i	0.470027	+	0.341495i	0.797452	−	0.603383i	$-0.206181\pi$
$733$	12.7255	+	9.24562i	0.470027	+	0.341495i	−0.327425	+	0.944877i	$0.606181\pi$
$734$		0			0
$735$	5.37124	−	16.5310i	0.198121	−	0.609754i
$736$		0			0
$737$	0.508645	−	5.63394i	0.0187362	−	0.207529i
$738$		0			0
$739$	−5.72911	+	17.6324i	−0.210749	+	0.648618i	0.788680	+	0.614805i	$0.210765\pi$
$739$	−5.72911	+	17.6324i	−0.210749	+	0.648618i	−0.999428	+	0.0338132i	$0.989235\pi$
$740$		0			0
$741$	15.5667	+	11.3099i	0.571856	+	0.415478i
$742$		0			0
$743$	7.79743	+	23.9980i	0.286060	+	0.880402i	0.986079	+	0.166277i	$0.0531748\pi$
$743$	7.79743	+	23.9980i	0.286060	+	0.880402i	−0.700019	+	0.714124i	$0.746825\pi$
$744$		0			0
$745$	−4.96885	+	3.61008i	−0.182044	+	0.132263i
$746$		0			0
$747$	38.3290			1.40238
$748$		0			0
$749$	−0.566786			−0.0207099
$750$		0			0
$751$	36.2453	−	26.3337i	1.32261	−	0.960932i	0.322713	−	0.946497i	$-0.395405\pi$
$751$	36.2453	−	26.3337i	1.32261	−	0.960932i	0.999896	−	0.0144348i	$-0.00459489\pi$
$752$		0			0
$753$	15.0985	+	46.4683i	0.550219	+	1.69340i
$754$		0			0
$755$	−35.5940	−	25.8606i	−1.29540	−	0.941163i
$756$		0			0
$757$	−1.04255	+	3.20862i	−0.0378920	+	0.116619i	−0.968213	−	0.250126i	$-0.919528\pi$
$757$	−1.04255	+	3.20862i	−0.0378920	+	0.116619i	0.930321	+	0.366745i	$0.119528\pi$
$758$		0			0
$759$	−38.7417	−	64.8836i	−1.40623	−	2.35513i
$760$		0			0
$761$	0.282181	−	0.868463i	0.0102290	−	0.0314818i	−0.945812	−	0.324716i	$-0.894731\pi$
$761$	0.282181	−	0.868463i	0.0102290	−	0.0314818i	0.956041	+	0.293234i	$0.0947314\pi$
$762$		0			0
$763$	6.73335	+	4.89206i	0.243763	+	0.177105i
$764$		0			0
$765$	1.19960	+	3.69199i	0.0433716	+	0.133484i
$766$		0			0
$767$	7.82925	−	5.68828i	0.282698	−	0.205392i
$768$		0			0
$769$	−35.3067			−1.27319			−0.636595	−	0.771198i	$-0.719658\pi$
$769$	−35.3067			−1.27319			−0.636595	+	0.771198i	$0.719658\pi$
$770$		0			0
$771$	−28.3148			−1.01973
$772$		0			0
$773$	−13.8361	+	10.0525i	−0.497652	+	0.361565i	−0.808119	−	0.589019i	$-0.799514\pi$
$773$	−13.8361	+	10.0525i	−0.497652	+	0.361565i	0.310468	+	0.950584i	$0.399514\pi$
$774$		0			0
$775$	0.101103	+	0.311162i	0.00363171	+	0.0111773i
$776$		0			0
$777$	−44.7796	−	32.5343i	−1.60646	−	1.16716i
$778$		0			0
$779$	26.6425	−	81.9972i	0.954566	−	2.93785i
$780$		0			0
$781$	25.1215	−	5.72647i	0.898919	−	0.204909i
$782$		0			0
$783$	−2.72572	+	8.38891i	−0.0974094	+	0.299795i
$784$		0			0
$785$	28.1039	+	20.4186i	1.00307	+	0.728773i
$786$		0			0
$787$	16.5355	+	50.8910i	0.589426	+	1.81407i	0.580718	+	0.814105i	$0.302772\pi$
$787$	16.5355	+	50.8910i	0.589426	+	1.81407i	0.00870856	+	0.999962i	$0.497228\pi$
$788$		0			0
$789$	−2.81473	+	2.04502i	−0.100207	+	0.0728047i
$790$		0			0
$791$	−40.0540			−1.42416
$792$		0			0
$793$	−5.68495			−0.201878
$794$		0			0
$795$	29.7032	−	21.5806i	1.05346	−	0.765385i
$796$		0			0
$797$	−6.85601	−	21.1006i	−0.242852	−	0.747423i	−0.995982	−	0.0895509i	$-0.971457\pi$
$797$	−6.85601	−	21.1006i	−0.242852	−	0.747423i	0.753130	−	0.657872i	$-0.228543\pi$
$798$		0			0
$799$	−1.83261	−	1.33147i	−0.0648330	−	0.0471039i
$800$		0			0
$801$	3.17077	−	9.75862i	0.112034	−	0.344804i
$802$		0			0
$803$	−17.0886	+	19.5485i	−0.603043	+	0.689851i
$804$		0			0
$805$	11.6417	−	35.8294i	0.410315	−	1.26282i
$806$		0			0
$807$	24.2025	+	17.5841i	0.851968	+	0.618991i
$808$		0			0
$809$	5.90737	+	18.1810i	0.207692	+	0.639210i	0.999592	+	0.0285595i	$0.00909200\pi$
$809$	5.90737	+	18.1810i	0.207692	+	0.639210i	−0.791900	+	0.610651i	$0.790908\pi$
$810$		0			0
$811$	6.16117	−	4.47635i	0.216348	−	0.157186i	−0.474333	−	0.880345i	$-0.657311\pi$
$811$	6.16117	−	4.47635i	0.216348	−	0.157186i	0.690681	+	0.723159i	$0.257311\pi$
$812$		0			0
$813$	−9.36892			−0.328582
$814$		0			0
$815$	−21.4423			−0.751093
$816$		0			0
$817$	−7.58054	+	5.50759i	−0.265210	+	0.192686i
$818$		0			0
$819$	2.40340	+	7.39689i	0.0839814	+	0.258468i
$820$		0			0
$821$	24.0607	+	17.4811i	0.839726	+	0.610096i	0.922294	−	0.386489i	$-0.126312\pi$
$821$	24.0607	+	17.4811i	0.839726	+	0.610096i	−0.0825684	+	0.996585i	$0.526312\pi$
$822$		0			0
$823$	4.46271	−	13.7348i	0.155560	−	0.478765i	−0.842657	−	0.538451i	$-0.819010\pi$
$823$	4.46271	−	13.7348i	0.155560	−	0.478765i	0.998217	+	0.0596857i	$0.0190098\pi$
$824$		0			0
$825$	1.94096	+	0.830246i	0.0675756	+	0.0289055i
$826$		0			0
$827$	9.87606	−	30.3954i	0.343424	−	1.05695i	−0.618998	−	0.785393i	$-0.712461\pi$
$827$	9.87606	−	30.3954i	0.343424	−	1.05695i	0.962422	−	0.271558i	$-0.0875390\pi$
$828$		0			0
$829$	35.0381	+	25.4566i	1.21692	+	0.884146i	0.995841	−	0.0911097i	$-0.0290414\pi$
$829$	35.0381	+	25.4566i	1.21692	+	0.884146i	0.221081	+	0.975255i	$0.429041\pi$
$830$		0			0
$831$	22.4138	+	68.9824i	0.777524	+	2.39297i
$832$		0			0
$833$	1.11824	−	0.812452i	0.0387449	−	0.0281498i
$834$		0			0
$835$	−1.51113			−0.0522947
$836$		0			0
$837$	3.21097			0.110987
$838$		0			0
$839$	6.11242	−	4.44093i	0.211024	−	0.153318i	−0.477253	−	0.878766i	$-0.658367\pi$
$839$	6.11242	−	4.44093i	0.211024	−	0.153318i	0.688277	+	0.725448i	$0.258367\pi$
$840$		0			0
$841$	−4.70748	−	14.4881i	−0.162327	−	0.499591i
$842$		0			0
$843$	11.4365	+	8.30911i	0.393894	+	0.286181i
$844$		0			0
$845$	0.674037	−	2.07447i	0.0231876	−	0.0713641i
$846$		0			0
$847$	−15.1324	−	15.8450i	−0.519957	−	0.544439i
$848$		0			0
$849$	−6.39589	+	19.6845i	−0.219506	+	0.675571i
$850$		0			0
$851$	74.1881	+	53.9008i	2.54313	+	1.84769i
$852$		0			0
$853$	−5.60593	−	17.2533i	−0.191943	−	0.590741i	−0.999999	−	0.00163415i	$-0.999480\pi$
$853$	−5.60593	−	17.2533i	−0.191943	−	0.590741i	0.808055	−	0.589107i	$-0.200520\pi$
$854$		0			0
$855$	50.4562	−	36.6586i	1.72557	−	1.25370i
$856$		0			0
$857$	21.3653			0.729824			0.364912	−	0.931042i	$-0.381099\pi$
$857$	21.3653			0.729824			0.364912	+	0.931042i	$0.381099\pi$
$858$		0			0
$859$	6.18695			0.211096			0.105548	−	0.994414i	$-0.466340\pi$
$859$	6.18695			0.211096			0.105548	+	0.994414i	$0.466340\pi$
$860$		0			0
$861$	49.8552	−	36.2219i	1.69906	−	1.23444i
$862$		0			0
$863$	2.14070	+	6.58839i	0.0728702	+	0.224272i	0.980858	−	0.194726i	$-0.0623817\pi$
$863$	2.14070	+	6.58839i	0.0728702	+	0.224272i	−0.907987	+	0.418997i	$0.862382\pi$
$864$		0			0
$865$	15.1217	+	10.9866i	0.514154	+	0.373555i
$866$		0			0
$867$	13.6353	−	41.9651i	0.463079	−	1.42521i
$868$		0			0
$869$	17.9081	+	7.66019i	0.607491	+	0.259854i
$870$		0			0
$871$	0.527061	−	1.62213i	0.0178588	−	0.0549637i
$872$		0			0
$873$	−8.45002	−	6.13930i	−0.285990	−	0.207784i
$874$		0			0
$875$	7.03805	+	21.6609i	0.237930	+	0.732272i
$876$		0			0
$877$	12.3629	−	8.98218i	0.417466	−	0.303307i	−0.359152	−	0.933279i	$-0.616934\pi$
$877$	12.3629	−	8.98218i	0.417466	−	0.303307i	0.776617	+	0.629973i	$0.216934\pi$
$878$		0			0
$879$	79.6738			2.68733
$880$		0			0
$881$	23.4247			0.789198			0.394599	−	0.918853i	$-0.370883\pi$
$881$	23.4247			0.789198			0.394599	+	0.918853i	$0.370883\pi$
$882$		0			0
$883$	−33.8871	+	24.6204i	−1.14039	+	0.828543i	−0.987174	−	0.159649i	$-0.948964\pi$
$883$	−33.8871	+	24.6204i	−1.14039	+	0.828543i	−0.153218	+	0.988192i	$0.548964\pi$
$884$		0			0
$885$	−17.1404	−	52.7526i	−0.576167	−	1.77326i
$886$		0			0
$887$	−27.6276	−	20.0726i	−0.927644	−	0.673973i	0.0177705	−	0.999842i	$-0.494343\pi$
$887$	−27.6276	−	20.0726i	−0.927644	−	0.673973i	−0.945415	+	0.325869i	$0.894343\pi$
$888$		0			0
$889$	6.45228	−	19.8581i	0.216403	−	0.666018i
$890$		0			0
$891$	−11.9342	+	13.6521i	−0.399809	+	0.457362i
$892$		0			0
$893$	−11.2460	+	34.6116i	−0.376332	+	1.15823i
$894$		0			0
$895$	−12.1344	−	8.81619i	−0.405610	−	0.294693i
$896$		0			0
$897$	−7.04100	−	21.6700i	−0.235092	−	0.723540i
$898$		0			0
$899$	4.05426	−	2.94559i	0.135217	−	0.0982409i
$900$		0			0
$901$	2.91966			0.0972679
$902$		0			0
$903$	−6.69735			−0.222874
$904$		0			0
$905$	−8.16030	+	5.92880i	−0.271258	+	0.197080i
$906$		0			0
$907$	10.3531	+	31.8636i	0.343769	+	1.05801i	0.962240	+	0.272204i	$0.0877526\pi$
$907$	10.3531	+	31.8636i	0.343769	+	1.05801i	−0.618471	+	0.785808i	$0.712247\pi$
$908$		0			0
$909$	48.2080	+	35.0251i	1.59896	+	1.16171i
$910$		0			0
$911$	15.9011	−	48.9384i	0.526825	−	1.62140i	−0.233852	−	0.972272i	$-0.575133\pi$
$911$	15.9011	−	48.9384i	0.526825	−	1.62140i	0.760678	−	0.649130i	$-0.224867\pi$
$912$		0			0
$913$	−31.7419	+	7.23558i	−1.05050	+	0.239463i
$914$		0			0
$915$	−10.0689	+	30.9890i	−0.332869	+	1.02446i
$916$		0			0
$917$	−17.7133	−	12.8695i	−0.584945	−	0.424988i
$918$		0			0
$919$	14.9179	+	45.9125i	0.492095	+	1.51451i	0.821435	+	0.570301i	$0.193174\pi$
$919$	14.9179	+	45.9125i	0.492095	+	1.51451i	−0.329341	+	0.944211i	$0.606826\pi$
$920$		0			0
$921$	57.2476	−	41.5928i	1.88637	−	1.37053i
$922$		0			0
$923$	7.76872			0.255711
$924$		0			0
$925$	−2.56172			−0.0842288
$926$		0			0
$927$	33.0151	−	23.9869i	1.08436	−	0.787832i
$928$		0			0
$929$	7.69403	+	23.6798i	0.252433	+	0.776908i	0.994325	+	0.106389i	$0.0339288\pi$
$929$	7.69403	+	23.6798i	0.252433	+	0.776908i	−0.741892	+	0.670520i	$0.766071\pi$
$930$		0			0
$931$	−17.9655	−	13.0527i	−0.588797	−	0.427786i
$932$		0			0
$933$	−15.7975	+	48.6198i	−0.517188	+	1.59174i
$934$		0			0
$935$	−1.69040	−	2.83104i	−0.0552820	−	0.0925850i
$936$		0			0
$937$	−16.8966	+	52.0024i	−0.551989	+	1.69885i	0.151778	+	0.988415i	$0.451500\pi$
$937$	−16.8966	+	52.0024i	−0.551989	+	1.69885i	−0.703767	+	0.710431i	$0.748500\pi$
$938$		0			0
$939$	9.14479	+	6.64408i	0.298429	+	0.216821i
$940$		0			0
$941$	8.56558	+	26.3621i	0.279230	+	0.859381i	0.988069	+	0.154011i	$0.0492191\pi$
$941$	8.56558	+	26.3621i	0.279230	+	0.859381i	−0.708839	+	0.705370i	$0.750781\pi$
$942$		0			0
$943$	−82.5970	+	60.0102i	−2.68973	+	1.95420i
$944$		0			0
$945$	10.3287			0.335992
$946$		0			0
$947$	36.2486			1.17792			0.588960	−	0.808162i	$-0.299537\pi$
$947$	36.2486			1.17792			0.588960	+	0.808162i	$0.299537\pi$
$948$		0			0
$949$	−6.33350	+	4.60156i	−0.205594	+	0.149373i
$950$		0			0
$951$	−6.89069	−	21.2074i	−0.223446	−	0.687696i
$952$		0			0
$953$	−20.3237	−	14.7660i	−0.658348	−	0.478318i	0.207757	−	0.978181i	$-0.433384\pi$
$953$	−20.3237	−	14.7660i	−0.658348	−	0.478318i	−0.866105	+	0.499863i	$0.833384\pi$
$954$		0			0
$955$	−0.741248	+	2.28133i	−0.0239862	+	0.0738220i
$956$		0			0
$957$	2.90749	−	32.2044i	0.0939857	−	1.04102i
$958$		0			0
$959$	−4.80862	+	14.7994i	−0.155278	+	0.477898i
$960$		0			0
$961$	23.6037	+	17.1491i	0.761408	+	0.553195i
$962$		0			0
$963$	0.343352	+	1.05673i	0.0110644	+	0.0340526i
$964$		0			0
$965$	2.97616	−	2.16231i	0.0958061	−	0.0696072i
$966$		0			0
$967$	−41.3428			−1.32949			−0.664747	−	0.747069i	$-0.731461\pi$
$967$	−41.3428			−1.32949			−0.664747	+	0.747069i	$0.731461\pi$
$968$		0			0
$969$	8.77001			0.281733
$970$		0			0
$971$	37.7347	−	27.4159i	1.21097	−	0.879818i	0.215647	−	0.976471i	$-0.430814\pi$
$971$	37.7347	−	27.4159i	1.21097	−	0.879818i	0.995318	+	0.0966536i	$0.0308139\pi$
$972$		0			0
$973$	−10.2271	−	31.4758i	−0.327866	−	1.00907i
$974$		0			0
$975$	0.514950	+	0.374133i	0.0164916	+	0.0119819i
$976$		0			0
$977$	10.6549	−	32.7923i	0.340880	−	1.04912i	−0.622873	−	0.782323i	$-0.714035\pi$
$977$	10.6549	−	32.7923i	0.340880	−	1.04912i	0.963753	−	0.266797i	$-0.0859652\pi$
$978$		0			0
$979$	−0.783660	+	8.68011i	−0.0250459	+	0.277417i
$980$		0			0
$981$	5.04190	−	15.5174i	0.160975	−	0.495432i
$982$		0			0
$983$	37.3343	+	27.1250i	1.19078	+	0.865152i	0.993346	−	0.115165i	$-0.0367396\pi$
$983$	37.3343	+	27.1250i	1.19078	+	0.865152i	0.197433	+	0.980316i	$0.436740\pi$
$984$		0			0
$985$	−2.00079	−	6.15780i	−0.0637505	−	0.196204i
$986$		0			0
$987$	−21.0442	+	15.2895i	−0.669845	+	0.486671i
$988$		0			0
$989$	11.0957			0.352824
$990$		0			0
$991$	−19.1947			−0.609738			−0.304869	−	0.952394i	$-0.598613\pi$
$991$	−19.1947			−0.609738			−0.304869	+	0.952394i	$0.598613\pi$
$992$		0			0
$993$	−29.9479	+	21.7584i	−0.950367	+	0.690482i
$994$		0			0
$995$	6.70321	+	20.6304i	0.212506	+	0.654027i
$996$		0			0
$997$	37.3445	+	27.1324i	1.18271	+	0.859291i	0.992475	−	0.122447i	$-0.0390743\pi$
$997$	37.3445	+	27.1324i	1.18271	+	0.859291i	0.190237	+	0.981738i	$0.439074\pi$
$998$		0			0
$999$	−7.76910	+	23.9108i	−0.245803	+	0.756505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.53.6	✓	28
11.4	even	5		6292.2.a.z.1.3		14
11.5	even	5	inner	572.2.n.b.313.6	yes	28
11.7	odd	10		6292.2.a.y.1.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.53.6	✓	28	1.1	even	1	trivial
572.2.n.b.313.6	yes	28	11.5	even	5	inner
6292.2.a.y.1.3		14	11.7	odd	10
6292.2.a.z.1.3		14	11.4	even	5

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.12584 - 1.54451i) q^{3} +(0.674037 + 2.07447i) q^{5} +(1.61142 + 1.17077i) q^{7} +(1.20663 - 3.71362i) q^{9} +O(q^{10})\)	\(q+(2.12584 - 1.54451i) q^{3} +(0.674037 + 2.07447i) q^{5} +(1.61142 + 1.17077i) q^{7} +(1.20663 - 3.71362i) q^{9} +(-0.298220 + 3.30319i) q^{11} +(-0.309017 + 0.951057i) q^{13} +(4.63695 + 3.36894i) q^{15} +(0.140846 + 0.433479i) q^{17} +(5.92410 - 4.30411i) q^{19} +5.23390 q^{21} -8.67119 q^{23} +(0.195971 - 0.142381i) q^{25} +(-0.734638 - 2.26098i) q^{27} +(-3.00169 - 2.18086i) q^{29} +(-0.417376 + 1.28455i) q^{31} +(4.46786 + 7.48266i) q^{33} +(-1.34257 + 4.13200i) q^{35} +(-8.55569 - 6.21607i) q^{37} +(0.811999 + 2.49908i) q^{39} +(9.52544 - 6.92064i) q^{41} -1.27961 q^{43} +8.51711 q^{45} +(-4.02075 + 2.92125i) q^{47} +(-0.937130 - 2.88419i) q^{49} +(0.968930 + 0.703969i) q^{51} +(1.97949 - 6.09223i) q^{53} +(-7.05339 + 1.60782i) q^{55} +(5.94594 - 18.2997i) q^{57} +(-7.82925 - 5.68828i) q^{59} +(1.75675 + 5.40671i) q^{61} +(6.29217 - 4.57153i) q^{63} -2.18123 q^{65} -1.70561 q^{67} +(-18.4336 + 13.3928i) q^{69} +(-2.40067 - 7.38850i) q^{71} +(6.33350 + 4.60156i) q^{73} +(0.196693 - 0.605360i) q^{75} +(-4.34783 + 4.97369i) q^{77} +(1.81477 - 5.58530i) q^{79} +(4.42313 + 3.21359i) q^{81} +(3.03332 + 9.33561i) q^{83} +(-0.804305 + 0.584362i) q^{85} -9.74948 q^{87} +2.62780 q^{89} +(-1.61142 + 1.17077i) q^{91} +(1.09673 + 3.37540i) q^{93} +(12.9218 + 9.38826i) q^{95} +(0.826593 - 2.54399i) q^{97} +(11.9069 + 5.09319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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