LMFDB - Embedded newform 252.2.w.a.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$-1.61108 - 0.635951i$ of defining polynomial
Character	$\chi$	$=$	252.101
Dual form			252.2.w.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43204 + 0.974295i) q^{3} +(1.09150 - 1.89054i) q^{5} +(-1.25859 - 2.32722i) q^{7} +(1.10150 - 2.79047i) q^{9} +O(q^{10})$	\(q+(-1.43204 + 0.974295i) q^{3} +(1.09150 - 1.89054i) q^{5} +(-1.25859 - 2.32722i) q^{7} +(1.10150 - 2.79047i) q^{9} +(-1.26889 + 0.732592i) q^{11} +(2.92752 - 1.69021i) q^{13} +(0.278862 + 3.77077i) q^{15} +(1.32136 - 2.28866i) q^{17} +(6.87816 - 3.97111i) q^{19} +(4.06975 + 2.10644i) q^{21} +(-3.47245 - 2.00482i) q^{23} +(0.117249 + 0.203081i) q^{25} +(1.14134 + 5.06925i) q^{27} +(-6.71261 - 3.87553i) q^{29} +0.706968i q^{31} +(1.10334 - 2.28537i) q^{33} +(-5.77345 - 0.160752i) q^{35} +(1.41738 + 2.45498i) q^{37} +(-2.54558 + 5.27272i) q^{39} +(3.74173 + 6.48086i) q^{41} +(-1.27112 + 2.20164i) q^{43} +(-4.07319 - 5.12822i) q^{45} -12.5508 q^{47} +(-3.83190 + 5.85803i) q^{49} +(0.337586 + 4.56485i) q^{51} +(-2.41675 - 1.39531i) q^{53} +3.19850i q^{55} +(-5.98079 + 12.3881i) q^{57} +13.4330 q^{59} -7.79493i q^{61} +(-7.88036 + 0.948624i) q^{63} -7.37945i q^{65} +5.84058 q^{67} +(6.92598 - 0.512200i) q^{69} +11.6854i q^{71} +(-3.95924 - 2.28587i) q^{73} +(-0.365767 - 0.176586i) q^{75} +(3.30191 + 2.03094i) q^{77} +9.38377 q^{79} +(-6.57340 - 6.14739i) q^{81} +(1.70847 - 2.95917i) q^{83} +(-2.88452 - 4.99614i) q^{85} +(13.3887 - 0.990137i) q^{87} +(4.61937 + 8.00099i) q^{89} +(-7.61803 - 4.68571i) q^{91} +(-0.688796 - 1.01241i) q^{93} -17.3379i q^{95} +(6.38394 + 3.68577i) q^{97} +(0.646596 + 4.34773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7} + 6 q^{9}+O(q^{10}) $ 16 * q - q^7 + 6 * q^9	$ 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.43204	+	0.974295i	−0.826791	+	0.562509i
$3$	−1.43204	+	0.974295i	−0.826791	+	0.562509i
$4$		0			0
$5$	1.09150	−	1.89054i	0.488134	−	0.845473i	−0.511773	−	0.859121i	$-0.671011\pi$
$5$	1.09150	−	1.89054i	0.488134	−	0.845473i	0.999907	+	0.0136476i	$0.00434429\pi$
$6$		0			0
$7$	−1.25859	−	2.32722i	−0.475703	−	0.879606i
$7$	−1.25859	−	2.32722i	−0.475703	−	0.879606i
$8$		0			0
$9$	1.10150	−	2.79047i	0.367166	−	0.930155i
$10$		0			0
$11$	−1.26889	+	0.732592i	−0.382584	+	0.220885i	−0.678942	−	0.734192i	$-0.737561\pi$
$11$	−1.26889	+	0.732592i	−0.382584	+	0.220885i	0.296358	+	0.955077i	$0.404228\pi$
$12$		0			0
$13$	2.92752	−	1.69021i	0.811948	−	0.468779i	−0.0356837	−	0.999363i	$-0.511361\pi$
$13$	2.92752	−	1.69021i	0.811948	−	0.468779i	0.847632	+	0.530585i	$0.178028\pi$
$14$		0			0
$15$	0.278862	+	3.77077i	0.0720017	+	0.973610i
$16$		0			0
$17$	1.32136	−	2.28866i	0.320476	−	0.555081i	−0.660110	−	0.751169i	$-0.729491\pi$
$17$	1.32136	−	2.28866i	0.320476	−	0.555081i	0.980586	+	0.196088i	$0.0628238\pi$
$18$		0			0
$19$	6.87816	−	3.97111i	1.57796	−	0.911034i	0.582813	−	0.812606i	$-0.301952\pi$
$19$	6.87816	−	3.97111i	1.57796	−	0.911034i	0.995144	−	0.0984279i	$-0.0313814\pi$
$20$		0			0
$21$	4.06975	+	2.10644i	0.888093	+	0.459663i
$22$		0			0
$23$	−3.47245	−	2.00482i	−0.724056	−	0.418034i	0.0921879	−	0.995742i	$-0.470614\pi$
$23$	−3.47245	−	2.00482i	−0.724056	−	0.418034i	−0.816244	+	0.577708i	$0.803947\pi$
$24$		0			0
$25$	0.117249	+	0.203081i	0.0234498	+	0.0406163i
$26$		0			0
$27$	1.14134	+	5.06925i	0.219651	+	0.975578i
$28$		0			0
$29$	−6.71261	−	3.87553i	−1.24650	−	0.719667i	−0.276091	−	0.961132i	$-0.589039\pi$
$29$	−6.71261	−	3.87553i	−1.24650	−	0.719667i	−0.970410	+	0.241464i	$0.922372\pi$
$30$		0			0
$31$			0.706968i			0.126975i	0.997983	+	0.0634876i	$0.0202223\pi$
$31$			0.706968i			0.126975i	−0.997983	+	0.0634876i	$0.979778\pi$
$32$		0			0
$33$	1.10334	−	2.28537i	0.192067	−	0.397833i
$34$		0			0
$35$	−5.77345	−	0.160752i	−0.975890	−	0.0271721i
$36$		0			0
$37$	1.41738	+	2.45498i	0.233016	+	0.403596i	0.958694	−	0.284438i	$-0.0918071\pi$
$37$	1.41738	+	2.45498i	0.233016	+	0.403596i	−0.725678	+	0.688034i	$0.758474\pi$
$38$		0			0
$39$	−2.54558	+	5.27272i	−0.407619	+	0.844310i
$40$		0			0
$41$	3.74173	+	6.48086i	0.584360	+	1.01214i	0.994955	+	0.100323i	$0.0319876\pi$
$41$	3.74173	+	6.48086i	0.584360	+	1.01214i	−0.410595	+	0.911818i	$0.634679\pi$
$42$		0			0
$43$	−1.27112	+	2.20164i	−0.193844	+	0.335748i	−0.946521	−	0.322642i	$-0.895429\pi$
$43$	−1.27112	+	2.20164i	−0.193844	+	0.335748i	0.752677	+	0.658390i	$0.228762\pi$
$44$		0			0
$45$	−4.07319	−	5.12822i	−0.607195	−	0.764470i
$46$		0			0
$47$	−12.5508			−1.83072			−0.915358	−	0.402640i	$-0.868093\pi$
$47$	−12.5508			−1.83072			−0.915358	+	0.402640i	$0.868093\pi$
$48$		0			0
$49$	−3.83190	+	5.85803i	−0.547414	+	0.836862i
$50$		0			0
$51$	0.337586	+	4.56485i	0.0472715	+	0.639206i
$52$		0			0
$53$	−2.41675	−	1.39531i	−0.331966	−	0.191661i	0.324748	−	0.945801i	$-0.394721\pi$
$53$	−2.41675	−	1.39531i	−0.331966	−	0.191661i	−0.656714	+	0.754140i	$0.728054\pi$
$54$		0			0
$55$			3.19850i			0.431286i
$56$		0			0
$57$	−5.98079	+	12.3881i	−0.792176	+	1.64085i
$58$		0			0
$59$	13.4330			1.74883			0.874414	−	0.485180i	$-0.161246\pi$
$59$	13.4330			1.74883			0.874414	+	0.485180i	$0.161246\pi$
$60$		0			0
$61$		−	7.79493i		−	0.998039i	−0.866591	−	0.499020i	$-0.833694\pi$
$61$		−	7.79493i		−	0.998039i	0.866591	−	0.499020i	$-0.166306\pi$
$62$		0			0
$63$	−7.88036	+	0.948624i	−0.992832	+	0.119515i
$64$		0			0
$65$		−	7.37945i		−	0.915308i
$66$		0			0
$67$	5.84058			0.713541			0.356770	−	0.934192i	$-0.383878\pi$
$67$	5.84058			0.713541			0.356770	+	0.934192i	$0.383878\pi$
$68$		0			0
$69$	6.92598	−	0.512200i	0.833791	−	0.0616616i
$70$		0			0
$71$			11.6854i			1.38680i	0.720554	+	0.693398i	$0.243887\pi$
$71$			11.6854i			1.38680i	−0.720554	+	0.693398i	$0.756113\pi$
$72$		0			0
$73$	−3.95924	−	2.28587i	−0.463394	−	0.267541i	0.250076	−	0.968226i	$-0.419544\pi$
$73$	−3.95924	−	2.28587i	−0.463394	−	0.267541i	−0.713470	+	0.700685i	$0.752878\pi$
$74$		0			0
$75$	−0.365767	−	0.176586i	−0.0422351	−	0.0203904i
$76$		0			0
$77$	3.30191	+	2.03094i	0.376288	+	0.231448i
$78$		0			0
$79$	9.38377			1.05576			0.527879	−	0.849320i	$-0.322988\pi$
$79$	9.38377			1.05576			0.527879	+	0.849320i	$0.322988\pi$
$80$		0			0
$81$	−6.57340	−	6.14739i	−0.730378	−	0.683043i
$82$		0			0
$83$	1.70847	−	2.95917i	0.187529	−	0.324811i	−0.756896	−	0.653535i	$-0.773285\pi$
$83$	1.70847	−	2.95917i	0.187529	−	0.324811i	0.944426	+	0.328724i	$0.106619\pi$
$84$		0			0
$85$	−2.88452	−	4.99614i	−0.312871	−	0.541908i
$86$		0			0
$87$	13.3887	−	0.990137i	1.43541	−	0.106154i
$88$		0			0
$89$	4.61937	+	8.00099i	0.489653	+	0.848103i	0.999929	−	0.0119070i	$-0.00379021\pi$
$89$	4.61937	+	8.00099i	0.489653	+	0.848103i	−0.510276	+	0.860010i	$0.670457\pi$
$90$		0			0
$91$	−7.61803	−	4.68571i	−0.798586	−	0.491196i
$92$		0			0
$93$	−0.688796	−	1.01241i	−0.0714248	−	0.104982i
$94$		0			0
$95$		−	17.3379i		−	1.77883i
$96$		0			0
$97$	6.38394	+	3.68577i	0.648191	+	0.374233i	0.787763	−	0.615979i	$-0.211239\pi$
$97$	6.38394	+	3.68577i	0.648191	+	0.374233i	−0.139572	+	0.990212i	$0.544573\pi$
$98$		0			0
$99$	0.646596	+	4.34773i	0.0649853	+	0.436964i
$100$		0			0
$101$	3.96357	+	6.86510i	0.394390	+	0.683103i	0.993023	−	0.117920i	$-0.0376226\pi$
$101$	3.96357	+	6.86510i	0.394390	+	0.683103i	−0.598633	+	0.801023i	$0.704289\pi$
$102$		0			0
$103$	−3.26825	−	1.88693i	−0.322031	−	0.185924i	0.330267	−	0.943888i	$-0.392861\pi$
$103$	−3.26825	−	1.88693i	−0.322031	−	0.185924i	−0.652297	+	0.757963i	$0.726195\pi$
$104$		0			0
$105$	8.42445	−	5.39483i	0.822142	−	0.526482i
$106$		0			0
$107$	−6.88241	+	3.97356i	−0.665347	+	0.384138i	−0.794311	−	0.607511i	$-0.792168\pi$
$107$	−6.88241	+	3.97356i	−0.665347	+	0.384138i	0.128964	+	0.991649i	$0.458835\pi$
$108$		0			0
$109$	0.505142	−	0.874932i	0.0483838	−	0.0838033i	−0.840819	−	0.541316i	$-0.817926\pi$
$109$	0.505142	−	0.874932i	0.0483838	−	0.0838033i	0.889203	+	0.457513i	$0.151260\pi$
$110$		0			0
$111$	−4.42163	−	2.13469i	−0.419682	−	0.202616i
$112$		0			0
$113$	−10.5557	+	6.09431i	−0.992992	+	0.573304i	−0.906167	−	0.422919i	$-0.861005\pi$
$113$	−10.5557	+	6.09431i	−0.992992	+	0.573304i	−0.0868250	+	0.996224i	$0.527672\pi$
$114$		0			0
$115$	−7.58037	+	4.37653i	−0.706873	+	0.408113i
$116$		0			0
$117$	−1.49180	−	10.0309i	−0.137917	−	0.927358i
$118$		0			0
$119$	−6.98925	−	0.194605i	−0.640703	−	0.0178394i
$120$		0			0
$121$	−4.42662	+	7.66713i	−0.402420	+	0.697012i
$122$		0			0
$123$	−11.6726	−	5.63533i	−1.05248	−	0.508121i
$124$		0			0
$125$	11.4269			1.02206
$126$		0			0
$127$	6.79350			0.602826			0.301413	−	0.953494i	$-0.402542\pi$
$127$	6.79350			0.602826			0.301413	+	0.953494i	$0.402542\pi$
$128$		0			0
$129$	−0.324751	−	4.39130i	−0.0285927	−	0.386632i
$130$		0			0
$131$	6.86790	−	11.8956i	0.600051	−	1.03932i	−0.392761	−	0.919640i	$-0.628480\pi$
$131$	6.86790	−	11.8956i	0.600051	−	1.03932i	0.992813	−	0.119679i	$-0.0381865\pi$
$132$		0			0
$133$	−17.8984	−	11.0090i	−1.55199	−	0.954600i
$134$		0			0
$135$	10.8294	+	3.37535i	0.932045	+	0.290504i
$136$		0			0
$137$	17.4028	−	10.0475i	1.48682	−	0.858416i	0.486933	−	0.873439i	$-0.338116\pi$
$137$	17.4028	−	10.0475i	1.48682	−	0.858416i	0.999887	+	0.0150235i	$0.00478229\pi$
$138$		0			0
$139$	8.51403	−	4.91558i	0.722151	−	0.416934i	−0.0933930	−	0.995629i	$-0.529771\pi$
$139$	8.51403	−	4.91558i	0.722151	−	0.416934i	0.815544	+	0.578695i	$0.196438\pi$
$140$		0			0
$141$	17.9732	−	12.2281i	1.51362	−	1.02980i
$142$		0			0
$143$	−2.47646	+	4.28936i	−0.207092	+	0.358694i
$144$		0			0
$145$	−14.6536	+	8.46029i	−1.21692	+	0.702589i
$146$		0			0
$147$	−0.220003	−	12.1224i	−0.0181456	−	0.999835i
$148$		0			0
$149$	17.3512	+	10.0177i	1.42146	+	0.820682i	0.996424	−	0.0844939i	$-0.0269274\pi$
$149$	17.3512	+	10.0177i	1.42146	+	0.820682i	0.425038	+	0.905175i	$0.360261\pi$
$150$		0			0
$151$	11.1168	+	19.2549i	0.904675	+	1.56694i	0.821353	+	0.570420i	$0.193220\pi$
$151$	11.1168	+	19.2549i	0.904675	+	1.56694i	0.0833218	+	0.996523i	$0.473447\pi$
$152$		0			0
$153$	−4.93094	−	6.20815i	−0.398643	−	0.501899i
$154$		0			0
$155$	1.33655	+	0.771657i	0.107354	+	0.0619810i
$156$		0			0
$157$			8.02869i			0.640759i	0.947289	+	0.320380i	$0.103811\pi$
$157$			8.02869i			0.640759i	−0.947289	+	0.320380i	$0.896189\pi$
$158$		0			0
$159$	4.82034	−	0.356480i	0.382278	−	0.0282707i
$160$		0			0
$161$	−0.295263	+	10.6044i	−0.0232700	+	0.835744i
$162$		0			0
$163$	−6.22604	−	10.7838i	−0.487661	−	0.844654i	0.512238	−	0.858844i	$-0.328817\pi$
$163$	−6.22604	−	10.7838i	−0.487661	−	0.844654i	−0.999899	+	0.0141893i	$0.995483\pi$
$164$		0			0
$165$	−3.11628	−	4.58039i	−0.242602	−	0.356583i
$166$		0			0
$167$	−9.85984	−	17.0777i	−0.762978	−	1.32152i	−0.941309	−	0.337546i	$-0.890403\pi$
$167$	−9.85984	−	17.0777i	−0.762978	−	1.32152i	0.178332	−	0.983970i	$-0.442930\pi$
$168$		0			0
$169$	−0.786412	+	1.36211i	−0.0604933	+	0.104777i
$170$		0			0
$171$	−3.50495	−	23.5674i	−0.268030	−	1.80225i
$172$		0			0
$173$	1.82747			0.138940			0.0694699	−	0.997584i	$-0.477869\pi$
$173$	1.82747			0.138940			0.0694699	+	0.997584i	$0.477869\pi$
$174$		0			0
$175$	0.325046	−	0.528460i	0.0245712	−	0.0399479i
$176$		0			0
$177$	−19.2367	+	13.0877i	−1.44592	+	0.983732i
$178$		0			0
$179$	12.1182	+	6.99645i	0.905757	+	0.522939i	0.879064	−	0.476705i	$-0.158169\pi$
$179$	12.1182	+	6.99645i	0.905757	+	0.522939i	0.0266934	+	0.999644i	$0.491502\pi$
$180$		0			0
$181$			16.3594i			1.21599i	0.793942	+	0.607994i	$0.208025\pi$
$181$			16.3594i			1.21599i	−0.793942	+	0.607994i	$0.791975\pi$
$182$		0			0
$183$	7.59456	+	11.1627i	0.561406	+	0.825170i
$184$		0			0
$185$	6.18830			0.454973
$186$		0			0
$187$			3.87206i			0.283153i
$188$		0			0
$189$	10.3608	−	9.03627i	0.753636	−	0.657292i
$190$		0			0
$191$		−	13.6631i		−	0.988624i	−0.869285	−	0.494312i	$-0.835420\pi$
$191$		−	13.6631i		−	0.988624i	0.869285	−	0.494312i	$-0.164580\pi$
$192$		0			0
$193$	−4.37769			−0.315113			−0.157557	−	0.987510i	$-0.550362\pi$
$193$	−4.37769			−0.315113			−0.157557	+	0.987510i	$0.550362\pi$
$194$		0			0
$195$	7.18976	+	10.5677i	0.514869	+	0.756768i
$196$		0			0
$197$		−	1.00603i		−	0.0716767i	−0.999358	−	0.0358384i	$-0.988590\pi$
$197$		−	1.00603i		−	0.0716767i	0.999358	−	0.0358384i	$-0.0114101\pi$
$198$		0			0
$199$	−5.67639	−	3.27726i	−0.402388	−	0.232319i	0.285126	−	0.958490i	$-0.407965\pi$
$199$	−5.67639	−	3.27726i	−0.402388	−	0.232319i	−0.687514	+	0.726171i	$0.741298\pi$
$200$		0			0
$201$	−8.36397	+	5.69045i	−0.589949	+	0.401373i
$202$		0			0
$203$	−0.570774	+	20.4994i	−0.0400605	+	1.43878i
$204$		0			0
$205$	16.3364			1.14098
$206$		0			0
$207$	−9.41928	+	7.48144i	−0.654685	+	0.519996i
$208$		0			0
$209$	−5.81840	+	10.0778i	−0.402467	+	0.697094i
$210$		0			0
$211$	−9.11202	−	15.7825i	−0.627297	−	1.08651i	−0.988092	−	0.153866i	$-0.950828\pi$
$211$	−9.11202	−	15.7825i	−0.627297	−	1.08651i	0.360794	−	0.932645i	$-0.382506\pi$
$212$		0			0
$213$	−11.3850	−	16.7339i	−0.780086	−	1.14659i
$214$		0			0
$215$	2.77486	+	4.80620i	0.189244	+	0.327780i
$216$		0			0
$217$	1.64527	−	0.889784i	0.111688	−	0.0604024i
$218$		0			0
$219$	7.89692	−	0.584004i	0.533625	−	0.0394633i
$220$		0			0
$221$		−	8.93345i		−	0.600929i
$222$		0			0
$223$	−8.71705	−	5.03279i	−0.583737	−	0.337021i	0.178880	−	0.983871i	$-0.442753\pi$
$223$	−8.71705	−	5.03279i	−0.583737	−	0.337021i	−0.762617	+	0.646850i	$0.776086\pi$
$224$		0			0
$225$	0.695841	−	0.103486i	0.0463894	−	0.00689904i
$226$		0			0
$227$	9.94372	+	17.2230i	0.659988	+	1.14313i	0.980618	+	0.195928i	$0.0627720\pi$
$227$	9.94372	+	17.2230i	0.659988	+	1.14313i	−0.320630	+	0.947204i	$0.603895\pi$
$228$		0			0
$229$	−15.3854	−	8.88275i	−1.01669	−	0.586988i	−0.103549	−	0.994624i	$-0.533020\pi$
$229$	−15.3854	−	8.88275i	−1.01669	−	0.586988i	−0.913145	+	0.407636i	$0.866353\pi$
$230$		0			0
$231$	−6.70722	+	0.308634i	−0.441303	+	0.0203066i
$232$		0			0
$233$	−13.9077	+	8.02962i	−0.911124	+	0.526038i	−0.880793	−	0.473502i	$-0.842990\pi$
$233$	−13.9077	+	8.02962i	−0.911124	+	0.526038i	−0.0303317	+	0.999540i	$0.509656\pi$
$234$		0			0
$235$	−13.6992	+	23.7277i	−0.893636	+	1.54782i
$236$		0			0
$237$	−13.4380	+	9.14256i	−0.872890	+	0.593873i
$238$		0			0
$239$	−7.11117	+	4.10564i	−0.459983	+	0.265572i	−0.712037	−	0.702142i	$-0.752227\pi$
$239$	−7.11117	+	4.10564i	−0.459983	+	0.265572i	0.252054	+	0.967713i	$0.418894\pi$
$240$		0			0
$241$	−24.6614	+	14.2382i	−1.58858	+	0.917166i	−0.595037	+	0.803698i	$0.702863\pi$
$241$	−24.6614	+	14.2382i	−1.58858	+	0.917166i	−0.993542	+	0.113468i	$0.963804\pi$
$242$		0			0
$243$	15.4028	+	2.39890i	0.988088	+	0.153890i
$244$		0			0
$245$	6.89230	+	13.6384i	0.440333	+	0.871325i
$246$		0			0
$247$	13.4240	−	23.2510i	0.854147	−	1.47943i
$248$		0			0
$249$	0.436489	+	5.90221i	0.0276613	+	0.374038i
$250$		0			0
$251$	0.656343			0.0414280			0.0207140	−	0.999785i	$-0.493406\pi$
$251$	0.656343			0.0414280			0.0207140	+	0.999785i	$0.493406\pi$
$252$		0			0
$253$	5.87486			0.369349
$254$		0			0
$255$	8.99848	+	4.34432i	0.563507	+	0.272052i
$256$		0			0
$257$	−3.82042	+	6.61716i	−0.238311	+	0.412767i	−0.960230	−	0.279211i	$-0.909927\pi$
$257$	−3.82042	+	6.61716i	−0.238311	+	0.412767i	0.721918	+	0.691978i	$0.243261\pi$
$258$		0			0
$259$	3.92937	−	6.38837i	0.244159	−	0.396954i
$260$		0			0
$261$	−18.2085	+	14.4624i	−1.12708	+	0.895201i
$262$		0			0
$263$	−5.73888	+	3.31334i	−0.353874	+	0.204310i	−0.666390	−	0.745603i	$-0.732162\pi$
$263$	−5.73888	+	3.31334i	−0.353874	+	0.204310i	0.312516	+	0.949913i	$0.398828\pi$
$264$		0			0
$265$	−5.27577	+	3.04597i	−0.324088	+	0.187112i
$266$		0			0
$267$	−14.4105	−	6.95714i	−0.881907	−	0.425770i
$268$		0			0
$269$	4.38347	−	7.59239i	0.267265	−	0.462916i	−0.700890	−	0.713270i	$-0.747214\pi$
$269$	4.38347	−	7.59239i	0.267265	−	0.462916i	0.968154	+	0.250354i	$0.0805469\pi$
$270$		0			0
$271$	14.2608	−	8.23346i	0.866280	−	0.500147i	0.000169619	−	1.00000i	$-0.499946\pi$
$271$	14.2608	−	8.23346i	0.866280	−	0.500147i	0.866110	+	0.499853i	$0.166613\pi$
$272$		0			0
$273$	15.4746	−	0.712068i	0.936566	−	0.0430963i
$274$		0			0
$275$	−0.297551	−	0.171791i	−0.0179430	−	0.0103594i
$276$		0			0
$277$	8.88732	+	15.3933i	0.533987	+	0.924893i	0.999212	+	0.0397001i	$0.0126402\pi$
$277$	8.88732	+	15.3933i	0.533987	+	0.924893i	−0.465225	+	0.885193i	$0.654026\pi$
$278$		0			0
$279$	1.97277	+	0.778725i	0.118107	+	0.0466210i
$280$		0			0
$281$	−14.0252	−	8.09748i	−0.836676	−	0.483055i	0.0194568	−	0.999811i	$-0.493806\pi$
$281$	−14.0252	−	8.09748i	−0.836676	−	0.483055i	−0.856133	+	0.516755i	$0.827140\pi$
$282$		0			0
$283$			28.3729i			1.68660i	0.537447	+	0.843298i	$0.319389\pi$
$283$			28.3729i			1.68660i	−0.537447	+	0.843298i	$0.680611\pi$
$284$		0			0
$285$	16.8922	+	24.8286i	1.00061	+	1.47072i
$286$		0			0
$287$	10.3731	−	16.8646i	0.612304	−	0.995484i
$288$		0			0
$289$	5.00804	+	8.67417i	0.294590	+	0.510246i
$290$		0			0
$291$	−12.7331	+	0.941657i	−0.746429	+	0.0552009i
$292$		0			0
$293$	−4.38260	−	7.59088i	−0.256034	−	0.443464i	0.709142	−	0.705066i	$-0.249083\pi$
$293$	−4.38260	−	7.59088i	−0.256034	−	0.443464i	−0.965176	+	0.261602i	$0.915749\pi$
$294$		0			0
$295$	14.6621	−	25.3956i	0.853663	−	1.47859i
$296$		0			0
$297$	−5.16193	−	5.59617i	−0.299525	−	0.324723i
$298$		0			0
$299$	−13.5542			−0.783861
$300$		0			0
$301$	6.72353	+	0.187206i	0.387538	+	0.0107904i
$302$		0			0
$303$	−12.3646	−	5.96944i	−0.710330	−	0.342936i
$304$		0			0
$305$	−14.7366	−	8.50818i	−0.843816	−	0.487177i
$306$		0			0
$307$		−	12.8497i		−	0.733372i	−0.930345	−	0.366686i	$-0.880492\pi$
$307$		−	12.8497i		−	0.733372i	0.930345	−	0.366686i	$-0.119508\pi$
$308$		0			0
$309$	6.51871	−	0.482080i	0.370836	−	0.0274246i
$310$		0			0
$311$	−6.59343			−0.373879			−0.186939	−	0.982371i	$-0.559857\pi$
$311$	−6.59343			−0.373879			−0.186939	+	0.982371i	$0.559857\pi$
$312$		0			0
$313$			3.41458i			0.193004i	0.995333	+	0.0965018i	$0.0307654\pi$
$313$			3.41458i			0.193004i	−0.995333	+	0.0965018i	$0.969235\pi$
$314$		0			0
$315$	−6.80802	+	15.9335i	−0.383588	+	0.897753i
$316$		0			0
$317$		−	32.1010i		−	1.80297i	−0.432810	−	0.901485i	$-0.642478\pi$
$317$		−	32.1010i		−	1.80297i	0.432810	−	0.901485i	$-0.357522\pi$
$318$		0			0
$319$	11.3567			0.635854
$320$		0			0
$321$	5.98449	−	12.3958i	0.334022	−	0.691866i
$322$		0			0
$323$		−	20.9890i		−	1.16786i
$324$		0			0
$325$	0.686498	+	0.396350i	0.0380801	+	0.0219855i
$326$		0			0
$327$	0.129056	+	1.74510i	0.00713681	+	0.0965042i
$328$		0			0
$329$	15.7963	+	29.2084i	0.870877	+	1.61031i
$330$		0			0
$331$	−28.8833			−1.58757			−0.793784	−	0.608199i	$-0.791892\pi$
$331$	−28.8833			−1.58757			−0.793784	+	0.608199i	$0.791892\pi$
$332$		0			0
$333$	8.41178	−	1.25100i	0.460963	−	0.0685544i
$334$		0			0
$335$	6.37501	−	11.0418i	0.348304	−	0.603280i
$336$		0			0
$337$	4.82568	+	8.35833i	0.262872	+	0.455307i	0.967004	−	0.254762i	$-0.0819971\pi$
$337$	4.82568	+	8.35833i	0.262872	+	0.455307i	−0.704132	+	0.710069i	$0.748664\pi$
$338$		0			0
$339$	9.17851	−	19.0116i	0.498508	−	1.03257i
$340$		0			0
$341$	−0.517919	−	0.897063i	−0.0280469	−	0.0485787i
$342$		0			0
$343$	18.4557	+	1.54481i	0.996515	+	0.0834117i
$344$		0			0
$345$	6.59139	−	13.6529i	0.354869	−	0.735047i
$346$		0			0
$347$		−	12.3273i		−	0.661766i	−0.943672	−	0.330883i	$-0.892653\pi$
$347$		−	12.3273i		−	0.661766i	0.943672	−	0.330883i	$-0.107347\pi$
$348$		0			0
$349$	−10.2211	−	5.90115i	−0.547123	−	0.315881i	0.200838	−	0.979624i	$-0.435634\pi$
$349$	−10.2211	−	5.90115i	−0.547123	−	0.315881i	−0.747961	+	0.663743i	$0.768967\pi$
$350$		0			0
$351$	11.9094	+	12.9112i	0.635676	+	0.689151i
$352$		0			0
$353$	6.59855	+	11.4290i	0.351205	+	0.608305i	0.986461	−	0.163997i	$-0.0524386\pi$
$353$	6.59855	+	11.4290i	0.351205	+	0.608305i	−0.635256	+	0.772302i	$0.719105\pi$
$354$		0			0
$355$	22.0916	+	12.7546i	1.17250	+	0.676943i
$356$		0			0
$357$	10.1985	−	6.53091i	0.539763	−	0.345652i
$358$		0			0
$359$	−5.22483	+	3.01656i	−0.275756	+	0.159208i	−0.631501	−	0.775375i	$-0.717561\pi$
$359$	−5.22483	+	3.01656i	−0.275756	+	0.159208i	0.355745	+	0.934583i	$0.384227\pi$
$360$		0			0
$361$	22.0394	−	38.1733i	1.15997	−	2.00912i
$362$		0			0
$363$	−1.13093	−	15.2925i	−0.0593585	−	0.802648i
$364$		0			0
$365$	−8.64304	+	4.99006i	−0.452397	+	0.261192i
$366$		0			0
$367$	14.8755	−	8.58836i	0.776494	−	0.448309i	−0.0586924	−	0.998276i	$-0.518693\pi$
$367$	14.8755	−	8.58836i	0.776494	−	0.448309i	0.835186	+	0.549967i	$0.185360\pi$
$368$		0			0
$369$	22.2061	−	3.30250i	1.15601	−	0.171921i
$370$		0			0
$371$	−0.205496	+	7.38043i	−0.0106688	+	0.383173i
$372$		0			0
$373$	−2.35902	+	4.08595i	−0.122146	+	0.211562i	−0.920614	−	0.390475i	$-0.872311\pi$
$373$	−2.35902	+	4.08595i	−0.122146	+	0.211562i	0.798468	+	0.602037i	$0.205644\pi$
$374$		0			0
$375$	−16.3639	+	11.1332i	−0.845026	+	0.574916i
$376$		0			0
$377$	−26.2017			−1.34946
$378$		0			0
$379$	9.34015			0.479771			0.239886	−	0.970801i	$-0.422890\pi$
$379$	9.34015			0.479771			0.239886	+	0.970801i	$0.422890\pi$
$380$		0			0
$381$	−9.72859	+	6.61887i	−0.498411	+	0.339095i
$382$		0			0
$383$	2.85036	−	4.93696i	0.145646	−	0.252267i	−0.783968	−	0.620802i	$-0.786807\pi$
$383$	2.85036	−	4.93696i	0.145646	−	0.252267i	0.929614	+	0.368535i	$0.120140\pi$
$384$		0			0
$385$	7.44361	−	4.02560i	0.379362	−	0.205164i
$386$		0			0
$387$	4.74347	+	5.97212i	0.241124	+	0.303580i
$388$		0			0
$389$	6.63671	−	3.83171i	0.336495	−	0.194275i	−0.322226	−	0.946663i	$-0.604431\pi$
$389$	6.63671	−	3.83171i	0.336495	−	0.194275i	0.658721	+	0.752387i	$0.271098\pi$
$390$		0			0
$391$	−9.17668	+	5.29816i	−0.464085	+	0.267939i
$392$		0			0
$393$	1.75464	+	23.7263i	0.0885100	+	1.19683i
$394$		0			0
$395$	10.2424	−	17.7404i	0.515351	−	0.892615i
$396$		0			0
$397$	−1.12810	+	0.651310i	−0.0566178	+	0.0326883i	−0.528042	−	0.849218i	$-0.677074\pi$
$397$	−1.12810	+	0.651310i	−0.0566178	+	0.0326883i	0.471424	+	0.881907i	$0.343740\pi$
$398$		0			0
$399$	36.3573	−	1.67299i	1.82014	−	0.0837542i
$400$		0			0
$401$	−8.18778	−	4.72722i	−0.408878	−	0.236066i	0.281429	−	0.959582i	$-0.409191\pi$
$401$	−8.18778	−	4.72722i	−0.408878	−	0.236066i	−0.690308	+	0.723516i	$0.742525\pi$
$402$		0			0
$403$	1.19492	+	2.06966i	0.0595233	+	0.103097i
$404$		0			0
$405$	−18.7967	+	5.71736i	−0.934018	+	0.284098i
$406$		0			0
$407$	−3.59700	−	2.07673i	−0.178296	−	0.102940i
$408$		0			0
$409$		−	19.0736i		−	0.943126i	−0.881832	−	0.471563i	$-0.843690\pi$
$409$		−	19.0736i		−	0.943126i	0.881832	−	0.471563i	$-0.156310\pi$
$410$		0			0
$411$	−15.1323	+	31.3439i	−0.746422	+	1.54608i
$412$		0			0
$413$	−16.9067	−	31.2615i	−0.831922	−	1.53828i
$414$		0			0
$415$	−3.72961	−	6.45987i	−0.183079	−	0.317102i
$416$		0			0
$417$	−7.40324	+	15.3345i	−0.362538	+	0.750934i
$418$		0			0
$419$	−4.20003	−	7.27466i	−0.205185	−	0.355390i	0.745007	−	0.667057i	$-0.232446\pi$
$419$	−4.20003	−	7.27466i	−0.205185	−	0.355390i	−0.950192	+	0.311666i	$0.899113\pi$
$420$		0			0
$421$	19.7178	−	34.1522i	0.960985	−	1.66448i	0.240951	−	0.970537i	$-0.422541\pi$
$421$	19.7178	−	34.1522i	0.960985	−	1.66448i	0.720035	−	0.693938i	$-0.244126\pi$
$422$		0			0
$423$	−13.8247	+	35.0225i	−0.672178	+	1.70285i
$424$		0			0
$425$	0.619711			0.0300604
$426$		0			0
$427$	−18.1405	+	9.81063i	−0.877881	+	0.474770i
$428$		0			0
$429$	−0.632697	−	8.55535i	−0.0305469	−	0.413056i
$430$		0			0
$431$	10.3340	+	5.96634i	0.497772	+	0.287389i	0.727793	−	0.685797i	$-0.240546\pi$
$431$	10.3340	+	5.96634i	0.497772	+	0.287389i	−0.230021	+	0.973186i	$0.573880\pi$
$432$		0			0
$433$		−	12.2121i		−	0.586875i	−0.955978	−	0.293437i	$-0.905201\pi$
$433$		−	12.2121i		−	0.586875i	0.955978	−	0.293437i	$-0.0947992\pi$
$434$		0			0
$435$	12.7419	−	26.3925i	0.610925	−	1.26542i
$436$		0			0
$437$	−31.8454			−1.52337
$438$		0			0
$439$		−	16.7015i		−	0.797120i	−0.917142	−	0.398560i	$-0.869510\pi$
$439$		−	16.7015i		−	0.797120i	0.917142	−	0.398560i	$-0.130490\pi$
$440$		0			0
$441$	12.1258	+	17.1454i	0.577419	+	0.816448i
$442$		0			0
$443$			30.2997i			1.43958i	0.694190	+	0.719791i	$0.255763\pi$
$443$			30.2997i			1.43958i	−0.694190	+	0.719791i	$0.744237\pi$
$444$		0			0
$445$	20.1682			0.956065
$446$		0			0
$447$	−34.6078	+	2.55936i	−1.63689	+	0.121054i
$448$		0			0
$449$		−	30.1253i		−	1.42170i	−0.703343	−	0.710851i	$-0.748310\pi$
$449$		−	30.1253i		−	1.42170i	0.703343	−	0.710851i	$-0.251690\pi$
$450$		0			0
$451$	−9.49566	−	5.48232i	−0.447133	−	0.258152i
$452$		0			0
$453$	−34.6798	−	16.7428i	−1.62940	−	0.786646i
$454$		0			0
$455$	−17.1736	+	9.28770i	−0.805110	+	0.435414i
$456$		0			0
$457$	25.2318			1.18029			0.590146	−	0.807297i	$-0.299070\pi$
$457$	25.2318			1.18029			0.590146	+	0.807297i	$0.299070\pi$
$458$		0			0
$459$	13.1099	+	4.08615i	0.611918	+	0.190725i
$460$		0			0
$461$	−12.3174	+	21.3344i	−0.573680	+	0.993643i	0.422503	+	0.906361i	$0.361151\pi$
$461$	−12.3174	+	21.3344i	−0.573680	+	0.993643i	−0.996184	+	0.0872820i	$0.972182\pi$
$462$		0			0
$463$	−6.33215	−	10.9676i	−0.294280	−	0.509708i	0.680537	−	0.732713i	$-0.261746\pi$
$463$	−6.33215	−	10.9676i	−0.294280	−	0.509708i	−0.974817	+	0.223006i	$0.928413\pi$
$464$		0			0
$465$	−2.66582	+	0.197146i	−0.123624	+	0.00914244i
$466$		0			0
$467$	10.4723	+	18.1385i	0.484599	+	0.839350i	0.999843	−	0.0176932i	$-0.00563223\pi$
$467$	10.4723	+	18.1385i	0.484599	+	0.839350i	−0.515245	+	0.857043i	$0.672299\pi$
$468$		0			0
$469$	−7.35090	−	13.5923i	−0.339433	−	0.627635i
$470$		0			0
$471$	−7.82231	−	11.4974i	−0.360433	−	0.529774i
$472$		0			0
$473$		−	3.72485i		−	0.171269i
$474$		0			0
$475$	1.61291	+	0.931217i	0.0740056	+	0.0427271i
$476$		0			0
$477$	−6.55562	+	5.20692i	−0.300161	+	0.238409i
$478$		0			0
$479$	15.8852	+	27.5141i	0.725816	+	1.25715i	0.958637	+	0.284630i	$0.0918707\pi$
$479$	15.8852	+	27.5141i	0.725816	+	1.25715i	−0.232822	+	0.972519i	$0.574796\pi$
$480$		0			0
$481$	8.29884	+	4.79134i	0.378394	+	0.218466i
$482$		0			0
$483$	−9.90898	−	15.4736i	−0.450874	−	0.704075i
$484$		0			0
$485$	13.9362	−	8.04605i	0.632809	−	0.365352i
$486$		0			0
$487$	−17.7821	+	30.7995i	−0.805784	+	1.39566i	0.109977	+	0.993934i	$0.464922\pi$
$487$	−17.7821	+	30.7995i	−0.805784	+	1.39566i	−0.915761	+	0.401724i	$0.868411\pi$
$488$		0			0
$489$	19.4226	+	9.37691i	0.878320	+	0.424038i
$490$		0			0
$491$	2.75734	−	1.59195i	0.124437	−	0.0718437i	−0.436490	−	0.899709i	$-0.643778\pi$
$491$	2.75734	−	1.59195i	0.124437	−	0.0718437i	0.560926	+	0.827866i	$0.310445\pi$
$492$		0			0
$493$	−17.7395	+	10.2419i	−0.798947	+	0.461272i
$494$		0			0
$495$	8.92531	+	3.52315i	0.401163	+	0.158354i
$496$		0			0
$497$	27.1944	−	14.7071i	1.21983	−	0.659703i
$498$		0			0
$499$	−16.0214	+	27.7498i	−0.717215	+	1.24225i	0.244884	+	0.969552i	$0.421250\pi$
$499$	−16.0214	+	27.7498i	−0.717215	+	1.24225i	−0.962099	+	0.272700i	$0.912083\pi$
$500$		0			0
$501$	30.7585	+	14.8497i	1.37419	+	0.663435i
$502$		0			0
$503$	11.6608			0.519930			0.259965	−	0.965618i	$-0.416289\pi$
$503$	11.6608			0.519930			0.259965	+	0.965618i	$0.416289\pi$
$504$		0			0
$505$	17.3050			0.770061
$506$		0			0
$507$	−0.200916	−	2.71679i	−0.00892299	−	0.120657i
$508$		0			0
$509$	−13.4427	+	23.2834i	−0.595836	+	1.03202i	0.397592	+	0.917562i	$0.369846\pi$
$509$	−13.4427	+	23.2834i	−0.595836	+	1.03202i	−0.993428	+	0.114457i	$0.963487\pi$
$510$		0			0
$511$	−0.336655	+	12.0910i	−0.0148927	+	0.534875i
$512$		0			0
$513$	27.9809	+	30.3347i	1.23539	+	1.33931i
$514$		0			0
$515$	−7.13461	+	4.11917i	−0.314388	+	0.181512i
$516$		0			0
$517$	15.9255	−	9.19459i	0.700402	−	0.404378i
$518$		0			0
$519$	−2.61701	+	1.78049i	−0.114874	+	0.0781549i
$520$		0			0
$521$	17.0385	−	29.5116i	0.746471	−	1.29293i	−0.203033	−	0.979172i	$-0.565080\pi$
$521$	17.0385	−	29.5116i	0.746471	−	1.29293i	0.949504	−	0.313754i	$-0.101587\pi$
$522$		0			0
$523$	4.71003	−	2.71933i	0.205955	−	0.118908i	−0.393475	−	0.919335i	$-0.628727\pi$
$523$	4.71003	−	2.71933i	0.205955	−	0.118908i	0.599430	+	0.800427i	$0.295394\pi$
$524$		0			0
$525$	0.0493959	+	1.07347i	0.00215581	+	0.0468500i
$526$		0			0
$527$	1.61801	+	0.934157i	0.0704815	+	0.0406925i
$528$		0			0
$529$	−3.46140	−	5.99532i	−0.150496	−	0.260666i
$530$		0			0
$531$	14.7964	−	37.4843i	0.642111	−	1.62668i
$532$		0			0
$533$	21.9080	+	12.6486i	0.948940	+	0.547871i
$534$		0			0
$535$			17.3486i			0.750045i
$536$		0			0
$537$	−24.1704	+	1.78748i	−1.04303	+	0.0771356i
$538$		0			0
$539$	0.570698	−	10.2404i	0.0245817	−	0.441085i
$540$		0			0
$541$	11.8329	+	20.4952i	0.508737	+	0.881158i	0.999949	+	0.0101183i	$0.00322080\pi$
$541$	11.8329	+	20.4952i	0.508737	+	0.881158i	−0.491212	+	0.871040i	$0.663446\pi$
$542$		0			0
$543$	−15.9389	−	23.4274i	−0.684004	−	1.00537i
$544$		0			0
$545$	−1.10273	−	1.90998i	−0.0472356	−	0.0818145i
$546$		0			0
$547$	−12.0824	+	20.9273i	−0.516606	+	0.894788i	0.483208	+	0.875505i	$0.339471\pi$
$547$	−12.0824	+	20.9273i	−0.516606	+	0.894788i	−0.999814	+	0.0192822i	$0.993862\pi$
$548$		0			0
$549$	−21.7515	−	8.58611i	−0.928331	−	0.366446i
$550$		0			0
$551$	−61.5605			−2.62257
$552$		0			0
$553$	−11.8103	−	21.8381i	−0.502226	−	0.928650i
$554$		0			0
$555$	−8.86192	+	6.02923i	−0.376167	+	0.255927i
$556$		0			0
$557$	−7.36315	−	4.25111i	−0.311987	−	0.180126i	0.335829	−	0.941923i	$-0.390984\pi$
$557$	−7.36315	−	4.25111i	−0.311987	−	0.180126i	−0.647815	+	0.761798i	$0.724317\pi$
$558$		0			0
$559$			8.59381i			0.363480i
$560$		0			0
$561$	−3.77253	−	5.54496i	−0.159276	−	0.234108i
$562$		0			0
$563$	0.947553			0.0399346			0.0199673	−	0.999801i	$-0.493644\pi$
$563$	0.947553			0.0399346			0.0199673	+	0.999801i	$0.493644\pi$
$564$		0			0
$565$			26.6078i			1.11940i
$566$		0			0
$567$	−6.03311	+	23.0348i	−0.253367	+	0.967370i
$568$		0			0
$569$		−	18.2280i		−	0.764158i	−0.924130	−	0.382079i	$-0.875208\pi$
$569$		−	18.2280i		−	0.764158i	0.924130	−	0.382079i	$-0.124792\pi$
$570$		0			0
$571$	−12.2424			−0.512330			−0.256165	−	0.966633i	$-0.582459\pi$
$571$	−12.2424			−0.512330			−0.256165	+	0.966633i	$0.582459\pi$
$572$		0			0
$573$	13.3118	+	19.5661i	0.556110	+	0.817385i
$574$		0			0
$575$		−	0.940253i		−	0.0392112i
$576$		0			0
$577$	−10.2500	−	5.91784i	−0.426713	−	0.246363i	0.271232	−	0.962514i	$-0.412569\pi$
$577$	−10.2500	−	5.91784i	−0.426713	−	0.246363i	−0.697945	+	0.716151i	$0.745902\pi$
$578$		0			0
$579$	6.26905	−	4.26516i	0.260533	−	0.177254i
$580$		0			0
$581$	−9.03690	−	0.251618i	−0.374914	−	0.0104389i
$582$		0			0
$583$	4.08878			0.169340
$584$		0			0
$585$	−20.5921	−	8.12845i	−0.851378	−	0.336070i
$586$		0			0
$587$	3.57681	−	6.19521i	0.147631	−	0.255704i	−0.782721	−	0.622373i	$-0.786169\pi$
$587$	3.57681	−	6.19521i	0.147631	−	0.255704i	0.930351	+	0.366669i	$0.119502\pi$
$588$		0			0
$589$	2.80745	+	4.86264i	0.115679	+	0.200362i
$590$		0			0
$591$	0.980171	+	1.44068i	0.0403188	+	0.0592617i
$592$		0			0
$593$	13.4811	+	23.3500i	0.553603	+	0.958869i	0.998011	+	0.0630442i	$0.0200809\pi$
$593$	13.4811	+	23.3500i	0.553603	+	0.958869i	−0.444408	+	0.895825i	$0.646586\pi$
$594$		0			0
$595$	−7.99668	+	13.0010i	−0.327832	+	0.532990i
$596$		0			0
$597$	11.3219	−	0.837289i	0.463373	−	0.0342680i
$598$		0			0
$599$			35.2441i			1.44004i	0.693955	+	0.720018i	$0.255867\pi$
$599$			35.2441i			1.44004i	−0.693955	+	0.720018i	$0.744133\pi$
$600$		0			0
$601$	3.39266	+	1.95875i	0.138389	+	0.0798991i	0.567596	−	0.823307i	$-0.307874\pi$
$601$	3.39266	+	1.95875i	0.138389	+	0.0798991i	−0.429207	+	0.903206i	$0.641207\pi$
$602$		0			0
$603$	6.43340	−	16.2979i	0.261988	−	0.663704i
$604$		0			0
$605$	9.66332	+	16.7374i	0.392870	+	0.680470i
$606$		0			0
$607$	−12.5377	−	7.23862i	−0.508888	−	0.293807i	0.223488	−	0.974707i	$-0.428256\pi$
$607$	−12.5377	−	7.23862i	−0.508888	−	0.293807i	−0.732376	+	0.680900i	$0.761589\pi$
$608$		0			0
$609$	−19.1551	−	29.9122i	−0.776204	−	1.21210i
$610$		0			0
$611$	−36.7426	+	21.2134i	−1.48645	+	0.858201i
$612$		0			0
$613$	−6.51761	+	11.2888i	−0.263244	+	0.455952i	−0.967102	−	0.254389i	$-0.918126\pi$
$613$	−6.51761	+	11.2888i	−0.263244	+	0.455952i	0.703858	+	0.710341i	$0.251459\pi$
$614$		0			0
$615$	−23.3944	+	15.9165i	−0.943355	+	0.641814i
$616$		0			0
$617$	−3.14491	+	1.81571i	−0.126609	+	0.0730979i	−0.561967	−	0.827160i	$-0.689955\pi$
$617$	−3.14491	+	1.81571i	−0.126609	+	0.0730979i	0.435358	+	0.900258i	$0.356622\pi$
$618$		0			0
$619$	−14.2737	+	8.24091i	−0.573708	+	0.331230i	−0.758629	−	0.651523i	$-0.774130\pi$
$619$	−14.2737	+	8.24091i	−0.573708	+	0.331230i	0.184921	+	0.982753i	$0.440797\pi$
$620$		0			0
$621$	6.19969	−	19.8909i	0.248785	−	0.798195i
$622$		0			0
$623$	12.8062	−	20.8203i	0.513068	−	0.834147i
$624$		0			0
$625$	11.8863	−	20.5876i	0.475450	−	0.823504i
$626$		0			0
$627$	−1.48651	−	20.1006i	−0.0593655	−	0.802742i
$628$		0			0
$629$	7.49147			0.298704
$630$		0			0
$631$	−34.8383			−1.38689			−0.693446	−	0.720508i	$-0.743909\pi$
$631$	−34.8383			−1.38689			−0.693446	+	0.720508i	$0.743909\pi$
$632$		0			0
$633$	28.4256	+	13.7234i	1.12982	+	0.545457i
$634$		0			0
$635$	7.41512	−	12.8434i	0.294260	−	0.509673i
$636$		0			0
$637$	−1.31669	+	23.6262i	−0.0521692	+	0.936105i
$638$		0			0
$639$	32.6076	+	12.8714i	1.28994	+	0.509185i
$640$		0			0
$641$	7.25538	−	4.18889i	0.286570	−	0.165451i	−0.349824	−	0.936815i	$-0.613759\pi$
$641$	7.25538	−	4.18889i	0.286570	−	0.165451i	0.636394	+	0.771364i	$0.280425\pi$
$642$		0			0
$643$	−18.0021	+	10.3935i	−0.709934	+	0.409881i	−0.811037	−	0.584995i	$-0.801096\pi$
$643$	−18.0021	+	10.3935i	−0.709934	+	0.409881i	0.101103	+	0.994876i	$0.467763\pi$
$644$		0			0
$645$	−8.65637	−	4.17915i	−0.340844	−	0.164554i
$646$		0			0
$647$	4.74770	−	8.22325i	0.186651	−	0.323289i	−0.757480	−	0.652858i	$-0.773570\pi$
$647$	4.74770	−	8.22325i	0.186651	−	0.323289i	0.944132	+	0.329568i	$0.106903\pi$
$648$		0			0
$649$	−17.0450	+	9.84091i	−0.669073	+	0.386290i
$650$		0			0
$651$	−1.48919	+	2.87719i	−0.0583659	+	0.112766i
$652$		0			0
$653$	−6.64747	−	3.83792i	−0.260136	−	0.150189i	0.364261	−	0.931297i	$-0.381322\pi$
$653$	−6.64747	−	3.83792i	−0.260136	−	0.150189i	−0.624396	+	0.781108i	$0.714655\pi$
$654$		0			0
$655$	−14.9927	−	25.9680i	−0.585811	−	1.01465i
$656$		0			0
$657$	−10.7397	+	8.53025i	−0.418997	+	0.332797i
$658$		0			0
$659$	38.0493	+	21.9678i	1.48219	+	0.855743i	0.999796	−	0.0202102i	$-0.00643354\pi$
$659$	38.0493	+	21.9678i	1.48219	+	0.855743i	0.482395	+	0.875954i	$0.339767\pi$
$660$		0			0
$661$		−	25.5938i		−	0.995484i	−0.867325	−	0.497742i	$-0.834163\pi$
$661$		−	25.5938i		−	0.995484i	0.867325	−	0.497742i	$-0.165837\pi$
$662$		0			0
$663$	8.70382	+	12.7931i	0.338028	+	0.496843i
$664$		0			0
$665$	−40.3490	+	21.8213i	−1.56467	+	0.846193i
$666$		0			0
$667$	15.5395	+	26.9151i	0.601691	+	1.04216i
$668$		0			0
$669$	17.3866	−	1.28580i	0.672206	−	0.0497119i
$670$		0			0
$671$	5.71051	+	9.89089i	0.220452	+	0.381834i
$672$		0			0
$673$	−7.64671	+	13.2445i	−0.294759	+	0.510538i	−0.974929	−	0.222517i	$-0.928573\pi$
$673$	−7.64671	+	13.2445i	−0.294759	+	0.510538i	0.680170	+	0.733055i	$0.261906\pi$
$674$		0			0
$675$	−0.895649	+	0.826150i	−0.0344736	+	0.0317985i
$676$		0			0
$677$	45.2918			1.74070			0.870352	−	0.492430i	$-0.163891\pi$
$677$	45.2918			1.74070			0.870352	+	0.492430i	$0.163891\pi$
$678$		0			0
$679$	0.542827	−	19.4957i	0.0208318	−	0.748177i
$680$		0			0
$681$	−31.0202	−	14.9760i	−1.18870	−	0.573882i
$682$		0			0
$683$	24.0891	+	13.9079i	0.921744	+	0.532169i	0.884191	−	0.467126i	$-0.154710\pi$
$683$	24.0891	+	13.9079i	0.921744	+	0.532169i	0.0375529	+	0.999295i	$0.488044\pi$
$684$		0			0
$685$		−	43.8674i		−	1.67609i
$686$		0			0
$687$	30.6869	−	2.26940i	1.17078	−	0.0865831i
$688$		0			0
$689$	−9.43345			−0.359386
$690$		0			0
$691$		−	16.2946i		−	0.619875i	−0.950757	−	0.309938i	$-0.899692\pi$
$691$		−	16.2946i		−	0.619875i	0.950757	−	0.309938i	$-0.100308\pi$
$692$		0			0
$693$	9.30433	−	6.97679i	0.353442	−	0.265026i
$694$		0			0
$695$		−	21.4614i		−	0.814079i
$696$		0			0
$697$	19.7766			0.749093
$698$		0			0
$699$	12.0932	−	25.0490i	0.457408	−	0.947439i
$700$		0			0
$701$			0.393403i			0.0148586i	0.999972	+	0.00742932i	$0.00236485\pi$
$701$			0.393403i			0.0148586i	−0.999972	+	0.00742932i	$0.997635\pi$
$702$		0			0
$703$	19.4980	+	11.2572i	0.735379	+	0.424572i
$704$		0			0
$705$	−3.49992	−	47.3261i	−0.131815	−	1.78240i
$706$		0			0
$707$	10.9881	−	17.8644i	0.413250	−	0.671862i
$708$		0			0
$709$	−32.6366			−1.22569			−0.612846	−	0.790202i	$-0.709975\pi$
$709$	−32.6366			−1.22569			−0.612846	+	0.790202i	$0.709975\pi$
$710$		0			0
$711$	10.3362	−	26.1851i	0.387638	−	0.982018i
$712$		0			0
$713$	1.41734	−	2.45491i	0.0530799	−	0.0919372i
$714$		0			0
$715$	5.40612	+	9.36368i	0.202178	+	0.350182i
$716$		0			0
$717$	6.18341	−	12.8078i	0.230924	−	0.478317i
$718$		0			0
$719$	0.106604	+	0.184643i	0.00397565	+	0.00688602i	0.868006	−	0.496553i	$-0.165401\pi$
$719$	0.106604	+	0.184643i	0.00397565	+	0.00688602i	−0.864031	+	0.503439i	$0.832068\pi$
$720$		0			0
$721$	−0.277900	+	9.98081i	−0.0103495	+	0.371705i
$722$		0			0
$723$	21.4439	−	44.4172i	0.797508	−	1.65190i
$724$		0			0
$725$		−	1.81761i		−	0.0675042i
$726$		0			0
$727$	31.8208	+	18.3717i	1.18017	+	0.681370i	0.956053	−	0.293193i	$-0.0947180\pi$
$727$	31.8208	+	18.3717i	1.18017	+	0.681370i	0.224114	+	0.974563i	$0.428051\pi$
$728$		0			0
$729$	−24.3947	+	11.5715i	−0.903507	+	0.428574i
$730$		0			0
$731$	3.35920	+	5.81831i	0.124245	+	0.215198i
$732$		0			0
$733$	9.41829	+	5.43765i	0.347873	+	0.200844i	0.663748	−	0.747956i	$-0.268965\pi$
$733$	9.41829	+	5.43765i	0.347873	+	0.200844i	−0.315875	+	0.948801i	$0.602298\pi$
$734$		0			0
$735$	−23.1579	−	12.8156i	−0.854192	−	0.472712i
$736$		0			0
$737$	−7.41104	+	4.27877i	−0.272989	+	0.157610i
$738$		0			0
$739$	6.91282	−	11.9734i	0.254292	−	0.440447i	−0.710411	−	0.703787i	$-0.751491\pi$
$739$	6.91282	−	11.9734i	0.254292	−	0.440447i	0.964703	+	0.263340i	$0.0848242\pi$
$740$		0			0
$741$	3.42961	+	46.3753i	0.125990	+	1.70364i
$742$		0			0
$743$	−15.8751	+	9.16552i	−0.582403	+	0.336250i	−0.762088	−	0.647474i	$-0.775825\pi$
$743$	−15.8751	+	9.16552i	−0.582403	+	0.336250i	0.179685	+	0.983724i	$0.442492\pi$
$744$		0			0
$745$	37.8776	−	21.8687i	1.38773	−	0.801206i
$746$		0			0
$747$	−6.37557	−	8.02696i	−0.233270	−	0.293691i
$748$		0			0
$749$	17.9095	+	11.0158i	0.654398	+	0.402508i
$750$		0			0
$751$	9.97084	−	17.2700i	0.363841	−	0.630191i	−0.624748	−	0.780826i	$-0.714798\pi$
$751$	9.97084	−	17.2700i	0.363841	−	0.630191i	0.988589	+	0.150635i	$0.0481318\pi$
$752$		0			0
$753$	−0.939912	+	0.639471i	−0.0342523	+	0.0233036i
$754$		0			0
$755$	48.5362			1.76641
$756$		0			0
$757$	−46.9292			−1.70567			−0.852836	−	0.522178i	$-0.825119\pi$
$757$	−46.9292			−1.70567			−0.852836	+	0.522178i	$0.825119\pi$
$758$		0			0
$759$	−8.41306	+	5.72385i	−0.305375	+	0.207762i
$760$		0			0
$761$	26.7769	−	46.3789i	0.970661	−	1.68123i	0.277093	−	0.960843i	$-0.410629\pi$
$761$	26.7769	−	46.3789i	0.970661	−	1.68123i	0.693568	−	0.720391i	$-0.256038\pi$
$762$		0			0
$763$	−2.67193	−	0.0743955i	−0.0967302	−	0.00269330i
$764$		0			0
$765$	−17.1189	+	2.54592i	−0.618934	+	0.0920479i
$766$		0			0
$767$	39.3254	−	22.7045i	1.41996	−	0.819813i
$768$		0			0
$769$	−34.7306	+	20.0517i	−1.25242	+	0.723085i	−0.971589	−	0.236673i	$-0.923943\pi$
$769$	−34.7306	+	20.0517i	−1.25242	+	0.723085i	−0.280830	+	0.959758i	$0.590610\pi$
$770$		0			0
$771$	−0.976058	−	13.1983i	−0.0351519	−	0.475325i
$772$		0			0
$773$	−7.82375	+	13.5511i	−0.281401	+	0.487400i	−0.971730	−	0.236095i	$-0.924132\pi$
$773$	−7.82375	+	13.5511i	−0.281401	+	0.487400i	0.690329	+	0.723495i	$0.257466\pi$
$774$		0			0
$775$	−0.143572	+	0.0828913i	−0.00515726	+	0.00297755i
$776$		0			0
$777$	0.597130	+	12.9768i	0.0214219	+	0.465540i
$778$		0			0
$779$	51.4724	+	29.7176i	1.84419	+	1.06474i
$780$		0			0
$781$	−8.56060	−	14.8274i	−0.306322	−	0.530566i
$782$		0			0
$783$	11.9847	−	38.4512i	0.428297	−	1.37413i
$784$		0			0
$785$	15.1785	+	8.76333i	0.541745	+	0.312777i
$786$		0			0
$787$		−	46.1788i		−	1.64610i	−0.567972	−	0.823048i	$-0.692272\pi$
$787$		−	46.1788i		−	1.64610i	0.567972	−	0.823048i	$-0.307728\pi$
$788$		0			0
$789$	4.99015	−	10.3362i	0.177654	−	0.367979i
$790$		0			0
$791$	27.4680	+	16.8951i	0.976651	+	0.600720i
$792$		0			0
$793$	−13.1750	−	22.8198i	−0.467859	−	0.810356i
$794$		0			0
$795$	4.58747	−	9.50212i	0.162701	−	0.337005i
$796$		0			0
$797$	−16.9388	−	29.3388i	−0.600002	−	1.03923i	−0.992820	−	0.119618i	$-0.961833\pi$
$797$	−16.9388	−	29.3388i	−0.600002	−	1.03923i	0.392818	−	0.919616i	$-0.371500\pi$
$798$		0			0
$799$	−16.5840	+	28.7244i	−0.586701	+	1.01620i
$800$		0			0
$801$	27.4147	−	4.07712i	0.968652	−	0.144058i
$802$		0			0
$803$	6.69844			0.236383
$804$		0			0
$805$	19.7257	+	12.1329i	0.695240	+	0.427629i
$806$		0			0
$807$	1.11991	+	15.1434i	0.0394226	+	0.533073i
$808$		0			0
$809$	−33.7873	−	19.5071i	−1.18790	−	0.685834i	−0.230070	−	0.973174i	$-0.573896\pi$
$809$	−33.7873	−	19.5071i	−1.18790	−	0.685834i	−0.957829	+	0.287340i	$0.907229\pi$
$810$		0			0
$811$			7.73397i			0.271577i	0.990738	+	0.135788i	$0.0433567\pi$
$811$			7.73397i			0.271577i	−0.990738	+	0.135788i	$0.956643\pi$
$812$		0			0
$813$	−12.4002	+	25.6849i	−0.434895	+	0.900807i
$814$		0			0
$815$	−27.1829			−0.952177
$816$		0			0
$817$			20.1910i			0.706394i
$818$		0			0
$819$	−21.4666	+	16.0965i	−0.750102	+	0.562459i
$820$		0			0
$821$		−	0.512269i		−	0.0178783i	−0.999960	−	0.00893915i	$-0.997155\pi$
$821$		−	0.512269i		−	0.0178783i	0.999960	−	0.00893915i	$-0.00284546\pi$
$822$		0			0
$823$	−48.3506			−1.68540			−0.842698	−	0.538387i	$-0.819034\pi$
$823$	−48.3506			−1.68540			−0.842698	+	0.538387i	$0.819034\pi$
$824$		0			0
$825$	0.593482	−	0.0438900i	0.0206624	−	0.00152805i
$826$		0			0
$827$			17.3086i			0.601879i	0.953643	+	0.300940i	$0.0973003\pi$
$827$			17.3086i			0.601879i	−0.953643	+	0.300940i	$0.902700\pi$
$828$		0			0
$829$	33.0205	+	19.0644i	1.14685	+	0.662134i	0.948118	−	0.317919i	$-0.102984\pi$
$829$	33.0205	+	19.0644i	1.14685	+	0.662134i	0.198733	+	0.980054i	$0.436317\pi$
$830$		0			0
$831$	−27.7246	−	13.3850i	−0.961757	−	0.464320i
$832$		0			0
$833$	8.34372	+	16.5104i	0.289093	+	0.572053i
$834$		0			0
$835$	−43.0481			−1.48974
$836$		0			0
$837$	−3.58380	+	0.806892i	−0.123874	+	0.0278903i
$838$		0			0
$839$	−15.2026	+	26.3317i	−0.524852	+	0.909071i	0.474729	+	0.880132i	$0.342546\pi$
$839$	−15.2026	+	26.3317i	−0.524852	+	0.909071i	−0.999581	+	0.0289389i	$0.990787\pi$
$840$		0			0
$841$	15.5394	+	26.9151i	0.535842	+	0.928106i
$842$		0			0
$843$	27.9741	−	2.06878i	0.963479	−	0.0712526i
$844$		0			0
$845$	1.71674	+	2.97348i	0.0590577	+	0.102291i
$846$		0			0
$847$	23.4144	+	0.651937i	0.804528	+	0.0224008i
$848$		0			0
$849$	−27.6436	−	40.6313i	−0.948726	−	1.39446i
$850$		0			0
$851$		−	11.3664i		−	0.389635i
$852$		0			0
$853$	27.7143	+	16.0008i	0.948919	+	0.547858i	0.892745	−	0.450563i	$-0.148777\pi$
$853$	27.7143	+	16.0008i	0.948919	+	0.547858i	0.0561738	+	0.998421i	$0.482110\pi$
$854$		0			0
$855$	−48.3807	−	19.0976i	−1.65459	−	0.653126i
$856$		0			0
$857$	−22.5774	−	39.1053i	−0.771230	−	1.33581i	−0.936889	−	0.349627i	$-0.886308\pi$
$857$	−22.5774	−	39.1053i	−0.771230	−	1.33581i	0.165659	−	0.986183i	$-0.447025\pi$
$858$		0			0
$859$	−15.7911	−	9.11701i	−0.538786	−	0.311068i	0.205801	−	0.978594i	$-0.434020\pi$
$859$	−15.7911	−	9.11701i	−0.538786	−	0.311068i	−0.744587	+	0.667526i	$0.767353\pi$
$860$		0			0
$861$	1.57635	+	34.2572i	0.0537220	+	1.16748i
$862$		0			0
$863$	−6.61966	+	3.82186i	−0.225336	+	0.130098i	−0.608419	−	0.793616i	$-0.708196\pi$
$863$	−6.61966	+	3.82186i	−0.225336	+	0.130098i	0.383083	+	0.923714i	$0.374862\pi$
$864$		0			0
$865$	1.99468	−	3.45489i	0.0678213	−	0.117470i
$866$		0			0
$867$	−15.6229	−	7.54249i	−0.530583	−	0.256157i
$868$		0			0
$869$	−11.9069	+	6.87448i	−0.403915	+	0.233201i
$870$		0			0
$871$	17.0984	−	9.87179i	0.579358	−	0.334493i
$872$		0			0
$873$	17.3169	−	13.7543i	0.586089	−	0.465513i
$874$		0			0
$875$	−14.3818	−	26.5930i	−0.486194	−	0.899006i
$876$		0			0
$877$	−8.01581	+	13.8838i	−0.270675	+	0.468822i	−0.969035	−	0.246924i	$-0.920580\pi$
$877$	−8.01581	+	13.8838i	−0.270675	+	0.468822i	0.698360	+	0.715747i	$0.253913\pi$
$878$		0			0
$879$	13.6718	+	6.60053i	0.461139	+	0.222630i
$880$		0			0
$881$	24.7532			0.833958			0.416979	−	0.908916i	$-0.363089\pi$
$881$	24.7532			0.833958			0.416979	+	0.908916i	$0.363089\pi$
$882$		0			0
$883$	−11.6958			−0.393595			−0.196798	−	0.980444i	$-0.563054\pi$
$883$	−11.6958			−0.393595			−0.196798	+	0.980444i	$0.563054\pi$
$884$		0			0
$885$	3.74595	+	50.6528i	0.125919	+	1.70268i
$886$		0			0
$887$	27.5429	−	47.7058i	0.924801	−	1.60180i	0.132921	−	0.991127i	$-0.457564\pi$
$887$	27.5429	−	47.7058i	0.924801	−	1.60180i	0.791880	−	0.610676i	$-0.209102\pi$
$888$		0			0
$889$	−8.55024	−	15.8100i	−0.286766	−	0.530249i
$890$		0			0
$891$	12.8444	+	2.98472i	0.430305	+	0.0999920i
$892$		0			0
$893$	−86.3261	+	49.8404i	−2.88879	+	1.66785i
$894$		0			0
$895$	26.4541	−	15.2733i	0.884262	−	0.510529i
$896$		0			0
$897$	19.4102	−	13.2058i	0.648089	−	0.440929i
$898$		0			0
$899$	2.73987	−	4.74560i	0.0913799	−	0.158275i
$900$		0			0
$901$	−6.38677	+	3.68741i	−0.212774	+	0.122845i
$902$		0			0
$903$	−9.81078	+	6.28261i	−0.326482	+	0.209072i
$904$		0			0
$905$	30.9281	+	17.8563i	1.02808	+	0.593565i
$906$		0			0
$907$	12.9383	+	22.4098i	0.429610	+	0.744107i	0.996839	−	0.0794540i	$-0.0253177\pi$
$907$	12.9383	+	22.4098i	0.429610	+	0.744107i	−0.567228	+	0.823560i	$0.691984\pi$
$908$		0			0
$909$	23.5227	−	3.49830i	0.780199	−	0.116031i
$910$		0			0
$911$	−3.86306	−	2.23034i	−0.127989	−	0.0738944i	0.434639	−	0.900605i	$-0.356876\pi$
$911$	−3.86306	−	2.23034i	−0.127989	−	0.0738944i	−0.562627	+	0.826711i	$0.690209\pi$
$912$		0			0
$913$			5.00646i			0.165690i
$914$		0			0
$915$	29.3929	−	2.17371i	0.971701	−	0.0718606i
$916$		0			0
$917$	−36.3274	−	1.01148i	−1.19964	−	0.0334020i
$918$		0			0
$919$	−21.2352	−	36.7805i	−0.700485	−	1.21328i	−0.968296	−	0.249804i	$-0.919634\pi$
$919$	−21.2352	−	36.7805i	−0.700485	−	1.21328i	0.267811	−	0.963471i	$-0.413700\pi$
$920$		0			0
$921$	12.5194	+	18.4014i	0.412529	+	0.606346i
$922$		0			0
$923$	19.7507	+	34.2091i	0.650101	+	1.12601i
$924$		0			0
$925$	−0.332373	+	0.575688i	−0.0109284	+	0.0189285i
$926$		0			0
$927$	−8.86538	+	7.04150i	−0.291177	+	0.231273i
$928$		0			0
$929$	−15.4502			−0.506903			−0.253452	−	0.967348i	$-0.581566\pi$
$929$	−15.4502			−0.506903			−0.253452	+	0.967348i	$0.581566\pi$
$930$		0			0
$931$	−3.09354	+	55.5093i	−0.101387	+	1.81925i
$932$		0			0
$933$	9.44207	−	6.42394i	0.309120	−	0.210310i
$934$		0			0
$935$	7.32027	+	4.22636i	0.239398	+	0.138217i
$936$		0			0
$937$			46.1410i			1.50736i	0.657241	+	0.753680i	$0.271723\pi$
$937$			46.1410i			1.50736i	−0.657241	+	0.753680i	$0.728277\pi$
$938$		0			0
$939$	−3.32681	−	4.88983i	−0.108566	−	0.159574i
$940$		0			0
$941$	−41.0104			−1.33690			−0.668451	−	0.743756i	$-0.733042\pi$
$941$	−41.0104			−1.33690			−0.668451	+	0.743756i	$0.733042\pi$
$942$		0			0
$943$		−	30.0060i		−	0.977128i
$944$		0			0
$945$	−5.77458	−	29.4505i	−0.187847	−	0.958026i
$946$		0			0
$947$		−	9.82254i		−	0.319190i	−0.987183	−	0.159595i	$-0.948981\pi$
$947$		−	9.82254i		−	0.319190i	0.987183	−	0.159595i	$-0.0510188\pi$
$948$		0			0
$949$	−15.4544			−0.501670
$950$		0			0
$951$	31.2758	+	45.9700i	1.01419	+	1.49068i
$952$		0			0
$953$			17.0826i			0.553359i	0.960962	+	0.276679i	$0.0892340\pi$
$953$			17.0826i			0.553359i	−0.960962	+	0.276679i	$0.910766\pi$
$954$		0			0
$955$	−25.8305	−	14.9132i	−0.835855	−	0.482581i
$956$		0			0
$957$	−16.2633	+	11.0648i	−0.525719	+	0.357674i
$958$		0			0
$959$	−45.2857	−	27.8544i	−1.46235	−	0.899466i
$960$		0			0
$961$	30.5002			0.983877
$962$		0			0
$963$	3.50712	+	23.5820i	0.113015	+	0.759919i
$964$		0			0
$965$	−4.77826	+	8.27619i	−0.153818	+	0.266420i
$966$		0			0
$967$	21.3240	+	36.9343i	0.685735	+	1.18773i	0.973205	+	0.229938i	$0.0738523\pi$
$967$	21.3240	+	36.9343i	0.685735	+	1.18773i	−0.287471	+	0.957789i	$0.592814\pi$
$968$		0			0
$969$	20.4495	+	30.0571i	0.656931	+	0.965574i
$970$		0			0
$971$	11.7562	+	20.3623i	0.377275	+	0.653459i	0.990665	−	0.136321i	$-0.0435280\pi$
$971$	11.7562	+	20.3623i	0.377275	+	0.653459i	−0.613390	+	0.789780i	$0.710195\pi$
$972$		0			0
$973$	−22.1553	−	13.6273i	−0.710267	−	0.436872i
$974$		0			0
$975$	−1.36926	+	0.101261i	−0.0438513	+	0.00324295i
$976$		0			0
$977$			34.8654i			1.11544i	0.830028	+	0.557722i	$0.188325\pi$
$977$			34.8654i			1.11544i	−0.830028	+	0.557722i	$0.811675\pi$
$978$		0			0
$979$	−11.7229	−	6.76824i	−0.374666	−	0.216314i
$980$		0			0
$981$	−1.88505	−	2.37332i	−0.0601851	−	0.0757742i
$982$		0			0
$983$	−13.1804	−	22.8292i	−0.420390	−	0.728137i	0.575587	−	0.817740i	$-0.304773\pi$
$983$	−13.1804	−	22.8292i	−0.420390	−	0.728137i	−0.995978	+	0.0896033i	$0.971440\pi$
$984$		0			0
$985$	−1.90194	−	1.09808i	−0.0606008	−	0.0349879i
$986$		0			0
$987$	−51.0785	−	26.4374i	−1.62585	−	0.841513i
$988$		0			0
$989$	8.82780	−	5.09673i	0.280708	−	0.162067i
$990$		0			0
$991$	0.0805213	−	0.139467i	0.00255784	−	0.00443031i	−0.864744	−	0.502214i	$-0.832519\pi$
$991$	0.0805213	−	0.139467i	0.00255784	−	0.00443031i	0.867301	+	0.497783i	$0.165852\pi$
$992$		0			0
$993$	41.3621	−	28.1408i	1.31259	−	0.893022i
$994$		0			0
$995$	−12.3916	+	7.15427i	−0.392839	+	0.226806i
$996$		0			0
$997$	14.5820	−	8.41890i	0.461816	−	0.266629i	−0.250992	−	0.967989i	$-0.580757\pi$
$997$	14.5820	−	8.41890i	0.461816	−	0.266629i	0.712807	+	0.701360i	$0.247423\pi$
$998$		0			0
$999$	−10.8272	+	9.98704i	−0.342557	+	0.315976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.w.a.101.2	yes	16
3.2	odd	2		756.2.w.a.521.3		16
4.3	odd	2		1008.2.ca.d.353.7		16
7.2	even	3		1764.2.bm.a.1685.5		16
7.3	odd	6		1764.2.x.b.1469.2		16
7.4	even	3		1764.2.x.a.1469.7		16
7.5	odd	6		252.2.bm.a.173.4	yes	16
7.6	odd	2		1764.2.w.b.1109.7		16
9.2	odd	6		2268.2.t.a.1781.3		16
9.4	even	3		756.2.bm.a.17.3		16
9.5	odd	6		252.2.bm.a.185.4	yes	16
9.7	even	3		2268.2.t.b.1781.6		16
12.11	even	2		3024.2.ca.d.2033.3		16
21.2	odd	6		5292.2.bm.a.4625.6		16
21.5	even	6		756.2.bm.a.89.3		16
21.11	odd	6		5292.2.x.a.4409.3		16
21.17	even	6		5292.2.x.b.4409.6		16
21.20	even	2		5292.2.w.b.521.6		16
28.19	even	6		1008.2.df.d.929.5		16
36.23	even	6		1008.2.df.d.689.5		16
36.31	odd	6		3024.2.df.d.17.3		16
63.4	even	3		5292.2.x.b.881.6		16
63.5	even	6	inner	252.2.w.a.5.2	✓	16
63.13	odd	6		5292.2.bm.a.2285.6		16
63.23	odd	6		1764.2.w.b.509.7		16
63.31	odd	6		5292.2.x.a.881.3		16
63.32	odd	6		1764.2.x.b.293.2		16
63.40	odd	6		756.2.w.a.341.3		16
63.41	even	6		1764.2.bm.a.1697.5		16
63.47	even	6		2268.2.t.b.2105.6		16
63.58	even	3		5292.2.w.b.1097.6		16
63.59	even	6		1764.2.x.a.293.7		16
63.61	odd	6		2268.2.t.a.2105.3		16
84.47	odd	6		3024.2.df.d.1601.3		16
252.103	even	6		3024.2.ca.d.2609.3		16
252.131	odd	6		1008.2.ca.d.257.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.2	✓	16	63.5	even	6	inner
252.2.w.a.101.2	yes	16	1.1	even	1	trivial
252.2.bm.a.173.4	yes	16	7.5	odd	6
252.2.bm.a.185.4	yes	16	9.5	odd	6
756.2.w.a.341.3		16	63.40	odd	6
756.2.w.a.521.3		16	3.2	odd	2
756.2.bm.a.17.3		16	9.4	even	3
756.2.bm.a.89.3		16	21.5	even	6
1008.2.ca.d.257.7		16	252.131	odd	6
1008.2.ca.d.353.7		16	4.3	odd	2
1008.2.df.d.689.5		16	36.23	even	6
1008.2.df.d.929.5		16	28.19	even	6
1764.2.w.b.509.7		16	63.23	odd	6
1764.2.w.b.1109.7		16	7.6	odd	2
1764.2.x.a.293.7		16	63.59	even	6
1764.2.x.a.1469.7		16	7.4	even	3
1764.2.x.b.293.2		16	63.32	odd	6
1764.2.x.b.1469.2		16	7.3	odd	6
1764.2.bm.a.1685.5		16	7.2	even	3
1764.2.bm.a.1697.5		16	63.41	even	6
2268.2.t.a.1781.3		16	9.2	odd	6
2268.2.t.a.2105.3		16	63.61	odd	6
2268.2.t.b.1781.6		16	9.7	even	3
2268.2.t.b.2105.6		16	63.47	even	6
3024.2.ca.d.2033.3		16	12.11	even	2
3024.2.ca.d.2609.3		16	252.103	even	6
3024.2.df.d.17.3		16	36.31	odd	6
3024.2.df.d.1601.3		16	84.47	odd	6
5292.2.w.b.521.6		16	21.20	even	2
5292.2.w.b.1097.6		16	63.58	even	3
5292.2.x.a.881.3		16	63.31	odd	6
5292.2.x.a.4409.3		16	21.11	odd	6
5292.2.x.b.881.6		16	63.4	even	3
5292.2.x.b.4409.6		16	21.17	even	6
5292.2.bm.a.2285.6		16	63.13	odd	6
5292.2.bm.a.4625.6		16	21.2	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43204 + 0.974295i) q^{3} +(1.09150 - 1.89054i) q^{5} +(-1.25859 - 2.32722i) q^{7} +(1.10150 - 2.79047i) q^{9} +O(q^{10})\)	\(q+(-1.43204 + 0.974295i) q^{3} +(1.09150 - 1.89054i) q^{5} +(-1.25859 - 2.32722i) q^{7} +(1.10150 - 2.79047i) q^{9} +(-1.26889 + 0.732592i) q^{11} +(2.92752 - 1.69021i) q^{13} +(0.278862 + 3.77077i) q^{15} +(1.32136 - 2.28866i) q^{17} +(6.87816 - 3.97111i) q^{19} +(4.06975 + 2.10644i) q^{21} +(-3.47245 - 2.00482i) q^{23} +(0.117249 + 0.203081i) q^{25} +(1.14134 + 5.06925i) q^{27} +(-6.71261 - 3.87553i) q^{29} +0.706968i q^{31} +(1.10334 - 2.28537i) q^{33} +(-5.77345 - 0.160752i) q^{35} +(1.41738 + 2.45498i) q^{37} +(-2.54558 + 5.27272i) q^{39} +(3.74173 + 6.48086i) q^{41} +(-1.27112 + 2.20164i) q^{43} +(-4.07319 - 5.12822i) q^{45} -12.5508 q^{47} +(-3.83190 + 5.85803i) q^{49} +(0.337586 + 4.56485i) q^{51} +(-2.41675 - 1.39531i) q^{53} +3.19850i q^{55} +(-5.98079 + 12.3881i) q^{57} +13.4330 q^{59} -7.79493i q^{61} +(-7.88036 + 0.948624i) q^{63} -7.37945i q^{65} +5.84058 q^{67} +(6.92598 - 0.512200i) q^{69} +11.6854i q^{71} +(-3.95924 - 2.28587i) q^{73} +(-0.365767 - 0.176586i) q^{75} +(3.30191 + 2.03094i) q^{77} +9.38377 q^{79} +(-6.57340 - 6.14739i) q^{81} +(1.70847 - 2.95917i) q^{83} +(-2.88452 - 4.99614i) q^{85} +(13.3887 - 0.990137i) q^{87} +(4.61937 + 8.00099i) q^{89} +(-7.61803 - 4.68571i) q^{91} +(-0.688796 - 1.01241i) q^{93} -17.3379i q^{95} +(6.38394 + 3.68577i) q^{97} +(0.646596 + 4.34773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7} + 6 q^{9}+O(q^{10}) \) 16 * q - q^7 + 6 * q^9	\( 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Introduction

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