LMFDB - Embedded newform 459.2.o.a.370.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(64,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.64"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.o (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			370.11
Character	$\chi$	$=$	459.370
Dual form			459.2.o.a.361.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15506 + 0.666877i) q^{2} +(-0.110551 - 0.191481i) q^{4} +(0.0545182 - 0.203465i) q^{5} +(-0.965572 - 3.60357i) q^{7} -2.96240i q^{8} +(0.198658 - 0.198658i) q^{10} +(-0.0436083 - 0.162748i) q^{11} +(0.706706 + 1.22405i) q^{13} +(1.28784 - 4.80627i) q^{14} +(1.75445 - 3.03880i) q^{16} +(4.12302 + 0.0270617i) q^{17} -5.28066i q^{19} +(-0.0449866 + 0.0120541i) q^{20} +(0.0581627 - 0.217066i) q^{22} +(-6.79301 - 1.82018i) q^{23} +(4.29170 + 2.47781i) q^{25} +1.88514i q^{26} +(-0.583267 + 0.583267i) q^{28} +(3.22202 - 0.863336i) q^{29} +(-1.82059 + 6.79453i) q^{31} +(-1.07802 + 0.622394i) q^{32} +(4.74430 + 2.78080i) q^{34} -0.785840 q^{35} +(6.83838 + 6.83838i) q^{37} +(3.52155 - 6.09950i) q^{38} +(-0.602745 - 0.161505i) q^{40} +(-3.60410 - 0.965717i) q^{41} +(5.92513 + 3.42088i) q^{43} +(-0.0263422 + 0.0263422i) q^{44} +(-6.63253 - 6.63253i) q^{46} +(-1.01890 + 1.76479i) q^{47} +(-5.99118 + 3.45901i) q^{49} +(3.30479 + 5.72407i) q^{50} +(0.156255 - 0.270641i) q^{52} -6.04183i q^{53} -0.0354910 q^{55} +(-10.6752 + 2.86041i) q^{56} +(4.29737 + 1.15148i) q^{58} +(-0.580968 + 0.335422i) q^{59} +(-0.801711 - 2.99203i) q^{61} +(-6.63401 + 6.63401i) q^{62} -8.67806 q^{64} +(0.287580 - 0.0770567i) q^{65} +(-2.21819 - 3.84202i) q^{67} +(-0.450623 - 0.792469i) q^{68} +(-0.907696 - 0.524058i) q^{70} +(5.52395 + 5.52395i) q^{71} +(-4.07769 - 4.07769i) q^{73} +(3.33841 + 12.4591i) q^{74} +(-1.01114 + 0.583784i) q^{76} +(-0.544367 + 0.314290i) q^{77} +(0.350417 + 1.30778i) q^{79} +(-0.522640 - 0.522640i) q^{80} +(-3.51896 - 3.51896i) q^{82} +(3.07278 + 1.77407i) q^{83} +(0.230286 - 0.837414i) q^{85} +(4.56261 + 7.90266i) q^{86} +(-0.482126 + 0.129185i) q^{88} +15.8264 q^{89} +(3.72857 - 3.72857i) q^{91} +(0.402447 + 1.50195i) q^{92} +(-2.35380 + 1.35897i) q^{94} +(-1.07443 - 0.287893i) q^{95} +(-8.66597 + 2.32204i) q^{97} -9.22692 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 24 q^{4} + 2 q^{5} - 2 q^{7} - 16 q^{10} - 4 q^{13} - 16 q^{16} + 8 q^{17} - 18 q^{20} - 4 q^{22} + 8 q^{23} + 10 q^{29} - 2 q^{31} + 20 q^{34} + 128 q^{35} - 8 q^{37} + 24 q^{38} - 20 q^{40} - 32 q^{41}+ \cdots - 208 q^{98}+O(q^{100}) $ 64 * q + 24 * q^4 + 2 * q^5 - 2 * q^7 - 16 * q^10 - 4 * q^13 - 16 * q^16 + 8 * q^17 - 18 * q^20 - 4 * q^22 + 8 * q^23 + 10 * q^29 - 2 * q^31 + 20 * q^34 + 128 * q^35 - 8 * q^37 + 24 * q^38 - 20 * q^40 - 32 * q^41 - 20 * q^44 - 40 * q^46 + 64 * q^47 - 48 * q^50 + 36 * q^52 - 16 * q^55 - 12 * q^56 - 10 * q^58 - 2 * q^61 + 28 * q^62 - 8 * q^64 - 8 * q^65 - 4 * q^67 + 60 * q^68 + 84 * q^71 - 44 * q^73 + 14 * q^74 + 10 * q^79 - 204 * q^80 - 52 * q^82 + 22 * q^85 - 32 * q^86 + 16 * q^88 - 128 * q^89 + 44 * q^91 - 136 * q^92 - 4 * q^95 - 44 * q^97 - 208 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.15506	+	0.666877i	0.816754	+	0.471553i	0.849296	−	0.527917i	$-0.177027\pi$
$2$	1.15506	+	0.666877i	0.816754	+	0.471553i	−0.0325421	+	0.999470i	$0.510360\pi$
$3$		0			0
$3$		0			0
$4$	−0.110551	−	0.191481i	−0.0552757	−	0.0957403i
$5$	0.0545182	−	0.203465i	0.0243813	−	0.0909923i	−0.952663	−	0.304028i	$-0.901668\pi$
$5$	0.0545182	−	0.203465i	0.0243813	−	0.0909923i	0.977044	+	0.213036i	$0.0683351\pi$
$6$		0			0
$7$	−0.965572	−	3.60357i	−0.364952	−	1.36202i	−0.867486	−	0.497462i	$-0.834265\pi$
$7$	−0.965572	−	3.60357i	−0.364952	−	1.36202i	0.502534	−	0.864558i	$-0.332401\pi$
$8$		−	2.96240i		−	1.04737i
$9$		0			0
$10$	0.198658	−	0.198658i	0.0628212	−	0.0628212i
$11$	−0.0436083	−	0.162748i	−0.0131484	−	0.0490704i	0.959040	−	0.283271i	$-0.0914195\pi$
$11$	−0.0436083	−	0.162748i	−0.0131484	−	0.0490704i	−0.972188	+	0.234200i	$0.924753\pi$
$12$		0			0
$13$	0.706706	+	1.22405i	0.196005	+	0.339491i	0.947230	−	0.320556i	$-0.103870\pi$
$13$	0.706706	+	1.22405i	0.196005	+	0.339491i	−0.751225	+	0.660047i	$0.770536\pi$
$14$	1.28784	−	4.80627i	0.344188	−	1.28453i
$15$		0			0
$16$	1.75445	−	3.03880i	0.438614	−	0.759701i
$17$	4.12302	+	0.0270617i	0.999978	+	0.00656344i
$17$	4.12302	+	0.0270617i	0.999978	+	0.00656344i
$18$		0			0
$19$		−	5.28066i		−	1.21147i	−0.795667	−	0.605734i	$-0.792880\pi$
$19$		−	5.28066i		−	1.21147i	0.795667	−	0.605734i	$-0.207120\pi$
$20$	−0.0449866	+	0.0120541i	−0.0100593	+	0.00269539i
$21$		0			0
$22$	0.0581627	−	0.217066i	0.0124003	−	0.0462786i
$23$	−6.79301	−	1.82018i	−1.41644	−	0.379534i	−0.532221	−	0.846605i	$-0.678642\pi$
$23$	−6.79301	−	1.82018i	−1.41644	−	0.379534i	−0.884220	+	0.467071i	$0.845309\pi$
$24$		0			0
$25$	4.29170	+	2.47781i	0.858340	+	0.495563i
$26$			1.88514i			0.369707i
$27$		0			0
$28$	−0.583267	+	0.583267i	−0.110227	+	0.110227i
$29$	3.22202	−	0.863336i	0.598313	−	0.160318i	0.0530634	−	0.998591i	$-0.483101\pi$
$29$	3.22202	−	0.863336i	0.598313	−	0.160318i	0.545250	+	0.838274i	$0.316435\pi$
$30$		0			0
$31$	−1.82059	+	6.79453i	−0.326987	+	1.22033i	0.585311	+	0.810809i	$0.300972\pi$
$31$	−1.82059	+	6.79453i	−0.326987	+	1.22033i	−0.912299	+	0.409525i	$0.865694\pi$
$32$	−1.07802	+	0.622394i	−0.190568	+	0.110025i
$33$		0			0
$34$	4.74430	+	2.78080i	0.813641	+	0.476903i
$35$	−0.785840			−0.132831
$36$		0			0
$37$	6.83838	+	6.83838i	1.12422	+	1.12422i	0.991099	+	0.133124i	$0.0425007\pi$
$37$	6.83838	+	6.83838i	1.12422	+	1.12422i	0.133124	+	0.991099i	$0.457499\pi$
$38$	3.52155	−	6.09950i	0.571271	−	0.989470i
$39$		0			0
$40$	−0.602745	−	0.161505i	−0.0953023	−	0.0255362i
$41$	−3.60410	−	0.965717i	−0.562867	−	0.150820i	−0.0338436	−	0.999427i	$-0.510775\pi$
$41$	−3.60410	−	0.965717i	−0.562867	−	0.150820i	−0.529023	+	0.848607i	$0.677441\pi$
$42$		0			0
$43$	5.92513	+	3.42088i	0.903574	+	0.521679i	0.878358	−	0.478003i	$-0.158639\pi$
$43$	5.92513	+	3.42088i	0.903574	+	0.521679i	0.0252162	+	0.999682i	$0.491973\pi$
$44$	−0.0263422	+	0.0263422i	−0.00397123	+	0.00397123i
$45$		0			0
$46$	−6.63253	−	6.63253i	−0.977913	−	0.977913i
$47$	−1.01890	+	1.76479i	−0.148622	+	0.257421i	−0.930719	−	0.365736i	$-0.880817\pi$
$47$	−1.01890	+	1.76479i	−0.148622	+	0.257421i	0.782096	+	0.623158i	$0.214151\pi$
$48$		0			0
$49$	−5.99118	+	3.45901i	−0.855882	+	0.494144i
$50$	3.30479	+	5.72407i	0.467368	+	0.809506i
$51$		0			0
$52$	0.156255	−	0.270641i	0.0216686	−	0.0375311i
$53$		−	6.04183i		−	0.829909i	−0.909842	−	0.414954i	$-0.863798\pi$
$53$		−	6.04183i		−	0.829909i	0.909842	−	0.414954i	$-0.136202\pi$
$54$		0			0
$55$	−0.0354910			−0.00478560
$56$	−10.6752	+	2.86041i	−1.42654	+	0.382239i
$57$		0			0
$58$	4.29737	+	1.15148i	0.564273	+	0.151196i
$59$	−0.580968	+	0.335422i	−0.0756355	+	0.0436682i	−0.537341	−	0.843365i	$-0.680571\pi$
$59$	−0.580968	+	0.335422i	−0.0756355	+	0.0436682i	0.461705	+	0.887033i	$0.347238\pi$
$60$		0			0
$61$	−0.801711	−	2.99203i	−0.102649	−	0.383090i	0.895419	−	0.445224i	$-0.146876\pi$
$61$	−0.801711	−	2.99203i	−0.102649	−	0.383090i	−0.998068	+	0.0621342i	$0.980209\pi$
$62$	−6.63401	+	6.63401i	−0.842520	+	0.842520i
$63$		0			0
$64$	−8.67806			−1.08476
$65$	0.287580	−	0.0770567i	0.0356699	−	0.00955771i
$66$		0			0
$67$	−2.21819	−	3.84202i	−0.270995	−	0.469377i	0.698122	−	0.715979i	$-0.254019\pi$
$67$	−2.21819	−	3.84202i	−0.270995	−	0.469377i	−0.969117	+	0.246602i	$0.920686\pi$
$68$	−0.450623	−	0.792469i	−0.0546461	−	0.0961010i
$69$		0			0
$70$	−0.907696	−	0.524058i	−0.108490	−	0.0626370i
$71$	5.52395	+	5.52395i	0.655572	+	0.655572i	0.954329	−	0.298757i	$-0.0965721\pi$
$71$	5.52395	+	5.52395i	0.655572	+	0.655572i	−0.298757	+	0.954329i	$0.596572\pi$
$72$		0			0
$73$	−4.07769	−	4.07769i	−0.477257	−	0.477257i	0.426996	−	0.904253i	$-0.359572\pi$
$73$	−4.07769	−	4.07769i	−0.477257	−	0.477257i	−0.904253	+	0.426996i	$0.859572\pi$
$74$	3.33841	+	12.4591i	0.388083	+	1.44834i
$75$		0			0
$76$	−1.01114	+	0.583784i	−0.115986	+	0.0669647i
$77$	−0.544367	+	0.314290i	−0.0620364	+	0.0358167i
$78$		0			0
$79$	0.350417	+	1.30778i	0.0394250	+	0.147136i	0.982833	−	0.184499i	$-0.0590663\pi$
$79$	0.350417	+	1.30778i	0.0394250	+	0.147136i	−0.943408	+	0.331635i	$0.892400\pi$
$80$	−0.522640	−	0.522640i	−0.0584329	−	0.0584329i
$81$		0			0
$82$	−3.51896	−	3.51896i	−0.388604	−	0.388604i
$83$	3.07278	+	1.77407i	0.337282	+	0.194730i	0.659069	−	0.752082i	$-0.270950\pi$
$83$	3.07278	+	1.77407i	0.337282	+	0.194730i	−0.321788	+	0.946812i	$0.604284\pi$
$84$		0			0
$85$	0.230286	−	0.837414i	0.0249780	−	0.0908303i
$86$	4.56261	+	7.90266i	0.491998	+	0.852166i
$87$		0			0
$88$	−0.482126	+	0.129185i	−0.0513948	+	0.0137712i
$89$	15.8264			1.67759			0.838797	−	0.544444i	$-0.183259\pi$
$89$	15.8264			1.67759			0.838797	+	0.544444i	$0.183259\pi$
$90$		0			0
$91$	3.72857	−	3.72857i	0.390860	−	0.390860i
$92$	0.402447	+	1.50195i	0.0419580	+	0.156589i
$93$		0			0
$94$	−2.35380	+	1.35897i	−0.242776	+	0.140167i
$95$	−1.07443	−	0.287893i	−0.110234	−	0.0295371i
$96$		0			0
$97$	−8.66597	+	2.32204i	−0.879895	+	0.235767i	−0.670362	−	0.742034i	$-0.733861\pi$
$97$	−8.66597	+	2.32204i	−0.879895	+	0.235767i	−0.209533	+	0.977801i	$0.567195\pi$
$98$	−9.22692			−0.932060
$99$		0			0
$100$		−	1.09570i		−	0.109570i
$101$	−7.35059	+	12.7316i	−0.731411	+	1.26684i	0.224870	+	0.974389i	$0.427804\pi$
$101$	−7.35059	+	12.7316i	−0.731411	+	1.26684i	−0.956280	+	0.292452i	$0.905529\pi$
$102$		0			0
$103$	7.74773	+	13.4195i	0.763406	+	1.32226i	0.941085	+	0.338170i	$0.109808\pi$
$103$	7.74773	+	13.4195i	0.763406	+	1.32226i	−0.177679	+	0.984088i	$0.556859\pi$
$104$	3.62613	−	2.09355i	0.355571	−	0.205289i
$105$		0			0
$106$	4.02915	−	6.97870i	0.391346	−	0.677831i
$107$	−11.1012	−	11.1012i	−1.07320	−	1.07320i	−0.997101	−	0.0760947i	$-0.975755\pi$
$107$	−11.1012	−	11.1012i	−1.07320	−	1.07320i	−0.0760947	−	0.997101i	$-0.524245\pi$
$108$		0			0
$109$	−10.4007	+	10.4007i	−0.996204	+	0.996204i	−0.999993	−	0.00378912i	$-0.998794\pi$
$109$	−10.4007	+	10.4007i	−0.996204	+	0.996204i	0.00378912	+	0.999993i	$0.498794\pi$
$110$	−0.0409944	−	0.0236681i	−0.00390866	−	0.00225667i
$111$		0			0
$112$	−12.6446	−	3.38811i	−1.19480	−	0.320146i
$113$	13.5285	+	3.62495i	1.27265	+	0.341006i	0.831047	−	0.556203i	$-0.187742\pi$
$113$	13.5285	+	3.62495i	1.27265	+	0.341006i	0.441606	+	0.897209i	$0.354409\pi$
$114$		0			0
$115$	−0.740686	+	1.28291i	−0.0690693	+	0.119632i
$116$	−0.521510	−	0.521510i	−0.0484210	−	0.0484210i
$117$		0			0
$118$	−0.894740			−0.0823675
$119$	−3.88355	−	14.8837i	−0.356005	−	1.36439i
$120$		0			0
$121$	9.50169	−	5.48581i	0.863790	−	0.498710i
$122$	1.06929	−	3.99063i	0.0968085	−	0.361294i
$123$		0			0
$124$	1.50229	−	0.402537i	0.134910	−	0.0361489i
$125$	1.48286	−	1.48286i	0.132631	−	0.132631i
$126$		0			0
$127$			0.370683i			0.0328928i	0.999865	+	0.0164464i	$0.00523529\pi$
$127$			0.370683i			0.0328928i	−0.999865	+	0.0164464i	$0.994765\pi$
$128$	−7.86768	−	4.54240i	−0.695411	−	0.401496i
$129$		0			0
$130$	0.383560	+	0.102775i	0.0336405	+	0.00901393i
$131$	−0.674611	+	2.51768i	−0.0589410	+	0.219971i	−0.989114	−	0.147150i	$-0.952990\pi$
$131$	−0.674611	+	2.51768i	−0.0589410	+	0.219971i	0.930173	+	0.367121i	$0.119657\pi$
$132$		0			0
$133$	−19.0292	+	5.09886i	−1.65004	+	0.442127i
$134$		−	5.91703i		−	0.511154i
$135$		0			0
$136$	0.0801678	−	12.2140i	0.00687433	−	1.04734i
$137$	5.56708	−	9.64246i	0.475628	−	0.823811i	−0.523983	−	0.851729i	$-0.675554\pi$
$137$	5.56708	−	9.64246i	0.475628	−	0.823811i	0.999610	+	0.0279179i	$0.00888769\pi$
$138$		0			0
$139$	2.63093	−	9.81876i	0.223152	−	0.832816i	−0.759984	−	0.649942i	$-0.774793\pi$
$139$	2.63093	−	9.81876i	0.223152	−	0.832816i	0.983136	−	0.182874i	$-0.0585402\pi$
$140$	0.0868757	+	0.150473i	0.00734234	+	0.0127173i
$141$		0			0
$142$	2.69672	+	10.0643i	0.226304	+	0.844578i
$143$	0.168394	−	0.168394i	0.0140818	−	0.0140818i
$144$		0			0
$145$		−	0.702634i		−	0.0583506i
$146$	−1.99068	−	7.42931i	−0.164750	−	0.614854i
$147$		0			0
$148$	0.553425	−	2.06541i	0.0454912	−	0.169776i
$149$	7.83470	+	13.5701i	0.641843	+	1.11171i	0.985021	+	0.172435i	$0.0551634\pi$
$149$	7.83470	+	13.5701i	0.641843	+	1.11171i	−0.343178	+	0.939271i	$0.611503\pi$
$150$		0			0
$151$	−0.491938	−	0.284020i	−0.0400333	−	0.0231132i	0.479850	−	0.877351i	$-0.340691\pi$
$151$	−0.491938	−	0.284020i	−0.0400333	−	0.0231132i	−0.519883	+	0.854237i	$0.674024\pi$
$152$	−15.6435			−1.26885
$153$		0			0
$154$	−0.838372			−0.0675579
$155$	1.28319	+	0.740852i	0.103069	+	0.0595067i
$156$		0			0
$157$	4.92247	+	8.52597i	0.392856	+	0.680447i	0.992825	−	0.119577i	$-0.0381537\pi$
$157$	4.92247	+	8.52597i	0.392856	+	0.680447i	−0.599969	+	0.800023i	$0.704820\pi$
$158$	−0.467370	+	1.74425i	−0.0371820	+	0.138765i
$159$		0			0
$160$	0.0678636	+	0.253271i	0.00536509	+	0.0200228i
$161$			26.2366i			2.06773i
$162$		0			0
$163$	6.29369	−	6.29369i	0.492960	−	0.492960i	−0.416278	−	0.909237i	$-0.636666\pi$
$163$	6.29369	−	6.29369i	0.492960	−	0.492960i	0.909237	+	0.416278i	$0.136666\pi$
$164$	0.213523	+	0.796877i	0.0166733	+	0.0622257i
$165$		0			0
$166$	2.36617	+	4.09833i	0.183651	+	0.318092i
$167$	1.96230	−	7.32340i	0.151847	−	0.566701i	−0.847508	−	0.530783i	$-0.821898\pi$
$167$	1.96230	−	7.32340i	0.151847	−	0.566701i	0.999355	−	0.0359181i	$-0.0114355\pi$
$168$		0			0
$169$	5.50113	−	9.52824i	0.423164	−	0.732942i
$170$	0.824446	−	0.813694i	0.0632322	−	0.0624075i
$171$		0			0
$172$		−	1.51273i		−	0.115345i
$173$	3.48458	−	0.933690i	0.264928	−	0.0709872i	−0.123910	−	0.992293i	$-0.539543\pi$
$173$	3.48458	−	0.933690i	0.264928	−	0.0709872i	0.388838	+	0.921306i	$0.372877\pi$
$174$		0			0
$175$	4.78502	−	17.8579i	0.361713	−	1.34993i
$176$	−0.571069	−	0.153017i	−0.0430459	−	0.0115341i
$177$		0			0
$178$	18.2805	+	10.5543i	1.37018	+	0.791075i
$179$			5.94978i			0.444708i	0.974966	+	0.222354i	$0.0713740\pi$
$179$			5.94978i			0.444708i	−0.974966	+	0.222354i	$0.928626\pi$
$180$		0			0
$181$	−10.2138	+	10.2138i	−0.759183	+	0.759183i	−0.976174	−	0.216991i	$-0.930376\pi$
$181$	−10.2138	+	10.2138i	−0.759183	+	0.759183i	0.216991	+	0.976174i	$0.430376\pi$
$182$	6.79323	−	1.82024i	0.503548	−	0.134925i
$183$		0			0
$184$	−5.39211	+	20.1236i	−0.397512	+	1.48353i
$185$	1.76419	−	1.01855i	0.129706	−	0.0748856i
$186$		0			0
$187$	−0.175393	−	0.672194i	−0.0128260	−	0.0491557i
$188$	0.450564			0.0328608
$189$		0			0
$190$	−1.04905	−	1.04905i	−0.0761058	−	0.0761058i
$191$	3.81360	−	6.60535i	0.275942	−	0.477946i	−0.694430	−	0.719560i	$-0.744343\pi$
$191$	3.81360	−	6.60535i	0.275942	−	0.477946i	0.970372	+	0.241614i	$0.0776767\pi$
$192$		0			0
$193$	−0.507121	−	0.135883i	−0.0365034	−	0.00978105i	0.240521	−	0.970644i	$-0.422682\pi$
$193$	−0.507121	−	0.135883i	−0.0365034	−	0.00978105i	−0.277025	+	0.960863i	$0.589348\pi$
$194$	−11.5583	−	3.09703i	−0.829835	−	0.222353i
$195$		0			0
$196$	1.32466	+	0.764796i	0.0946189	+	0.0546283i
$197$	13.4803	−	13.4803i	0.960430	−	0.960430i	−0.0388165	−	0.999246i	$-0.512359\pi$
$197$	13.4803	−	13.4803i	0.960430	−	0.960430i	0.999246	+	0.0388165i	$0.0123588\pi$
$198$		0			0
$199$	15.0652	+	15.0652i	1.06795	+	1.06795i	0.997517	+	0.0704282i	$0.0224366\pi$
$199$	15.0652	+	15.0652i	1.06795	+	1.06795i	0.0704282	+	0.997517i	$0.477563\pi$
$200$	7.34029	−	12.7137i	0.519037	−	0.898998i
$201$		0			0
$202$	−16.9808	+	9.80387i	−1.19476	+	0.689798i
$203$	−6.22218	−	10.7771i	−0.436711	−	0.756406i
$204$		0			0
$205$	−0.392979	+	0.680660i	−0.0274468	+	0.0475393i
$206$			20.6671i			1.43995i
$207$		0			0
$208$	4.95953			0.343882
$209$	−0.859419	+	0.230281i	−0.0594472	+	0.0159288i
$210$		0			0
$211$	−26.2576	−	7.03571i	−1.80765	−	0.484358i	−0.812519	−	0.582934i	$-0.801905\pi$
$211$	−26.2576	−	7.03571i	−1.80765	−	0.484358i	−0.995130	+	0.0985760i	$0.968571\pi$
$212$	−1.15689	+	0.667932i	−0.0794557	+	0.0458737i
$213$		0			0
$214$	−5.41948	−	20.2258i	−0.370468	−	1.38260i
$215$	1.01906	−	1.01906i	0.0694991	−	0.0694991i
$216$		0			0
$217$	26.2424			1.78145
$218$	−18.9494	+	5.07748i	−1.28342	+	0.343890i
$219$		0			0
$220$	0.00392358	+	0.00679583i	0.000264527	+	0.000458175i
$221$	2.88064	+	5.06591i	0.193773	+	0.340770i
$222$		0			0
$223$	18.2255	+	10.5225i	1.22047	+	0.704638i	0.965018	−	0.262183i	$-0.0844425\pi$
$223$	18.2255	+	10.5225i	1.22047	+	0.704638i	0.255452	+	0.966822i	$0.417776\pi$
$224$	3.28374	+	3.28374i	0.219404	+	0.219404i
$225$		0			0
$226$	13.2089	+	13.2089i	0.878641	+	0.878641i
$227$	3.71004	+	13.8461i	0.246244	+	0.918995i	0.972754	+	0.231839i	$0.0744743\pi$
$227$	3.71004	+	13.8461i	0.246244	+	0.918995i	−0.726510	+	0.687156i	$0.758859\pi$
$228$		0			0
$229$	20.1226	−	11.6178i	1.32974	−	0.767723i	0.344477	−	0.938795i	$-0.388056\pi$
$229$	20.1226	−	11.6178i	1.32974	−	0.767723i	0.985259	+	0.171072i	$0.0547229\pi$
$230$	−1.71108	+	0.987892i	−0.112825	+	0.0651397i
$231$		0			0
$232$	−2.55755	−	9.54491i	−0.167911	−	0.626654i
$233$	−17.8322	−	17.8322i	−1.16823	−	1.16823i	−0.982625	−	0.185602i	$-0.940576\pi$
$233$	−17.8322	−	17.8322i	−1.16823	−	1.16823i	−0.185602	−	0.982625i	$-0.559424\pi$
$234$		0			0
$235$	0.303524	+	0.303524i	0.0197997	+	0.0197997i
$236$	0.128453	+	0.0741627i	0.00836161	+	0.00482758i
$237$		0			0
$238$	5.43983	−	19.7815i	0.352612	−	1.28224i
$239$	−12.6575	−	21.9234i	−0.818746	−	1.41811i	−0.906607	−	0.421977i	$-0.861336\pi$
$239$	−12.6575	−	21.9234i	−0.818746	−	1.41811i	0.0878604	−	0.996133i	$-0.471997\pi$
$240$		0			0
$241$	−27.5291	+	7.37641i	−1.77331	+	0.475156i	−0.989337	−	0.145642i	$-0.953475\pi$
$241$	−27.5291	+	7.37641i	−1.77331	+	0.475156i	−0.783970	+	0.620798i	$0.786809\pi$
$242$	14.6334			0.940672
$243$		0			0
$244$	−0.484285	+	0.484285i	−0.0310032	+	0.0310032i
$245$	0.377158	+	1.40757i	0.0240957	+	0.0899265i
$246$		0			0
$247$	6.46380	−	3.73188i	0.411282	−	0.237454i
$248$	20.1281	+	5.39332i	1.27814	+	0.342476i
$249$		0			0
$250$	2.70168	−	0.723912i	0.170869	−	0.0457842i
$251$	−22.9319			−1.44745			−0.723723	−	0.690090i	$-0.757571\pi$
$251$	−22.9319			−1.44745			−0.723723	+	0.690090i	$0.757571\pi$
$252$		0			0
$253$			1.18493i			0.0744956i
$254$	−0.247200	+	0.428163i	−0.0155107	+	0.0268653i
$255$		0			0
$256$	2.61961	+	4.53730i	0.163726	+	0.283581i
$257$	−7.44836	+	4.30031i	−0.464616	+	0.268246i	−0.713983	−	0.700163i	$-0.753111\pi$
$257$	−7.44836	+	4.30031i	−0.464616	+	0.268246i	0.249367	+	0.968409i	$0.419777\pi$
$258$		0			0
$259$	18.0396	−	31.2455i	1.12093	−	1.94150i
$260$	−0.0465472	−	0.0465472i	−0.00288673	−	0.00288673i
$261$		0			0
$262$	−2.45820	+	2.45820i	−0.151868	+	0.151868i
$263$	21.1728	+	12.2241i	1.30557	+	0.753770i	0.981353	−	0.192213i	$-0.0615666\pi$
$263$	21.1728	+	12.2241i	1.30557	+	0.753770i	0.324215	+	0.945983i	$0.394900\pi$
$264$		0			0
$265$	−1.22930	−	0.329390i	−0.0755152	−	0.0202342i
$266$	−25.3803	−	6.80062i	−1.55616	−	0.416973i
$267$		0			0
$268$	−0.490447	+	0.849480i	−0.0299588	+	0.0518902i
$269$	7.74991	+	7.74991i	0.472521	+	0.472521i	0.902729	−	0.430209i	$-0.141560\pi$
$269$	7.74991	+	7.74991i	0.472521	+	0.472521i	−0.430209	+	0.902729i	$0.641560\pi$
$270$		0			0
$271$	−9.92166			−0.602698			−0.301349	−	0.953514i	$-0.597437\pi$
$271$	−9.92166			−0.602698			−0.301349	+	0.953514i	$0.597437\pi$
$272$	7.31588	−	12.4816i	0.443590	−	0.756806i
$273$		0			0
$274$	12.8607	−	7.42511i	0.776941	−	0.448567i
$275$	0.216106	−	0.806520i	0.0130317	−	0.0486350i
$276$		0			0
$277$	−23.2183	+	6.22133i	−1.39505	+	0.373803i	−0.876566	−	0.481282i	$-0.840171\pi$
$277$	−23.2183	+	6.22133i	−1.39505	+	0.373803i	−0.518487	+	0.855086i	$0.673505\pi$
$278$	9.58679	−	9.58679i	0.574978	−	0.574978i
$279$		0			0
$280$			2.32798i			0.139123i
$281$	−6.00066	−	3.46448i	−0.357969	−	0.206674i	0.310220	−	0.950665i	$-0.399597\pi$
$281$	−6.00066	−	3.46448i	−0.357969	−	0.206674i	−0.668190	+	0.743991i	$0.732931\pi$
$282$		0			0
$283$	10.1538	+	2.72072i	0.603584	+	0.161730i	0.547654	−	0.836705i	$-0.315521\pi$
$283$	10.1538	+	2.72072i	0.603584	+	0.161730i	0.0559298	+	0.998435i	$0.482188\pi$
$284$	0.447049	−	1.66841i	0.0265274	−	0.0990018i
$285$		0			0
$286$	0.306804	−	0.0822078i	0.0181417	−	0.00486105i
$287$			13.9201i			0.821677i
$288$		0			0
$289$	16.9985	+	0.223152i	0.999914	+	0.0131266i
$290$	0.468570	−	0.811588i	0.0275154	−	0.0476581i
$291$		0			0
$292$	−0.330004	+	1.23159i	−0.0193120	+	0.0720735i
$293$	−0.926817	−	1.60529i	−0.0541452	−	0.0937822i	0.837682	−	0.546158i	$-0.183910\pi$
$293$	−0.926817	−	1.60529i	−0.0541452	−	0.0937822i	−0.891828	+	0.452375i	$0.850577\pi$
$294$		0			0
$295$	0.0365732	+	0.136493i	0.00212938	+	0.00794694i
$296$	20.2580	−	20.2580i	1.17747	−	1.17747i
$297$		0			0
$298$			20.8991i			1.21065i
$299$	−2.57267	−	9.60132i	−0.148781	−	0.555259i
$300$		0			0
$301$	6.60621	−	24.6547i	0.380776	−	1.42107i
$302$	−0.378813	−	0.656123i	−0.0217982	−	0.0377556i
$303$		0			0
$304$	−16.0469	−	9.26468i	−0.920353	−	0.531366i
$305$	−0.652480			−0.0373609
$306$		0			0
$307$	2.47808			0.141431			0.0707157	−	0.997497i	$-0.477472\pi$
$307$	2.47808			0.141431			0.0707157	+	0.997497i	$0.477472\pi$
$308$	0.120361	+	0.0694904i	0.00685820	+	0.00395959i
$309$		0			0
$310$	0.988113	+	1.71146i	0.0561211	+	0.0972045i
$311$	−0.0785321	+	0.293086i	−0.00445315	+	0.0166194i	−0.968117	−	0.250500i	$-0.919405\pi$
$311$	−0.0785321	+	0.293086i	−0.00445315	+	0.0166194i	0.963664	+	0.267119i	$0.0860717\pi$
$312$		0			0
$313$	2.04909	+	7.64730i	0.115821	+	0.432251i	0.999347	−	0.0361315i	$-0.0115035\pi$
$313$	2.04909	+	7.64730i	0.115821	+	0.432251i	−0.883526	+	0.468383i	$0.844837\pi$
$314$			13.1307i			0.741010i
$315$		0			0
$316$	0.211674	−	0.211674i	0.0119076	−	0.0119076i
$317$	3.88088	+	14.4836i	0.217972	+	0.813482i	0.985099	+	0.171987i	$0.0550187\pi$
$317$	3.88088	+	14.4836i	0.217972	+	0.813482i	−0.767127	+	0.641495i	$0.778315\pi$
$318$		0			0
$319$	−0.281013	−	0.486729i	−0.0157337	−	0.0272516i
$320$	−0.473112	+	1.76568i	−0.0264478	+	0.0987045i
$321$		0			0
$322$	−17.4966	+	30.3049i	−0.975045	+	1.68883i
$323$	0.142904	−	21.7723i	0.00795139	−	1.21144i
$324$		0			0
$325$			7.00435i			0.388531i
$326$	11.4667	−	3.07250i	0.635083	−	0.170170i
$327$		0			0
$328$	−2.86084	+	10.6768i	−0.157964	+	0.589528i
$329$	7.34337	+	1.96765i	0.404853	+	0.108480i
$330$		0			0
$331$	−6.97954	−	4.02964i	−0.383630	−	0.221489i	0.295766	−	0.955260i	$-0.404425\pi$
$331$	−6.97954	−	4.02964i	−0.383630	−	0.221489i	−0.679397	+	0.733771i	$0.737758\pi$
$332$		−	0.784504i		−	0.0430552i
$333$		0			0
$334$	7.15038	−	7.15038i	0.391251	−	0.391251i
$335$	−0.902647	+	0.241864i	−0.0493169	+	0.0132144i
$336$		0			0
$337$	−1.08054	+	4.03263i	−0.0588608	+	0.219671i	−0.989091	−	0.147305i	$-0.952940\pi$
$337$	−1.08054	+	4.03263i	−0.0588608	+	0.219671i	0.930230	+	0.366976i	$0.119607\pi$
$338$	12.7083	−	7.33715i	0.691242	−	0.399089i
$339$		0			0
$340$	−0.185807	+	0.0484820i	−0.0100768	+	0.00262930i
$341$	1.18519			0.0641817
$342$		0			0
$343$	−0.216280	−	0.216280i	−0.0116780	−	0.0116780i
$344$	10.1340	−	17.5526i	0.546389	−	0.946374i
$345$		0			0
$346$	4.64757	+	1.24531i	0.249855	+	0.0669484i
$347$	−6.16352	−	1.65151i	−0.330875	−	0.0886578i	0.0895570	−	0.995982i	$-0.471455\pi$
$347$	−6.16352	−	1.65151i	−0.330875	−	0.0886578i	−0.420432	+	0.907324i	$0.638122\pi$
$348$		0			0
$349$	−14.6553	−	8.46127i	−0.784482	−	0.452921i	0.0535341	−	0.998566i	$-0.482951\pi$
$349$	−14.6553	−	8.46127i	−0.784482	−	0.452921i	−0.838017	+	0.545645i	$0.816285\pi$
$350$	17.4360	−	17.4360i	0.931996	−	0.931996i
$351$		0			0
$352$	0.148304	+	0.148304i	0.00790463	+	0.00790463i
$353$	−10.6249	+	18.4029i	−0.565507	+	0.979486i	0.431496	+	0.902115i	$0.357986\pi$
$353$	−10.6249	+	18.4029i	−0.565507	+	0.979486i	−0.997002	+	0.0773711i	$0.975347\pi$
$354$		0			0
$355$	1.42508	−	0.822773i	0.0756357	−	0.0436683i
$356$	−1.74963	−	3.03045i	−0.0927302	−	0.160613i
$357$		0			0
$358$	−3.96777	+	6.87238i	−0.209703	+	0.363217i
$359$		−	12.4405i		−	0.656585i	−0.944576	−	0.328292i	$-0.893527\pi$
$359$		−	12.4405i		−	0.656585i	0.944576	−	0.328292i	$-0.106473\pi$
$360$		0			0
$361$	−8.88541			−0.467653
$362$	−18.6089	+	4.98623i	−0.978060	+	0.262071i
$363$		0			0
$364$	−1.12615	−	0.301750i	−0.0590261	−	0.0158160i
$365$	−1.05197	+	0.607358i	−0.0550629	+	0.0317906i
$366$		0			0
$367$	−0.575434	−	2.14755i	−0.0300374	−	0.112101i	0.949279	−	0.314434i	$-0.101815\pi$
$367$	−0.575434	−	2.14755i	−0.0300374	−	0.112101i	−0.979317	+	0.202332i	$0.935148\pi$
$368$	−17.4492	+	17.4492i	−0.909603	+	0.909603i
$369$		0			0
$370$	2.71700			0.141250
$371$	−21.7721	+	5.83382i	−1.13035	+	0.302877i
$372$		0			0
$373$	0.870398	+	1.50757i	0.0450675	+	0.0780592i	0.887679	−	0.460462i	$-0.152316\pi$
$373$	0.870398	+	1.50757i	0.0450675	+	0.0780592i	−0.842612	+	0.538522i	$0.818983\pi$
$374$	0.245680	−	0.893393i	0.0127038	−	0.0461962i
$375$		0			0
$376$	5.22803	+	3.01840i	0.269615	+	0.155662i
$377$	3.33378	+	3.33378i	0.171699	+	0.171699i
$378$		0			0
$379$	−21.5308	−	21.5308i	−1.10596	−	1.10596i	−0.993676	−	0.112289i	$-0.964182\pi$
$379$	−21.5308	−	21.5308i	−1.10596	−	1.10596i	−0.112289	−	0.993676i	$-0.535818\pi$
$380$	0.0636538	+	0.237559i	0.00326537	+	0.0121865i
$381$		0			0
$382$	8.80991	−	5.08640i	0.450754	−	0.260243i
$383$	11.7895	−	6.80666i	0.602415	−	0.347804i	−0.167576	−	0.985859i	$-0.553594\pi$
$383$	11.7895	−	6.80666i	0.602415	−	0.347804i	0.769991	+	0.638055i	$0.220261\pi$
$384$		0			0
$385$	0.0342691	+	0.127894i	0.00174652	+	0.00651809i
$386$	−0.495140	−	0.495140i	−0.0252020	−	0.0252020i
$387$		0			0
$388$	1.40266	+	1.40266i	0.0712092	+	0.0712092i
$389$	−26.2082	−	15.1313i	−1.32881	−	0.767187i	−0.343692	−	0.939082i	$-0.611678\pi$
$389$	−26.2082	−	15.1313i	−1.32881	−	0.767187i	−0.985115	+	0.171895i	$0.945011\pi$
$390$		0			0
$391$	−27.9584	−	7.68847i	−1.41392	−	0.388823i
$392$	10.2470	+	17.7483i	0.517550	+	0.896423i
$393$		0			0
$394$	24.5603	−	6.58090i	1.23733	−	0.331541i
$395$	0.285190			0.0143495
$396$		0			0
$397$	3.67871	−	3.67871i	0.184629	−	0.184629i	−0.608740	−	0.793370i	$-0.708325\pi$
$397$	3.67871	−	3.67871i	0.184629	−	0.184629i	0.793370	+	0.608740i	$0.208325\pi$
$398$	7.35465	+	27.4479i	0.368655	+	1.37584i
$399$		0			0
$400$	15.0592	−	8.69443i	0.752959	−	0.434721i
$401$	−28.3899	−	7.60705i	−1.41772	−	0.379878i	−0.533048	−	0.846085i	$-0.678954\pi$
$401$	−28.3899	−	7.60705i	−1.41772	−	0.379878i	−0.884676	+	0.466207i	$0.845620\pi$
$402$		0			0
$403$	−9.60347	+	2.57324i	−0.478383	+	0.128182i
$404$	3.25047			0.161717
$405$		0			0
$406$		−	16.5977i		−	0.823730i
$407$	0.814725	−	1.41114i	0.0403844	−	0.0699478i
$408$		0			0
$409$	−6.22602	−	10.7838i	−0.307857	−	0.533224i	0.670036	−	0.742328i	$-0.266279\pi$
$409$	−6.22602	−	10.7838i	−0.307857	−	0.533224i	−0.977893	+	0.209104i	$0.932945\pi$
$410$	−0.907832	+	0.524137i	−0.0448346	+	0.0258853i
$411$		0			0
$412$	1.71304	−	2.96708i	0.0843955	−	0.146177i
$413$	1.76968	+	1.76968i	0.0870803	+	0.0870803i
$414$		0			0
$415$	0.528484	−	0.528484i	0.0259422	−	0.0259422i
$416$	−1.52368	−	0.879699i	−0.0747047	−	0.0431308i
$417$		0			0
$418$	−1.14625	−	0.307137i	−0.0560650	−	0.0150226i
$419$	22.6398	+	6.06633i	1.10603	+	0.296360i	0.765217	−	0.643772i	$-0.222632\pi$
$419$	22.6398	+	6.06633i	1.10603	+	0.296360i	0.340812	+	0.940132i	$0.389298\pi$
$420$		0			0
$421$	−18.8404	+	32.6325i	−0.918223	+	1.59041i	−0.116110	+	0.993236i	$0.537043\pi$
$421$	−18.8404	+	32.6325i	−0.918223	+	1.59041i	−0.802113	+	0.597172i	$0.796291\pi$
$422$	−25.6373	−	25.6373i	−1.24800	−	1.24800i
$423$		0			0
$424$	−17.8983			−0.869219
$425$	17.6277	+	10.3322i	0.855069	+	0.501186i
$426$		0			0
$427$	−10.0079	+	5.77804i	−0.484314	+	0.279619i
$428$	−0.898413	+	3.35292i	−0.0434264	+	0.162070i
$429$		0			0
$430$	1.85666	−	0.497490i	0.0895361	−	0.0239911i
$431$	−7.01607	+	7.01607i	−0.337952	+	0.337952i	−0.855596	−	0.517644i	$-0.826809\pi$
$431$	−7.01607	+	7.01607i	−0.337952	+	0.337952i	0.517644	+	0.855596i	$0.326809\pi$
$432$		0			0
$433$			13.7702i			0.661756i	0.943674	+	0.330878i	$0.107345\pi$
$433$			13.7702i			0.661756i	−0.943674	+	0.330878i	$0.892655\pi$
$434$	30.3117	+	17.5005i	1.45501	+	0.840050i
$435$		0			0
$436$	3.14133	+	0.841718i	0.150443	+	0.0403110i
$437$	−9.61177	+	35.8716i	−0.459793	+	1.71597i
$438$		0			0
$439$	−11.7336	+	3.14401i	−0.560015	+	0.150056i	−0.527713	−	0.849423i	$-0.676950\pi$
$439$	−11.7336	+	3.14401i	−0.560015	+	0.150056i	−0.0323018	+	0.999478i	$0.510284\pi$
$440$			0.105139i			0.00501229i
$441$		0			0
$442$	−0.0510152	+	7.77247i	−0.00242655	+	0.369699i
$443$	−17.4660	+	30.2520i	−0.829835	+	1.43732i	0.0683324	+	0.997663i	$0.478232\pi$
$443$	−17.4660	+	30.2520i	−0.829835	+	1.43732i	−0.898167	+	0.439654i	$0.855101\pi$
$444$		0			0
$445$	0.862827	−	3.22012i	0.0409019	−	0.152648i
$446$	14.0344	+	24.3083i	0.664549	+	1.15103i
$447$		0			0
$448$	8.37929	+	31.2719i	0.395884	+	1.47746i
$449$	−4.84668	+	4.84668i	−0.228729	+	0.228729i	−0.812162	−	0.583433i	$-0.801709\pi$
$449$	−4.84668	+	4.84668i	−0.228729	+	0.228729i	0.583433	+	0.812162i	$0.301709\pi$
$450$		0			0
$451$			0.628675i			0.0296031i
$452$	−0.801485	−	2.99118i	−0.0376987	−	0.140693i
$453$		0			0
$454$	−4.94827	+	18.4672i	−0.232234	+	0.866709i
$455$	−0.555358	−	0.961908i	−0.0260356	−	0.0450950i
$456$		0			0
$457$	17.7446	+	10.2448i	0.830056	+	0.479233i	0.853872	−	0.520483i	$-0.174248\pi$
$457$	17.7446	+	10.2448i	0.830056	+	0.479233i	−0.0238158	+	0.999716i	$0.507582\pi$
$458$	30.9904			1.44809
$459$		0			0
$460$	0.327535			0.0152714
$461$	11.3518	+	6.55396i	0.528706	+	0.305248i	0.740489	−	0.672068i	$-0.234594\pi$
$461$	11.3518	+	6.55396i	0.528706	+	0.305248i	−0.211784	+	0.977317i	$0.567927\pi$
$462$		0			0
$463$	−8.92097	−	15.4516i	−0.414593	−	0.718096i	0.580793	−	0.814051i	$-0.302743\pi$
$463$	−8.92097	−	15.4516i	−0.414593	−	0.718096i	−0.995386	+	0.0959556i	$0.969409\pi$
$464$	3.02937	−	11.3058i	0.140635	−	0.524857i
$465$		0			0
$466$	−8.70547	−	32.4892i	−0.403273	−	1.50503i
$467$			24.8641i			1.15058i	0.817951	+	0.575288i	$0.195110\pi$
$467$			24.8641i			1.15058i	−0.817951	+	0.575288i	$0.804890\pi$
$468$		0			0
$469$	−11.7031	+	11.7031i	−0.540400	+	0.540400i
$470$	0.148177	+	0.553003i	0.00683489	+	0.0255081i
$471$		0			0
$472$	0.993654	+	1.72106i	0.0457367	+	0.0792182i
$473$	0.298357	−	1.11348i	0.0137185	−	0.0511980i
$474$		0			0
$475$	13.0845	−	22.6630i	0.600358	−	1.03985i
$476$	−2.42060	+	2.38904i	−0.110948	+	0.109501i
$477$		0			0
$478$		−	33.7640i		−	1.54433i
$479$	−24.1589	+	6.47337i	−1.10385	+	0.295776i	−0.764331	−	0.644824i	$-0.776931\pi$
$479$	−24.1589	+	6.47337i	−1.10385	+	0.295776i	−0.339518	+	0.940599i	$0.610264\pi$
$480$		0			0
$481$	−3.53780	+	13.2032i	−0.161310	+	0.602016i
$482$	−36.7171	−	9.83831i	−1.67242	−	0.448123i
$483$		0			0
$484$	−2.10085	−	1.21293i	−0.0954932	−	0.0551330i
$485$			1.88981i			0.0858120i
$486$		0			0
$487$	−12.2325	+	12.2325i	−0.554308	+	0.554308i	−0.927681	−	0.373373i	$-0.878201\pi$
$487$	−12.2325	+	12.2325i	−0.554308	+	0.554308i	0.373373	+	0.927681i	$0.378201\pi$
$488$	−8.86359	+	2.37499i	−0.401236	+	0.107511i
$489$		0			0
$490$	−0.503036	+	1.87735i	−0.0227248	+	0.0848102i
$491$	−5.79286	+	3.34451i	−0.261428	+	0.150936i	−0.624986	−	0.780636i	$-0.714895\pi$
$491$	−5.79286	+	3.34451i	−0.261428	+	0.150936i	0.363558	+	0.931572i	$0.381562\pi$
$492$		0			0
$493$	13.3078	−	3.47236i	0.599353	−	0.156387i
$494$	9.95480			0.447888
$495$		0			0
$496$	17.4531	+	17.4531i	0.783668	+	0.783668i
$497$	14.5721	−	25.2397i	0.653649	−	1.13215i
$498$		0			0
$499$	−11.4893	−	3.07856i	−0.514334	−	0.137815i	−0.00768931	−	0.999970i	$-0.502448\pi$
$499$	−11.4893	−	3.07856i	−0.514334	−	0.137815i	−0.506644	+	0.862155i	$0.669114\pi$
$500$	−0.447870	−	0.120006i	−0.0200294	−	0.00536685i
$501$		0			0
$502$	−26.4878	−	15.2927i	−1.18221	−	0.682548i
$503$	−5.14169	+	5.14169i	−0.229257	+	0.229257i	−0.812382	−	0.583125i	$-0.801830\pi$
$503$	−5.14169	+	5.14169i	−0.229257	+	0.229257i	0.583125	+	0.812382i	$0.301830\pi$
$504$		0			0
$505$	2.18969	+	2.18969i	0.0974399	+	0.0974399i
$506$	−0.790199	+	1.36866i	−0.0351286	+	0.0608446i
$507$		0			0
$508$	0.0709786	−	0.0409795i	0.00314916	−	0.00181817i
$509$	3.49778	+	6.05834i	0.155036	+	0.268531i	0.933072	−	0.359689i	$-0.117117\pi$
$509$	3.49778	+	6.05834i	0.155036	+	0.268531i	−0.778036	+	0.628220i	$0.783784\pi$
$510$		0			0
$511$	−10.7569	+	18.6315i	−0.475858	+	0.824210i
$512$			25.1574i			1.11181i
$513$		0			0
$514$	−11.4711			−0.505969
$515$	3.15278	−	0.844785i	0.138928	−	0.0372257i
$516$		0			0
$517$	0.331649	+	0.0888652i	0.0145859	+	0.00390829i
$518$	41.6738	−	24.0604i	1.83104	−	1.05715i
$519$		0			0
$520$	−0.228273	−	0.851927i	−0.0100104	−	0.0373595i
$521$	5.20499	−	5.20499i	0.228035	−	0.228035i	−0.583837	−	0.811871i	$-0.698449\pi$
$521$	5.20499	−	5.20499i	0.228035	−	0.228035i	0.811871	+	0.583837i	$0.198449\pi$
$522$		0			0
$523$	−26.8971			−1.17613			−0.588065	−	0.808814i	$-0.700110\pi$
$523$	−26.8971			−1.17613			−0.588065	+	0.808814i	$0.700110\pi$
$524$	0.556666	−	0.149158i	0.0243181	−	0.00651601i
$525$		0			0
$526$	16.3039	+	28.2392i	0.710885	+	1.23129i
$527$	−7.69019	+	27.9647i	−0.334990	+	1.21816i
$528$		0			0
$529$	22.9134	+	13.2290i	0.996233	+	0.575175i
$530$	−1.20026	−	1.20026i	−0.0521358	−	0.0521358i
$531$		0			0
$532$	3.08004	+	3.08004i	0.133537	+	0.133537i
$533$	−1.36496	−	5.09408i	−0.0591228	−	0.220649i
$534$		0			0
$535$	−2.86393	+	1.65349i	−0.123818	+	0.0714866i
$536$	−11.3816	+	6.57117i	−0.491610	+	0.283831i
$537$		0			0
$538$	3.78341	+	14.1199i	0.163114	+	0.608751i
$539$	0.824212	+	0.824212i	0.0355013	+	0.0355013i
$540$		0			0
$541$	−0.960273	−	0.960273i	−0.0412854	−	0.0412854i	0.686163	−	0.727448i	$-0.259294\pi$
$541$	−0.960273	−	0.960273i	−0.0412854	−	0.0412854i	−0.727448	+	0.686163i	$0.759294\pi$
$542$	−11.4602	−	6.61653i	−0.492256	−	0.284204i
$543$		0			0
$544$	−4.46153	+	2.53697i	−0.191286	+	0.108772i
$545$	1.54914	+	2.68320i	0.0663581	+	0.114936i
$546$		0			0
$547$	24.5966	−	6.59064i	1.05168	−	0.281796i	0.308732	−	0.951149i	$-0.400096\pi$
$547$	24.5966	−	6.59064i	1.05168	−	0.281796i	0.742944	+	0.669354i	$0.233429\pi$
$548$	−2.46179			−0.105163
$549$		0			0
$550$	0.787466	−	0.787466i	0.0335777	−	0.0335777i
$551$	−4.55899	−	17.0144i	−0.194219	−	0.724837i
$552$		0			0
$553$	4.37430	−	2.52550i	0.186014	−	0.107395i
$554$	−30.9675	−	8.29771i	−1.31568	−	0.352536i
$555$		0			0
$556$	−2.17095	+	0.581705i	−0.0920690	+	0.0246698i
$557$	−25.8012			−1.09323			−0.546616	−	0.837384i	$-0.684084\pi$
$557$	−25.8012			−1.09323			−0.546616	+	0.837384i	$0.684084\pi$
$558$		0			0
$559$			9.67022i			0.409007i
$560$	−1.37872	+	2.38801i	−0.0582616	+	0.100912i
$561$		0			0
$562$	−4.62077	−	8.00340i	−0.194915	−	0.337603i
$563$	8.72945	−	5.03995i	0.367902	−	0.212409i	−0.304639	−	0.952468i	$-0.598536\pi$
$563$	8.72945	−	5.03995i	0.367902	−	0.212409i	0.672542	+	0.740059i	$0.265203\pi$
$564$		0			0
$565$	1.47510	−	2.55495i	0.0620579	−	0.107487i
$566$	9.91397	+	9.91397i	0.416715	+	0.416715i
$567$		0			0
$568$	16.3642	−	16.3642i	0.686625	−	0.686625i
$569$	−33.2481	−	19.1958i	−1.39383	−	0.804730i	−0.400096	−	0.916473i	$-0.631023\pi$
$569$	−33.2481	−	19.1958i	−1.39383	−	0.804730i	−0.993737	+	0.111743i	$0.964357\pi$
$570$		0			0
$571$	−4.91094	−	1.31588i	−0.205516	−	0.0550680i	0.154592	−	0.987978i	$-0.450594\pi$
$571$	−4.91094	−	1.31588i	−0.205516	−	0.0550680i	−0.360108	+	0.932910i	$0.617260\pi$
$572$	−0.0508603	−	0.0136280i	−0.00212658	−	0.000569814i
$573$		0			0
$574$	−9.28299	+	16.0786i	−0.387464	+	0.671108i
$575$	−24.6435	−	24.6435i	−1.02771	−	1.02771i
$576$		0			0
$577$	15.5111			0.645734			0.322867	−	0.946444i	$-0.395353\pi$
$577$	15.5111			0.645734			0.322867	+	0.946444i	$0.395353\pi$
$578$	19.4856	+	11.5937i	0.810493	+	0.482233i
$579$		0			0
$580$	−0.134541	+	0.0776772i	−0.00558650	+	0.00322537i
$581$	3.42599	−	12.7860i	0.142134	−	0.530451i
$582$		0			0
$583$	−0.983296	+	0.263473i	−0.0407240	+	0.0109120i
$584$	−12.0798	+	12.0798i	−0.499864	+	0.499864i
$585$		0			0
$586$		−	2.47229i		−	0.102129i
$587$	19.4261	+	11.2157i	0.801801	+	0.462920i	0.844101	−	0.536185i	$-0.180135\pi$
$587$	19.4261	+	11.2157i	0.801801	+	0.462920i	−0.0422994	+	0.999105i	$0.513468\pi$
$588$		0			0
$589$	35.8796	+	9.61392i	1.47839	+	0.396135i
$590$	−0.0487796	+	0.182048i	−0.00200823	+	0.00749480i
$591$		0			0
$592$	32.7781	−	8.78287i	1.34717	−	0.360974i
$593$		−	29.6938i		−	1.21938i	−0.792640	−	0.609690i	$-0.791294\pi$
$593$		−	29.6938i		−	1.21938i	0.792640	−	0.609690i	$-0.208706\pi$
$594$		0			0
$595$	−3.24003	−	0.0212662i	−0.132828	−	0.000871829i
$596$	1.73227	−	3.00038i	0.0709566	−	0.122900i
$597$		0			0
$598$	3.43130	−	12.8058i	0.140316	−	0.523668i
$599$	−2.71859	−	4.70873i	−0.111078	−	0.192393i	0.805127	−	0.593103i	$-0.202097\pi$
$599$	−2.71859	−	4.70873i	−0.111078	−	0.192393i	−0.916205	+	0.400709i	$0.868764\pi$
$600$		0			0
$601$	3.66085	+	13.6625i	0.149329	+	0.557304i	0.999524	+	0.0308368i	$0.00981721\pi$
$601$	3.66085	+	13.6625i	0.149329	+	0.557304i	−0.850195	+	0.526468i	$0.823516\pi$
$602$	24.0722	−	24.0722i	0.981111	−	0.981111i
$603$		0			0
$604$			0.125595i			0.00511040i
$605$	−0.598153	−	2.23234i	−0.0243184	−	0.0907574i
$606$		0			0
$607$	8.56899	−	31.9799i	0.347804	−	1.29802i	−0.541497	−	0.840703i	$-0.682142\pi$
$607$	8.56899	−	31.9799i	0.347804	−	1.29802i	0.889302	−	0.457321i	$-0.151191\pi$
$608$	3.28665	+	5.69265i	0.133291	+	0.230867i
$609$		0			0
$610$	−0.753657	−	0.435124i	−0.0305147	−	0.0176177i
$611$	−2.88026			−0.116523
$612$		0			0
$613$	−0.832327			−0.0336174			−0.0168087	−	0.999859i	$-0.505351\pi$
$613$	−0.832327			−0.0336174			−0.0168087	+	0.999859i	$0.505351\pi$
$614$	2.86234	+	1.65257i	0.115515	+	0.0666924i
$615$		0			0
$616$	0.931055	+	1.61263i	0.0375133	+	0.0649749i
$617$	11.1408	−	41.5778i	0.448510	−	1.67386i	−0.257990	−	0.966148i	$-0.583060\pi$
$617$	11.1408	−	41.5778i	0.448510	−	1.67386i	0.706500	−	0.707713i	$-0.250273\pi$
$618$		0			0
$619$	−8.25515	−	30.8086i	−0.331803	−	1.23830i	−0.907294	−	0.420496i	$-0.861856\pi$
$619$	−8.25515	−	30.8086i	−0.331803	−	1.23830i	0.575492	−	0.817808i	$-0.304811\pi$
$620$		−	0.327609i		−	0.0131571i
$621$		0			0
$622$	−0.286162	+	0.286162i	−0.0114740	+	0.0114740i
$623$	−15.2815	−	57.0315i	−0.612242	−	2.28492i
$624$		0			0
$625$	12.1682	+	21.0760i	0.486728	+	0.843038i
$626$	−2.73298	+	10.1996i	−0.109232	+	0.407659i
$627$		0			0
$628$	1.08837	−	1.88512i	0.0434308	−	0.0752243i
$629$	28.0097	+	28.3798i	1.11682	+	1.13158i
$630$		0			0
$631$		−	2.37358i		−	0.0944907i	−0.998883	−	0.0472454i	$-0.984956\pi$
$631$		−	2.37358i		−	0.0944907i	0.998883	−	0.0472454i	$-0.0150443\pi$
$632$	3.87416	−	1.03808i	0.154106	−	0.0412925i
$633$		0			0
$634$	−5.17613	+	19.3176i	−0.205570	+	0.767200i
$635$	0.0754209	+	0.0202090i	0.00299299	+	0.000801969i
$636$		0			0
$637$	−8.46800	−	4.88900i	−0.335514	−	0.193709i
$638$		−	0.749604i		−	0.0296771i
$639$		0			0
$640$	−1.35315	+	1.35315i	−0.0534880	+	0.0534880i
$641$	26.9829	−	7.23006i	1.06576	−	0.285570i	0.317011	−	0.948422i	$-0.397321\pi$
$641$	26.9829	−	7.23006i	1.06576	−	0.285570i	0.748751	+	0.662852i	$0.230654\pi$
$642$		0			0
$643$	−4.39087	+	16.3869i	−0.173159	+	0.646238i	0.823699	+	0.567027i	$0.191907\pi$
$643$	−4.39087	+	16.3869i	−0.173159	+	0.646238i	−0.996858	+	0.0792105i	$0.974760\pi$
$644$	5.02379	−	2.90049i	0.197965	−	0.114295i
$645$		0			0
$646$	14.6845	−	25.0531i	0.577753	−	0.985699i
$647$	−6.19196			−0.243431			−0.121716	−	0.992565i	$-0.538840\pi$
$647$	−6.19196			−0.243431			−0.121716	+	0.992565i	$0.538840\pi$
$648$		0			0
$649$	0.0799243	+	0.0799243i	0.00313730	+	0.00313730i
$650$	−4.67103	+	8.09047i	−0.183213	+	0.317334i
$651$		0			0
$652$	−1.90089	−	0.509343i	−0.0744447	−	0.0199474i
$653$	22.9921	+	6.16071i	0.899749	+	0.241087i	0.678909	−	0.734223i	$-0.262453\pi$
$653$	22.9921	+	6.16071i	0.899749	+	0.241087i	0.220841	+	0.975310i	$0.429120\pi$
$654$		0			0
$655$	0.475481	+	0.274519i	0.0185786	+	0.0107264i
$656$	−9.25786	+	9.25786i	−0.361459	+	0.361459i
$657$		0			0
$658$	7.16988	+	7.16988i	0.279511	+	0.279511i
$659$	22.6425	−	39.2180i	0.882027	−	1.52772i	0.0329442	−	0.999457i	$-0.489512\pi$
$659$	22.6425	−	39.2180i	0.882027	−	1.52772i	0.849083	−	0.528259i	$-0.177155\pi$
$660$		0			0
$661$	−32.5396	+	18.7867i	−1.26564	+	0.730720i	−0.974161	−	0.225856i	$-0.927482\pi$
$661$	−32.5396	+	18.7867i	−1.26564	+	0.730720i	−0.291483	+	0.956576i	$0.594149\pi$
$662$	−5.37454	−	9.30898i	−0.208888	−	0.361804i
$663$		0			0
$664$	5.25551	−	9.10281i	0.203953	−	0.353258i
$665$			4.14976i			0.160921i
$666$		0			0
$667$	−23.4586			−0.908321
$668$	−1.61922	+	0.433869i	−0.0626496	+	0.0167869i
$669$		0			0
$670$	−1.20391	−	0.322586i	−0.0465110	−	0.0124626i
$671$	−0.451986	+	0.260954i	−0.0174487	+	0.0100740i
$672$		0			0
$673$	−4.27274	−	15.9461i	−0.164702	−	0.614677i	−0.998078	−	0.0619701i	$-0.980262\pi$
$673$	−4.27274	−	15.9461i	−0.164702	−	0.614677i	0.833376	−	0.552707i	$-0.186405\pi$
$674$	−3.93736	+	3.93736i	−0.151661	+	0.151661i
$675$		0			0
$676$	−2.43263			−0.0935627
$677$	−2.07862	+	0.556966i	−0.0798880	+	0.0214059i	−0.298542	−	0.954397i	$-0.596500\pi$
$677$	−2.07862	+	0.556966i	−0.0798880	+	0.0214059i	0.218654	+	0.975803i	$0.429834\pi$
$678$		0			0
$679$	16.7352	+	28.9863i	0.642239	+	1.11239i
$680$	−2.48076	−	0.682199i	−0.0951327	−	0.0261611i
$681$		0			0
$682$	1.36897	+	0.790376i	0.0524206	+	0.0302651i
$683$	7.82243	+	7.82243i	0.299317	+	0.299317i	0.840746	−	0.541429i	$-0.182117\pi$
$683$	7.82243	+	7.82243i	0.299317	+	0.299317i	−0.541429	+	0.840746i	$0.682117\pi$
$684$		0			0
$685$	−1.65839	−	1.65839i	−0.0633640	−	0.0633640i
$686$	−0.105585	−	0.394049i	−0.00403126	−	0.0150449i
$687$		0			0
$688$	20.7907	−	12.0035i	0.792640	−	0.457631i
$689$	7.39550	−	4.26979i	0.281746	−	0.162666i
$690$		0			0
$691$	−3.03050	−	11.3100i	−0.115286	−	0.430252i	0.884023	−	0.467444i	$-0.154825\pi$
$691$	−3.03050	−	11.3100i	−0.115286	−	0.430252i	−0.999308	+	0.0371926i	$0.988158\pi$
$692$	−0.564008	−	0.564008i	−0.0214404	−	0.0214404i
$693$		0			0
$694$	−6.01791	−	6.01791i	−0.228437	−	0.228437i
$695$	−1.85434	−	1.07060i	−0.0703391	−	0.0406103i
$696$		0			0
$697$	−14.8337	−	4.07920i	−0.561865	−	0.154511i
$698$	−11.2852	−	19.5466i	−0.427153	−	0.739850i
$699$		0			0
$700$	−3.94844	+	1.05798i	−0.149237	+	0.0399879i
$701$	−38.5387			−1.45559			−0.727793	−	0.685797i	$-0.759454\pi$
$701$	−38.5387			−1.45559			−0.727793	+	0.685797i	$0.759454\pi$
$702$		0			0
$703$	36.1112	−	36.1112i	1.36196	−	1.36196i
$704$	0.378435	+	1.41234i	0.0142628	+	0.0532295i
$705$		0			0
$706$	−24.5449	+	14.1710i	−0.923759	+	0.533333i
$707$	52.9766	+	14.1950i	1.99239	+	0.533860i
$708$		0			0
$709$	−3.81483	+	1.02218i	−0.143269	+	0.0383888i	−0.329741	−	0.944072i	$-0.606961\pi$
$709$	−3.81483	+	1.02218i	−0.143269	+	0.0383888i	0.186472	+	0.982460i	$0.440295\pi$
$710$	2.19475			0.0823676
$711$		0			0
$712$		−	46.8842i		−	1.75706i
$713$	24.7346	−	42.8415i	0.926317	−	1.60443i
$714$		0			0
$715$	−0.0250817	−	0.0434428i	−0.000938002	−	0.00162467i
$716$	1.13927	−	0.657757i	0.0425764	−	0.0245815i
$717$		0			0
$718$	8.29628	−	14.3696i	0.309614	−	0.536268i
$719$	15.6084	+	15.6084i	0.582096	+	0.582096i	0.935479	−	0.353383i	$-0.114969\pi$
$719$	15.6084	+	15.6084i	0.582096	+	0.582096i	−0.353383	+	0.935479i	$0.614969\pi$
$720$		0			0
$721$	40.8769	−	40.8769i	1.52233	−	1.52233i
$722$	−10.2632	−	5.92547i	−0.381957	−	0.220523i
$723$		0			0
$724$	3.08488	+	0.826592i	0.114649	+	0.0307200i
$725$	15.9671	+	4.27838i	0.593004	+	0.158895i
$726$		0			0
$727$	14.0561	−	24.3459i	0.521311	−	0.902938i	−0.478381	−	0.878152i	$-0.658776\pi$
$727$	14.0561	−	24.3459i	0.521311	−	0.902938i	0.999693	−	0.0247856i	$-0.00789032\pi$
$728$	−11.0455	−	11.0455i	−0.409374	−	0.409374i
$729$		0			0
$730$	−1.62013			−0.0599637
$731$	24.3368	+	14.2647i	0.900131	+	0.527598i
$732$		0			0
$733$	−5.78305	+	3.33885i	−0.213602	+	0.123323i	−0.602984	−	0.797753i	$-0.706022\pi$
$733$	−5.78305	+	3.33885i	−0.213602	+	0.123323i	0.389382	+	0.921076i	$0.372688\pi$
$734$	0.767488	−	2.86430i	0.0283285	−	0.105723i
$735$		0			0
$736$	8.45586	−	2.26574i	0.311687	−	0.0835163i
$737$	−0.528550	+	0.528550i	−0.0194694	+	0.0194694i
$738$		0			0
$739$			5.62966i			0.207090i	0.994625	+	0.103545i	$0.0330186\pi$
$739$			5.62966i			0.207090i	−0.994625	+	0.103545i	$0.966981\pi$
$740$	−0.390066	−	0.225205i	−0.0143391	−	0.00827870i
$741$		0			0
$742$	−29.0386	−	7.78088i	−1.06604	−	0.285645i
$743$	2.63795	−	9.84496i	0.0967770	−	0.361177i	−0.900506	−	0.434844i	$-0.856804\pi$
$743$	2.63795	−	9.84496i	0.0967770	−	0.361177i	0.997283	+	0.0736672i	$0.0234703\pi$
$744$		0			0
$745$	3.18817	−	0.854268i	0.116806	−	0.0312980i
$746$			2.32179i			0.0850069i
$747$		0			0
$748$	−0.109322	+	0.107896i	−0.00399721	+	0.00394508i
$749$	−29.2849	+	50.7230i	−1.07005	+	1.85338i
$750$		0			0
$751$	−4.31973	+	16.1215i	−0.157629	+	0.588281i	0.841237	+	0.540667i	$0.181828\pi$
$751$	−4.31973	+	16.1215i	−0.157629	+	0.588281i	−0.998866	+	0.0476133i	$0.984838\pi$
$752$	3.57524	+	6.19249i	0.130376	+	0.225817i
$753$		0			0
$754$	1.62751	+	6.07396i	0.0592705	+	0.221200i
$755$	−0.0846077	+	0.0846077i	−0.00307919	+	0.00307919i
$756$		0			0
$757$		−	17.3458i		−	0.630446i	−0.949018	−	0.315223i	$-0.897921\pi$
$757$		−	17.3458i		−	0.630446i	0.949018	−	0.315223i	$-0.102079\pi$
$758$	−10.5111	−	39.2279i	−0.381780	−	1.42482i
$759$		0			0
$760$	−0.852854	+	3.18289i	−0.0309362	+	0.115456i
$761$	−3.20919	−	5.55848i	−0.116333	−	0.201495i	0.801979	−	0.597353i	$-0.203781\pi$
$761$	−3.20919	−	5.55848i	−0.116333	−	0.201495i	−0.918312	+	0.395858i	$0.870447\pi$
$762$		0			0
$763$	47.5221	+	27.4369i	1.72042	+	0.993282i
$764$	−1.68639			−0.0610116
$765$		0			0
$766$	18.1568			0.656032
$767$	−0.821147	−	0.474089i	−0.0296499	−	0.0171184i
$768$		0			0
$769$	−14.8709	−	25.7572i	−0.536258	−	0.928827i	−0.999101	−	0.0423865i	$-0.986504\pi$
$769$	−14.8709	−	25.7572i	−0.536258	−	0.928827i	0.462843	−	0.886440i	$-0.346829\pi$
$770$	−0.0457066	+	0.170579i	−0.00164715	+	0.00614725i
$771$		0			0
$772$	0.0300440	+	0.112126i	0.00108131	+	0.00403550i
$773$			52.2434i			1.87906i	0.342461	+	0.939532i	$0.388740\pi$
$773$			52.2434i			1.87906i	−0.342461	+	0.939532i	$0.611260\pi$
$774$		0			0
$775$	−24.6490	+	24.6490i	−0.885419	+	0.885419i
$776$	6.87881	+	25.6721i	0.246935	+	0.921574i
$777$		0			0
$778$	−20.1814	−	34.9552i	−0.723539	−	1.25321i
$779$	−5.09963	+	19.0321i	−0.182713	+	0.681895i
$780$		0			0
$781$	0.658123	−	1.13990i	0.0235495	−	0.0407889i
$782$	−27.1665	−	27.5255i	−0.971473	−	0.984310i
$783$		0			0
$784$			24.2747i			0.866953i
$785$	2.00310	−	0.536729i	0.0714937	−	0.0191567i
$786$		0			0
$787$	−10.8164	+	40.3675i	−0.385564	+	1.43895i	0.451711	+	0.892164i	$0.350814\pi$
$787$	−10.8164	+	40.3675i	−0.385564	+	1.43895i	−0.837275	+	0.546781i	$0.815853\pi$
$788$	−4.07147	−	1.09095i	−0.145040	−	0.0388634i
$789$		0			0
$790$	0.329413	+	0.190187i	0.0117200	+	0.00676654i
$791$		−	52.2509i		−	1.85783i
$792$		0			0
$793$	3.09582	−	3.09582i	0.109936	−	0.109936i
$794$	6.70240	−	1.79590i	0.237859	−	0.0637342i
$795$		0			0
$796$	1.21922	−	4.55018i	0.0432140	−	0.161277i
$797$	−9.12386	+	5.26766i	−0.323184	+	0.186590i	−0.652811	−	0.757521i	$-0.726410\pi$
$797$	−9.12386	+	5.26766i	−0.323184	+	0.186590i	0.329627	+	0.944111i	$0.393077\pi$
$798$		0			0
$799$	−4.24871	+	7.24869i	−0.150309	+	0.256440i
$800$	−6.16871			−0.218097
$801$		0			0
$802$	−27.7192	−	27.7192i	−0.978799	−	0.978799i
$803$	−0.485816	+	0.841458i	−0.0171441	+	0.0296944i
$804$		0			0
$805$	5.33822	+	1.43037i	0.188148	+	0.0504140i
$806$	−12.8087	−	3.43207i	−0.451166	−	0.120890i
$807$		0			0
$808$	37.7161	+	21.7754i	1.32685	+	0.766056i
$809$	6.93423	−	6.93423i	0.243795	−	0.243795i	−0.574623	−	0.818418i	$-0.694851\pi$
$809$	6.93423	−	6.93423i	0.243795	−	0.243795i	0.818418	+	0.574623i	$0.194851\pi$
$810$		0			0
$811$	16.3558	+	16.3558i	0.574330	+	0.574330i	0.933335	−	0.359006i	$-0.116884\pi$
$811$	16.3558	+	16.3558i	0.574330	+	0.574330i	−0.359006	+	0.933335i	$0.616884\pi$
$812$	−1.37574	+	2.38285i	−0.0482790	+	0.0836217i
$813$		0			0
$814$	1.88212	−	1.08664i	0.0659682	−	0.0380868i
$815$	−0.937423	−	1.62366i	−0.0328365	−	0.0568745i
$816$		0			0
$817$	18.0645	−	31.2886i	0.631997	−	1.09465i
$818$		−	16.6080i		−	0.580683i
$819$		0			0
$820$	0.173777			0.00606857
$821$	−3.91441	+	1.04886i	−0.136614	+	0.0366056i	−0.326478	−	0.945205i	$-0.605862\pi$
$821$	−3.91441	+	1.04886i	−0.136614	+	0.0366056i	0.189864	+	0.981810i	$0.439195\pi$
$822$		0			0
$823$	37.2278	+	9.97516i	1.29768	+	0.347712i	0.840572	−	0.541700i	$-0.182219\pi$
$823$	37.2278	+	9.97516i	1.29768	+	0.347712i	0.457107	+	0.889412i	$0.348886\pi$
$824$	39.7538	−	22.9519i	1.38489	−	0.799567i
$825$		0			0
$826$	0.863936	+	3.22425i	0.0300602	+	0.112186i
$827$	9.84615	−	9.84615i	0.342384	−	0.342384i	−0.514879	−	0.857263i	$-0.672163\pi$
$827$	9.84615	−	9.84615i	0.342384	−	0.342384i	0.857263	+	0.514879i	$0.172163\pi$
$828$		0			0
$829$	−3.18743			−0.110704			−0.0553519	−	0.998467i	$-0.517628\pi$
$829$	−3.18743			−0.110704			−0.0553519	+	0.998467i	$0.517628\pi$
$830$	0.962866	−	0.257999i	0.0334216	−	0.00895528i
$831$		0			0
$832$	−6.13283	−	10.6224i	−0.212618	−	0.368265i
$833$	−24.7953	+	14.0994i	−0.859107	+	0.488516i
$834$		0			0
$835$	−1.38307	−	0.798517i	−0.0478632	−	0.0276338i
$836$	0.139104	+	0.139104i	0.00481102	+	0.00481102i
$837$		0			0
$838$	22.1050	+	22.1050i	0.763604	+	0.763604i
$839$	9.75283	+	36.3981i	0.336705	+	1.25660i	0.902009	+	0.431718i	$0.142092\pi$
$839$	9.75283	+	36.3981i	0.336705	+	1.25660i	−0.565304	+	0.824883i	$0.691241\pi$
$840$		0			0
$841$	−15.4787	+	8.93663i	−0.533748	+	0.308160i
$842$	−43.5236	+	25.1284i	−1.49992	+	0.865981i
$843$		0			0
$844$	1.55561	+	5.80563i	0.0535464	+	0.199838i
$845$	−1.63875	−	1.63875i	−0.0563747	−	0.0563747i
$846$		0			0
$847$	−28.9430	−	28.9430i	−0.994494	−	0.994494i
$848$	−18.3599	−	10.6001i	−0.630482	−	0.364009i
$849$		0			0
$850$	13.4708	+	23.6899i	0.462045	+	0.812556i
$851$	−34.0061	−	58.9003i	−1.16571	−	2.01908i
$852$		0			0
$853$	−35.5719	+	9.53147i	−1.21796	+	0.326351i	−0.809880	−	0.586595i	$-0.800468\pi$
$853$	−35.5719	+	9.53147i	−1.21796	+	0.326351i	−0.408079	+	0.912946i	$0.633801\pi$
$854$	−15.4130			−0.527420
$855$		0			0
$856$	−32.8863	+	32.8863i	−1.12403	+	1.12403i
$857$	5.30869	+	19.8123i	0.181341	+	0.676775i	0.995384	+	0.0959705i	$0.0305954\pi$
$857$	5.30869	+	19.8123i	0.181341	+	0.676775i	−0.814043	+	0.580805i	$0.802738\pi$
$858$		0			0
$859$	9.51344	−	5.49259i	0.324594	−	0.187405i	−0.328844	−	0.944384i	$-0.606659\pi$
$859$	9.51344	−	5.49259i	0.324594	−	0.187405i	0.653439	+	0.756979i	$0.273326\pi$
$860$	−0.307787	−	0.0824714i	−0.0104955	−	0.00281225i
$861$		0			0
$862$	−12.7829	+	3.42516i	−0.435386	+	0.116661i
$863$	20.0046			0.680966			0.340483	−	0.940251i	$-0.389409\pi$
$863$	20.0046			0.680966			0.340483	+	0.940251i	$0.389409\pi$
$864$		0			0
$865$		−	0.759893i		−	0.0258371i
$866$	−9.18305	+	15.9055i	−0.312053	+	0.540491i
$867$		0			0
$868$	−2.90114	−	5.02492i	−0.0984710	−	0.170557i
$869$	0.197557	−	0.114060i	0.00670166	−	0.00386921i
$870$		0			0
$871$	3.13521	−	5.43035i	0.106233	−	0.184000i
$872$	30.8110	+	30.8110i	1.04339	+	1.04339i
$873$		0			0
$874$	−35.0241	+	35.0241i	−1.18471	+	1.18471i
$875$	−6.77538	−	3.91177i	−0.229050	−	0.132242i
$876$		0			0
$877$	37.6541	+	10.0894i	1.27149	+	0.340694i	0.830601	−	0.556868i	$-0.187997\pi$
$877$	37.6541	+	10.0894i	1.27149	+	0.340694i	0.440887	+	0.897563i	$0.354664\pi$
$878$	−15.6498	−	4.19334i	−0.528153	−	0.141518i
$879$		0			0
$880$	−0.0622673	+	0.107850i	−0.00209903	+	0.00363563i
$881$	31.2239	+	31.2239i	1.05196	+	1.05196i	0.998574	+	0.0533851i	$0.0170011\pi$
$881$	31.2239	+	31.2239i	1.05196	+	1.05196i	0.0533851	+	0.998574i	$0.482999\pi$
$882$		0			0
$883$	20.6430			0.694694			0.347347	−	0.937737i	$-0.387083\pi$
$883$	20.6430			0.694694			0.347347	+	0.937737i	$0.387083\pi$
$884$	0.651564	−	1.11163i	0.0219145	−	0.0373881i
$885$		0			0
$886$	−40.3487	+	23.2953i	−1.35554	+	0.782622i
$887$	−10.0495	+	37.5051i	−0.337428	+	1.25930i	0.563785	+	0.825922i	$0.309345\pi$
$887$	−10.0495	+	37.5051i	−0.337428	+	1.25930i	−0.901213	+	0.433377i	$0.857322\pi$
$888$		0			0
$889$	1.33578	−	0.357921i	0.0448006	−	0.0120043i
$890$	3.14404	−	3.14404i	0.105388	−	0.105388i
$891$		0			0
$892$		−	4.65310i		−	0.155797i
$893$	9.31927	+	5.38049i	0.311858	+	0.180051i
$894$		0			0
$895$	1.21057	+	0.324372i	0.0404650	+	0.0108426i
$896$	−8.77204	+	32.7377i	−0.293053	+	1.09369i
$897$		0			0
$898$	−8.83037	+	2.36609i	−0.294673	+	0.0789574i
$899$			23.4639i			0.782564i
$900$		0			0
$901$	0.163502	−	24.9105i	0.00544705	−	0.829891i
$902$	−0.419249	+	0.726160i	−0.0139595	+	0.0241785i
$903$		0			0
$904$	10.7386	−	40.0768i	0.357159	−	1.33294i
$905$	1.52131	+	2.63498i	0.0505699	+	0.0875896i
$906$		0			0
$907$	−2.56868	−	9.58646i	−0.0852917	−	0.318313i	0.910078	−	0.414438i	$-0.136022\pi$
$907$	−2.56868	−	9.58646i	−0.0852917	−	0.318313i	−0.995369	+	0.0961250i	$0.969355\pi$
$908$	2.24110	−	2.24110i	0.0743735	−	0.0743735i
$909$		0			0
$910$		−	1.48142i		−	0.0491086i
$911$	3.42063	+	12.7660i	0.113331	+	0.422956i	0.999157	−	0.0410619i	$-0.0130741\pi$
$911$	3.42063	+	12.7660i	0.113331	+	0.422956i	−0.885826	+	0.464018i	$0.846407\pi$
$912$		0			0
$913$	0.154728	−	0.577454i	0.00512076	−	0.0191109i
$914$	13.6641	+	23.6669i	0.451968	+	0.782831i
$915$		0			0
$916$	−4.44915	−	2.56872i	−0.147004	−	0.0848728i
$917$	9.72402			0.321115
$918$		0			0
$919$	−18.4170			−0.607522			−0.303761	−	0.952748i	$-0.598242\pi$
$919$	−18.4170			−0.607522			−0.303761	+	0.952748i	$0.598242\pi$
$920$	3.80048	+	2.19421i	0.125298	+	0.0723410i
$921$		0			0
$922$	8.74137	+	15.1405i	0.287882	+	0.498625i
$923$	−2.85778	+	10.6654i	−0.0940651	+	0.351056i
$924$		0			0
$925$	12.4040	+	46.2925i	0.407843	+	1.52209i
$926$		−	23.7968i		−	0.782010i
$927$		0			0
$928$	−2.93605	+	2.93605i	−0.0963807	+	0.0963807i
$929$	−7.54349	−	28.1527i	−0.247494	−	0.923660i	−0.972113	−	0.234511i	$-0.924651\pi$
$929$	−7.54349	−	28.1527i	−0.247494	−	0.923660i	0.724620	−	0.689149i	$-0.242016\pi$
$930$		0			0
$931$	18.2659	+	31.6374i	0.598639	+	1.03687i
$932$	−1.44315	+	5.38590i	−0.0472718	+	0.176421i
$933$		0			0
$934$	−16.5813	+	28.7197i	−0.542557	+	0.939737i
$935$	−0.146330		0.000960448i	−0.00478550		3.14100e-5i
$936$		0			0
$937$			42.0254i			1.37291i	0.727173	+	0.686455i	$0.240834\pi$
$937$			42.0254i			1.37291i	−0.727173	+	0.686455i	$0.759166\pi$
$938$	−21.3224	+	5.71332i	−0.696201	+	0.186547i
$939$		0			0
$940$	0.0245640	−	0.0916740i	0.000801189	−	0.00299008i
$941$	5.30484	+	1.42143i	0.172933	+	0.0463372i	0.344246	−	0.938879i	$-0.388134\pi$
$941$	5.30484	+	1.42143i	0.172933	+	0.0463372i	−0.171314	+	0.985217i	$0.554801\pi$
$942$		0			0
$943$	22.7249	+	13.1203i	0.740026	+	0.427254i
$944$			2.35393i			0.0766139i
$945$		0			0
$946$	1.08718	−	1.08718i	0.0353472	−	0.0353472i
$947$	33.0702	−	8.86114i	1.07464	−	0.287948i	0.322241	−	0.946658i	$-0.395564\pi$
$947$	33.0702	−	8.86114i	1.07464	−	0.287948i	0.752398	+	0.658709i	$0.228897\pi$
$948$		0			0
$949$	2.10957	−	7.87302i	0.0684796	−	0.255569i
$950$	30.2269	−	17.4515i	0.980690	−	0.566201i
$951$		0			0
$952$	−44.0915	+	11.5046i	−1.42901	+	0.372868i
$953$	34.1762			1.10707			0.553537	−	0.832824i	$-0.313278\pi$
$953$	34.1762			1.10707			0.553537	+	0.832824i	$0.313278\pi$
$954$		0			0
$955$	−1.13605	−	1.13605i	−0.0367616	−	0.0367616i
$956$	−2.79861	+	4.84733i	−0.0905135	+	0.156774i
$957$		0			0
$958$	−32.2221	−	8.63387i	−1.04105	−	0.278948i
$959$	−40.1227	−	10.7508i	−1.29563	−	0.347162i
$960$		0			0
$961$	−16.0043	−	9.24010i	−0.516268	−	0.298068i
$962$	−12.8913	+	12.8913i	−0.415633	+	0.415633i
$963$		0			0
$964$	4.45582	+	4.45582i	0.143512	+	0.143512i
$965$	−0.0552947	+	0.0957733i	−0.00178000	+	0.00308305i
$966$		0			0
$967$	30.6398	−	17.6899i	0.985309	−	0.568868i	0.0814401	−	0.996678i	$-0.474048\pi$
$967$	30.6398	−	17.6899i	0.985309	−	0.568868i	0.903869	+	0.427810i	$0.140715\pi$
$968$	−16.2512	−	28.1478i	−0.522332	−	0.904706i
$969$		0			0
$970$	−1.26027	+	2.18285i	−0.0404649	+	0.0700872i
$971$			44.6796i			1.43384i	0.697157	+	0.716919i	$0.254448\pi$
$971$			44.6796i			1.43384i	−0.697157	+	0.716919i	$0.745552\pi$
$972$		0			0
$973$	−37.9229			−1.21575
$974$	−22.2869	+	5.97176i	−0.714118	+	0.191347i
$975$		0			0
$976$	−10.4988	−	2.81313i	−0.336057	−	0.0900462i
$977$	−5.43870	+	3.14004i	−0.173999	+	0.100459i	−0.584470	−	0.811415i	$-0.698698\pi$
$977$	−5.43870	+	3.14004i	−0.173999	+	0.100459i	0.410471	+	0.911874i	$0.365364\pi$
$978$		0			0
$979$	−0.690162	−	2.57572i	−0.0220577	−	0.0823203i
$980$	0.227827	−	0.227827i	0.00727768	−	0.00727768i
$981$		0			0
$982$	−8.92150			−0.284697
$983$	−21.6274	+	5.79503i	−0.689806	+	0.184833i	−0.586660	−	0.809833i	$-0.699557\pi$
$983$	−21.6274	+	5.79503i	−0.689806	+	0.184833i	−0.103146	+	0.994666i	$0.532891\pi$
$984$		0			0
$985$	−2.00784	−	3.47768i	−0.0639751	−	0.110808i
$986$	17.6870	+	4.86386i	0.563268	+	0.154897i
$987$		0			0
$988$	−1.42916	−	0.825128i	−0.0454677	−	0.0262508i
$989$	−34.0229	−	34.0229i	−1.08186	−	1.08186i
$990$		0			0
$991$	6.63161	+	6.63161i	0.210660	+	0.210660i	0.804548	−	0.593888i	$-0.202408\pi$
$991$	6.63161	+	6.63161i	0.210660	+	0.210660i	−0.593888	+	0.804548i	$0.702408\pi$
$992$	−2.26625	−	8.45775i	−0.0719534	−	0.268534i
$993$		0			0
$994$	33.6635	−	19.4356i	1.06774	−	0.616461i
$995$	3.88657	−	2.24391i	0.123213	−	0.0711368i
$996$		0			0
$997$	7.85176	+	29.3031i	0.248668	+	0.928040i	0.971504	+	0.237021i	$0.0761711\pi$
$997$	7.85176	+	29.3031i	0.248668	+	0.928040i	−0.722837	+	0.691019i	$0.757162\pi$
$998$	−11.2179	−	11.2179i	−0.355097	−	0.355097i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.o.a.370.11		64
3.2	odd	2		153.2.n.a.115.6	yes	64
9.4	even	3	inner	459.2.o.a.64.6		64
9.5	odd	6		153.2.n.a.13.11	yes	64
17.4	even	4	inner	459.2.o.a.208.6		64
51.38	odd	4		153.2.n.a.106.11	yes	64
153.4	even	12	inner	459.2.o.a.361.11		64
153.140	odd	12		153.2.n.a.4.6	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.n.a.4.6	✓	64	153.140	odd	12
153.2.n.a.13.11	yes	64	9.5	odd	6
153.2.n.a.106.11	yes	64	51.38	odd	4
153.2.n.a.115.6	yes	64	3.2	odd	2
459.2.o.a.64.6		64	9.4	even	3	inner
459.2.o.a.208.6		64	17.4	even	4	inner
459.2.o.a.361.11		64	153.4	even	12	inner
459.2.o.a.370.11		64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.15506 + 0.666877i) q^{2} +(-0.110551 - 0.191481i) q^{4} +(0.0545182 - 0.203465i) q^{5} +(-0.965572 - 3.60357i) q^{7} -2.96240i q^{8} +(0.198658 - 0.198658i) q^{10} +(-0.0436083 - 0.162748i) q^{11} +(0.706706 + 1.22405i) q^{13} +(1.28784 - 4.80627i) q^{14} +(1.75445 - 3.03880i) q^{16} +(4.12302 + 0.0270617i) q^{17} -5.28066i q^{19} +(-0.0449866 + 0.0120541i) q^{20} +(0.0581627 - 0.217066i) q^{22} +(-6.79301 - 1.82018i) q^{23} +(4.29170 + 2.47781i) q^{25} +1.88514i q^{26} +(-0.583267 + 0.583267i) q^{28} +(3.22202 - 0.863336i) q^{29} +(-1.82059 + 6.79453i) q^{31} +(-1.07802 + 0.622394i) q^{32} +(4.74430 + 2.78080i) q^{34} -0.785840 q^{35} +(6.83838 + 6.83838i) q^{37} +(3.52155 - 6.09950i) q^{38} +(-0.602745 - 0.161505i) q^{40} +(-3.60410 - 0.965717i) q^{41} +(5.92513 + 3.42088i) q^{43} +(-0.0263422 + 0.0263422i) q^{44} +(-6.63253 - 6.63253i) q^{46} +(-1.01890 + 1.76479i) q^{47} +(-5.99118 + 3.45901i) q^{49} +(3.30479 + 5.72407i) q^{50} +(0.156255 - 0.270641i) q^{52} -6.04183i q^{53} -0.0354910 q^{55} +(-10.6752 + 2.86041i) q^{56} +(4.29737 + 1.15148i) q^{58} +(-0.580968 + 0.335422i) q^{59} +(-0.801711 - 2.99203i) q^{61} +(-6.63401 + 6.63401i) q^{62} -8.67806 q^{64} +(0.287580 - 0.0770567i) q^{65} +(-2.21819 - 3.84202i) q^{67} +(-0.450623 - 0.792469i) q^{68} +(-0.907696 - 0.524058i) q^{70} +(5.52395 + 5.52395i) q^{71} +(-4.07769 - 4.07769i) q^{73} +(3.33841 + 12.4591i) q^{74} +(-1.01114 + 0.583784i) q^{76} +(-0.544367 + 0.314290i) q^{77} +(0.350417 + 1.30778i) q^{79} +(-0.522640 - 0.522640i) q^{80} +(-3.51896 - 3.51896i) q^{82} +(3.07278 + 1.77407i) q^{83} +(0.230286 - 0.837414i) q^{85} +(4.56261 + 7.90266i) q^{86} +(-0.482126 + 0.129185i) q^{88} +15.8264 q^{89} +(3.72857 - 3.72857i) q^{91} +(0.402447 + 1.50195i) q^{92} +(-2.35380 + 1.35897i) q^{94} +(-1.07443 - 0.287893i) q^{95} +(-8.66597 + 2.32204i) q^{97} -9.22692 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 24 q^{4} + 2 q^{5} - 2 q^{7} - 16 q^{10} - 4 q^{13} - 16 q^{16} + 8 q^{17} - 18 q^{20} - 4 q^{22} + 8 q^{23} + 10 q^{29} - 2 q^{31} + 20 q^{34} + 128 q^{35} - 8 q^{37} + 24 q^{38} - 20 q^{40} - 32 q^{41}+ \cdots - 208 q^{98}+O(q^{100}) \) 64 * q + 24 * q^4 + 2 * q^5 - 2 * q^7 - 16 * q^10 - 4 * q^13 - 16 * q^16 + 8 * q^17 - 18 * q^20 - 4 * q^22 + 8 * q^23 + 10 * q^29 - 2 * q^31 + 20 * q^34 + 128 * q^35 - 8 * q^37 + 24 * q^38 - 20 * q^40 - 32 * q^41 - 20 * q^44 - 40 * q^46 + 64 * q^47 - 48 * q^50 + 36 * q^52 - 16 * q^55 - 12 * q^56 - 10 * q^58 - 2 * q^61 + 28 * q^62 - 8 * q^64 - 8 * q^65 - 4 * q^67 + 60 * q^68 + 84 * q^71 - 44 * q^73 + 14 * q^74 + 10 * q^79 - 204 * q^80 - 52 * q^82 + 22 * q^85 - 32 * q^86 + 16 * q^88 - 128 * q^89 + 44 * q^91 - 136 * q^92 - 4 * q^95 - 44 * q^97 - 208 * q^98

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