LMFDB - Embedded newform 726.2.b.c.725.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(725,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.725"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.185640625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			725.1
Root			$1.71634 + 0.232753i$ of defining polynomial
Character	$\chi$	$=$	726.725
Dual form			726.2.b.c.725.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(-1.71634 - 0.232753i) q^{3} +1.00000 q^{4} -2.65532i q^{5} +(1.71634 + 0.232753i) q^{6} +1.64108i q^{7} -1.00000 q^{8} +(2.89165 + 0.798968i) q^{9} +2.65532i q^{10} +(-1.71634 - 0.232753i) q^{12} -1.50641i q^{13} -1.64108i q^{14} +(-0.618034 + 4.55743i) q^{15} +1.00000 q^{16} +6.79026 q^{17} +(-2.89165 - 0.798968i) q^{18} +5.48844i q^{19} -2.65532i q^{20} +(0.381966 - 2.81665i) q^{21} -4.78856i q^{23} +(1.71634 + 0.232753i) q^{24} -2.05072 q^{25} +1.50641i q^{26} +(-4.77710 - 2.04434i) q^{27} +1.64108i q^{28} -0.464026 q^{29} +(0.618034 - 4.55743i) q^{30} -5.19231 q^{31} -1.00000 q^{32} -6.79026 q^{34} +4.35758 q^{35} +(2.89165 + 0.798968i) q^{36} +1.00696 q^{37} -5.48844i q^{38} +(-0.350622 + 2.58551i) q^{39} +2.65532i q^{40} +1.57428 q^{41} +(-0.381966 + 2.81665i) q^{42} -3.42500i q^{43} +(2.12151 - 7.67826i) q^{45} +4.78856i q^{46} -10.0129i q^{47} +(-1.71634 - 0.232753i) q^{48} +4.30687 q^{49} +2.05072 q^{50} +(-11.6544 - 1.58046i) q^{51} -1.50641i q^{52} -9.82493i q^{53} +(4.77710 + 2.04434i) q^{54} -1.64108i q^{56} +(1.27745 - 9.42004i) q^{57} +0.464026 q^{58} -6.11223i q^{59} +(-0.618034 + 4.55743i) q^{60} -13.9034i q^{61} +5.19231 q^{62} +(-1.31117 + 4.74542i) q^{63} +1.00000 q^{64} -4.00000 q^{65} +11.7972 q^{67} +6.79026 q^{68} +(-1.11455 + 8.21881i) q^{69} -4.35758 q^{70} +0.898056i q^{71} +(-2.89165 - 0.798968i) q^{72} -4.62724i q^{73} -1.00696 q^{74} +(3.51973 + 0.477311i) q^{75} +5.48844i q^{76} +(0.350622 - 2.58551i) q^{78} +3.17739i q^{79} -2.65532i q^{80} +(7.72330 + 4.62067i) q^{81} -1.57428 q^{82} +1.87418 q^{83} +(0.381966 - 2.81665i) q^{84} -18.0303i q^{85} +3.42500i q^{86} +(0.796426 + 0.108003i) q^{87} +12.8092i q^{89} +(-2.12151 + 7.67826i) q^{90} +2.47214 q^{91} -4.78856i q^{92} +(8.91178 + 1.20853i) q^{93} +10.0129i q^{94} +14.5736 q^{95} +(1.71634 + 0.232753i) q^{96} -3.59099 q^{97} -4.30687 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 3 q^{3} + 8 q^{4} + 3 q^{6} - 8 q^{8} + 7 q^{9} - 3 q^{12} + 4 q^{15} + 8 q^{16} - 10 q^{17} - 7 q^{18} + 12 q^{21} + 3 q^{24} + 14 q^{25} - 15 q^{27} - 2 q^{29} - 4 q^{30} - 22 q^{31} - 8 q^{32}+ \cdots - 22 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 3 * q^3 + 8 * q^4 + 3 * q^6 - 8 * q^8 + 7 * q^9 - 3 * q^12 + 4 * q^15 + 8 * q^16 - 10 * q^17 - 7 * q^18 + 12 * q^21 + 3 * q^24 + 14 * q^25 - 15 * q^27 - 2 * q^29 - 4 * q^30 - 22 * q^31 - 8 * q^32 + 10 * q^34 - 8 * q^35 + 7 * q^36 - 24 * q^37 + 8 * q^39 + 2 * q^41 - 12 * q^42 - 8 * q^45 - 3 * q^48 + 22 * q^49 - 14 * q^50 - 20 * q^51 + 15 * q^54 + 30 * q^57 + 2 * q^58 + 4 * q^60 + 22 * q^62 - 14 * q^63 + 8 * q^64 - 32 * q^65 - 2 * q^67 - 10 * q^68 - 16 * q^69 + 8 * q^70 - 7 * q^72 + 24 * q^74 + 21 * q^75 - 8 * q^78 + 19 * q^81 - 2 * q^82 + 24 * q^83 + 12 * q^84 + 42 * q^87 + 8 * q^90 - 16 * q^91 - 18 * q^93 + 20 * q^95 + 3 * q^96 - 16 * q^97 - 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.71634	−	0.232753i	−0.990930	−	0.134380i
$3$	−1.71634	−	0.232753i	−0.990930	−	0.134380i
$4$	1.00000			0.500000
$5$		−	2.65532i		−	1.18749i	−0.804652	−	0.593747i	$-0.797648\pi$
$5$		−	2.65532i		−	1.18749i	0.804652	−	0.593747i	$-0.202352\pi$
$6$	1.71634	+	0.232753i	0.700693	+	0.0950211i
$7$			1.64108i			0.620269i	0.950693	+	0.310134i	$0.100374\pi$
$7$			1.64108i			0.620269i	−0.950693	+	0.310134i	$0.899626\pi$
$8$	−1.00000			−0.353553
$9$	2.89165	+	0.798968i	0.963884	+	0.266323i
$10$			2.65532i			0.839685i
$11$		0			0
$11$		0			0
$12$	−1.71634	−	0.232753i	−0.495465	−	0.0671901i
$13$		−	1.50641i		−	0.417803i	−0.977937	−	0.208902i	$-0.933011\pi$
$13$		−	1.50641i		−	0.417803i	0.977937	−	0.208902i	$-0.0669888\pi$
$14$		−	1.64108i		−	0.438596i
$15$	−0.618034	+	4.55743i	−0.159576	+	1.17672i
$16$	1.00000			0.250000
$17$	6.79026			1.64688			0.823440	−	0.567403i	$-0.192052\pi$
$17$	6.79026			1.64688			0.823440	+	0.567403i	$0.192052\pi$
$18$	−2.89165	−	0.798968i	−0.681569	−	0.188319i
$19$			5.48844i			1.25914i	0.776946	+	0.629568i	$0.216768\pi$
$19$			5.48844i			1.25914i	−0.776946	+	0.629568i	$0.783232\pi$
$20$		−	2.65532i		−	0.593747i
$21$	0.381966	−	2.81665i	0.0833518	−	0.614643i
$22$		0			0
$23$		−	4.78856i		−	0.998485i	−0.866462	−	0.499242i	$-0.833612\pi$
$23$		−	4.78856i		−	0.998485i	0.866462	−	0.499242i	$-0.166388\pi$
$24$	1.71634	+	0.232753i	0.350347	+	0.0475106i
$25$	−2.05072			−0.410143
$26$			1.50641i			0.295431i
$27$	−4.77710	−	2.04434i	−0.919353	−	0.393434i
$28$			1.64108i			0.310134i
$29$	−0.464026			−0.0861674			−0.0430837	−	0.999071i	$-0.513718\pi$
$29$	−0.464026			−0.0861674			−0.0430837	+	0.999071i	$0.513718\pi$
$30$	0.618034	−	4.55743i	0.112837	−	0.832069i
$31$	−5.19231			−0.932567			−0.466283	−	0.884635i	$-0.654407\pi$
$31$	−5.19231			−0.932567			−0.466283	+	0.884635i	$0.654407\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−6.79026			−1.16452
$35$	4.35758			0.736566
$36$	2.89165	+	0.798968i	0.481942	+	0.133161i
$37$	1.00696			0.165543			0.0827716	−	0.996569i	$-0.473623\pi$
$37$	1.00696			0.165543			0.0827716	+	0.996569i	$0.473623\pi$
$38$		−	5.48844i		−	0.890343i
$39$	−0.350622	+	2.58551i	−0.0561445	+	0.414014i
$40$			2.65532i			0.419843i
$41$	1.57428			0.245861			0.122930	−	0.992415i	$-0.460771\pi$
$41$	1.57428			0.245861			0.122930	+	0.992415i	$0.460771\pi$
$42$	−0.381966	+	2.81665i	−0.0589386	+	0.434618i
$43$		−	3.42500i		−	0.522308i	−0.965297	−	0.261154i	$-0.915897\pi$
$43$		−	3.42500i		−	0.522308i	0.965297	−	0.261154i	$-0.0841030\pi$
$44$		0			0
$45$	2.12151	−	7.67826i	0.316257	−	1.14461i
$46$			4.78856i			0.706035i
$47$		−	10.0129i		−	1.46053i	−0.683162	−	0.730267i	$-0.739396\pi$
$47$		−	10.0129i		−	1.46053i	0.683162	−	0.730267i	$-0.260604\pi$
$48$	−1.71634	−	0.232753i	−0.247732	−	0.0335950i
$49$	4.30687			0.615267
$50$	2.05072			0.290015
$51$	−11.6544	−	1.58046i	−1.63194	−	0.221308i
$52$		−	1.50641i		−	0.208902i
$53$		−	9.82493i		−	1.34956i	−0.738020	−	0.674779i	$-0.764239\pi$
$53$		−	9.82493i		−	1.34956i	0.738020	−	0.674779i	$-0.235761\pi$
$54$	4.77710	+	2.04434i	0.650081	+	0.278200i
$55$		0			0
$56$		−	1.64108i		−	0.219298i
$57$	1.27745	−	9.42004i	0.169203	−	1.24771i
$58$	0.464026			0.0609296
$59$		−	6.11223i		−	0.795744i	−0.917441	−	0.397872i	$-0.869749\pi$
$59$		−	6.11223i		−	0.795744i	0.917441	−	0.397872i	$-0.130251\pi$
$60$	−0.618034	+	4.55743i	−0.0797878	+	0.588362i
$61$		−	13.9034i		−	1.78015i	−0.455813	−	0.890076i	$-0.650651\pi$
$61$		−	13.9034i		−	1.78015i	0.455813	−	0.890076i	$-0.349349\pi$
$62$	5.19231			0.659424
$63$	−1.31117	+	4.74542i	−0.165192	+	0.597867i
$64$	1.00000			0.125000
$65$	−4.00000			−0.496139
$66$		0			0
$67$	11.7972			1.44126			0.720630	−	0.693320i	$-0.243853\pi$
$67$	11.7972			1.44126			0.720630	+	0.693320i	$0.243853\pi$
$68$	6.79026			0.823440
$69$	−1.11455	+	8.21881i	−0.134177	+	0.989428i
$70$	−4.35758			−0.520831
$71$			0.898056i			0.106580i	0.998579	+	0.0532898i	$0.0169707\pi$
$71$			0.898056i			0.106580i	−0.998579	+	0.0532898i	$0.983029\pi$
$72$	−2.89165	−	0.798968i	−0.340784	−	0.0941593i
$73$		−	4.62724i		−	0.541577i	−0.962639	−	0.270788i	$-0.912716\pi$
$73$		−	4.62724i		−	0.541577i	0.962639	−	0.270788i	$-0.0872844\pi$
$74$	−1.00696			−0.117057
$75$	3.51973	+	0.477311i	0.406423	+	0.0551151i
$76$			5.48844i			0.629568i
$77$		0			0
$78$	0.350622	−	2.58551i	0.0397001	−	0.292752i
$79$			3.17739i			0.357484i	0.983896	+	0.178742i	$0.0572028\pi$
$79$			3.17739i			0.357484i	−0.983896	+	0.178742i	$0.942797\pi$
$80$		−	2.65532i		−	0.296874i
$81$	7.72330	+	4.62067i	0.858145	+	0.513408i
$82$	−1.57428			−0.173850
$83$	1.87418			0.205718			0.102859	−	0.994696i	$-0.467201\pi$
$83$	1.87418			0.205718			0.102859	+	0.994696i	$0.467201\pi$
$84$	0.381966	−	2.81665i	0.0416759	−	0.307321i
$85$		−	18.0303i		−	1.95566i
$86$			3.42500i			0.369327i
$87$	0.796426	+	0.108003i	0.0853859	+	0.0115792i
$88$		0			0
$89$			12.8092i			1.35777i	0.734244	+	0.678886i	$0.237537\pi$
$89$			12.8092i			1.35777i	−0.734244	+	0.678886i	$0.762463\pi$
$90$	−2.12151	+	7.67826i	−0.223627	+	0.809359i
$91$	2.47214			0.259150
$92$		−	4.78856i		−	0.499242i
$93$	8.91178	+	1.20853i	0.924108	+	0.125318i
$94$			10.0129i			1.03275i
$95$	14.5736			1.49522
$96$	1.71634	+	0.232753i	0.175173	+	0.0237553i
$97$	−3.59099			−0.364610			−0.182305	−	0.983242i	$-0.558356\pi$
$97$	−3.59099			−0.364610			−0.182305	+	0.983242i	$0.558356\pi$
$98$	−4.30687			−0.435059
$99$		0			0
$100$	−2.05072			−0.205072
$101$	−12.1722			−1.21118			−0.605591	−	0.795776i	$-0.707063\pi$
$101$	−12.1722			−1.21118			−0.605591	+	0.795776i	$0.707063\pi$
$102$	11.6544	+	1.58046i	1.15396	+	0.156488i
$103$	0.886596			0.0873589			0.0436795	−	0.999046i	$-0.486092\pi$
$103$	0.886596			0.0873589			0.0436795	+	0.999046i	$0.486092\pi$
$104$			1.50641i			0.147716i
$105$	−7.47910	−	1.01424i	−0.729885	−	0.0989798i
$106$			9.82493i			0.954281i
$107$	−2.23177			−0.215753			−0.107877	−	0.994164i	$-0.534405\pi$
$107$	−2.23177			−0.215753			−0.107877	+	0.994164i	$0.534405\pi$
$108$	−4.77710	−	2.04434i	−0.459676	−	0.196717i
$109$		−	4.73524i		−	0.453554i	−0.973947	−	0.226777i	$-0.927181\pi$
$109$		−	4.73524i		−	0.453554i	0.973947	−	0.226777i	$-0.0728188\pi$
$110$		0			0
$111$	−1.72829	−	0.234373i	−0.164042	−	0.0222457i
$112$			1.64108i			0.155067i
$113$		−	3.89575i		−	0.366481i	−0.983068	−	0.183241i	$-0.941341\pi$
$113$		−	3.89575i		−	0.366481i	0.983068	−	0.183241i	$-0.0586588\pi$
$114$	−1.27745	+	9.42004i	−0.119644	+	0.882268i
$115$	−12.7152			−1.18570
$116$	−0.464026			−0.0430837
$117$	1.20357	−	4.35602i	0.111270	−	0.402714i
$118$			6.11223i			0.562676i
$119$			11.1433i			1.02151i
$120$	0.618034	−	4.55743i	0.0564185	−	0.416035i
$121$		0			0
$122$			13.9034i			1.25876i
$123$	−2.70200	−	0.366418i	−0.243631	−	0.0330388i
$124$	−5.19231			−0.466283
$125$		−	7.83129i		−	0.700452i
$126$	1.31117	−	4.74542i	0.116808	−	0.422756i
$127$		−	0.236376i		−	0.0209749i	−0.999945	−	0.0104875i	$-0.996662\pi$
$127$		−	0.236376i		−	0.0209749i	0.999945	−	0.0104875i	$-0.00333833\pi$
$128$	−1.00000			−0.0883883
$129$	−0.797180	+	5.87847i	−0.0701878	+	0.517571i
$130$	4.00000			0.350823
$131$	−5.26741			−0.460216			−0.230108	−	0.973165i	$-0.573908\pi$
$131$	−5.26741			−0.460216			−0.230108	+	0.973165i	$0.573908\pi$
$132$		0			0
$133$	−9.00696			−0.781002
$134$	−11.7972			−1.01912
$135$	−5.42838	+	12.6847i	−0.467201	+	1.09173i
$136$	−6.79026			−0.582260
$137$			0.927773i			0.0792650i	0.999214	+	0.0396325i	$0.0126187\pi$
$137$			0.927773i			0.0792650i	−0.999214	+	0.0396325i	$0.987381\pi$
$138$	1.11455	−	8.21881i	0.0948771	−	0.699632i
$139$		−	8.45318i		−	0.716990i	−0.933532	−	0.358495i	$-0.883290\pi$
$139$		−	8.45318i		−	0.716990i	0.933532	−	0.358495i	$-0.116710\pi$
$140$	4.35758			0.368283
$141$	−2.33054	+	17.1856i	−0.196267	+	1.44729i
$142$		−	0.898056i		−	0.0753632i
$143$		0			0
$144$	2.89165	+	0.798968i	0.240971	+	0.0665807i
$145$			1.23214i			0.102323i
$146$			4.62724i			0.382953i
$147$	−7.39205	−	1.00244i	−0.609686	−	0.0826796i
$148$	1.00696			0.0827716
$149$	−18.0716			−1.48048			−0.740241	−	0.672341i	$-0.765289\pi$
$149$	−18.0716			−1.48048			−0.740241	+	0.672341i	$0.765289\pi$
$150$	−3.51973	−	0.477311i	−0.287385	−	0.0389723i
$151$			13.3299i			1.08477i	0.840129	+	0.542387i	$0.182479\pi$
$151$			13.3299i			1.08477i	−0.840129	+	0.542387i	$0.817521\pi$
$152$		−	5.48844i		−	0.445172i
$153$	19.6351	+	5.42520i	1.58740	+	0.438602i
$154$		0			0
$155$			13.7872i			1.10742i
$156$	−0.350622	+	2.58551i	−0.0280722	+	0.207007i
$157$	9.70820			0.774799			0.387400	−	0.921912i	$-0.373373\pi$
$157$	9.70820			0.774799			0.387400	+	0.921912i	$0.373373\pi$
$158$		−	3.17739i		−	0.252780i
$159$	−2.28678	+	16.8629i	−0.181354	+	1.33732i
$160$			2.65532i			0.209921i
$161$	7.85840			0.619329
$162$	−7.72330	−	4.62067i	−0.606800	−	0.363034i
$163$	7.08206			0.554710			0.277355	−	0.960768i	$-0.410542\pi$
$163$	7.08206			0.554710			0.277355	+	0.960768i	$0.410542\pi$
$164$	1.57428			0.122930
$165$		0			0
$166$	−1.87418			−0.145465
$167$	−2.53482			−0.196151			−0.0980753	−	0.995179i	$-0.531269\pi$
$167$	−2.53482			−0.196151			−0.0980753	+	0.995179i	$0.531269\pi$
$168$	−0.381966	+	2.81665i	−0.0294693	+	0.217309i
$169$	10.7307			0.825441
$170$			18.0303i			1.38286i
$171$	−4.38509	+	15.8707i	−0.335336	+	1.21366i
$172$		−	3.42500i		−	0.261154i
$173$	0.949284			0.0721727			0.0360864	−	0.999349i	$-0.488511\pi$
$173$	0.949284			0.0721727			0.0360864	+	0.999349i	$0.488511\pi$
$174$	−0.796426	−	0.108003i	−0.0603769	−	0.00818772i
$175$		−	3.36538i		−	0.254399i
$176$		0			0
$177$	−1.42264	+	10.4907i	−0.106932	+	0.788526i
$178$		−	12.8092i		−	0.960090i
$179$			18.5656i			1.38766i	0.720139	+	0.693830i	$0.244078\pi$
$179$			18.5656i			1.38766i	−0.720139	+	0.693830i	$0.755922\pi$
$180$	2.12151	−	7.67826i	0.158128	−	0.572303i
$181$	12.8793			0.957310			0.478655	−	0.878003i	$-0.341125\pi$
$181$	12.8793			0.957310			0.478655	+	0.878003i	$0.341125\pi$
$182$	−2.47214			−0.183247
$183$	−3.23607	+	23.8630i	−0.239217	+	1.76401i
$184$			4.78856i			0.353018i
$185$		−	2.67380i		−	0.196582i
$186$	−8.91178	−	1.20853i	−0.653443	−	0.0886135i
$187$		0			0
$188$		−	10.0129i		−	0.730267i
$189$	3.35492	−	7.83959i	0.244035	−	0.570246i
$190$	−14.5736			−1.05728
$191$		−	3.22883i		−	0.233630i	−0.993154	−	0.116815i	$-0.962732\pi$
$191$		−	3.22883i		−	0.233630i	0.993154	−	0.116815i	$-0.0372684\pi$
$192$	−1.71634	−	0.232753i	−0.123866	−	0.0167975i
$193$			9.76512i			0.702909i	0.936205	+	0.351454i	$0.114313\pi$
$193$			9.76512i			0.702909i	−0.936205	+	0.351454i	$0.885687\pi$
$194$	3.59099			0.257818
$195$	6.86536	+	0.931013i	0.491639	+	0.0666712i
$196$	4.30687			0.307633
$197$	−13.9679			−0.995175			−0.497587	−	0.867414i	$-0.665781\pi$
$197$	−13.9679			−0.995175			−0.497587	+	0.867414i	$0.665781\pi$
$198$		0			0
$199$	15.9679			1.13194			0.565969	−	0.824427i	$-0.308502\pi$
$199$	15.9679			1.13194			0.565969	+	0.824427i	$0.308502\pi$
$200$	2.05072			0.145007
$201$	−20.2481	−	2.74584i	−1.42819	−	0.193677i
$202$	12.1722			0.856435
$203$		−	0.761502i		−	0.0534470i
$204$	−11.6544	−	1.58046i	−0.815972	−	0.110654i
$205$		−	4.18021i		−	0.291959i
$206$	−0.886596			−0.0617721
$207$	3.82591	−	13.8469i	0.265919	−	0.962423i
$208$		−	1.50641i		−	0.104451i
$209$		0			0
$210$	7.47910	+	1.01424i	0.516107	+	0.0699893i
$211$		−	2.26810i		−	0.156142i	−0.996948	−	0.0780712i	$-0.975124\pi$
$211$		−	2.26810i		−	0.156142i	0.996948	−	0.0780712i	$-0.0248761\pi$
$212$		−	9.82493i		−	0.674779i
$213$	0.209025	−	1.54137i	0.0143222	−	0.105613i
$214$	2.23177			0.152560
$215$	−9.09447			−0.620238
$216$	4.77710	+	2.04434i	0.325040	+	0.139100i
$217$		−	8.52098i		−	0.578442i
$218$			4.73524i			0.320711i
$219$	−1.07700	+	7.94191i	−0.0727772	+	0.536665i
$220$		0			0
$221$		−	10.2289i		−	0.688072i
$222$	1.72829	+	0.234373i	0.115995	+	0.0157301i
$223$	4.40134			0.294735			0.147368	−	0.989082i	$-0.452920\pi$
$223$	4.40134			0.294735			0.147368	+	0.989082i	$0.452920\pi$
$224$		−	1.64108i		−	0.109649i
$225$	−5.92996	−	1.63846i	−0.395330	−	0.109230i
$226$			3.89575i			0.259142i
$227$	12.7334			0.845144			0.422572	−	0.906329i	$-0.361127\pi$
$227$	12.7334			0.845144			0.422572	+	0.906329i	$0.361127\pi$
$228$	1.27745	−	9.42004i	0.0846014	−	0.623857i
$229$	6.42337			0.424468			0.212234	−	0.977219i	$-0.431926\pi$
$229$	6.42337			0.424468			0.212234	+	0.977219i	$0.431926\pi$
$230$	12.7152			0.838413
$231$		0			0
$232$	0.464026			0.0304648
$233$	16.8103			1.10128			0.550641	−	0.834742i	$-0.314383\pi$
$233$	16.8103			1.10128			0.550641	+	0.834742i	$0.314383\pi$
$234$	−1.20357	+	4.35602i	−0.0786801	+	0.284762i
$235$	−26.5875			−1.73438
$236$		−	6.11223i		−	0.397872i
$237$	0.739548	−	5.45348i	0.0480388	−	0.354242i
$238$		−	11.1433i		−	0.722316i
$239$	12.0387			0.778722			0.389361	−	0.921085i	$-0.372696\pi$
$239$	12.0387			0.778722			0.389361	+	0.921085i	$0.372696\pi$
$240$	−0.618034	+	4.55743i	−0.0398939	+	0.294181i
$241$			20.5642i			1.32466i	0.749214	+	0.662328i	$0.230432\pi$
$241$			20.5642i			1.32466i	−0.749214	+	0.662328i	$0.769568\pi$
$242$		0			0
$243$	−12.1803	−	9.72827i	−0.781369	−	0.624069i
$244$		−	13.9034i		−	0.890076i
$245$		−	11.4361i		−	0.730626i
$246$	2.70200	+	0.366418i	0.172273	+	0.0233620i
$247$	8.26785			0.526071
$248$	5.19231			0.329712
$249$	−3.21674	−	0.436223i	−0.203853	−	0.0276445i
$250$			7.83129i			0.495294i
$251$		−	16.3658i		−	1.03300i	−0.856287	−	0.516500i	$-0.827234\pi$
$251$		−	16.3658i		−	1.03300i	0.856287	−	0.516500i	$-0.172766\pi$
$252$	−1.31117	+	4.74542i	−0.0825958	+	0.298934i
$253$		0			0
$254$			0.236376i			0.0148315i
$255$	−4.19661	+	30.9462i	−0.262802	+	1.93792i
$256$	1.00000			0.0625000
$257$		−	8.53623i		−	0.532475i	−0.963907	−	0.266238i	$-0.914219\pi$
$257$		−	8.53623i		−	0.532475i	0.963907	−	0.266238i	$-0.0857806\pi$
$258$	0.797180	−	5.87847i	0.0496303	−	0.365978i
$259$			1.65250i			0.102681i
$260$	−4.00000			−0.248069
$261$	−1.34180	−	0.370742i	−0.0830554	−	0.0229483i
$262$	5.26741			0.325422
$263$	13.5666			0.836553			0.418276	−	0.908320i	$-0.362634\pi$
$263$	13.5666			0.836553			0.418276	+	0.908320i	$0.362634\pi$
$264$		0			0
$265$	−26.0883			−1.60259
$266$	9.00696			0.552252
$267$	2.98138	−	21.9849i	0.182458	−	1.34546i
$268$	11.7972			0.720630
$269$			11.8485i			0.722414i	0.932486	+	0.361207i	$0.117635\pi$
$269$			11.8485i			0.722414i	−0.932486	+	0.361207i	$0.882365\pi$
$270$	5.42838	−	12.6847i	0.330361	−	0.771967i
$271$			21.6515i			1.31523i	0.753352	+	0.657617i	$0.228436\pi$
$271$			21.6515i			1.31523i	−0.753352	+	0.657617i	$0.771564\pi$
$272$	6.79026			0.411720
$273$	−4.24303	−	0.575398i	−0.256800	−	0.0348247i
$274$		−	0.927773i		−	0.0560488i
$275$		0			0
$276$	−1.11455	+	8.21881i	−0.0670883	+	0.494714i
$277$			4.07356i			0.244756i	0.992484	+	0.122378i	$0.0390521\pi$
$277$			4.07356i			0.244756i	−0.992484	+	0.122378i	$0.960948\pi$
$278$			8.45318i			0.506988i
$279$	−15.0144	−	4.14849i	−0.898886	−	0.248364i
$280$	−4.35758			−0.260415
$281$	17.8647			1.06572			0.532858	−	0.846205i	$-0.321118\pi$
$281$	17.8647			1.06572			0.532858	+	0.846205i	$0.321118\pi$
$282$	2.33054	−	17.1856i	0.138782	−	1.02339i
$283$		−	3.03967i		−	0.180690i	−0.995911	−	0.0903448i	$-0.971203\pi$
$283$		−	3.03967i		−	0.180690i	0.995911	−	0.0903448i	$-0.0287969\pi$
$284$			0.898056i			0.0532898i
$285$	−25.0132	−	3.39205i	−1.48165	−	0.200927i
$286$		0			0
$287$			2.58351i			0.152500i
$288$	−2.89165	−	0.798968i	−0.170392	−	0.0470796i
$289$	29.1077			1.71222
$290$		−	1.23214i		−	0.0723535i
$291$	6.16337	+	0.835815i	0.361303	+	0.0489963i
$292$		−	4.62724i		−	0.270788i
$293$	−23.3411			−1.36360			−0.681801	−	0.731538i	$-0.738803\pi$
$293$	−23.3411			−1.36360			−0.681801	+	0.731538i	$0.738803\pi$
$294$	7.39205	+	1.00244i	0.431113	+	0.0584633i
$295$	−16.2299			−0.944942
$296$	−1.00696			−0.0585284
$297$		0			0
$298$	18.0716			1.04686
$299$	−7.21355			−0.417170
$300$	3.51973	+	0.477311i	0.203212	+	0.0275575i
$301$	5.62069			0.323971
$302$		−	13.3299i		−	0.767051i
$303$	20.8917	+	2.83313i	1.20020	+	0.162759i
$304$			5.48844i			0.314784i
$305$	−36.9180			−2.11392
$306$	−19.6351	−	5.42520i	−1.12246	−	0.310138i
$307$		−	30.0216i		−	1.71342i	−0.515794	−	0.856712i	$-0.672503\pi$
$307$		−	30.0216i		−	1.71342i	0.515794	−	0.856712i	$-0.327497\pi$
$308$		0			0
$309$	−1.52170	−	0.206358i	−0.0865666	−	0.0117393i
$310$		−	13.7872i		−	0.783063i
$311$		−	0.495224i		−	0.0280816i	−0.999901	−	0.0140408i	$-0.995531\pi$
$311$		−	0.495224i		−	0.0280816i	0.999901	−	0.0140408i	$-0.00446947\pi$
$312$	0.350622	−	2.58551i	0.0198501	−	0.146376i
$313$	−28.3789			−1.60407			−0.802035	−	0.597277i	$-0.796249\pi$
$313$	−28.3789			−1.60407			−0.802035	+	0.597277i	$0.796249\pi$
$314$	−9.70820			−0.547866
$315$	12.6006	+	3.48157i	0.709964	+	0.196164i
$316$			3.17739i			0.178742i
$317$			6.64071i			0.372979i	0.982457	+	0.186490i	$0.0597111\pi$
$317$			6.64071i			0.372979i	−0.982457	+	0.186490i	$0.940289\pi$
$318$	2.28678	−	16.8629i	0.128236	−	0.945626i
$319$		0			0
$320$		−	2.65532i		−	0.148437i
$321$	3.83047	+	0.519451i	0.213796	+	0.0289929i
$322$	−7.85840			−0.437932
$323$			37.2680i			2.07365i
$324$	7.72330	+	4.62067i	0.429072	+	0.256704i
$325$			3.08922i			0.171359i
$326$	−7.08206			−0.392239
$327$	−1.10214	+	8.12728i	−0.0609486	+	0.449440i
$328$	−1.57428			−0.0869250
$329$	16.4320			0.905924
$330$		0			0
$331$	7.41016			0.407299			0.203650	−	0.979044i	$-0.434720\pi$
$331$	7.41016			0.407299			0.203650	+	0.979044i	$0.434720\pi$
$332$	1.87418			0.102859
$333$	2.91178	+	0.804529i	0.159564	+	0.0440879i
$334$	2.53482			0.138699
$335$		−	31.3254i		−	1.71149i
$336$	0.381966	−	2.81665i	0.0208380	−	0.153661i
$337$		−	34.2137i		−	1.86374i	−0.362792	−	0.931870i	$-0.618176\pi$
$337$		−	34.2137i		−	1.86374i	0.362792	−	0.931870i	$-0.381824\pi$
$338$	−10.7307			−0.583675
$339$	−0.906749	+	6.68644i	−0.0492478	+	0.363157i
$340$		−	18.0303i		−	0.977831i
$341$		0			0
$342$	4.38509	−	15.8707i	0.237119	−	0.858188i
$343$			18.5554i			1.00190i
$344$			3.42500i			0.184664i
$345$	21.8236	+	2.95950i	1.17494	+	0.159334i
$346$	−0.949284			−0.0510338
$347$	20.9245			1.12329			0.561644	−	0.827379i	$-0.310169\pi$
$347$	20.9245			1.12329			0.561644	+	0.827379i	$0.310169\pi$
$348$	0.796426	+	0.108003i	0.0426929	+	0.00578960i
$349$		−	29.4529i		−	1.57658i	−0.615306	−	0.788288i	$-0.710968\pi$
$349$		−	29.4529i		−	1.57658i	0.615306	−	0.788288i	$-0.289032\pi$
$350$			3.36538i			0.179887i
$351$	−3.07962	+	7.19627i	−0.164378	+	0.384109i
$352$		0			0
$353$		−	24.3265i		−	1.29477i	−0.762163	−	0.647385i	$-0.775863\pi$
$353$		−	24.3265i		−	1.29477i	0.762163	−	0.647385i	$-0.224137\pi$
$354$	1.42264	−	10.4907i	0.0756125	−	0.557572i
$355$	2.38462			0.126563
$356$			12.8092i			0.678886i
$357$	2.59365	−	19.1258i	0.137271	−	1.01224i
$358$		−	18.5656i		−	0.981224i
$359$	−32.7277			−1.72730			−0.863650	−	0.504092i	$-0.831827\pi$
$359$	−32.7277			−1.72730			−0.863650	+	0.504092i	$0.831827\pi$
$360$	−2.12151	+	7.67826i	−0.111814	+	0.404680i
$361$	−11.1230			−0.585422
$362$	−12.8793			−0.676920
$363$		0			0
$364$	2.47214			0.129575
$365$	−12.2868			−0.643120
$366$	3.23607	−	23.8630i	0.169152	−	1.24734i
$367$	−11.9030			−0.621329			−0.310665	−	0.950520i	$-0.600552\pi$
$367$	−11.9030			−0.621329			−0.310665	+	0.950520i	$0.600552\pi$
$368$		−	4.78856i		−	0.249621i
$369$	4.55226	+	1.25780i	0.236981	+	0.0654783i
$370$			2.67380i			0.139004i
$371$	16.1235			0.837088
$372$	8.91178	+	1.20853i	0.462054	+	0.0626592i
$373$			27.7804i			1.43841i	0.694796	+	0.719207i	$0.255495\pi$
$373$			27.7804i			1.43841i	−0.694796	+	0.719207i	$0.744505\pi$
$374$		0			0
$375$	−1.82276	+	13.4412i	−0.0941268	+	0.694099i
$376$			10.0129i			0.516377i
$377$			0.699013i			0.0360010i
$378$	−3.35492	+	7.83959i	−0.172559	+	0.403225i
$379$	−7.86465			−0.403980			−0.201990	−	0.979388i	$-0.564741\pi$
$379$	−7.86465			−0.403980			−0.201990	+	0.979388i	$0.564741\pi$
$380$	14.5736			0.747608
$381$	−0.0550172	+	0.405701i	−0.00281862	+	0.0207847i
$382$			3.22883i			0.165201i
$383$			12.9561i			0.662023i	0.943627	+	0.331012i	$0.107390\pi$
$383$			12.9561i			0.662023i	−0.943627	+	0.331012i	$0.892610\pi$
$384$	1.71634	+	0.232753i	0.0875867	+	0.0118776i
$385$		0			0
$386$		−	9.76512i		−	0.497032i
$387$	2.73647	−	9.90391i	0.139102	−	0.503444i
$388$	−3.59099			−0.182305
$389$			25.8976i			1.31306i	0.754299	+	0.656531i	$0.227977\pi$
$389$			25.8976i			1.31306i	−0.754299	+	0.656531i	$0.772023\pi$
$390$	−6.86536	−	0.931013i	−0.347641	−	0.0471437i
$391$		−	32.5156i		−	1.64439i
$392$	−4.30687			−0.217530
$393$	9.04067	+	1.22601i	0.456042	+	0.0618439i
$394$	13.9679			0.703695
$395$	8.43698			0.424511
$396$		0			0
$397$	−17.9986			−0.903323			−0.451661	−	0.892189i	$-0.649168\pi$
$397$	−17.9986			−0.903323			−0.451661	+	0.892189i	$0.649168\pi$
$398$	−15.9679			−0.800401
$399$	15.4590	+	2.09640i	0.773919	+	0.104951i
$400$	−2.05072			−0.102536
$401$		−	3.76803i		−	0.188166i	−0.995564	−	0.0940832i	$-0.970008\pi$
$401$		−	3.76803i		−	0.188166i	0.995564	−	0.0940832i	$-0.0299920\pi$
$402$	20.2481	+	2.74584i	1.00988	+	0.136950i
$403$			7.82175i			0.389629i
$404$	−12.1722			−0.605591
$405$	12.2694	−	20.5078i	0.609669	−	1.01904i
$406$			0.761502i			0.0377927i
$407$		0			0
$408$	11.6544	+	1.58046i	0.576979	+	0.0782442i
$409$			14.3741i			0.710752i	0.934724	+	0.355376i	$0.115647\pi$
$409$			14.3741i			0.710752i	−0.934724	+	0.355376i	$0.884353\pi$
$410$			4.18021i			0.206446i
$411$	0.215942	−	1.59237i	0.0106516	−	0.0785461i
$412$	0.886596			0.0436795
$413$	10.0306			0.493575
$414$	−3.82591	+	13.8469i	−0.188033	+	0.680536i
$415$		−	4.97656i		−	0.244290i
$416$			1.50641i			0.0738579i
$417$	−1.96751	+	14.5085i	−0.0963492	+	0.710486i
$418$		0			0
$419$		−	31.1601i		−	1.52227i	−0.648595	−	0.761134i	$-0.724643\pi$
$419$		−	31.1601i		−	1.52227i	0.648595	−	0.761134i	$-0.275357\pi$
$420$	−7.47910	−	1.01424i	−0.364943	−	0.0494899i
$421$	−10.8166			−0.527169			−0.263584	−	0.964636i	$-0.584905\pi$
$421$	−10.8166			−0.527169			−0.263584	+	0.964636i	$0.584905\pi$
$422$			2.26810i			0.110409i
$423$	8.00000	−	28.9539i	0.388973	−	1.40779i
$424$			9.82493i			0.477141i
$425$	−13.9249			−0.675457
$426$	−0.209025	+	1.54137i	−0.0101273	+	0.0746796i
$427$	22.8166			1.10417
$428$	−2.23177			−0.107877
$429$		0			0
$430$	9.09447			0.438574
$431$	39.8322			1.91865			0.959324	−	0.282308i	$-0.0911001\pi$
$431$	39.8322			1.91865			0.959324	+	0.282308i	$0.0911001\pi$
$432$	−4.77710	−	2.04434i	−0.229838	−	0.0983585i
$433$	16.1553			0.776374			0.388187	−	0.921581i	$-0.373101\pi$
$433$	16.1553			0.776374			0.388187	+	0.921581i	$0.373101\pi$
$434$			8.52098i			0.409020i
$435$	0.286784	−	2.11477i	0.0137502	−	0.101395i
$436$		−	4.73524i		−	0.226777i
$437$	26.2818			1.25723
$438$	1.07700	−	7.94191i	0.0514612	−	0.379479i
$439$		−	6.13994i		−	0.293043i	−0.989207	−	0.146522i	$-0.953192\pi$
$439$		−	6.13994i		−	0.293043i	0.989207	−	0.146522i	$-0.0468078\pi$
$440$		0			0
$441$	12.4540	+	3.44105i	0.593046	+	0.163859i
$442$			10.2289i			0.486540i
$443$			1.63784i			0.0778160i	0.999243	+	0.0389080i	$0.0123879\pi$
$443$			1.63784i			0.0778160i	−0.999243	+	0.0389080i	$0.987612\pi$
$444$	−1.72829	−	0.234373i	−0.0820208	−	0.0111229i
$445$	34.0125			1.61235
$446$	−4.40134			−0.208409
$447$	31.0170	+	4.20622i	1.46705	+	0.198948i
$448$			1.64108i			0.0775336i
$449$			18.2818i			0.862772i	0.902167	+	0.431386i	$0.141975\pi$
$449$			18.2818i			0.862772i	−0.902167	+	0.431386i	$0.858025\pi$
$450$	5.92996	+	1.63846i	0.279541	+	0.0772376i
$451$		0			0
$452$		−	3.89575i		−	0.183241i
$453$	3.10258	−	22.8787i	0.145772	−	1.07493i
$454$	−12.7334			−0.597607
$455$		−	6.56431i		−	0.307740i
$456$	−1.27745	+	9.42004i	−0.0598222	+	0.441134i
$457$			27.9848i			1.30907i	0.756031	+	0.654536i	$0.227136\pi$
$457$			27.9848i			1.30907i	−0.756031	+	0.654536i	$0.772864\pi$
$458$	−6.42337			−0.300144
$459$	−32.4378	−	13.8816i	−1.51406	−	0.647939i
$460$	−12.7152			−0.592848
$461$	30.3359			1.41288			0.706441	−	0.707772i	$-0.250300\pi$
$461$	30.3359			1.41288			0.706441	+	0.707772i	$0.250300\pi$
$462$		0			0
$463$	−10.9632			−0.509503			−0.254752	−	0.967007i	$-0.581994\pi$
$463$	−10.9632			−0.509503			−0.254752	+	0.967007i	$0.581994\pi$
$464$	−0.464026			−0.0215419
$465$	3.20903	−	23.6636i	0.148815	−	1.09737i
$466$	−16.8103			−0.778724
$467$			32.2185i			1.49089i	0.666565	+	0.745447i	$0.267764\pi$
$467$			32.2185i			1.49089i	−0.666565	+	0.745447i	$0.732236\pi$
$468$	1.20357	−	4.35602i	0.0556352	−	0.201357i
$469$			19.3602i			0.893969i
$470$	26.5875			1.22639
$471$	−16.6626	−	2.25962i	−0.767771	−	0.104118i
$472$			6.11223i			0.281338i
$473$		0			0
$474$	−0.739548	+	5.45348i	−0.0339686	+	0.250487i
$475$		−	11.2552i		−	0.516426i
$476$			11.1433i			0.510754i
$477$	7.84980	−	28.4103i	0.359418	−	1.30082i
$478$	−12.0387			−0.550639
$479$	−18.8328			−0.860493			−0.430247	−	0.902711i	$-0.641573\pi$
$479$	−18.8328			−0.860493			−0.430247	+	0.902711i	$0.641573\pi$
$480$	0.618034	−	4.55743i	0.0282093	−	0.208017i
$481$		−	1.51690i		−	0.0691645i
$482$		−	20.5642i		−	0.936674i
$483$	−13.4877	−	1.82907i	−0.613712	−	0.0832255i
$484$		0			0
$485$			9.53523i			0.432972i
$486$	12.1803	+	9.72827i	0.552511	+	0.441283i
$487$	−26.8604			−1.21716			−0.608579	−	0.793493i	$-0.708260\pi$
$487$	−26.8604			−1.21716			−0.608579	+	0.793493i	$0.708260\pi$
$488$			13.9034i			0.629379i
$489$	−12.1552	−	1.64837i	−0.549678	−	0.0745420i
$490$			11.4361i			0.516630i
$491$	−19.0395			−0.859239			−0.429619	−	0.903010i	$-0.641352\pi$
$491$	−19.0395			−0.859239			−0.429619	+	0.903010i	$0.641352\pi$
$492$	−2.70200	−	0.366418i	−0.121815	−	0.0165194i
$493$	−3.15086			−0.141907
$494$	−8.26785			−0.371988
$495$		0			0
$496$	−5.19231			−0.233142
$497$	−1.47378			−0.0661080
$498$	3.21674	+	0.436223i	0.144146	+	0.0195476i
$499$	10.6200			0.475416			0.237708	−	0.971337i	$-0.423604\pi$
$499$	10.6200			0.475416			0.237708	+	0.971337i	$0.423604\pi$
$500$		−	7.83129i		−	0.350226i
$501$	4.35062	+	0.589989i	0.194371	+	0.0263587i
$502$			16.3658i			0.730442i
$503$	−30.9691			−1.38084			−0.690422	−	0.723407i	$-0.742575\pi$
$503$	−30.9691			−1.38084			−0.690422	+	0.723407i	$0.742575\pi$
$504$	1.31117	−	4.74542i	0.0584041	−	0.211378i
$505$			32.3211i			1.43827i
$506$		0			0
$507$	−18.4176	−	2.49761i	−0.817954	−	0.110923i
$508$		−	0.236376i		−	0.0104875i
$509$			20.5756i			0.911995i	0.889981	+	0.455998i	$0.150717\pi$
$509$			20.5756i			0.911995i	−0.889981	+	0.455998i	$0.849283\pi$
$510$	4.19661	−	30.9462i	0.185829	−	1.37032i
$511$	7.59365			0.335923
$512$	−1.00000			−0.0441942
$513$	11.2203	−	26.2188i	0.495387	−	1.15759i
$514$			8.53623i			0.376517i
$515$		−	2.35420i		−	0.103738i
$516$	−0.797180	+	5.87847i	−0.0350939	+	0.258785i
$517$		0			0
$518$		−	1.65250i		−	0.0726066i
$519$	−1.62930	−	0.220949i	−0.0715181	−	0.00969859i
$520$	4.00000			0.175412
$521$			3.82984i			0.167788i	0.996475	+	0.0838941i	$0.0267357\pi$
$521$			3.82984i			0.167788i	−0.996475	+	0.0838941i	$0.973264\pi$
$522$	1.34180	+	0.370742i	0.0587290	+	0.0162269i
$523$			9.63169i			0.421165i	0.977576	+	0.210582i	$0.0675360\pi$
$523$			9.63169i			0.421165i	−0.977576	+	0.210582i	$0.932464\pi$
$524$	−5.26741			−0.230108
$525$	−0.783304	+	5.77614i	−0.0341862	+	0.252092i
$526$	−13.5666			−0.591532
$527$	−35.2572			−1.53583
$528$		0			0
$529$	0.0696480			0.00302817
$530$	26.0883			1.13320
$531$	4.88347	−	17.6744i	0.211925	−	0.767005i
$532$	−9.00696			−0.390501
$533$		−	2.37151i		−	0.102721i
$534$	−2.98138	+	21.9849i	−0.129017	+	0.951382i
$535$			5.92605i			0.256206i
$536$	−11.7972			−0.509562
$537$	4.32121	−	31.8649i	0.186474	−	1.37507i
$538$		−	11.8485i		−	0.510824i
$539$		0			0
$540$	−5.42838	+	12.6847i	−0.233600	+	0.545863i
$541$		−	2.78903i		−	0.119910i	−0.998201	−	0.0599550i	$-0.980904\pi$
$541$		−	2.78903i		−	0.119910i	0.998201	−	0.0599550i	$-0.0190957\pi$
$542$		−	21.6515i		−	0.930011i
$543$	−22.1052	−	2.99770i	−0.948627	−	0.128643i
$544$	−6.79026			−0.291130
$545$	−12.5736			−0.538592
$546$	4.24303	+	0.575398i	0.181585	+	0.0246247i
$547$			33.1227i			1.41623i	0.706099	+	0.708113i	$0.250453\pi$
$547$			33.1227i			1.41623i	−0.706099	+	0.708113i	$0.749547\pi$
$548$			0.927773i			0.0396325i
$549$	11.1084	−	40.2039i	0.474095	−	1.71586i
$550$		0			0
$551$		−	2.54678i		−	0.108496i
$552$	1.11455	−	8.21881i	0.0474386	−	0.349816i
$553$	−5.21434			−0.221736
$554$		−	4.07356i		−	0.173069i
$555$	−0.622335	+	4.58915i	−0.0264167	+	0.194799i
$556$		−	8.45318i		−	0.358495i
$557$	27.4015			1.16104			0.580519	−	0.814247i	$-0.302850\pi$
$557$	27.4015			1.16104			0.580519	+	0.814247i	$0.302850\pi$
$558$	15.0144	+	4.14849i	0.635609	+	0.175620i
$559$	−5.15946			−0.218222
$560$	4.35758			0.184141
$561$		0			0
$562$	−17.8647			−0.753575
$563$	−21.2562			−0.895844			−0.447922	−	0.894073i	$-0.647836\pi$
$563$	−21.2562			−0.895844			−0.447922	+	0.894073i	$0.647836\pi$
$564$	−2.33054	+	17.1856i	−0.0981334	+	0.723644i
$565$	−10.3445			−0.435195
$566$			3.03967i			0.127767i
$567$	−7.58288	+	12.6745i	−0.318451	+	0.532280i
$568$		−	0.898056i		−	0.0376816i
$569$	36.9079			1.54726			0.773630	−	0.633637i	$-0.218439\pi$
$569$	36.9079			1.54726			0.773630	+	0.633637i	$0.218439\pi$
$570$	25.0132	+	3.39205i	1.04769	+	0.142077i
$571$		−	26.4505i		−	1.10692i	−0.832876	−	0.553460i	$-0.813307\pi$
$571$		−	26.4505i		−	1.10692i	0.832876	−	0.553460i	$-0.186693\pi$
$572$		0			0
$573$	−0.751520	+	5.54177i	−0.0313952	+	0.231511i
$574$		−	2.58351i		−	0.107834i
$575$			9.81998i			0.409522i
$576$	2.89165	+	0.798968i	0.120485	+	0.0332903i
$577$	−24.4912			−1.01958			−0.509790	−	0.860299i	$-0.670277\pi$
$577$	−24.4912			−1.01958			−0.509790	+	0.860299i	$0.670277\pi$
$578$	−29.1077			−1.21072
$579$	2.27286	−	16.7603i	0.0944570	−	0.696533i
$580$			1.23214i			0.0511617i
$581$			3.07568i			0.127601i
$582$	−6.16337	−	0.835815i	−0.255480	−	0.0346456i
$583$		0			0
$584$			4.62724i			0.191476i
$585$	−11.5666	−	3.19587i	−0.478220	−	0.132133i
$586$	23.3411			0.964212
$587$		−	41.4212i		−	1.70964i	−0.518927	−	0.854819i	$-0.673668\pi$
$587$		−	41.4212i		−	1.70964i	0.518927	−	0.854819i	$-0.326332\pi$
$588$	−7.39205	−	1.00244i	−0.304843	−	0.0413398i
$589$		−	28.4977i		−	1.17423i
$590$	16.2299			0.668175
$591$	23.9738	+	3.25108i	0.986148	+	0.133732i
$592$	1.00696			0.0413858
$593$	−2.94808			−0.121063			−0.0605316	−	0.998166i	$-0.519280\pi$
$593$	−2.94808			−0.121063			−0.0605316	+	0.998166i	$0.519280\pi$
$594$		0			0
$595$	29.5891			1.21304
$596$	−18.0716			−0.740241
$597$	−27.4064	−	3.71659i	−1.12167	−	0.152110i
$598$	7.21355			0.294984
$599$			27.7430i			1.13355i	0.823873	+	0.566775i	$0.191809\pi$
$599$			27.7430i			1.13355i	−0.823873	+	0.566775i	$0.808191\pi$
$600$	−3.51973	−	0.477311i	−0.143692	−	0.0194861i
$601$			4.44136i			0.181167i	0.995889	+	0.0905834i	$0.0288732\pi$
$601$			4.44136i			0.181167i	−0.995889	+	0.0905834i	$0.971127\pi$
$602$	−5.62069			−0.229082
$603$	34.1135	+	9.42560i	1.38921	+	0.383840i
$604$			13.3299i			0.542387i
$605$		0			0
$606$	−20.8917	−	2.83313i	−0.848667	−	0.115088i
$607$		−	40.6397i		−	1.64951i	−0.565488	−	0.824756i	$-0.691312\pi$
$607$		−	40.6397i		−	1.64951i	0.565488	−	0.824756i	$-0.308688\pi$
$608$		−	5.48844i		−	0.222586i
$609$	−0.177242	+	1.30700i	−0.00718221	+	0.0529622i
$610$	36.9180			1.49477
$611$	−15.0836			−0.610216
$612$	19.6351	+	5.42520i	0.793701	+	0.219301i
$613$			28.8714i			1.16610i	0.812435	+	0.583052i	$0.198142\pi$
$613$			28.8714i			1.16610i	−0.812435	+	0.583052i	$0.801858\pi$
$614$			30.0216i			1.21157i
$615$	−0.972957	+	7.17467i	−0.0392334	+	0.289310i
$616$		0			0
$617$			31.6428i			1.27389i	0.770909	+	0.636946i	$0.219802\pi$
$617$			31.6428i			1.27389i	−0.770909	+	0.636946i	$0.780198\pi$
$618$	1.52170	+	0.206358i	0.0612118	+	0.00830094i
$619$	0.954383			0.0383599			0.0191799	−	0.999816i	$-0.493894\pi$
$619$	0.954383			0.0383599			0.0191799	+	0.999816i	$0.493894\pi$
$620$			13.7872i			0.553709i
$621$	−9.78947	+	22.8754i	−0.392838	+	0.917960i
$622$			0.495224i			0.0198567i
$623$	−21.0209			−0.842184
$624$	−0.350622	+	2.58551i	−0.0140361	+	0.103503i
$625$	−31.0481			−1.24193
$626$	28.3789			1.13425
$627$		0			0
$628$	9.70820			0.387400
$629$	6.83752			0.272630
$630$	−12.6006	−	3.48157i	−0.502020	−	0.138709i
$631$	7.11650			0.283303			0.141652	−	0.989917i	$-0.454759\pi$
$631$	7.11650			0.283303			0.141652	+	0.989917i	$0.454759\pi$
$632$		−	3.17739i		−	0.126390i
$633$	−0.527907	+	3.89283i	−0.0209824	+	0.154726i
$634$		−	6.64071i		−	0.263736i
$635$	−0.627652			−0.0249076
$636$	−2.28678	+	16.8629i	−0.0906769	+	0.668658i
$637$		−	6.48791i		−	0.257060i
$638$		0			0
$639$	−0.717518	+	2.59687i	−0.0283846	+	0.102730i
$640$			2.65532i			0.104961i
$641$			32.8449i			1.29730i	0.761088	+	0.648648i	$0.224665\pi$
$641$			32.8449i			1.29730i	−0.761088	+	0.648648i	$0.775335\pi$
$642$	−3.83047	−	0.519451i	−0.151177	−	0.0205011i
$643$	3.29640			0.129997			0.0649987	−	0.997885i	$-0.479296\pi$
$643$	3.29640			0.129997			0.0649987	+	0.997885i	$0.479296\pi$
$644$	7.85840			0.309664
$645$	15.6092	+	2.11677i	0.614612	+	0.0833477i
$646$		−	37.2680i		−	1.46629i
$647$		−	5.82245i		−	0.228904i	−0.993429	−	0.114452i	$-0.963489\pi$
$647$		−	5.82245i		−	0.228904i	0.993429	−	0.114452i	$-0.0365113\pi$
$648$	−7.72330	−	4.62067i	−0.303400	−	0.181517i
$649$		0			0
$650$		−	3.08922i		−	0.121169i
$651$	−1.98329	+	14.6249i	−0.0777311	+	0.573196i
$652$	7.08206			0.277355
$653$			4.37774i			0.171314i	0.996325	+	0.0856570i	$0.0272989\pi$
$653$			4.37774i			0.171314i	−0.996325	+	0.0856570i	$0.972701\pi$
$654$	1.10214	−	8.12728i	0.0430972	−	0.317802i
$655$			13.9867i			0.546504i
$656$	1.57428			0.0614652
$657$	3.69701	−	13.3804i	0.144234	−	0.522017i
$658$	−16.4320			−0.640585
$659$	15.3805			0.599141			0.299570	−	0.954074i	$-0.403157\pi$
$659$	15.3805			0.599141			0.299570	+	0.954074i	$0.403157\pi$
$660$		0			0
$661$	12.6047			0.490266			0.245133	−	0.969489i	$-0.421168\pi$
$661$	12.6047			0.490266			0.245133	+	0.969489i	$0.421168\pi$
$662$	−7.41016			−0.288004
$663$	−2.38082	+	17.5563i	−0.0924632	+	0.681831i
$664$	−1.87418			−0.0727325
$665$			23.9163i			0.927436i
$666$	−2.91178	−	0.804529i	−0.112829	−	0.0311749i
$667$			2.22202i			0.0860369i
$668$	−2.53482			−0.0980753
$669$	−7.55420	−	1.02443i	−0.292062	−	0.0396066i
$670$			31.3254i			1.21021i
$671$		0			0
$672$	−0.381966	+	2.81665i	−0.0147347	+	0.108655i
$673$			32.2330i			1.24249i	0.783615	+	0.621246i	$0.213373\pi$
$673$			32.2330i			1.24249i	−0.783615	+	0.621246i	$0.786627\pi$
$674$			34.2137i			1.31786i
$675$	9.79647	+	4.19237i	0.377066	+	0.161364i
$676$	10.7307			0.412720
$677$	−9.11198			−0.350202			−0.175101	−	0.984550i	$-0.556025\pi$
$677$	−9.11198			−0.350202			−0.175101	+	0.984550i	$0.556025\pi$
$678$	0.906749	−	6.68644i	0.0348235	−	0.256791i
$679$		−	5.89309i		−	0.226156i
$680$			18.0303i			0.691431i
$681$	−21.8548	−	2.96374i	−0.837479	−	0.113571i
$682$		0			0
$683$			28.1535i			1.07726i	0.842541	+	0.538632i	$0.181059\pi$
$683$			28.1535i			1.07726i	−0.842541	+	0.538632i	$0.818941\pi$
$684$	−4.38509	+	15.8707i	−0.167668	+	0.606830i
$685$	2.46353			0.0941268
$686$		−	18.5554i		−	0.708450i
$687$	−11.0247	−	1.49506i	−0.420618	−	0.0570401i
$688$		−	3.42500i		−	0.130577i
$689$	−14.8004			−0.563849
$690$	−21.8236	−	2.95950i	−0.830809	−	0.112666i
$691$	10.7376			0.408478			0.204239	−	0.978921i	$-0.434528\pi$
$691$	10.7376			0.408478			0.204239	+	0.978921i	$0.434528\pi$
$692$	0.949284			0.0360864
$693$		0			0
$694$	−20.9245			−0.794285
$695$	−22.4459			−0.851421
$696$	−0.796426	−	0.108003i	−0.0301885	−	0.00409386i
$697$	10.6898			0.404904
$698$			29.4529i			1.11481i
$699$	−28.8523	−	3.91266i	−1.09129	−	0.147990i
$700$		−	3.36538i		−	0.127199i
$701$	−41.5341			−1.56872			−0.784360	−	0.620306i	$-0.787008\pi$
$701$	−41.5341			−1.56872			−0.784360	+	0.620306i	$0.787008\pi$
$702$	3.07962	−	7.19627i	0.116233	−	0.271606i
$703$			5.52664i			0.208441i
$704$		0			0
$705$	45.6332	+	6.18832i	1.71865	+	0.233066i
$706$			24.3265i			0.915541i
$707$		−	19.9756i		−	0.751258i
$708$	−1.42264	+	10.4907i	−0.0534661	+	0.394263i
$709$	30.2145			1.13473			0.567364	−	0.823467i	$-0.307963\pi$
$709$	30.2145			1.13473			0.567364	+	0.823467i	$0.307963\pi$
$710$	−2.38462			−0.0894934
$711$	−2.53863	+	9.18791i	−0.0952062	+	0.344573i
$712$		−	12.8092i		−	0.480045i
$713$			24.8637i			0.931154i
$714$	−2.59365	+	19.1258i	−0.0970649	+	0.715764i
$715$		0			0
$716$			18.5656i			0.693830i
$717$	−20.6626	−	2.80206i	−0.771658	−	0.104645i
$718$	32.7277			1.22139
$719$			50.2334i			1.87339i	0.350148	+	0.936695i	$0.386131\pi$
$719$			50.2334i			1.87339i	−0.350148	+	0.936695i	$0.613869\pi$
$720$	2.12151	−	7.67826i	0.0790642	−	0.286152i
$721$			1.45497i			0.0541860i
$722$	11.1230			0.413956
$723$	4.78639	−	35.2952i	0.178008	−	1.31264i
$724$	12.8793			0.478655
$725$	0.951585			0.0353410
$726$		0			0
$727$	42.9707			1.59369			0.796847	−	0.604181i	$-0.206499\pi$
$727$	42.9707			1.59369			0.796847	+	0.604181i	$0.206499\pi$
$728$	−2.47214			−0.0916235
$729$	18.6413	+	19.5320i	0.690420	+	0.723409i
$730$	12.2868			0.454754
$731$		−	23.2567i		−	0.860179i
$732$	−3.23607	+	23.8630i	−0.119609	+	0.882003i
$733$			34.4677i			1.27309i	0.771238	+	0.636547i	$0.219638\pi$
$733$			34.4677i			1.27309i	−0.771238	+	0.636547i	$0.780362\pi$
$734$	11.9030			0.439346
$735$	−2.66179	+	19.6282i	−0.0981816	+	0.723999i
$736$			4.78856i			0.176509i
$737$		0			0
$738$	−4.55226	−	1.25780i	−0.167571	−	0.0463002i
$739$			1.13944i			0.0419151i	0.999780	+	0.0209576i	$0.00667149\pi$
$739$			1.13944i			0.0419151i	−0.999780	+	0.0209576i	$0.993329\pi$
$740$		−	2.67380i		−	0.0982908i
$741$	−14.1905	−	1.92437i	−0.521299	−	0.0706935i
$742$	−16.1235			−0.591911
$743$	−14.6641			−0.537973			−0.268987	−	0.963144i	$-0.586689\pi$
$743$	−14.6641			−0.537973			−0.268987	+	0.963144i	$0.586689\pi$
$744$	−8.91178	−	1.20853i	−0.326722	−	0.0443068i
$745$			47.9858i			1.75807i
$746$		−	27.7804i		−	1.01711i
$747$	5.41949	+	1.49741i	0.198289	+	0.0547875i
$748$		0			0
$749$		−	3.66250i		−	0.133825i
$750$	1.82276	−	13.4412i	0.0665577	−	0.490802i
$751$	−30.7152			−1.12081			−0.560406	−	0.828218i	$-0.689355\pi$
$751$	−30.7152			−1.12081			−0.560406	+	0.828218i	$0.689355\pi$
$752$		−	10.0129i		−	0.365134i
$753$	−3.80920	+	28.0893i	−0.138815	+	1.02363i
$754$		−	0.699013i		−	0.0254566i
$755$	35.3952			1.28816
$756$	3.35492	−	7.83959i	0.122017	−	0.285123i
$757$	36.8080			1.33781			0.668905	−	0.743348i	$-0.266763\pi$
$757$	36.8080			1.33781			0.668905	+	0.743348i	$0.266763\pi$
$758$	7.86465			0.285657
$759$		0			0
$760$	−14.5736			−0.528639
$761$	−17.7995			−0.645232			−0.322616	−	0.946530i	$-0.604562\pi$
$761$	−17.7995			−0.645232			−0.322616	+	0.946530i	$0.604562\pi$
$762$	0.0550172	−	0.405701i	0.00199306	−	0.0146970i
$763$	7.77089			0.281325
$764$		−	3.22883i		−	0.116815i
$765$	14.4056	−	52.1374i	0.520837	−	1.88503i
$766$		−	12.9561i		−	0.468121i
$767$	−9.20752			−0.332464
$768$	−1.71634	−	0.232753i	−0.0619331	−	0.00839876i
$769$		−	15.5249i		−	0.559841i	−0.960023	−	0.279920i	$-0.909692\pi$
$769$		−	15.5249i		−	0.559841i	0.960023	−	0.279920i	$-0.0903081\pi$
$770$		0			0
$771$	−1.98683	+	14.6511i	−0.0715541	+	0.527645i
$772$			9.76512i			0.351454i
$773$			34.8051i			1.25185i	0.779883	+	0.625926i	$0.215279\pi$
$773$			34.8051i			1.25185i	−0.779883	+	0.625926i	$0.784721\pi$
$774$	−2.73647	+	9.90391i	−0.0983603	+	0.355989i
$775$	10.6480			0.382486
$776$	3.59099			0.128909
$777$	0.384624	−	2.83625i	0.0137983	−	0.101750i
$778$		−	25.8976i		−	0.928474i
$779$			8.64034i			0.309572i
$780$	6.86536	+	0.931013i	0.245819	+	0.0333356i
$781$		0			0
$782$			32.5156i			1.16276i
$783$	2.21670	+	0.948628i	0.0792183	+	0.0339012i
$784$	4.30687			0.153817
$785$		−	25.7784i		−	0.920070i
$786$	−9.04067	−	1.22601i	−0.322470	−	0.0437302i
$787$		−	18.8902i		−	0.673362i	−0.941619	−	0.336681i	$-0.890696\pi$
$787$		−	18.8902i		−	0.673362i	0.941619	−	0.336681i	$-0.109304\pi$
$788$	−13.9679			−0.497587
$789$	−23.2849	−	3.15767i	−0.828965	−	0.112416i
$790$	−8.43698			−0.300174
$791$	6.39323			0.227317
$792$		0			0
$793$	−20.9443			−0.743753
$794$	17.9986			0.638746
$795$	44.7764	+	6.07214i	1.58806	+	0.215357i
$796$	15.9679			0.565969
$797$		−	45.2566i		−	1.60307i	−0.597947	−	0.801535i	$-0.704017\pi$
$797$		−	45.2566i		−	1.60307i	0.597947	−	0.801535i	$-0.295983\pi$
$798$	−15.4590	−	2.09640i	−0.547243	−	0.0742117i
$799$		−	67.9904i		−	2.40533i
$800$	2.05072			0.0725037
$801$	−10.2341	+	37.0397i	−0.361605	+	1.30873i
$802$			3.76803i			0.133054i
$803$		0			0
$804$	−20.2481	−	2.74584i	−0.714094	−	0.0968384i
$805$		−	20.8666i		−	0.735450i
$806$		−	7.82175i		−	0.275510i
$807$	2.75777	−	20.3360i	0.0970781	−	0.715861i
$808$	12.1722			0.428218
$809$	−24.4669			−0.860211			−0.430105	−	0.902779i	$-0.641524\pi$
$809$	−24.4669			−0.860211			−0.430105	+	0.902779i	$0.641524\pi$
$810$	−12.2694	+	20.5078i	−0.431101	+	0.720571i
$811$			12.1210i			0.425627i	0.977093	+	0.212814i	$0.0682627\pi$
$811$			12.1210i			0.425627i	−0.977093	+	0.212814i	$0.931737\pi$
$812$		−	0.761502i		−	0.0267235i
$813$	5.03945	−	37.1613i	0.176741	−	1.30330i
$814$		0			0
$815$		−	18.8051i		−	0.658715i
$816$	−11.6544	−	1.58046i	−0.407986	−	0.0553270i
$817$	18.7979			0.657656
$818$		−	14.3741i		−	0.502577i
$819$	7.14856	+	1.97516i	0.249791	+	0.0690176i
$820$		−	4.18021i		−	0.145979i
$821$	38.6073			1.34740			0.673702	−	0.739003i	$-0.264703\pi$
$821$	38.6073			1.34740			0.673702	+	0.739003i	$0.264703\pi$
$822$	−0.215942	+	1.59237i	−0.00753185	+	0.0555405i
$823$	−7.14045			−0.248900			−0.124450	−	0.992226i	$-0.539717\pi$
$823$	−7.14045			−0.248900			−0.124450	+	0.992226i	$0.539717\pi$
$824$	−0.886596			−0.0308860
$825$		0			0
$826$	−10.0306			−0.349010
$827$	−14.4318			−0.501841			−0.250921	−	0.968008i	$-0.580733\pi$
$827$	−14.4318			−0.501841			−0.250921	+	0.968008i	$0.580733\pi$
$828$	3.82591	−	13.8469i	0.132960	−	0.481212i
$829$	−55.6805			−1.93386			−0.966932	−	0.255032i	$-0.917914\pi$
$829$	−55.6805			−1.93386			−0.966932	+	0.255032i	$0.917914\pi$
$830$			4.97656i			0.172739i
$831$	0.948134	−	6.99162i	0.0328904	−	0.242536i
$832$		−	1.50641i		−	0.0522254i
$833$	29.2448			1.01327
$834$	1.96751	−	14.5085i	0.0681292	−	0.502390i
$835$			6.73076i			0.232928i
$836$		0			0
$837$	24.8042	+	10.6149i	0.857358	+	0.366903i
$838$			31.1601i			1.07641i
$839$		−	41.3981i		−	1.42922i	−0.699522	−	0.714611i	$-0.746604\pi$
$839$		−	41.3981i		−	1.42922i	0.699522	−	0.714611i	$-0.253396\pi$
$840$	7.47910	+	1.01424i	0.258053	+	0.0349947i
$841$	−28.7847			−0.992575
$842$	10.8166			0.372764
$843$	−30.6618	−	4.15806i	−1.05605	−	0.143211i
$844$		−	2.26810i		−	0.0780712i
$845$		−	28.4935i		−	0.980206i
$846$	−8.00000	+	28.9539i	−0.275046	+	0.995455i
$847$		0			0
$848$		−	9.82493i		−	0.337389i
$849$	−0.707493	+	5.21711i	−0.0242811	+	0.179051i
$850$	13.9249			0.477620
$851$		−	4.82189i		−	0.165292i
$852$	0.209025	−	1.54137i	0.00716109	−	0.0528065i
$853$			37.3680i			1.27946i	0.768602	+	0.639728i	$0.220953\pi$
$853$			37.3680i			1.27946i	−0.768602	+	0.639728i	$0.779047\pi$
$854$	−22.8166			−0.780768
$855$	42.1417	+	11.6438i	1.44122	+	0.398210i
$856$	2.23177			0.0762802
$857$	−34.9831			−1.19500			−0.597499	−	0.801869i	$-0.703839\pi$
$857$	−34.9831			−1.19500			−0.597499	+	0.801869i	$0.703839\pi$
$858$		0			0
$859$	3.21505			0.109696			0.0548481	−	0.998495i	$-0.482533\pi$
$859$	3.21505			0.109696			0.0548481	+	0.998495i	$0.482533\pi$
$860$	−9.09447			−0.310119
$861$	0.601321	−	4.43419i	0.0204930	−	0.151117i
$862$	−39.8322			−1.35669
$863$			45.2723i			1.54109i	0.637388	+	0.770543i	$0.280015\pi$
$863$			45.2723i			1.54109i	−0.637388	+	0.770543i	$0.719985\pi$
$864$	4.77710	+	2.04434i	0.162520	+	0.0695499i
$865$		−	2.52065i		−	0.0857047i
$866$	−16.1553			−0.548979
$867$	−49.9587	−	6.77491i	−1.69669	−	0.230088i
$868$		−	8.52098i		−	0.289221i
$869$		0			0
$870$	−0.286784	+	2.11477i	−0.00972288	+	0.0716973i
$871$		−	17.7715i		−	0.602163i
$872$			4.73524i			0.160355i
$873$	−10.3839	−	2.86909i	−0.351442	−	0.0971039i
$874$	−26.2818			−0.888994
$875$	12.8517			0.434468
$876$	−1.07700	+	7.94191i	−0.0363886	+	0.268332i
$877$		−	47.7756i		−	1.61327i	−0.591052	−	0.806634i	$-0.701287\pi$
$877$		−	47.7756i		−	1.61327i	0.591052	−	0.806634i	$-0.298713\pi$
$878$			6.13994i			0.207213i
$879$	40.0613	+	5.43271i	1.35123	+	0.183241i
$880$		0			0
$881$		−	34.4685i		−	1.16127i	−0.814163	−	0.580636i	$-0.802804\pi$
$881$		−	34.4685i		−	1.16127i	0.814163	−	0.580636i	$-0.197196\pi$
$882$	−12.4540	−	3.44105i	−0.419347	−	0.115866i
$883$	−37.1200			−1.24919			−0.624593	−	0.780950i	$-0.714735\pi$
$883$	−37.1200			−1.24919			−0.624593	+	0.780950i	$0.714735\pi$
$884$		−	10.2289i		−	0.344036i
$885$	27.8560	+	3.77756i	0.936371	+	0.126981i
$886$		−	1.63784i		−	0.0550242i
$887$	42.9793			1.44310			0.721552	−	0.692361i	$-0.243429\pi$
$887$	42.9793			1.44310			0.721552	+	0.692361i	$0.243429\pi$
$888$	1.72829	+	0.234373i	0.0579975	+	0.00786505i
$889$	0.387911			0.0130101
$890$	−34.0125			−1.14010
$891$		0			0
$892$	4.40134			0.147368
$893$	54.9553			1.83901
$894$	−31.0170	−	4.20622i	−1.03736	−	0.140677i
$895$	49.2976			1.64784
$896$		−	1.64108i		−	0.0548245i
$897$	12.3809	+	1.67898i	0.413386	+	0.0560594i
$898$		−	18.2818i		−	0.610072i
$899$	2.40937			0.0803569
$900$	−5.92996	−	1.63846i	−0.197665	−	0.0546152i
$901$		−	66.7138i		−	2.22256i
$902$		0			0
$903$	−9.64702	−	1.30823i	−0.321033	−	0.0435353i
$904$			3.89575i			0.129571i
$905$		−	34.1986i		−	1.13680i
$906$	−3.10258	+	22.8787i	−0.103076	+	0.760093i
$907$	−37.8374			−1.25637			−0.628185	−	0.778064i	$-0.716202\pi$
$907$	−37.8374			−1.25637			−0.628185	+	0.778064i	$0.716202\pi$
$908$	12.7334			0.422572
$909$	−35.1979	−	9.72522i	−1.16744	−	0.322565i
$910$			6.56431i			0.217605i
$911$		−	20.3155i		−	0.673084i	−0.941668	−	0.336542i	$-0.890743\pi$
$911$		−	20.3155i		−	0.673084i	0.941668	−	0.336542i	$-0.109257\pi$
$912$	1.27745	−	9.42004i	0.0423007	−	0.311929i
$913$		0			0
$914$		−	27.9848i		−	0.925654i
$915$	63.3639	+	8.59279i	2.09475	+	0.284069i
$916$	6.42337			0.212234
$917$		−	8.64423i		−	0.285458i
$918$	32.4378	+	13.8816i	1.07061	+	0.458162i
$919$		−	33.3847i		−	1.10126i	−0.834749	−	0.550630i	$-0.814388\pi$
$919$		−	33.3847i		−	1.10126i	0.834749	−	0.550630i	$-0.185612\pi$
$920$	12.7152			0.419207
$921$	−6.98763	+	51.5273i	−0.230250	+	1.69788i
$922$	−30.3359			−0.999058
$923$	1.35284			0.0445293
$924$		0			0
$925$	−2.06499			−0.0678964
$926$	10.9632			0.360273
$927$	2.56373	+	0.708362i	0.0842039	+	0.0232657i
$928$	0.464026			0.0152324
$929$		−	23.5418i		−	0.772382i	−0.922419	−	0.386191i	$-0.873790\pi$
$929$		−	23.5418i		−	0.772382i	0.922419	−	0.386191i	$-0.126210\pi$
$930$	−3.20903	+	23.6636i	−0.105228	+	0.775960i
$931$			23.6380i			0.774704i
$932$	16.8103			0.550641
$933$	−0.115265	+	0.849973i	−0.00377360	+	0.0278269i
$934$		−	32.2185i		−	1.05422i
$935$		0			0
$936$	−1.20357	+	4.35602i	−0.0393400	+	0.142381i
$937$		−	24.8579i		−	0.812073i	−0.913857	−	0.406036i	$-0.866911\pi$
$937$		−	24.8579i		−	0.812073i	0.913857	−	0.406036i	$-0.133089\pi$
$938$		−	19.3602i		−	0.632131i
$939$	48.7079	+	6.60528i	1.58952	+	0.215555i
$940$	−26.5875			−0.867188
$941$	−7.06663			−0.230366			−0.115183	−	0.993344i	$-0.536745\pi$
$941$	−7.06663			−0.230366			−0.115183	+	0.993344i	$0.536745\pi$
$942$	16.6626	+	2.25962i	0.542896	+	0.0736223i
$943$		−	7.53853i		−	0.245488i
$944$		−	6.11223i		−	0.198936i
$945$	−20.8166	−	8.90839i	−0.677164	−	0.289790i
$946$		0			0
$947$			11.7619i			0.382210i	0.981570	+	0.191105i	$0.0612071\pi$
$947$			11.7619i			0.382210i	−0.981570	+	0.191105i	$0.938793\pi$
$948$	0.739548	−	5.45348i	0.0240194	−	0.177121i
$949$	−6.97052			−0.226273
$950$			11.2552i			0.365168i
$951$	1.54565	−	11.3977i	0.0501210	−	0.369596i
$952$		−	11.1433i		−	0.361158i
$953$	2.71982			0.0881036			0.0440518	−	0.999029i	$-0.485973\pi$
$953$	2.71982			0.0881036			0.0440518	+	0.999029i	$0.485973\pi$
$954$	−7.84980	+	28.4103i	−0.254147	+	0.919816i
$955$	−8.57357			−0.277434
$956$	12.0387			0.389361
$957$		0			0
$958$	18.8328			0.608461
$959$	−1.52255			−0.0491656
$960$	−0.618034	+	4.55743i	−0.0199470	+	0.147090i
$961$	−4.03989			−0.130319
$962$			1.51690i			0.0489067i
$963$	−6.45349	−	1.78311i	−0.207961	−	0.0574599i
$964$			20.5642i			0.662328i
$965$	25.9295			0.834700
$966$	13.4877	+	1.82907i	0.433960	+	0.0588493i
$967$			21.8182i			0.701625i	0.936446	+	0.350812i	$0.114095\pi$
$967$			21.8182i			0.701625i	−0.936446	+	0.350812i	$0.885905\pi$
$968$		0			0
$969$	8.67424	−	63.9646i	0.278657	−	2.05484i
$970$		−	9.53523i		−	0.306158i
$971$			44.3702i			1.42391i	0.702226	+	0.711954i	$0.252189\pi$
$971$			44.3702i			1.42391i	−0.702226	+	0.711954i	$0.747811\pi$
$972$	−12.1803	−	9.72827i	−0.390685	−	0.312035i
$973$	13.8723			0.444726
$974$	26.8604			0.860661
$975$	0.719026	−	5.30215i	0.0230273	−	0.169805i
$976$		−	13.9034i		−	0.445038i
$977$		−	31.3275i		−	1.00226i	−0.865373	−	0.501128i	$-0.832919\pi$
$977$		−	31.3275i		−	1.00226i	0.865373	−	0.501128i	$-0.167081\pi$
$978$	12.1552	+	1.64837i	0.388681	+	0.0527091i
$979$		0			0
$980$		−	11.4361i		−	0.365313i
$981$	3.78330	−	13.6927i	0.120792	−	0.437173i
$982$	19.0395			0.607573
$983$		−	38.4222i		−	1.22548i	−0.790285	−	0.612740i	$-0.790067\pi$
$983$		−	38.4222i		−	1.22548i	0.790285	−	0.612740i	$-0.209933\pi$
$984$	2.70200	+	0.366418i	0.0861366	+	0.0116810i
$985$			37.0893i			1.18176i
$986$	3.15086			0.100344
$987$	−28.2029	−	3.82459i	−0.897707	−	0.121738i
$988$	8.26785			0.263035
$989$	−16.4008			−0.521517
$990$		0			0
$991$	−28.2808			−0.898371			−0.449185	−	0.893439i	$-0.648286\pi$
$991$	−28.2808			−0.898371			−0.449185	+	0.893439i	$0.648286\pi$
$992$	5.19231			0.164856
$993$	−12.7184	−	1.72474i	−0.403605	−	0.0547329i
$994$	1.47378			0.0467454
$995$		−	42.4000i		−	1.34417i
$996$	−3.21674	−	0.436223i	−0.101926	−	0.0138222i
$997$			23.6328i			0.748457i	0.927337	+	0.374228i	$0.122092\pi$
$997$			23.6328i			0.748457i	−0.927337	+	0.374228i	$0.877908\pi$
$998$	−10.6200			−0.336170
$999$	−4.81035	−	2.05857i	−0.152193	−	0.0651303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.b.c.725.1		8
3.2	odd	2		726.2.b.e.725.2		8
11.2	odd	10		66.2.h.a.29.1	✓	8
11.3	even	5		726.2.h.f.233.2		8
11.4	even	5		726.2.h.h.215.2		8
11.5	even	5		66.2.h.b.41.1	yes	8
11.6	odd	10		726.2.h.d.239.1		8
11.7	odd	10		726.2.h.c.215.2		8
11.8	odd	10		726.2.h.a.233.2		8
11.9	even	5		726.2.h.j.161.1		8
11.10	odd	2		726.2.b.e.725.1		8
33.2	even	10		66.2.h.b.29.2	yes	8
33.5	odd	10		66.2.h.a.41.1	yes	8
33.8	even	10		726.2.h.h.233.2		8
33.14	odd	10		726.2.h.c.233.2		8
33.17	even	10		726.2.h.j.239.1		8
33.20	odd	10		726.2.h.d.161.2		8
33.26	odd	10		726.2.h.a.215.2		8
33.29	even	10		726.2.h.f.215.2		8
33.32	even	2	inner	726.2.b.c.725.2		8
44.27	odd	10		528.2.bn.a.305.2		8
44.35	even	10		528.2.bn.b.161.2		8
132.35	odd	10		528.2.bn.a.161.1		8
132.71	even	10		528.2.bn.b.305.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.h.a.29.1	✓	8	11.2	odd	10
66.2.h.a.41.1	yes	8	33.5	odd	10
66.2.h.b.29.2	yes	8	33.2	even	10
66.2.h.b.41.1	yes	8	11.5	even	5
528.2.bn.a.161.1		8	132.35	odd	10
528.2.bn.a.305.2		8	44.27	odd	10
528.2.bn.b.161.2		8	44.35	even	10
528.2.bn.b.305.2		8	132.71	even	10
726.2.b.c.725.1		8	1.1	even	1	trivial
726.2.b.c.725.2		8	33.32	even	2	inner
726.2.b.e.725.1		8	11.10	odd	2
726.2.b.e.725.2		8	3.2	odd	2
726.2.h.a.215.2		8	33.26	odd	10
726.2.h.a.233.2		8	11.8	odd	10
726.2.h.c.215.2		8	11.7	odd	10
726.2.h.c.233.2		8	33.14	odd	10
726.2.h.d.161.2		8	33.20	odd	10
726.2.h.d.239.1		8	11.6	odd	10
726.2.h.f.215.2		8	33.29	even	10
726.2.h.f.233.2		8	11.3	even	5
726.2.h.h.215.2		8	11.4	even	5
726.2.h.h.233.2		8	33.8	even	10
726.2.h.j.161.1		8	11.9	even	5
726.2.h.j.239.1		8	33.17	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.71634 - 0.232753i) q^{3} +1.00000 q^{4} -2.65532i q^{5} +(1.71634 + 0.232753i) q^{6} +1.64108i q^{7} -1.00000 q^{8} +(2.89165 + 0.798968i) q^{9} +2.65532i q^{10} +(-1.71634 - 0.232753i) q^{12} -1.50641i q^{13} -1.64108i q^{14} +(-0.618034 + 4.55743i) q^{15} +1.00000 q^{16} +6.79026 q^{17} +(-2.89165 - 0.798968i) q^{18} +5.48844i q^{19} -2.65532i q^{20} +(0.381966 - 2.81665i) q^{21} -4.78856i q^{23} +(1.71634 + 0.232753i) q^{24} -2.05072 q^{25} +1.50641i q^{26} +(-4.77710 - 2.04434i) q^{27} +1.64108i q^{28} -0.464026 q^{29} +(0.618034 - 4.55743i) q^{30} -5.19231 q^{31} -1.00000 q^{32} -6.79026 q^{34} +4.35758 q^{35} +(2.89165 + 0.798968i) q^{36} +1.00696 q^{37} -5.48844i q^{38} +(-0.350622 + 2.58551i) q^{39} +2.65532i q^{40} +1.57428 q^{41} +(-0.381966 + 2.81665i) q^{42} -3.42500i q^{43} +(2.12151 - 7.67826i) q^{45} +4.78856i q^{46} -10.0129i q^{47} +(-1.71634 - 0.232753i) q^{48} +4.30687 q^{49} +2.05072 q^{50} +(-11.6544 - 1.58046i) q^{51} -1.50641i q^{52} -9.82493i q^{53} +(4.77710 + 2.04434i) q^{54} -1.64108i q^{56} +(1.27745 - 9.42004i) q^{57} +0.464026 q^{58} -6.11223i q^{59} +(-0.618034 + 4.55743i) q^{60} -13.9034i q^{61} +5.19231 q^{62} +(-1.31117 + 4.74542i) q^{63} +1.00000 q^{64} -4.00000 q^{65} +11.7972 q^{67} +6.79026 q^{68} +(-1.11455 + 8.21881i) q^{69} -4.35758 q^{70} +0.898056i q^{71} +(-2.89165 - 0.798968i) q^{72} -4.62724i q^{73} -1.00696 q^{74} +(3.51973 + 0.477311i) q^{75} +5.48844i q^{76} +(0.350622 - 2.58551i) q^{78} +3.17739i q^{79} -2.65532i q^{80} +(7.72330 + 4.62067i) q^{81} -1.57428 q^{82} +1.87418 q^{83} +(0.381966 - 2.81665i) q^{84} -18.0303i q^{85} +3.42500i q^{86} +(0.796426 + 0.108003i) q^{87} +12.8092i q^{89} +(-2.12151 + 7.67826i) q^{90} +2.47214 q^{91} -4.78856i q^{92} +(8.91178 + 1.20853i) q^{93} +10.0129i q^{94} +14.5736 q^{95} +(1.71634 + 0.232753i) q^{96} -3.59099 q^{97} -4.30687 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 3 q^{3} + 8 q^{4} + 3 q^{6} - 8 q^{8} + 7 q^{9} - 3 q^{12} + 4 q^{15} + 8 q^{16} - 10 q^{17} - 7 q^{18} + 12 q^{21} + 3 q^{24} + 14 q^{25} - 15 q^{27} - 2 q^{29} - 4 q^{30} - 22 q^{31} - 8 q^{32}+ \cdots - 22 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 3 * q^3 + 8 * q^4 + 3 * q^6 - 8 * q^8 + 7 * q^9 - 3 * q^12 + 4 * q^15 + 8 * q^16 - 10 * q^17 - 7 * q^18 + 12 * q^21 + 3 * q^24 + 14 * q^25 - 15 * q^27 - 2 * q^29 - 4 * q^30 - 22 * q^31 - 8 * q^32 + 10 * q^34 - 8 * q^35 + 7 * q^36 - 24 * q^37 + 8 * q^39 + 2 * q^41 - 12 * q^42 - 8 * q^45 - 3 * q^48 + 22 * q^49 - 14 * q^50 - 20 * q^51 + 15 * q^54 + 30 * q^57 + 2 * q^58 + 4 * q^60 + 22 * q^62 - 14 * q^63 + 8 * q^64 - 32 * q^65 - 2 * q^67 - 10 * q^68 - 16 * q^69 + 8 * q^70 - 7 * q^72 + 24 * q^74 + 21 * q^75 - 8 * q^78 + 19 * q^81 - 2 * q^82 + 24 * q^83 + 12 * q^84 + 42 * q^87 + 8 * q^90 - 16 * q^91 - 18 * q^93 + 20 * q^95 + 3 * q^96 - 16 * q^97 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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