LMFDB - Embedded newform 990.2.z.a.611.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(161,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			611.4
Character	$\chi$	$=$	990.611
Dual form			990.2.z.a.431.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.951057 - 0.309017i) q^{5} +(1.97378 + 2.71668i) q^{7} +(-0.809017 - 0.587785i) q^{8} -1.00000i q^{10} +(3.27288 - 0.536907i) q^{11} +(2.94348 - 0.956394i) q^{13} +(-1.97378 + 2.71668i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-0.169746 + 0.522426i) q^{17} +(-1.98338 + 2.72988i) q^{19} +(0.951057 - 0.309017i) q^{20} +(1.52200 + 2.94678i) q^{22} -3.45661i q^{23} +(0.809017 + 0.587785i) q^{25} +(1.81917 + 2.50387i) q^{26} +(-3.19365 - 1.03768i) q^{28} +(-0.129183 + 0.0938569i) q^{29} +(3.08374 + 9.49078i) q^{31} +1.00000 q^{32} -0.549311 q^{34} +(-1.03768 - 3.19365i) q^{35} +(-3.95771 + 2.87544i) q^{37} +(-3.20917 - 1.04272i) q^{38} +(0.587785 + 0.809017i) q^{40} +(0.817355 + 0.593843i) q^{41} +8.23066i q^{43} +(-2.33223 + 2.35812i) q^{44} +(3.28743 - 1.06815i) q^{46} +(-2.87791 + 3.96110i) q^{47} +(-1.32141 + 4.06689i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-1.81917 + 2.50387i) q^{52} +(-2.18282 + 0.709241i) q^{53} +(-3.27861 - 0.500746i) q^{55} -3.35800i q^{56} +(-0.129183 - 0.0938569i) q^{58} +(5.88811 + 8.10429i) q^{59} +(8.78757 + 2.85525i) q^{61} +(-8.07334 + 5.86563i) q^{62} +(0.309017 + 0.951057i) q^{64} -3.09496 q^{65} +2.23583 q^{67} +(-0.169746 - 0.522426i) q^{68} +(2.71668 - 1.97378i) q^{70} +(-12.4922 - 4.05895i) q^{71} +(-3.15954 - 4.34873i) q^{73} +(-3.95771 - 2.87544i) q^{74} -3.37432i q^{76} +(7.91856 + 7.83163i) q^{77} +(14.6412 - 4.75721i) q^{79} +(-0.587785 + 0.809017i) q^{80} +(-0.312202 + 0.960859i) q^{82} +(2.13488 - 6.57048i) q^{83} +(0.322877 - 0.444402i) q^{85} +(-7.82782 + 2.54341i) q^{86} +(-2.96340 - 1.48938i) q^{88} +1.34287i q^{89} +(8.40801 + 6.10878i) q^{91} +(2.03174 + 2.79645i) q^{92} +(-4.65656 - 1.51301i) q^{94} +(2.72988 - 1.98338i) q^{95} +(-1.71164 - 5.26787i) q^{97} -4.27619 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{2} - 8 q^{4} - 8 q^{8} - 8 q^{16} + 4 q^{17} + 8 q^{25} - 8 q^{29} + 32 q^{31} + 32 q^{32} + 24 q^{34} + 16 q^{37} + 32 q^{41} - 20 q^{46} - 20 q^{47} + 16 q^{49} + 8 q^{50} - 40 q^{53} + 8 q^{55}+ \cdots + 16 q^{98}+O(q^{100}) $ 32 * q - 8 * q^2 - 8 * q^4 - 8 * q^8 - 8 * q^16 + 4 * q^17 + 8 * q^25 - 8 * q^29 + 32 * q^31 + 32 * q^32 + 24 * q^34 + 16 * q^37 + 32 * q^41 - 20 * q^46 - 20 * q^47 + 16 * q^49 + 8 * q^50 - 40 * q^53 + 8 * q^55 - 8 * q^58 + 40 * q^59 - 28 * q^62 - 8 * q^64 + 8 * q^65 + 4 * q^68 - 40 * q^71 + 40 * q^73 + 16 * q^74 - 28 * q^77 + 20 * q^79 - 8 * q^82 - 24 * q^83 - 24 * q^91 + 20 * q^94 + 16 * q^95 + 48 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.951057	−	0.309017i	−0.425325	−	0.138197i
$5$	−0.951057	−	0.309017i	−0.425325	−	0.138197i
$6$		0			0
$7$	1.97378	+	2.71668i	0.746021	+	1.02681i	0.998250	+	0.0591416i	$0.0188364\pi$
$7$	1.97378	+	2.71668i	0.746021	+	1.02681i	−0.252229	+	0.967668i	$0.581164\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$		0			0
$10$		−	1.00000i		−	0.316228i
$11$	3.27288	−	0.536907i	0.986810	−	0.161883i
$11$	3.27288	−	0.536907i	0.986810	−	0.161883i
$12$		0			0
$13$	2.94348	−	0.956394i	0.816374	−	0.265256i	0.129079	−	0.991634i	$-0.458798\pi$
$13$	2.94348	−	0.956394i	0.816374	−	0.265256i	0.687295	+	0.726378i	$0.258798\pi$
$14$	−1.97378	+	2.71668i	−0.527516	+	0.726064i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.169746	+	0.522426i	−0.0411696	+	0.126707i	−0.969529	−	0.244977i	$-0.921220\pi$
$17$	−0.169746	+	0.522426i	−0.0411696	+	0.126707i	0.928359	+	0.371684i	$0.121220\pi$
$18$		0			0
$19$	−1.98338	+	2.72988i	−0.455018	+	0.626278i	−0.973466	−	0.228831i	$-0.926510\pi$
$19$	−1.98338	+	2.72988i	−0.455018	+	0.626278i	0.518448	+	0.855109i	$0.326510\pi$
$20$	0.951057	−	0.309017i	0.212663	−	0.0690983i
$21$		0			0
$22$	1.52200	+	2.94678i	0.324492	+	0.628255i
$23$		−	3.45661i		−	0.720752i	−0.932807	−	0.360376i	$-0.882648\pi$
$23$		−	3.45661i		−	0.720752i	0.932807	−	0.360376i	$-0.117352\pi$
$24$		0			0
$25$	0.809017	+	0.587785i	0.161803	+	0.117557i
$26$	1.81917	+	2.50387i	0.356768	+	0.491050i
$27$		0			0
$28$	−3.19365	−	1.03768i	−0.603543	−	0.196103i
$29$	−0.129183	+	0.0938569i	−0.0239887	+	0.0174288i	−0.599715	−	0.800214i	$-0.704719\pi$
$29$	−0.129183	+	0.0938569i	−0.0239887	+	0.0174288i	0.575726	+	0.817642i	$0.304719\pi$
$30$		0			0
$31$	3.08374	+	9.49078i	0.553857	+	1.70460i	0.698944	+	0.715176i	$0.253654\pi$
$31$	3.08374	+	9.49078i	0.553857	+	1.70460i	−0.145088	+	0.989419i	$0.546346\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.549311			−0.0942061
$35$	−1.03768	−	3.19365i	−0.175400	−	0.539826i
$36$		0			0
$37$	−3.95771	+	2.87544i	−0.650643	+	0.472720i	−0.863490	−	0.504366i	$-0.831726\pi$
$37$	−3.95771	+	2.87544i	−0.650643	+	0.472720i	0.212847	+	0.977085i	$0.431726\pi$
$38$	−3.20917	−	1.04272i	−0.520596	−	0.169152i
$39$		0			0
$40$	0.587785	+	0.809017i	0.0929370	+	0.127917i
$41$	0.817355	+	0.593843i	0.127649	+	0.0927427i	0.649778	−	0.760124i	$-0.274862\pi$
$41$	0.817355	+	0.593843i	0.127649	+	0.0927427i	−0.522129	+	0.852867i	$0.674862\pi$
$42$		0			0
$43$			8.23066i			1.25516i	0.778551	+	0.627582i	$0.215955\pi$
$43$			8.23066i			1.25516i	−0.778551	+	0.627582i	$0.784045\pi$
$44$	−2.33223	+	2.35812i	−0.351597	+	0.355499i
$45$		0			0
$46$	3.28743	−	1.06815i	0.484705	−	0.157490i
$47$	−2.87791	+	3.96110i	−0.419786	+	0.577786i	−0.965571	−	0.260139i	$-0.916232\pi$
$47$	−2.87791	+	3.96110i	−0.419786	+	0.577786i	0.545785	+	0.837925i	$0.316232\pi$
$48$		0			0
$49$	−1.32141	+	4.06689i	−0.188773	+	0.580985i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$		0			0
$52$	−1.81917	+	2.50387i	−0.252273	+	0.347224i
$53$	−2.18282	+	0.709241i	−0.299833	+	0.0974218i	−0.455070	−	0.890455i	$-0.650386\pi$
$53$	−2.18282	+	0.709241i	−0.299833	+	0.0974218i	0.155237	+	0.987877i	$0.450386\pi$
$54$		0			0
$55$	−3.27861	−	0.500746i	−0.442087	−	0.0675206i
$56$		−	3.35800i		−	0.448732i
$57$		0			0
$58$	−0.129183	−	0.0938569i	−0.0169626	−	0.0123240i
$59$	5.88811	+	8.10429i	0.766566	+	1.05509i	0.996639	+	0.0819148i	$0.0261035\pi$
$59$	5.88811	+	8.10429i	0.766566	+	1.05509i	−0.230073	+	0.973173i	$0.573896\pi$
$60$		0			0
$61$	8.78757	+	2.85525i	1.12513	+	0.365578i	0.811724	−	0.584041i	$-0.198529\pi$
$61$	8.78757	+	2.85525i	1.12513	+	0.365578i	0.313408	+	0.949618i	$0.398529\pi$
$62$	−8.07334	+	5.86563i	−1.02532	+	0.744935i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−3.09496			−0.383882
$66$		0			0
$67$	2.23583			0.273151			0.136575	−	0.990630i	$-0.456390\pi$
$67$	2.23583			0.273151			0.136575	+	0.990630i	$0.456390\pi$
$68$	−0.169746	−	0.522426i	−0.0205848	−	0.0633534i
$69$		0			0
$70$	2.71668	−	1.97378i	0.324706	−	0.235912i
$71$	−12.4922	−	4.05895i	−1.48255	−	0.481709i	−0.547674	−	0.836692i	$-0.684487\pi$
$71$	−12.4922	−	4.05895i	−1.48255	−	0.481709i	−0.934873	+	0.354983i	$0.884487\pi$
$72$		0			0
$73$	−3.15954	−	4.34873i	−0.369796	−	0.508980i	0.583050	−	0.812437i	$-0.301859\pi$
$73$	−3.15954	−	4.34873i	−0.369796	−	0.508980i	−0.952845	+	0.303456i	$0.901859\pi$
$74$	−3.95771	−	2.87544i	−0.460074	−	0.334263i
$75$		0			0
$76$		−	3.37432i		−	0.387061i
$77$	7.91856	+	7.83163i	0.902404	+	0.892497i
$78$		0			0
$79$	14.6412	−	4.75721i	1.64726	−	0.535228i	0.669119	−	0.743155i	$-0.266672\pi$
$79$	14.6412	−	4.75721i	1.64726	−	0.535228i	0.978144	+	0.207927i	$0.0666716\pi$
$80$	−0.587785	+	0.809017i	−0.0657164	+	0.0904508i
$81$		0			0
$82$	−0.312202	+	0.960859i	−0.0344769	+	0.106109i
$83$	2.13488	−	6.57048i	0.234333	−	0.721203i	−0.762876	−	0.646545i	$-0.776213\pi$
$83$	2.13488	−	6.57048i	0.234333	−	0.721203i	0.997209	−	0.0746585i	$-0.0237867\pi$
$84$		0			0
$85$	0.322877	−	0.444402i	0.0350209	−	0.0482022i
$86$	−7.82782	+	2.54341i	−0.844096	+	0.274263i
$87$		0			0
$88$	−2.96340	−	1.48938i	−0.315899	−	0.158769i
$89$			1.34287i			0.142344i	0.997464	+	0.0711721i	$0.0226740\pi$
$89$			1.34287i			0.142344i	−0.997464	+	0.0711721i	$0.977326\pi$
$90$		0			0
$91$	8.40801	+	6.10878i	0.881399	+	0.640374i
$92$	2.03174	+	2.79645i	0.211824	+	0.291550i
$93$		0			0
$94$	−4.65656	−	1.51301i	−0.480287	−	0.156055i
$95$	2.72988	−	1.98338i	0.280080	−	0.203490i
$96$		0			0
$97$	−1.71164	−	5.26787i	−0.173790	−	0.534871i	0.825786	−	0.563984i	$-0.190732\pi$
$97$	−1.71164	−	5.26787i	−0.173790	−	0.534871i	−0.999576	+	0.0291124i	$0.990732\pi$
$98$	−4.27619			−0.431960
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−5.07506	−	15.6194i	−0.504987	−	1.55419i	−0.800792	−	0.598942i	$-0.795588\pi$
$101$	−5.07506	−	15.6194i	−0.504987	−	1.55419i	0.295805	−	0.955248i	$-0.404412\pi$
$102$		0			0
$103$	1.50443	−	1.09303i	0.148236	−	0.107700i	−0.511195	−	0.859465i	$-0.670797\pi$
$103$	1.50443	−	1.09303i	0.148236	−	0.107700i	0.659431	+	0.751765i	$0.270797\pi$
$104$	−2.94348	−	0.956394i	−0.288632	−	0.0937821i
$105$		0			0
$106$	−1.34906	−	1.85682i	−0.131032	−	0.180350i
$107$	6.29636	+	4.57457i	0.608692	+	0.442241i	0.848954	−	0.528468i	$-0.177233\pi$
$107$	6.29636	+	4.57457i	0.608692	+	0.442241i	−0.240261	+	0.970708i	$0.577233\pi$
$108$		0			0
$109$			1.45551i			0.139413i	0.997568	+	0.0697065i	$0.0222063\pi$
$109$			1.45551i			0.139413i	−0.997568	+	0.0697065i	$0.977794\pi$
$110$	−0.536907	−	3.27288i	−0.0511921	−	0.312057i
$111$		0			0
$112$	3.19365	−	1.03768i	0.301772	−	0.0980516i
$113$	3.77631	−	5.19764i	0.355245	−	0.488953i	−0.593571	−	0.804782i	$-0.702282\pi$
$113$	3.77631	−	5.19764i	0.355245	−	0.488953i	0.948816	+	0.315828i	$0.102282\pi$
$114$		0			0
$115$	−1.06815	+	3.28743i	−0.0996055	+	0.306554i
$116$	0.0493435	−	0.151864i	0.00458143	−	0.0141002i
$117$		0			0
$118$	−5.88811	+	8.10429i	−0.542044	+	0.746060i
$119$	−1.75431	+	0.570009i	−0.160817	+	0.0522527i
$120$		0			0
$121$	10.4235	−	3.51446i	0.947587	−	0.319496i
$122$			9.23980i			0.836532i
$123$		0			0
$124$	−8.07334	−	5.86563i	−0.725008	−	0.526749i
$125$	−0.587785	−	0.809017i	−0.0525731	−	0.0723607i
$126$		0			0
$127$	−16.4469	−	5.34391i	−1.45942	−	0.474195i	−0.531530	−	0.847040i	$-0.678383\pi$
$127$	−16.4469	−	5.34391i	−1.45942	−	0.474195i	−0.927894	+	0.372844i	$0.878383\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$		0			0
$130$	−0.956394	−	2.94348i	−0.0838813	−	0.258160i
$131$	2.63421			0.230152			0.115076	−	0.993357i	$-0.463289\pi$
$131$	2.63421			0.230152			0.115076	+	0.993357i	$0.463289\pi$
$132$		0			0
$133$	−11.3310			−0.982521
$134$	0.690911	+	2.12641i	0.0596856	+	0.183693i
$135$		0			0
$136$	0.444402	−	0.322877i	0.0381072	−	0.0276865i
$137$	−10.5401	−	3.42468i	−0.900501	−	0.292591i	−0.178057	−	0.984020i	$-0.556981\pi$
$137$	−10.5401	−	3.42468i	−0.900501	−	0.292591i	−0.722444	+	0.691430i	$0.756981\pi$
$138$		0			0
$139$	−10.9908	−	15.1276i	−0.932229	−	1.28310i	−0.958984	−	0.283460i	$-0.908518\pi$
$139$	−10.9908	−	15.1276i	−0.932229	−	1.28310i	0.0267554	−	0.999642i	$-0.491482\pi$
$140$	2.71668	+	1.97378i	0.229602	+	0.166815i
$141$		0			0
$142$		−	13.1350i		−	1.10227i
$143$	9.12015	−	4.71053i	0.762665	−	0.393915i
$144$		0			0
$145$	0.151864	−	0.0493435i	0.0126116	−	0.00409776i
$146$	3.15954	−	4.34873i	0.261485	−	0.359903i
$147$		0			0
$148$	1.51171	−	4.65256i	0.124262	−	0.382438i
$149$	−5.65044	+	17.3903i	−0.462902	+	1.42467i	0.398700	+	0.917082i	$0.369462\pi$
$149$	−5.65044	+	17.3903i	−0.462902	+	1.42467i	−0.861602	+	0.507585i	$0.830538\pi$
$150$		0			0
$151$	8.54451	−	11.7605i	0.695342	−	0.957056i	−0.304648	−	0.952465i	$-0.598539\pi$
$151$	8.54451	−	11.7605i	0.695342	−	0.957056i	0.999989	−	0.00459093i	$-0.00146134\pi$
$152$	3.20917	−	1.04272i	0.260298	−	0.0845760i
$153$		0			0
$154$	−5.00135	+	9.95111i	−0.403020	+	0.801883i
$155$		−	9.97920i		−	0.801549i
$156$		0			0
$157$	1.33771	+	0.971902i	0.106761	+	0.0775662i	0.639885	−	0.768471i	$-0.278982\pi$
$157$	1.33771	+	0.971902i	0.106761	+	0.0775662i	−0.533124	+	0.846037i	$0.678982\pi$
$158$	9.04876	+	12.4545i	0.719881	+	0.990831i
$159$		0			0
$160$	−0.951057	−	0.309017i	−0.0751876	−	0.0244299i
$161$	9.39050	−	6.82260i	0.740075	−	0.537696i
$162$		0			0
$163$	−1.37434	−	4.22980i	−0.107647	−	0.331303i	0.882696	−	0.469945i	$-0.155726\pi$
$163$	−1.37434	−	4.22980i	−0.107647	−	0.331303i	−0.990343	+	0.138642i	$0.955726\pi$
$164$	−1.01031			−0.0788917
$165$		0			0
$166$	6.90861			0.536212
$167$	−2.07344	−	6.38139i	−0.160447	−	0.493807i	0.838225	−	0.545325i	$-0.183594\pi$
$167$	−2.07344	−	6.38139i	−0.160447	−	0.493807i	−0.998672	+	0.0515186i	$0.983594\pi$
$168$		0			0
$169$	−2.76785	+	2.01096i	−0.212912	+	0.154689i
$170$	0.522426	+	0.169746i	0.0400682	+	0.0130190i
$171$		0			0
$172$	−4.83786	−	6.65874i	−0.368883	−	0.507724i
$173$	12.6840	+	9.21550i	0.964350	+	0.700641i	0.954157	−	0.299307i	$-0.0967554\pi$
$173$	12.6840	+	9.21550i	0.964350	+	0.700641i	0.0101931	+	0.999948i	$0.496755\pi$
$174$		0			0
$175$			3.35800i			0.253841i
$176$	0.500746	−	3.27861i	0.0377452	−	0.247134i
$177$		0			0
$178$	−1.27715	+	0.414971i	−0.0957263	+	0.0311034i
$179$	11.2192	−	15.4419i	0.838561	−	1.15418i	−0.147708	−	0.989031i	$-0.547190\pi$
$179$	11.2192	−	15.4419i	0.838561	−	1.15418i	0.986269	−	0.165149i	$-0.0528105\pi$
$180$		0			0
$181$	1.02360	−	3.15031i	0.0760835	−	0.234161i	−0.905781	−	0.423747i	$-0.860715\pi$
$181$	1.02360	−	3.15031i	0.0760835	−	0.234161i	0.981864	+	0.189586i	$0.0607146\pi$
$182$	−3.21157	+	9.88421i	−0.238058	+	0.732666i
$183$		0			0
$184$	−2.03174	+	2.79645i	−0.149782	+	0.206157i
$185$	4.65256	−	1.51171i	0.342063	−	0.111143i
$186$		0			0
$187$	−0.275065	+	1.80097i	−0.0201148	+	0.131700i
$188$		−	4.89619i		−	0.357092i
$189$		0			0
$190$	2.72988	+	1.98338i	0.198047	+	0.143889i
$191$	−10.6722	−	14.6890i	−0.772212	−	1.06286i	−0.996099	−	0.0882433i	$-0.971875\pi$
$191$	−10.6722	−	14.6890i	−0.772212	−	1.06286i	0.223887	−	0.974615i	$-0.428125\pi$
$192$		0			0
$193$	−24.3515	−	7.91228i	−1.75286	−	0.569538i	−0.756437	−	0.654067i	$-0.773062\pi$
$193$	−24.3515	−	7.91228i	−1.75286	−	0.569538i	−0.996421	+	0.0845285i	$0.973062\pi$
$194$	4.48112	−	3.25572i	0.321726	−	0.233747i
$195$		0			0
$196$	−1.32141	−	4.06689i	−0.0943867	−	0.290492i
$197$	2.09997			0.149617			0.0748084	−	0.997198i	$-0.476165\pi$
$197$	2.09997			0.149617			0.0748084	+	0.997198i	$0.476165\pi$
$198$		0			0
$199$	16.7840			1.18978			0.594892	−	0.803805i	$-0.297195\pi$
$199$	16.7840			1.18978			0.594892	+	0.803805i	$0.297195\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$		0			0
$202$	13.2867	−	9.65333i	0.934847	−	0.679206i
$203$	−0.509959	−	0.165696i	−0.0357921	−	0.0116296i
$204$		0			0
$205$	−0.593843	−	0.817355i	−0.0414758	−	0.0570866i
$206$	1.50443	+	1.09303i	0.104819	+	0.0761552i
$207$		0			0
$208$		−	3.09496i		−	0.214597i
$209$	−5.02566	+	9.99947i	−0.347632	+	0.691677i
$210$		0			0
$211$	18.5494	−	6.02706i	1.27699	−	0.414920i	0.409472	−	0.912323i	$-0.365713\pi$
$211$	18.5494	−	6.02706i	1.27699	−	0.414920i	0.867520	+	0.497403i	$0.165713\pi$
$212$	1.34906	−	1.85682i	0.0926536	−	0.127527i
$213$		0			0
$214$	−2.40500	+	7.40182i	−0.164402	+	0.505978i
$215$	2.54341	−	7.82782i	0.173459	−	0.533853i
$216$		0			0
$217$	−19.6968	+	27.1103i	−1.33711	+	1.84037i
$218$	−1.38428	+	0.449779i	−0.0937550	+	0.0304629i
$219$		0			0
$220$	2.94678	−	1.52200i	0.198672	−	0.102613i
$221$			1.70009i			0.114361i
$222$		0			0
$223$	19.1299	+	13.8987i	1.28104	+	0.930726i	0.999584	−	0.0288491i	$-0.00918422\pi$
$223$	19.1299	+	13.8987i	1.28104	+	0.930726i	0.281451	+	0.959576i	$0.409184\pi$
$224$	1.97378	+	2.71668i	0.131879	+	0.181516i
$225$		0			0
$226$	6.11020	+	1.98532i	0.406444	+	0.132062i
$227$	7.39873	−	5.37549i	0.491071	−	0.356784i	−0.314525	−	0.949249i	$-0.601845\pi$
$227$	7.39873	−	5.37549i	0.491071	−	0.356784i	0.805596	+	0.592465i	$0.201845\pi$
$228$		0			0
$229$	0.407956	+	1.25556i	0.0269585	+	0.0829698i	0.963631	−	0.267238i	$-0.0861110\pi$
$229$	0.407956	+	1.25556i	0.0269585	+	0.0829698i	−0.936672	+	0.350208i	$0.886111\pi$
$230$	−3.45661			−0.227922
$231$		0			0
$232$	0.159679			0.0104834
$233$	8.96716	+	27.5981i	0.587458	+	1.80801i	0.589166	+	0.808012i	$0.299456\pi$
$233$	8.96716	+	27.5981i	0.587458	+	1.80801i	−0.00170824	+	0.999999i	$0.500544\pi$
$234$		0			0
$235$	3.96110	−	2.87791i	0.258394	−	0.187734i
$236$	−9.52716	−	3.09556i	−0.620165	−	0.201504i
$237$		0			0
$238$	−1.08422	−	1.49230i	−0.0702797	−	0.0967317i
$239$	11.8944	+	8.64180i	0.769386	+	0.558991i	0.901775	−	0.432206i	$-0.142265\pi$
$239$	11.8944	+	8.64180i	0.769386	+	0.558991i	−0.132389	+	0.991198i	$0.542265\pi$
$240$		0			0
$241$		−	18.6117i		−	1.19888i	−0.800418	−	0.599442i	$-0.795389\pi$
$241$		−	18.6117i		−	1.19888i	0.800418	−	0.599442i	$-0.204611\pi$
$242$	6.56348	+	8.82727i	0.421916	+	0.567439i
$243$		0			0
$244$	−8.78757	+	2.85525i	−0.562566	+	0.182789i
$245$	2.51348	−	3.45951i	0.160580	−	0.221020i
$246$		0			0
$247$	−3.22718	+	9.93224i	−0.205341	+	0.631973i
$248$	3.08374	−	9.49078i	0.195818	−	0.602665i
$249$		0			0
$250$	0.587785	−	0.809017i	0.0371748	−	0.0511667i
$251$	12.5734	−	4.08536i	0.793629	−	0.257866i	0.115980	−	0.993252i	$-0.462999\pi$
$251$	12.5734	−	4.08536i	0.793629	−	0.257866i	0.677648	+	0.735386i	$0.262999\pi$
$252$		0			0
$253$	−1.85588	−	11.3130i	−0.116678	−	0.711245i
$254$		−	17.2933i		−	1.08508i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	14.2124	+	19.5617i	0.886547	+	1.22023i	0.974564	+	0.224108i	$0.0719469\pi$
$257$	14.2124	+	19.5617i	0.886547	+	1.22023i	−0.0880173	+	0.996119i	$0.528053\pi$
$258$		0			0
$259$	−15.6233	−	5.07632i	−0.970786	−	0.315427i
$260$	2.50387	−	1.81917i	0.155284	−	0.112820i
$261$		0			0
$262$	0.814017	+	2.50529i	0.0502901	+	0.154777i
$263$	−22.7988			−1.40583			−0.702916	−	0.711273i	$-0.748119\pi$
$263$	−22.7988			−1.40583			−0.702916	+	0.711273i	$0.748119\pi$
$264$		0			0
$265$	2.29515			0.140990
$266$	−3.50147	−	10.7764i	−0.214689	−	0.660744i
$267$		0			0
$268$	−1.80883	+	1.31419i	−0.110492	+	0.0802770i
$269$	11.8408	+	3.84730i	0.721945	+	0.234574i	0.646866	−	0.762604i	$-0.276079\pi$
$269$	11.8408	+	3.84730i	0.721945	+	0.234574i	0.0750785	+	0.997178i	$0.476079\pi$
$270$		0			0
$271$	−15.7854	−	21.7267i	−0.958895	−	1.31981i	−0.947461	−	0.319871i	$-0.896361\pi$
$271$	−15.7854	−	21.7267i	−0.958895	−	1.31981i	−0.0114334	−	0.999935i	$-0.503639\pi$
$272$	0.444402	+	0.322877i	0.0269458	+	0.0195773i
$273$		0			0
$274$		−	11.0825i		−	0.669519i
$275$	2.96340	+	1.48938i	0.178700	+	0.0898132i
$276$		0			0
$277$	−26.9192	+	8.74659i	−1.61742	+	0.525532i	−0.971331	−	0.237731i	$-0.923596\pi$
$277$	−26.9192	+	8.74659i	−1.61742	+	0.525532i	−0.646089	+	0.763262i	$0.723596\pi$
$278$	10.9908	−	15.1276i	0.659185	−	0.907290i
$279$		0			0
$280$	−1.03768	+	3.19365i	−0.0620132	+	0.190857i
$281$	1.44479	−	4.44659i	0.0861887	−	0.265261i	−0.898669	−	0.438628i	$-0.855465\pi$
$281$	1.44479	−	4.44659i	0.0861887	−	0.265261i	0.984857	+	0.173367i	$0.0554646\pi$
$282$		0			0
$283$	−8.06170	+	11.0960i	−0.479218	+	0.659587i	−0.978354	−	0.206936i	$-0.933651\pi$
$283$	−8.06170	+	11.0960i	−0.479218	+	0.659587i	0.499136	+	0.866524i	$0.333651\pi$
$284$	12.4922	−	4.05895i	0.741274	−	0.240854i
$285$		0			0
$286$	7.29826	+	7.21814i	0.431555	+	0.426818i
$287$			3.39261i			0.200260i
$288$		0			0
$289$	13.5092	+	9.81499i	0.794657	+	0.577352i
$290$	0.0938569	+	0.129183i	0.00551147	+	0.00758589i
$291$		0			0
$292$	5.11224	+	1.66107i	0.299171	+	0.0972066i
$293$	−3.47554	+	2.52513i	−0.203043	+	0.147520i	−0.684661	−	0.728862i	$-0.740050\pi$
$293$	−3.47554	+	2.52513i	−0.203043	+	0.147520i	0.481617	+	0.876382i	$0.340050\pi$
$294$		0			0
$295$	−3.09556	−	9.52716i	−0.180231	−	0.554693i
$296$	4.89199			0.284341
$297$		0			0
$298$	−18.2852			−1.05923
$299$	−3.30588	−	10.1744i	−0.191184	−	0.588403i
$300$		0			0
$301$	−22.3601	+	16.2456i	−1.28881	+	0.936378i
$302$	13.8253	+	4.49211i	0.795557	+	0.258492i
$303$		0			0
$304$	1.98338	+	2.72988i	0.113754	+	0.156570i
$305$	−7.47515	−	5.43102i	−0.428026	−	0.310979i
$306$		0			0
$307$		−	21.2828i		−	1.21467i	−0.794444	−	0.607337i	$-0.792238\pi$
$307$		−	21.2828i		−	1.21467i	0.794444	−	0.607337i	$-0.207762\pi$
$308$	−11.0096	−	1.68151i	−0.627328	−	0.0958128i
$309$		0			0
$310$	9.49078	−	3.08374i	0.539040	−	0.175145i
$311$	18.3415	−	25.2449i	1.04005	−	1.43151i	0.142926	−	0.989733i	$-0.454349\pi$
$311$	18.3415	−	25.2449i	1.04005	−	1.43151i	0.897126	−	0.441775i	$-0.145651\pi$
$312$		0			0
$313$	9.66847	−	29.7565i	0.546494	−	1.68194i	−0.170916	−	0.985286i	$-0.554673\pi$
$313$	9.66847	−	29.7565i	0.546494	−	1.68194i	0.717410	−	0.696651i	$-0.245327\pi$
$314$	−0.510959	+	1.57257i	−0.0288351	+	0.0887453i
$315$		0			0
$316$	−9.04876	+	12.4545i	−0.509032	+	0.700623i
$317$	−32.3173	+	10.5005i	−1.81512	+	0.589769i	−0.815178	+	0.579211i	$0.803361\pi$
$317$	−32.3173	+	10.5005i	−1.81512	+	0.589769i	−0.999944	+	0.0105576i	$0.996639\pi$
$318$		0			0
$319$	−0.372408	+	0.376542i	−0.0208508	+	0.0210823i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	9.39050	+	6.82260i	0.523312	+	0.380208i
$323$	−1.08949	−	1.49956i	−0.0606209	−	0.0834375i
$324$		0			0
$325$	2.94348	+	0.956394i	0.163275	+	0.0530512i
$326$	3.59808	−	2.61416i	0.199279	−	0.144785i
$327$		0			0
$328$	−0.312202	−	0.960859i	−0.0172385	−	0.0530545i
$329$	−16.4414			−0.906445
$330$		0			0
$331$	18.0703			0.993235			0.496618	−	0.867969i	$-0.334575\pi$
$331$	18.0703			0.993235			0.496618	+	0.867969i	$0.334575\pi$
$332$	2.13488	+	6.57048i	0.117167	+	0.360602i
$333$		0			0
$334$	5.42833	−	3.94391i	0.297025	−	0.215801i
$335$	−2.12641	−	0.690911i	−0.116178	−	0.0377485i
$336$		0			0
$337$	−9.56336	−	13.1628i	−0.520949	−	0.717025i	0.464768	−	0.885432i	$-0.346138\pi$
$337$	−9.56336	−	13.1628i	−0.520949	−	0.717025i	−0.985718	+	0.168407i	$0.946138\pi$
$338$	−2.76785	−	2.01096i	−0.150551	−	0.109382i
$339$		0			0
$340$			0.549311i			0.0297906i
$341$	15.1884	+	29.4065i	0.822497	+	1.59245i
$342$		0			0
$343$	8.69891	−	2.82645i	0.469697	−	0.152614i
$344$	4.83786	−	6.65874i	0.260840	−	0.359015i
$345$		0			0
$346$	−4.84487	+	14.9110i	−0.260462	+	0.801620i
$347$	1.31675	−	4.05253i	0.0706867	−	0.217551i	−0.909472	−	0.415765i	$-0.863514\pi$
$347$	1.31675	−	4.05253i	0.0706867	−	0.217551i	0.980159	+	0.198214i	$0.0635140\pi$
$348$		0			0
$349$	5.48459	−	7.54889i	0.293583	−	0.404083i	−0.636591	−	0.771202i	$-0.719656\pi$
$349$	5.48459	−	7.54889i	0.293583	−	0.404083i	0.930174	+	0.367119i	$0.119656\pi$
$350$	−3.19365	+	1.03768i	−0.170708	+	0.0554663i
$351$		0			0
$352$	3.27288	−	0.536907i	0.174445	−	0.0286172i
$353$		−	31.1139i		−	1.65603i	−0.560708	−	0.828013i	$-0.689471\pi$
$353$		−	31.1139i		−	1.65603i	0.560708	−	0.828013i	$-0.310529\pi$
$354$		0			0
$355$	10.6265	+	7.72058i	0.563994	+	0.409766i
$356$	−0.789321	−	1.08641i	−0.0418339	−	0.0575795i
$357$		0			0
$358$	18.1530	+	5.89827i	0.959417	+	0.311733i
$359$	5.66731	−	4.11754i	0.299109	−	0.217315i	−0.428100	−	0.903731i	$-0.640817\pi$
$359$	5.66731	−	4.11754i	0.299109	−	0.217315i	0.727209	+	0.686416i	$0.240817\pi$
$360$		0			0
$361$	2.35284	+	7.24130i	0.123834	+	0.381121i
$362$	3.31244			0.174098
$363$		0			0
$364$	−10.3929			−0.544734
$365$	1.66107	+	5.11224i	0.0869442	+	0.267587i
$366$		0			0
$367$	−10.3012	+	7.48424i	−0.537717	+	0.390674i	−0.823236	−	0.567699i	$-0.807834\pi$
$367$	−10.3012	+	7.48424i	−0.537717	+	0.390674i	0.285520	+	0.958373i	$0.407834\pi$
$368$	−3.28743	−	1.06815i	−0.171369	−	0.0556812i
$369$		0			0
$370$	2.87544	+	3.95771i	0.149487	+	0.205751i
$371$	−6.23520	−	4.53014i	−0.323716	−	0.235193i
$372$		0			0
$373$		−	3.89853i		−	0.201858i	−0.994894	−	0.100929i	$-0.967818\pi$
$373$		−	3.89853i		−	0.201858i	0.994894	−	0.100929i	$-0.0321815\pi$
$374$	−1.79783	+	0.294929i	−0.0929635	+	0.0152504i
$375$		0			0
$376$	4.65656	−	1.51301i	0.240144	−	0.0780274i
$377$	−0.290483	+	0.399816i	−0.0149606	+	0.0205915i
$378$		0			0
$379$	3.76119	−	11.5758i	0.193200	−	0.594607i	−0.806793	−	0.590834i	$-0.798799\pi$
$379$	3.76119	−	11.5758i	0.193200	−	0.594607i	0.999993	−	0.00377326i	$-0.00120107\pi$
$380$	−1.04272	+	3.20917i	−0.0534906	+	0.164627i
$381$		0			0
$382$	10.6722	−	14.6890i	0.546036	−	0.751554i
$383$	−26.9883	+	8.76903i	−1.37904	+	0.448077i	−0.902353	−	0.430998i	$-0.858162\pi$
$383$	−26.9883	+	8.76903i	−1.37904	+	0.448077i	−0.476685	+	0.879074i	$0.658162\pi$
$384$		0			0
$385$	−5.11089	−	9.89529i	−0.260475	−	0.504311i
$386$		−	25.6047i		−	1.30324i
$387$		0			0
$388$	4.48112	+	3.25572i	0.227494	+	0.165284i
$389$	15.3126	+	21.0759i	0.776377	+	1.06859i	0.995672	+	0.0929330i	$0.0296242\pi$
$389$	15.3126	+	21.0759i	0.776377	+	1.06859i	−0.219295	+	0.975659i	$0.570376\pi$
$390$		0			0
$391$	1.80582	+	0.586747i	0.0913243	+	0.0296731i
$392$	3.45951	−	2.51348i	0.174731	−	0.126950i
$393$		0			0
$394$	0.648927	+	1.99719i	0.0326925	+	0.100617i
$395$	−15.3947			−0.774590
$396$		0			0
$397$	−15.9672			−0.801371			−0.400686	−	0.916216i	$-0.631228\pi$
$397$	−15.9672			−0.801371			−0.400686	+	0.916216i	$0.631228\pi$
$398$	5.18653	+	15.9625i	0.259977	+	0.800128i
$399$		0			0
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	−15.3675	−	4.99321i	−0.767418	−	0.249349i	−0.100958	−	0.994891i	$-0.532191\pi$
$401$	−15.3675	−	4.99321i	−0.767418	−	0.249349i	−0.666459	+	0.745542i	$0.732191\pi$
$402$		0			0
$403$	18.1539	+	24.9866i	0.904308	+	1.24467i
$404$	13.2867	+	9.65333i	0.661037	+	0.480271i
$405$		0			0
$406$		−	0.536202i		−	0.0266113i
$407$	−11.4092	+	11.5359i	−0.565535	+	0.571813i
$408$		0			0
$409$	−12.1861	+	3.95950i	−0.602563	+	0.195785i	−0.594383	−	0.804182i	$-0.702604\pi$
$409$	−12.1861	+	3.95950i	−0.602563	+	0.195785i	−0.00817997	+	0.999967i	$0.502604\pi$
$410$	0.593843	−	0.817355i	0.0293278	−	0.0403663i
$411$		0			0
$412$	−0.574641	+	1.76856i	−0.0283105	+	0.0871309i
$413$	−10.3949	+	31.9922i	−0.511500	+	1.57423i
$414$		0			0
$415$	−4.06078	+	5.58918i	−0.199336	+	0.274362i
$416$	2.94348	−	0.956394i	0.144316	−	0.0468911i
$417$		0			0
$418$	−11.0631	−	1.68968i	−0.541112	−	0.0826449i
$419$			17.1588i			0.838260i	0.907926	+	0.419130i	$0.137665\pi$
$419$			17.1588i			0.838260i	−0.907926	+	0.419130i	$0.862335\pi$
$420$		0			0
$421$	14.0557	+	10.2121i	0.685033	+	0.497706i	0.875024	−	0.484080i	$-0.160846\pi$
$421$	14.0557	+	10.2121i	0.685033	+	0.497706i	−0.189991	+	0.981786i	$0.560846\pi$
$422$	11.4641	+	15.7790i	0.558066	+	0.768112i
$423$		0			0
$424$	2.18282	+	0.709241i	0.106007	+	0.0344438i
$425$	−0.444402	+	0.322877i	−0.0215567	+	0.0156618i
$426$		0			0
$427$	9.58795	+	29.5087i	0.463993	+	1.42803i
$428$	−7.78273			−0.376192
$429$		0			0
$430$	8.23066			0.396918
$431$	2.40515	+	7.40230i	0.115852	+	0.356556i	0.992124	−	0.125261i	$-0.0399768\pi$
$431$	2.40515	+	7.40230i	0.115852	+	0.356556i	−0.876272	+	0.481817i	$0.839977\pi$
$432$		0			0
$433$	29.6830	−	21.5659i	1.42647	−	1.03639i	0.435812	−	0.900038i	$-0.356461\pi$
$433$	29.6830	−	21.5659i	1.42647	−	1.03639i	0.990660	−	0.136354i	$-0.0435386\pi$
$434$	−31.8701	−	10.3552i	−1.52981	−	0.497066i
$435$		0			0
$436$	−0.855530	−	1.17754i	−0.0409725	−	0.0563937i
$437$	9.43613	+	6.85575i	0.451391	+	0.327955i
$438$		0			0
$439$		−	7.96864i		−	0.380322i	−0.981753	−	0.190161i	$-0.939099\pi$
$439$		−	7.96864i		−	0.380322i	0.981753	−	0.190161i	$-0.0609010\pi$
$440$	2.35812	+	2.33223i	0.112419	+	0.111185i
$441$		0			0
$442$	−1.61688	+	0.525358i	−0.0769074	+	0.0249887i
$443$	4.64628	−	6.39505i	0.220751	−	0.303838i	−0.684250	−	0.729248i	$-0.739870\pi$
$443$	4.64628	−	6.39505i	0.220751	−	0.303838i	0.905001	+	0.425410i	$0.139870\pi$
$444$		0			0
$445$	0.414971	−	1.27715i	0.0196715	−	0.0605426i
$446$	−7.30698	+	22.4886i	−0.345996	+	1.06487i
$447$		0			0
$448$	−1.97378	+	2.71668i	−0.0932526	+	0.128351i
$449$	−16.6643	+	5.41455i	−0.786435	+	0.255528i	−0.674585	−	0.738197i	$-0.735678\pi$
$449$	−16.6643	+	5.41455i	−0.786435	+	0.255528i	−0.111850	+	0.993725i	$0.535678\pi$
$450$		0			0
$451$	2.99394	+	1.50473i	0.140979	+	0.0708551i
$452$			6.42464i			0.302190i
$453$		0			0
$454$	7.39873	+	5.37549i	0.347240	+	0.252284i
$455$	−6.10878	−	8.40801i	−0.286384	−	0.394174i
$456$		0			0
$457$	−8.23587	−	2.67599i	−0.385258	−	0.125178i	0.109983	−	0.993933i	$-0.464920\pi$
$457$	−8.23587	−	2.67599i	−0.385258	−	0.125178i	−0.495241	+	0.868756i	$0.664920\pi$
$458$	−1.06804	+	0.775979i	−0.0499064	+	0.0362591i
$459$		0			0
$460$	−1.06815	−	3.28743i	−0.0498027	−	0.153277i
$461$	−31.4941			−1.46683			−0.733413	−	0.679783i	$-0.762074\pi$
$461$	−31.4941			−1.46683			−0.733413	+	0.679783i	$0.762074\pi$
$462$		0			0
$463$	−0.397627			−0.0184793			−0.00923965	−	0.999957i	$-0.502941\pi$
$463$	−0.397627			−0.0184793			−0.00923965	+	0.999957i	$0.502941\pi$
$464$	0.0493435	+	0.151864i	0.00229071	+	0.00705010i
$465$		0			0
$466$	−23.4763	+	17.0566i	−1.08752	+	0.790129i
$467$	−11.0418	−	3.58771i	−0.510956	−	0.166020i	0.0421811	−	0.999110i	$-0.486569\pi$
$467$	−11.0418	−	3.58771i	−0.510956	−	0.166020i	−0.553137	+	0.833090i	$0.686569\pi$
$468$		0			0
$469$	4.41306	+	6.07405i	0.203776	+	0.280474i
$470$	3.96110	+	2.87791i	0.182712	+	0.132748i
$471$		0			0
$472$		−	10.0174i		−	0.461090i
$473$	4.41910	+	26.9379i	0.203190	+	1.23861i
$474$		0			0
$475$	−3.20917	+	1.04272i	−0.147247	+	0.0478434i
$476$	1.08422	−	1.49230i	0.0496952	−	0.0683996i
$477$		0			0
$478$	−4.54326	+	13.9827i	−0.207804	+	0.639555i
$479$	3.50361	−	10.7830i	0.160084	−	0.492687i	−0.838557	−	0.544814i	$-0.816600\pi$
$479$	3.50361	−	10.7830i	0.160084	−	0.492687i	0.998640	+	0.0521270i	$0.0166001\pi$
$480$		0			0
$481$	−8.89936	+	12.2489i	−0.405776	+	0.558503i
$482$	17.7008	−	5.75133i	0.806248	−	0.261966i
$483$		0			0
$484$	−6.36701	+	8.97002i	−0.289410	+	0.407728i
$485$			5.53897i			0.251512i
$486$		0			0
$487$	−16.3926	−	11.9099i	−0.742820	−	0.539690i	0.150773	−	0.988568i	$-0.451824\pi$
$487$	−16.3926	−	11.9099i	−0.742820	−	0.539690i	−0.893593	+	0.448878i	$0.851824\pi$
$488$	−5.43102	−	7.47515i	−0.245851	−	0.338384i
$489$		0			0
$490$	4.06689	+	1.32141i	0.183724	+	0.0596954i
$491$	−10.0498	+	7.30162i	−0.453542	+	0.329518i	−0.790993	−	0.611826i	$-0.790435\pi$
$491$	−10.0498	+	7.30162i	−0.453542	+	0.329518i	0.337451	+	0.941343i	$0.390435\pi$
$492$		0			0
$493$	−0.0271049	−	0.0834204i	−0.00122074	−	0.00375707i
$494$	−10.4434			−0.469870
$495$		0			0
$496$	9.97920			0.448079
$497$	−13.6300	−	41.9487i	−0.611388	−	1.88166i
$498$		0			0
$499$	4.55484	−	3.30929i	0.203903	−	0.148144i	−0.481148	−	0.876639i	$-0.659780\pi$
$499$	4.55484	−	3.30929i	0.203903	−	0.148144i	0.685051	+	0.728495i	$0.259780\pi$
$500$	0.951057	+	0.309017i	0.0425325	+	0.0138197i
$501$		0			0
$502$	7.77081	+	10.6956i	0.346828	+	0.477368i
$503$	5.60339	+	4.07110i	0.249843	+	0.181521i	0.705657	−	0.708554i	$-0.250652\pi$
$503$	5.60339	+	4.07110i	0.249843	+	0.181521i	−0.455814	+	0.890075i	$0.650652\pi$
$504$		0			0
$505$			16.4232i			0.730824i
$506$	10.1859	−	5.26097i	0.452816	−	0.233878i
$507$		0			0
$508$	16.4469	−	5.34391i	0.729712	−	0.237098i
$509$	−9.58532	+	13.1931i	−0.424862	+	0.584772i	−0.966764	−	0.255669i	$-0.917704\pi$
$509$	−9.58532	+	13.1931i	−0.424862	+	0.584772i	0.541902	+	0.840441i	$0.317704\pi$
$510$		0			0
$511$	5.57787	−	17.1669i	0.246750	−	0.759419i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$		0			0
$514$	−14.2124	+	19.5617i	−0.626883	+	0.862831i
$515$	−1.76856	+	0.574641i	−0.0779323	+	0.0253217i
$516$		0			0
$517$	−7.29230	+	14.5094i	−0.320715	+	0.638122i
$518$		−	16.4273i		−	0.721775i
$519$		0			0
$520$	2.50387	+	1.81917i	0.109802	+	0.0797758i
$521$	−19.0794	−	26.2606i	−0.835885	−	1.15050i	−0.986799	−	0.161950i	$-0.948222\pi$
$521$	−19.0794	−	26.2606i	−0.835885	−	1.15050i	0.150914	−	0.988547i	$-0.451778\pi$
$522$		0			0
$523$	−8.97577	−	2.91640i	−0.392483	−	0.127525i	0.106126	−	0.994353i	$-0.466155\pi$
$523$	−8.97577	−	2.91640i	−0.392483	−	0.127525i	−0.498608	+	0.866827i	$0.666155\pi$
$524$	−2.13112	+	1.54835i	−0.0930986	+	0.0676401i
$525$		0			0
$526$	−7.04520	−	21.6829i	−0.307185	−	0.945419i
$527$	−5.48169			−0.238786
$528$		0			0
$529$	11.0519			0.480516
$530$	0.709241	+	2.18282i	0.0308075	+	0.0948157i
$531$		0			0
$532$	9.16696	−	6.66019i	0.397438	−	0.288756i
$533$	2.97381	+	0.966251i	0.128810	+	0.0418530i
$534$		0			0
$535$	−4.57457	−	6.29636i	−0.197776	−	0.272215i
$536$	−1.80883	−	1.31419i	−0.0781295	−	0.0567644i
$537$		0			0
$538$			12.4501i			0.536763i
$539$	−2.14128	+	14.0199i	−0.0922316	+	0.603881i
$540$		0			0
$541$	−17.0526	+	5.54071i	−0.733147	+	0.238214i	−0.651714	−	0.758465i	$-0.725950\pi$
$541$	−17.0526	+	5.54071i	−0.733147	+	0.238214i	−0.0814331	+	0.996679i	$0.525950\pi$
$542$	15.7854	−	21.7267i	0.678041	−	0.933243i
$543$		0			0
$544$	−0.169746	+	0.522426i	−0.00727782	+	0.0223988i
$545$	0.449779	−	1.38428i	0.0192664	−	0.0592959i
$546$		0			0
$547$	−10.7868	+	14.8468i	−0.461211	+	0.634802i	−0.974759	−	0.223258i	$-0.928331\pi$
$547$	−10.7868	+	14.8468i	−0.461211	+	0.634802i	0.513549	+	0.858061i	$0.328331\pi$
$548$	10.5401	−	3.42468i	0.450251	−	0.146295i
$549$		0			0
$550$	−0.500746	+	3.27861i	−0.0213519	+	0.139800i
$551$		−	0.538808i		−	0.0229540i
$552$		0			0
$553$	41.8224	+	30.3858i	1.77847	+	1.29213i
$554$	−16.6370	−	22.8989i	−0.706838	−	0.972880i
$555$		0			0
$556$	17.7835	+	5.77821i	0.754189	+	0.245051i
$557$	−35.9279	+	26.1032i	−1.52232	+	1.10603i	−0.561990	+	0.827144i	$0.689964\pi$
$557$	−35.9279	+	26.1032i	−1.52232	+	1.10603i	−0.960325	+	0.278883i	$0.910036\pi$
$558$		0			0
$559$	7.87175	+	24.2268i	0.332940	+	1.02468i
$560$	−3.35800			−0.141902
$561$		0			0
$562$	4.67542			0.197221
$563$	3.23085	+	9.94354i	0.136164	+	0.419070i	0.995769	−	0.0918887i	$-0.0292904\pi$
$563$	3.23085	+	9.94354i	0.136164	+	0.419070i	−0.859605	+	0.510959i	$0.829290\pi$
$564$		0			0
$565$	−5.19764	+	3.77631i	−0.218666	+	0.158870i
$566$	−13.0441	−	4.23829i	−0.548285	−	0.178148i
$567$		0			0
$568$	7.72058	+	10.6265i	0.323948	+	0.445877i
$569$	0.0789397	+	0.0573530i	0.00330932	+	0.00240436i	0.589439	−	0.807813i	$-0.299349\pi$
$569$	0.0789397	+	0.0573530i	0.00330932	+	0.00240436i	−0.586129	+	0.810217i	$0.699349\pi$
$570$		0			0
$571$			2.09993i			0.0878795i	0.999034	+	0.0439397i	$0.0139910\pi$
$571$			2.09993i			0.0878795i	−0.999034	+	0.0439397i	$0.986009\pi$
$572$	−4.60957	+	9.17159i	−0.192736	+	0.383483i
$573$		0			0
$574$	−3.22657	+	1.04837i	−0.134674	+	0.0437583i
$575$	2.03174	−	2.79645i	0.0847295	−	0.116620i
$576$		0			0
$577$	11.3441	−	34.9136i	0.472262	−	1.45347i	−0.377352	−	0.926070i	$-0.623165\pi$
$577$	11.3441	−	34.9136i	0.472262	−	1.45347i	0.849614	−	0.527404i	$-0.176835\pi$
$578$	−5.16005	+	15.8810i	−0.214630	+	0.660562i
$579$		0			0
$580$	−0.0938569	+	0.129183i	−0.00389720	+	0.00536403i
$581$	22.0637	−	7.16892i	0.915356	−	0.297417i
$582$		0			0
$583$	−6.76331	+	3.49323i	−0.280108	+	0.144675i
$584$			5.37533i			0.222433i
$585$		0			0
$586$	−3.47554	−	2.52513i	−0.143573	−	0.104312i
$587$	−2.79081	−	3.84122i	−0.115189	−	0.158544i	0.747529	−	0.664229i	$-0.231240\pi$
$587$	−2.79081	−	3.84122i	−0.115189	−	0.158544i	−0.862718	+	0.505685i	$0.831240\pi$
$588$		0			0
$589$	−32.0250	−	10.4055i	−1.31957	−	0.428753i
$590$	8.10429	−	5.88811i	0.333648	−	0.242410i
$591$		0			0
$592$	1.51171	+	4.65256i	0.0621309	+	0.191219i
$593$	−25.6824			−1.05465			−0.527326	−	0.849663i	$-0.676805\pi$
$593$	−25.6824			−1.05465			−0.527326	+	0.849663i	$0.676805\pi$
$594$		0			0
$595$	1.84459			0.0756208
$596$	−5.65044	−	17.3903i	−0.231451	−	0.712333i
$597$		0			0
$598$	8.65490	−	6.28815i	0.353925	−	0.257142i
$599$	−22.2810	−	7.23954i	−0.910378	−	0.295800i	−0.183864	−	0.982952i	$-0.558861\pi$
$599$	−22.2810	−	7.23954i	−0.910378	−	0.295800i	−0.726514	+	0.687152i	$0.758861\pi$
$600$		0			0
$601$	−14.0746	−	19.3720i	−0.574115	−	0.790202i	0.418919	−	0.908023i	$-0.362409\pi$
$601$	−14.0746	−	19.3720i	−0.574115	−	0.790202i	−0.993035	+	0.117821i	$0.962409\pi$
$602$	−22.3601	−	16.2456i	−0.911329	−	0.662119i
$603$		0			0
$604$			14.5368i			0.591493i
$605$	−10.9993	+	0.121424i	−0.447186	+	0.00493659i
$606$		0			0
$607$	20.2358	−	6.57500i	0.821344	−	0.266871i	0.131949	−	0.991256i	$-0.457876\pi$
$607$	20.2358	−	6.57500i	0.821344	−	0.266871i	0.689395	+	0.724385i	$0.257876\pi$
$608$	−1.98338	+	2.72988i	−0.0804365	+	0.110711i
$609$		0			0
$610$	2.85525	−	8.78757i	0.115606	−	0.355798i
$611$	−4.68269	+	14.4118i	−0.189441	+	0.583040i
$612$		0			0
$613$	−0.755360	+	1.03966i	−0.0305087	+	0.0419916i	−0.823999	−	0.566591i	$-0.808262\pi$
$613$	−0.755360	+	1.03966i	−0.0305087	+	0.0419916i	0.793490	+	0.608583i	$0.208262\pi$
$614$	20.2411	−	6.57675i	0.816866	−	0.265416i
$615$		0			0
$616$	−1.80293	−	10.9903i	−0.0726423	−	0.442813i
$617$		−	17.1621i		−	0.690918i	−0.938434	−	0.345459i	$-0.887723\pi$
$617$		−	17.1621i		−	0.690918i	0.938434	−	0.345459i	$-0.112277\pi$
$618$		0			0
$619$	7.85490	+	5.70692i	0.315715	+	0.229381i	0.734345	−	0.678776i	$-0.237489\pi$
$619$	7.85490	+	5.70692i	0.315715	+	0.229381i	−0.418630	+	0.908157i	$0.637489\pi$
$620$	5.86563	+	8.07334i	0.235569	+	0.324233i
$621$		0			0
$622$	29.6772	+	9.64270i	1.18995	+	0.386637i
$623$	−3.64816	+	2.65054i	−0.146160	+	0.106192i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	31.2878			1.25051
$627$		0			0
$628$	−1.65350			−0.0659817
$629$	−0.830398	−	2.55570i	−0.0331102	−	0.101903i
$630$		0			0
$631$	−15.7594	+	11.4499i	−0.627373	+	0.455813i	−0.855489	−	0.517821i	$-0.826743\pi$
$631$	−15.7594	+	11.4499i	−0.627373	+	0.455813i	0.228116	+	0.973634i	$0.426743\pi$
$632$	−14.6412	−	4.75721i	−0.582396	−	0.189232i
$633$		0			0
$634$	−19.9732	−	27.4908i	−0.793237	−	1.09180i
$635$	13.9905	+	10.1647i	0.555198	+	0.403375i
$636$		0			0
$637$			13.2346i			0.524374i
$638$	−0.473193	−	0.237823i	−0.0187339	−	0.00941551i
$639$		0			0
$640$	0.951057	−	0.309017i	0.0375938	−	0.0122150i
$641$	−19.8968	+	27.3856i	−0.785875	+	1.08166i	0.208734	+	0.977972i	$0.433066\pi$
$641$	−19.8968	+	27.3856i	−0.785875	+	1.08166i	−0.994609	+	0.103692i	$0.966934\pi$
$642$		0			0
$643$	−8.02179	+	24.6885i	−0.316349	+	0.973621i	0.658847	+	0.752277i	$0.271044\pi$
$643$	−8.02179	+	24.6885i	−0.316349	+	0.973621i	−0.975196	+	0.221344i	$0.928956\pi$
$644$	−3.58685	+	11.0392i	−0.141342	+	0.435005i
$645$		0			0
$646$	1.08949	−	1.49956i	0.0428654	−	0.0589992i
$647$	3.08581	−	1.00264i	0.121316	−	0.0394178i	−0.247730	−	0.968829i	$-0.579685\pi$
$647$	3.08581	−	1.00264i	0.121316	−	0.0394178i	0.369046	+	0.929411i	$0.379685\pi$
$648$		0			0
$649$	23.6223	+	23.3630i	0.927257	+	0.917077i
$650$			3.09496i			0.121394i
$651$		0			0
$652$	3.59808	+	2.61416i	0.140912	+	0.102378i
$653$	26.6424	+	36.6701i	1.04260	+	1.43501i	0.895054	+	0.445958i	$0.147137\pi$
$653$	26.6424	+	36.6701i	1.04260	+	1.43501i	0.147544	+	0.989055i	$0.452863\pi$
$654$		0			0
$655$	−2.50529	−	0.814017i	−0.0978897	−	0.0318063i
$656$	0.817355	−	0.593843i	0.0319124	−	0.0231857i
$657$		0			0
$658$	−5.08068	−	15.6367i	−0.198066	−	0.609583i
$659$	−4.94893			−0.192783			−0.0963916	−	0.995343i	$-0.530730\pi$
$659$	−4.94893			−0.192783			−0.0963916	+	0.995343i	$0.530730\pi$
$660$		0			0
$661$	−26.4352			−1.02821			−0.514105	−	0.857727i	$-0.671876\pi$
$661$	−26.4352			−1.02821			−0.514105	+	0.857727i	$0.671876\pi$
$662$	5.58404	+	17.1859i	0.217030	+	0.667949i
$663$		0			0
$664$	−5.58918	+	4.06078i	−0.216902	+	0.157589i
$665$	10.7764	+	3.50147i	0.417891	+	0.135781i
$666$		0			0
$667$	0.324426	+	0.446535i	0.0125618	+	0.0172899i
$668$	5.42833	+	3.94391i	0.210028	+	0.152595i
$669$		0			0
$670$		−	2.23583i		−	0.0863778i
$671$	30.2936	+	4.62679i	1.16947	+	0.178615i
$672$		0			0
$673$	−7.09244	+	2.30447i	−0.273393	+	0.0888309i	−0.442505	−	0.896766i	$-0.645910\pi$
$673$	−7.09244	+	2.30447i	−0.273393	+	0.0888309i	0.169112	+	0.985597i	$0.445910\pi$
$674$	9.56336	−	13.1628i	0.368367	−	0.507014i
$675$		0			0
$676$	1.05723	−	3.25380i	0.0406625	−	0.125146i
$677$	11.6497	−	35.8540i	0.447733	−	1.37798i	−0.431725	−	0.902006i	$-0.642095\pi$
$677$	11.6497	−	35.8540i	0.447733	−	1.37798i	0.879458	−	0.475976i	$-0.157905\pi$
$678$		0			0
$679$	10.9327	−	15.0476i	0.419560	−	0.577474i
$680$	−0.522426	+	0.169746i	−0.0200341	+	0.00650948i
$681$		0			0
$682$	−23.2738	+	23.5321i	−0.891199	+	0.901091i
$683$		−	0.633926i		−	0.0242565i	−0.999926	−	0.0121282i	$-0.996139\pi$
$683$		−	0.633926i		−	0.0242565i	0.999926	−	0.0121282i	$-0.00386063\pi$
$684$		0			0
$685$	8.96594	+	6.51414i	0.342571	+	0.248892i
$686$	5.37622	+	7.39974i	0.205265	+	0.282523i
$687$		0			0
$688$	7.82782	+	2.54341i	0.298433	+	0.0969667i
$689$	−5.74677	+	4.17527i	−0.218934	+	0.159065i
$690$		0			0
$691$	7.49393	+	23.0639i	0.285082	+	0.877393i	0.986374	+	0.164519i	$0.0526071\pi$
$691$	7.49393	+	23.0639i	0.285082	+	0.877393i	−0.701292	+	0.712875i	$0.747393\pi$
$692$	−15.6783			−0.596001
$693$		0			0
$694$	4.26108			0.161748
$695$	5.77821	+	17.7835i	0.219180	+	0.674567i
$696$		0			0
$697$	−0.448982	+	0.326205i	−0.0170064	+	0.0123559i
$698$	8.87425	+	2.88342i	0.335895	+	0.109139i
$699$		0			0
$700$	−1.97378	−	2.71668i	−0.0746021	−	0.102681i
$701$	1.05596	+	0.767198i	0.0398830	+	0.0289767i	0.607548	−	0.794283i	$-0.292153\pi$
$701$	1.05596	+	0.767198i	0.0398830	+	0.0289767i	−0.567665	+	0.823260i	$0.692153\pi$
$702$		0			0
$703$		−	16.5072i		−	0.622579i
$704$	1.52200	+	2.94678i	0.0573627	+	0.111061i
$705$		0			0
$706$	29.5911	−	9.61473i	1.11368	−	0.361855i
$707$	32.4159	−	44.6167i	1.21913	−	1.67798i
$708$		0			0
$709$	12.7638	−	39.2829i	0.479354	−	1.47530i	−0.360640	−	0.932705i	$-0.617442\pi$
$709$	12.7638	−	39.2829i	0.479354	−	1.47530i	0.839994	−	0.542596i	$-0.182558\pi$
$710$	−4.05895	+	12.4922i	−0.152330	+	0.468823i
$711$		0			0
$712$	0.789321	−	1.08641i	0.0295811	−	0.0407148i
$713$	32.8059	−	10.6593i	1.22859	−	0.399193i
$714$		0			0
$715$	−10.1294	+	1.66170i	−0.378819	+	0.0621442i
$716$			19.0872i			0.713322i
$717$		0			0
$718$	5.66731	+	4.11754i	0.211502	+	0.153665i
$719$	21.3225	+	29.3479i	0.795194	+	1.09449i	0.993442	+	0.114339i	$0.0364750\pi$
$719$	21.3225	+	29.3479i	0.795194	+	1.09449i	−0.198247	+	0.980152i	$0.563525\pi$
$720$		0			0
$721$	5.93884	+	1.92965i	0.221174	+	0.0718638i
$722$	−6.15982	+	4.47537i	−0.229245	+	0.166556i
$723$		0			0
$724$	1.02360	+	3.15031i	0.0380418	+	0.117080i
$725$	−0.159679			−0.00593033
$726$		0			0
$727$	24.1321			0.895008			0.447504	−	0.894282i	$-0.352313\pi$
$727$	24.1321			0.895008			0.447504	+	0.894282i	$0.352313\pi$
$728$	−3.21157	−	9.88421i	−0.119029	−	0.366333i
$729$		0			0
$730$	−4.34873	+	3.15954i	−0.160954	+	0.116940i
$731$	−4.29991	−	1.39713i	−0.159038	−	0.0516745i
$732$		0			0
$733$	12.1397	+	16.7088i	0.448389	+	0.617155i	0.972051	−	0.234772i	$-0.0754342\pi$
$733$	12.1397	+	16.7088i	0.448389	+	0.617155i	−0.523661	+	0.851927i	$0.675434\pi$
$734$	−10.3012	−	7.48424i	−0.380223	−	0.276248i
$735$		0			0
$736$		−	3.45661i		−	0.127412i
$737$	7.31761	−	1.20043i	0.269548	−	0.0442186i
$738$		0			0
$739$	−1.95695	+	0.635852i	−0.0719877	+	0.0233902i	−0.344789	−	0.938680i	$-0.612050\pi$
$739$	−1.95695	+	0.635852i	−0.0719877	+	0.0233902i	0.272802	+	0.962070i	$0.412050\pi$
$740$	−2.87544	+	3.95771i	−0.105703	+	0.145488i
$741$		0			0
$742$	2.38164	−	7.32992i	0.0874326	−	0.269090i
$743$	5.95344	−	18.3228i	0.218411	−	0.672199i	−0.780483	−	0.625177i	$-0.785027\pi$
$743$	5.95344	−	18.3228i	0.218411	−	0.672199i	0.998894	−	0.0470220i	$-0.0149731\pi$
$744$		0			0
$745$	10.7478	−	14.7930i	0.393768	−	0.541975i
$746$	3.70772	−	1.20471i	0.135749	−	0.0441076i
$747$		0			0
$748$	−0.836053	−	1.61870i	−0.0305691	−	0.0591855i
$749$			26.1344i			0.954931i
$750$		0			0
$751$	4.37428	+	3.17810i	0.159620	+	0.115971i	0.664728	−	0.747085i	$-0.268547\pi$
$751$	4.37428	+	3.17810i	0.159620	+	0.115971i	−0.505108	+	0.863056i	$0.668547\pi$
$752$	2.87791	+	3.96110i	0.104947	+	0.144447i
$753$		0			0
$754$	−0.470011	−	0.152716i	−0.0171168	−	0.00556159i
$755$	−11.7605	+	8.54451i	−0.428009	+	0.310966i
$756$		0			0
$757$	4.75889	+	14.6464i	0.172965	+	0.532331i	0.999535	−	0.0305033i	$-0.00971102\pi$
$757$	4.75889	+	14.6464i	0.172965	+	0.532331i	−0.826570	+	0.562834i	$0.809711\pi$
$758$	12.1715			0.442088
$759$		0			0
$760$	−3.37432			−0.122400
$761$	−12.3735	−	38.0818i	−0.448540	−	1.38046i	−0.878555	−	0.477642i	$-0.841492\pi$
$761$	−12.3735	−	38.0818i	−0.448540	−	1.38046i	0.430015	−	0.902822i	$-0.358508\pi$
$762$		0			0
$763$	−3.95417	+	2.87287i	−0.143151	+	0.104005i
$764$	17.2679	+	5.61070i	0.624732	+	0.202988i
$765$		0			0
$766$	−16.6797	−	22.9576i	−0.602662	−	0.829493i
$767$	25.0824	+	18.2234i	0.905673	+	0.658010i
$768$		0			0
$769$			9.10215i			0.328232i	0.986441	+	0.164116i	$0.0524771\pi$
$769$			9.10215i			0.328232i	−0.986441	+	0.164116i	$0.947523\pi$
$770$	7.83163	−	7.91856i	0.282232	−	0.285365i
$771$		0			0
$772$	24.3515	−	7.91228i	0.876429	−	0.284769i
$773$	22.1852	−	30.5352i	0.797945	−	1.09828i	−0.195128	−	0.980778i	$-0.562512\pi$
$773$	22.1852	−	30.5352i	0.797945	−	1.09828i	0.993073	−	0.117499i	$-0.0374876\pi$
$774$		0			0
$775$	−3.08374	+	9.49078i	−0.110771	+	0.340919i
$776$	−1.71164	+	5.26787i	−0.0614441	+	0.189106i
$777$		0			0
$778$	−15.3126	+	21.0759i	−0.548982	+	0.755608i
$779$	−3.24225	+	1.05347i	−0.116166	+	0.0377445i
$780$		0			0
$781$	−43.0646	−	6.57732i	−1.54097	−	0.235355i
$782$			1.89875i			0.0678992i
$783$		0			0
$784$	3.45951	+	2.51348i	0.123554	+	0.0897671i
$785$	−0.971902	−	1.33771i	−0.0346887	−	0.0477448i
$786$		0			0
$787$	−51.6380	−	16.7782i	−1.84070	−	0.598078i	−0.998239	−	0.0593128i	$-0.981109\pi$
$787$	−51.6380	−	16.7782i	−1.84070	−	0.598078i	−0.842456	−	0.538765i	$-0.818891\pi$
$788$	−1.69891	+	1.23433i	−0.0605213	+	0.0439713i
$789$		0			0
$790$	−4.75721	−	14.6412i	−0.169254	−	0.520910i
$791$	21.5740			0.767082
$792$		0			0
$793$	28.5968			1.01550
$794$	−4.93414	−	15.1857i	−0.175106	−	0.538921i
$795$		0			0
$796$	−13.5785	+	9.86538i	−0.481278	+	0.349669i
$797$	21.5827	+	7.01266i	0.764500	+	0.248401i	0.665209	−	0.746657i	$-0.268343\pi$
$797$	21.5827	+	7.01266i	0.764500	+	0.248401i	0.0992910	+	0.995058i	$0.468343\pi$
$798$		0			0
$799$	−1.58087	−	2.17588i	−0.0559271	−	0.0769770i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$		0			0
$802$		−	16.1584i		−	0.570572i
$803$	−12.6756	−	12.5365i	−0.447314	−	0.442403i
$804$		0			0
$805$	−11.0392	+	3.58685i	−0.389080	+	0.126420i
$806$	−18.1539	+	24.9866i	−0.639442	+	0.880117i
$807$		0			0
$808$	−5.07506	+	15.6194i	−0.178540	+	0.549489i
$809$	13.5233	−	41.6205i	0.475455	−	1.46330i	−0.369889	−	0.929076i	$-0.620604\pi$
$809$	13.5233	−	41.6205i	0.475455	−	1.46330i	0.845344	−	0.534223i	$-0.179396\pi$
$810$		0			0
$811$	30.2027	−	41.5704i	1.06056	−	1.45973i	0.181277	−	0.983432i	$-0.441977\pi$
$811$	30.2027	−	41.5704i	1.06056	−	1.45973i	0.879282	−	0.476302i	$-0.158023\pi$
$812$	0.509959	−	0.165696i	0.0178960	−	0.00581478i
$813$		0			0
$814$	−14.4969	−	7.28605i	−0.508117	−	0.255376i
$815$			4.44747i			0.155788i
$816$		0			0
$817$	−22.4687	−	16.3245i	−0.786082	−	0.571122i
$818$	−7.53142	−	10.3661i	−0.263330	−	0.362442i
$819$		0			0
$820$	0.960859	+	0.312202i	0.0335546	+	0.0109026i
$821$	−15.9529	+	11.5905i	−0.556761	+	0.404510i	−0.830272	−	0.557358i	$-0.811815\pi$
$821$	−15.9529	+	11.5905i	−0.556761	+	0.404510i	0.273511	+	0.961869i	$0.411815\pi$
$822$		0			0
$823$	6.42117	+	19.7623i	0.223828	+	0.688872i	0.998408	+	0.0563962i	$0.0179610\pi$
$823$	6.42117	+	19.7623i	0.223828	+	0.688872i	−0.774581	+	0.632475i	$0.782039\pi$
$824$	−1.85958			−0.0647815
$825$		0			0
$826$	−33.6386			−1.17044
$827$	−16.7719	−	51.6187i	−0.583218	−	1.79496i	−0.606313	−	0.795226i	$-0.707352\pi$
$827$	−16.7719	−	51.6187i	−0.583218	−	1.79496i	0.0230949	−	0.999733i	$-0.492648\pi$
$828$		0			0
$829$	21.4367	−	15.5746i	0.744526	−	0.540930i	−0.149599	−	0.988747i	$-0.547798\pi$
$829$	21.4367	−	15.5746i	0.744526	−	0.540930i	0.894125	+	0.447817i	$0.147798\pi$
$830$	−6.57048	−	2.13488i	−0.228065	−	0.0741027i
$831$		0			0
$832$	1.81917	+	2.50387i	0.0630683	+	0.0868061i
$833$	−1.90035	−	1.38068i	−0.0658431	−	0.0478378i
$834$		0			0
$835$			6.70979i			0.232202i
$836$	−1.81170	−	11.0437i	−0.0626588	−	0.381956i
$837$		0			0
$838$	−16.3189	+	5.30235i	−0.563729	+	0.183167i
$839$	22.7118	−	31.2601i	0.784099	−	1.07922i	−0.210719	−	0.977547i	$-0.567580\pi$
$839$	22.7118	−	31.2601i	0.784099	−	1.07922i	0.994818	−	0.101673i	$-0.0324196\pi$
$840$		0			0
$841$	−8.95361	+	27.5564i	−0.308745	+	0.950220i
$842$	−5.36880	+	16.5235i	−0.185021	+	0.569436i
$843$		0			0
$844$	−11.4641	+	15.7790i	−0.394612	+	0.543137i
$845$	3.25380	−	1.05723i	0.111934	−	0.0363696i
$846$		0			0
$847$	30.1213	+	21.3804i	1.03498	+	0.734641i
$848$			2.29515i			0.0788159i
$849$		0			0
$850$	−0.444402	−	0.322877i	−0.0152429	−	0.0110746i
$851$	9.93927	+	13.6802i	0.340714	+	0.468952i
$852$		0			0
$853$	−0.0479198	−	0.0155701i	−0.00164074	−	0.000533110i	0.308197	−	0.951323i	$-0.400275\pi$
$853$	−0.0479198	−	0.0155701i	−0.00164074	−	0.000533110i	−0.309837	+	0.950790i	$0.600275\pi$
$854$	−25.1016	+	18.2374i	−0.858958	+	0.624070i
$855$		0			0
$856$	−2.40500	−	7.40182i	−0.0822011	−	0.252989i
$857$	−3.06875			−0.104827			−0.0524133	−	0.998625i	$-0.516691\pi$
$857$	−3.06875			−0.104827			−0.0524133	+	0.998625i	$0.516691\pi$
$858$		0			0
$859$	38.5002			1.31361			0.656805	−	0.754061i	$-0.271908\pi$
$859$	38.5002			1.31361			0.656805	+	0.754061i	$0.271908\pi$
$860$	2.54341	+	7.82782i	0.0867297	+	0.266927i
$861$		0			0
$862$	−6.29678	+	4.57488i	−0.214469	+	0.155821i
$863$	44.4363	+	14.4382i	1.51263	+	0.491483i	0.943672	−	0.330883i	$-0.107347\pi$
$863$	44.4363	+	14.4382i	1.51263	+	0.491483i	0.568958	+	0.822367i	$0.307347\pi$
$864$		0			0
$865$	−9.21550	−	12.6840i	−0.313336	−	0.431270i
$866$	29.6830	+	21.5659i	1.00867	+	0.732840i
$867$		0			0
$868$		−	33.5102i		−	1.13741i
$869$	45.3647	−	23.4307i	1.53889	−	0.794833i
$870$		0			0
$871$	6.58113	−	2.13834i	0.222993	−	0.0724548i
$872$	0.855530	−	1.17754i	0.0289719	−	0.0398764i
$873$		0			0
$874$	−3.60428	+	11.0928i	−0.121917	+	0.375221i
$875$	1.03768	−	3.19365i	0.0350800	−	0.107965i
$876$		0			0
$877$	−4.12117	+	5.67230i	−0.139162	+	0.191540i	−0.872909	−	0.487882i	$-0.837770\pi$
$877$	−4.12117	+	5.67230i	−0.139162	+	0.191540i	0.733748	+	0.679422i	$0.237770\pi$
$878$	7.57862	−	2.46244i	0.255766	−	0.0831035i
$879$		0			0
$880$	−1.48938	+	2.96340i	−0.0502071	+	0.0998962i
$881$			17.4385i			0.587518i	0.955880	+	0.293759i	$0.0949062\pi$
$881$			17.4385i			0.587518i	−0.955880	+	0.293759i	$0.905094\pi$
$882$		0			0
$883$	−42.8737	−	31.1496i	−1.44282	−	1.04827i	−0.987445	−	0.157966i	$-0.949507\pi$
$883$	−42.8737	−	31.1496i	−1.44282	−	1.04827i	−0.455371	−	0.890302i	$-0.650493\pi$
$884$	−0.999290	−	1.37540i	−0.0336098	−	0.0462599i
$885$		0			0
$886$	7.51783	+	2.44269i	0.252567	+	0.0820638i
$887$	−12.2717	+	8.91595i	−0.412045	+	0.299368i	−0.774429	−	0.632661i	$-0.781963\pi$
$887$	−12.2717	+	8.91595i	−0.412045	+	0.299368i	0.362384	+	0.932029i	$0.381963\pi$
$888$		0			0
$889$	−17.9449	−	55.2286i	−0.601852	−	1.85231i
$890$	1.34287			0.0450132
$891$		0			0
$892$	−23.6459			−0.791723
$893$	−5.10537	−	15.7127i	−0.170845	−	0.525806i
$894$		0			0
$895$	−15.4419	+	11.2192i	−0.516165	+	0.375016i
$896$	−3.19365	−	1.03768i	−0.106692	−	0.0346665i
$897$		0			0
$898$	−10.2991	−	14.1755i	−0.343685	−	0.473042i
$899$	−1.28914	−	0.936617i	−0.0429953	−	0.0312379i
$900$		0			0
$901$		−	1.26075i		−	0.0420018i
$902$	−0.505907	+	3.31240i	−0.0168449	+	0.110291i
$903$		0			0
$904$	−6.11020	+	1.98532i	−0.203222	+	0.0660309i
$905$	−1.94700	+	2.67982i	−0.0647205	+	0.0890801i
$906$		0			0
$907$	15.2231	−	46.8519i	0.505475	−	1.55569i	−0.294496	−	0.955653i	$-0.595152\pi$
$907$	15.2231	−	46.8519i	0.505475	−	1.55569i	0.799971	−	0.600039i	$-0.204848\pi$
$908$	−2.82606	+	8.69773i	−0.0937862	+	0.288644i
$909$		0			0
$910$	6.10878	−	8.40801i	0.202504	−	0.278723i
$911$	34.1551	−	11.0977i	1.13161	−	0.367682i	0.317422	−	0.948284i	$-0.397183\pi$
$911$	34.1551	−	11.0977i	1.13161	−	0.367682i	0.814188	+	0.580602i	$0.197183\pi$
$912$		0			0
$913$	3.45946	−	22.6506i	0.114491	−	0.749625i
$914$		−	8.65970i		−	0.286437i
$915$		0			0
$916$	−1.06804	−	0.775979i	−0.0352892	−	0.0256391i
$917$	5.19937	+	7.15632i	0.171698	+	0.236323i
$918$		0			0
$919$	−4.16272	−	1.35255i	−0.137316	−	0.0446165i	0.239553	−	0.970883i	$-0.422999\pi$
$919$	−4.16272	−	1.35255i	−0.137316	−	0.0446165i	−0.376868	+	0.926267i	$0.622999\pi$
$920$	2.79645	−	2.03174i	0.0921963	−	0.0669845i
$921$		0			0
$922$	−9.73221	−	29.9527i	−0.320513	−	0.986438i
$923$	−40.6524			−1.33809
$924$		0			0
$925$	−4.89199			−0.160848
$926$	−0.122874	−	0.378166i	−0.00403787	−	0.0124273i
$927$		0			0
$928$	−0.129183	+	0.0938569i	−0.00424064	+	0.00308100i
$929$	−14.7720	−	4.79971i	−0.484653	−	0.157473i	0.0564913	−	0.998403i	$-0.482009\pi$
$929$	−14.7720	−	4.79971i	−0.484653	−	0.157473i	−0.541144	+	0.840930i	$0.682009\pi$
$930$		0			0
$931$	−8.48129	−	11.6735i	−0.277963	−	0.382583i
$932$	−23.4763	−	17.0566i	−0.768993	−	0.558706i
$933$		0			0
$934$		−	11.6101i		−	0.379894i
$935$	0.818134	−	1.62783i	0.0267559	−	0.0532357i
$936$		0			0
$937$	32.4805	−	10.5536i	1.06109	−	0.344770i	0.274080	−	0.961707i	$-0.411627\pi$
$937$	32.4805	−	10.5536i	1.06109	−	0.344770i	0.787013	+	0.616937i	$0.211627\pi$
$938$	−4.41306	+	6.07405i	−0.144091	+	0.198325i
$939$		0			0
$940$	−1.51301	+	4.65656i	−0.0493488	+	0.151880i
$941$	−11.9543	+	36.7916i	−0.389700	+	1.19937i	0.543313	+	0.839530i	$0.317170\pi$
$941$	−11.9543	+	36.7916i	−0.389700	+	1.19937i	−0.933013	+	0.359843i	$0.882830\pi$
$942$		0			0
$943$	2.05268	−	2.82527i	0.0668445	−	0.0920036i
$944$	9.52716	−	3.09556i	0.310083	−	0.100752i
$945$		0			0
$946$	−24.2539	+	12.5271i	−0.788563	+	0.407291i
$947$		−	39.6726i		−	1.28918i	−0.764526	−	0.644592i	$-0.777027\pi$
$947$		−	39.6726i		−	1.28918i	0.764526	−	0.644592i	$-0.222973\pi$
$948$		0			0
$949$	−13.4591	−	9.77863i	−0.436902	−	0.317428i
$950$	−1.98338	−	2.72988i	−0.0643492	−	0.0885691i
$951$		0			0
$952$	1.75431	+	0.570009i	0.0568574	+	0.0184741i
$953$	22.4624	−	16.3199i	0.727628	−	0.528653i	−0.161184	−	0.986924i	$-0.551531\pi$
$953$	22.4624	−	16.3199i	0.727628	−	0.528653i	0.888812	+	0.458271i	$0.151531\pi$
$954$		0			0
$955$	5.61070	+	17.2679i	0.181558	+	0.558778i
$956$	−14.7023			−0.475506
$957$		0			0
$958$	11.3379			0.366311
$959$	−11.5001	−	35.3937i	−0.371358	−	1.14292i
$960$		0			0
$961$	−55.4860	+	40.3129i	−1.78987	+	1.30042i
$962$	−14.3995	−	4.67867i	−0.464258	−	0.150846i
$963$		0			0
$964$	10.9397	+	15.0572i	0.352343	+	0.484959i
$965$	20.7146	+	15.0500i	0.666827	+	0.484478i
$966$		0			0
$967$			7.18678i			0.231111i	0.993301	+	0.115556i	$0.0368649\pi$
$967$			7.18678i			0.231111i	−0.993301	+	0.115556i	$0.963135\pi$
$968$	−10.4985	−	3.28350i	−0.337435	−	0.105536i
$969$		0			0
$970$	−5.26787	+	1.71164i	−0.169141	+	0.0549573i
$971$	−16.5408	+	22.7664i	−0.530818	+	0.730609i	−0.987255	−	0.159147i	$-0.949126\pi$
$971$	−16.5408	+	22.7664i	−0.530818	+	0.730609i	0.456437	+	0.889756i	$0.349126\pi$
$972$		0			0
$973$	19.4033	−	59.7171i	0.622040	−	1.91444i
$974$	6.26142	−	19.2707i	0.200629	−	0.617472i
$975$		0			0
$976$	5.43102	−	7.47515i	0.173843	−	0.239274i
$977$	28.1915	−	9.15999i	0.901927	−	0.293054i	0.178895	−	0.983868i	$-0.442748\pi$
$977$	28.1915	−	9.15999i	0.901927	−	0.293054i	0.723032	+	0.690814i	$0.242748\pi$
$978$		0			0
$979$	0.720998	+	4.39506i	0.0230432	+	0.140467i
$980$			4.27619i			0.136598i
$981$		0			0
$982$	−10.0498	−	7.30162i	−0.320703	−	0.233004i
$983$	−27.3665	−	37.6667i	−0.872855	−	1.20138i	−0.978349	−	0.206962i	$-0.933642\pi$
$983$	−27.3665	−	37.6667i	−0.872855	−	1.20138i	0.105494	−	0.994420i	$-0.466358\pi$
$984$		0			0
$985$	−1.99719	−	0.648927i	−0.0636359	−	0.0206765i
$986$	0.0709616	−	0.0515567i	0.00225988	−	0.00164190i
$987$		0			0
$988$	−3.22718	−	9.93224i	−0.102670	−	0.315987i
$989$	28.4501			0.904662
$990$		0			0
$991$	−29.6860			−0.943007			−0.471503	−	0.881864i	$-0.656288\pi$
$991$	−29.6860			−0.943007			−0.471503	+	0.881864i	$0.656288\pi$
$992$	3.08374	+	9.49078i	0.0979089	+	0.301333i
$993$		0			0
$994$	35.6837	−	25.9257i	1.13182	−	0.822315i
$995$	−15.9625	−	5.18653i	−0.506046	−	0.164424i
$996$		0			0
$997$	26.9056	+	37.0323i	0.852108	+	1.17283i	0.983394	+	0.181481i	$0.0580891\pi$
$997$	26.9056	+	37.0323i	0.852108	+	1.17283i	−0.131287	+	0.991344i	$0.541911\pi$
$998$	4.55484	+	3.30929i	0.144181	+	0.104754i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.z.a.611.4	yes	32
3.2	odd	2		990.2.z.b.611.8	yes	32
11.2	odd	10		990.2.z.b.431.8	yes	32
33.2	even	10	inner	990.2.z.a.431.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.z.a.431.4	✓	32	33.2	even	10	inner
990.2.z.a.611.4	yes	32	1.1	even	1	trivial
990.2.z.b.431.8	yes	32	11.2	odd	10
990.2.z.b.611.8	yes	32	3.2	odd	2

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.951057 - 0.309017i) q^{5} +(1.97378 + 2.71668i) q^{7} +(-0.809017 - 0.587785i) q^{8} -1.00000i q^{10} +(3.27288 - 0.536907i) q^{11} +(2.94348 - 0.956394i) q^{13} +(-1.97378 + 2.71668i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-0.169746 + 0.522426i) q^{17} +(-1.98338 + 2.72988i) q^{19} +(0.951057 - 0.309017i) q^{20} +(1.52200 + 2.94678i) q^{22} -3.45661i q^{23} +(0.809017 + 0.587785i) q^{25} +(1.81917 + 2.50387i) q^{26} +(-3.19365 - 1.03768i) q^{28} +(-0.129183 + 0.0938569i) q^{29} +(3.08374 + 9.49078i) q^{31} +1.00000 q^{32} -0.549311 q^{34} +(-1.03768 - 3.19365i) q^{35} +(-3.95771 + 2.87544i) q^{37} +(-3.20917 - 1.04272i) q^{38} +(0.587785 + 0.809017i) q^{40} +(0.817355 + 0.593843i) q^{41} +8.23066i q^{43} +(-2.33223 + 2.35812i) q^{44} +(3.28743 - 1.06815i) q^{46} +(-2.87791 + 3.96110i) q^{47} +(-1.32141 + 4.06689i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-1.81917 + 2.50387i) q^{52} +(-2.18282 + 0.709241i) q^{53} +(-3.27861 - 0.500746i) q^{55} -3.35800i q^{56} +(-0.129183 - 0.0938569i) q^{58} +(5.88811 + 8.10429i) q^{59} +(8.78757 + 2.85525i) q^{61} +(-8.07334 + 5.86563i) q^{62} +(0.309017 + 0.951057i) q^{64} -3.09496 q^{65} +2.23583 q^{67} +(-0.169746 - 0.522426i) q^{68} +(2.71668 - 1.97378i) q^{70} +(-12.4922 - 4.05895i) q^{71} +(-3.15954 - 4.34873i) q^{73} +(-3.95771 - 2.87544i) q^{74} -3.37432i q^{76} +(7.91856 + 7.83163i) q^{77} +(14.6412 - 4.75721i) q^{79} +(-0.587785 + 0.809017i) q^{80} +(-0.312202 + 0.960859i) q^{82} +(2.13488 - 6.57048i) q^{83} +(0.322877 - 0.444402i) q^{85} +(-7.82782 + 2.54341i) q^{86} +(-2.96340 - 1.48938i) q^{88} +1.34287i q^{89} +(8.40801 + 6.10878i) q^{91} +(2.03174 + 2.79645i) q^{92} +(-4.65656 - 1.51301i) q^{94} +(2.72988 - 1.98338i) q^{95} +(-1.71164 - 5.26787i) q^{97} -4.27619 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{2} - 8 q^{4} - 8 q^{8} - 8 q^{16} + 4 q^{17} + 8 q^{25} - 8 q^{29} + 32 q^{31} + 32 q^{32} + 24 q^{34} + 16 q^{37} + 32 q^{41} - 20 q^{46} - 20 q^{47} + 16 q^{49} + 8 q^{50} - 40 q^{53} + 8 q^{55}+ \cdots + 16 q^{98}+O(q^{100}) \) 32 * q - 8 * q^2 - 8 * q^4 - 8 * q^8 - 8 * q^16 + 4 * q^17 + 8 * q^25 - 8 * q^29 + 32 * q^31 + 32 * q^32 + 24 * q^34 + 16 * q^37 + 32 * q^41 - 20 * q^46 - 20 * q^47 + 16 * q^49 + 8 * q^50 - 40 * q^53 + 8 * q^55 - 8 * q^58 + 40 * q^59 - 28 * q^62 - 8 * q^64 + 8 * q^65 + 4 * q^68 - 40 * q^71 + 40 * q^73 + 16 * q^74 - 28 * q^77 + 20 * q^79 - 8 * q^82 - 24 * q^83 - 24 * q^91 + 20 * q^94 + 16 * q^95 + 48 * q^97 + 16 * q^98

Introduction

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