LMFDB - Embedded newform 459.2.e.b.154.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(154,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.154"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.152695449.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 3x^{5} - 5x^{4} + 6x^{3} - 16x + 16 $ x^8 - 2x^7 + 3x^5 - 5x^4 + 6x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			154.4
Root			$-1.37475 + 0.331768i$ of defining polynomial
Character	$\chi$	$=$	459.154
Dual form			459.2.e.b.307.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.974693 - 1.68822i) q^{2} +(-0.900054 - 1.55894i) q^{4} +(-0.974693 - 1.68822i) q^{5} +(0.900054 - 1.55894i) q^{7} +0.389667 q^{8} -3.80011 q^{10} +(0.194834 - 0.337462i) q^{11} +(-0.679914 - 1.17765i) q^{13} +(-1.75455 - 3.03897i) q^{14} +(2.17991 - 3.77572i) q^{16} +1.00000 q^{17} -7.91955 q^{19} +(-1.75455 + 3.03897i) q^{20} +(-0.379806 - 0.657843i) q^{22} +(0.905113 + 1.56770i) q^{23} +(0.599946 - 1.03914i) q^{25} -2.65083 q^{26} -3.24039 q^{28} +(-2.26947 + 3.93084i) q^{29} +(2.40005 + 4.15702i) q^{31} +(-3.85983 - 6.68542i) q^{32} +(0.974693 - 1.68822i) q^{34} -3.50911 q^{35} +7.20799 q^{37} +(-7.71913 + 13.3699i) q^{38} +(-0.379806 - 0.657843i) q^{40} +(1.00533 + 1.74128i) q^{41} +(6.28844 - 10.8919i) q^{43} -0.701443 q^{44} +3.52883 q^{46} +(2.07464 - 3.59338i) q^{47} +(1.87981 + 3.25592i) q^{49} +(-1.16953 - 2.02568i) q^{50} +(-1.22392 + 2.11989i) q^{52} +2.08855 q^{53} -0.759612 q^{55} +(0.350721 - 0.607467i) q^{56} +(4.42408 + 7.66273i) q^{58} +(5.80921 + 10.0619i) q^{59} +(-4.74444 + 8.21760i) q^{61} +9.35727 q^{62} -6.32894 q^{64} +(-1.32541 + 2.29569i) q^{65} +(1.81555 + 3.14463i) q^{67} +(-0.900054 - 1.55894i) q^{68} +(-3.42030 + 5.92414i) q^{70} +14.5198 q^{71} +0.111884 q^{73} +(7.02558 - 12.1687i) q^{74} +(7.12802 + 12.3461i) q^{76} +(-0.350721 - 0.607467i) q^{77} +(-5.36841 + 9.29835i) q^{79} -8.49899 q^{80} +3.91955 q^{82} +(-2.10527 + 3.64644i) q^{83} +(-0.974693 - 1.68822i) q^{85} +(-12.2586 - 21.2325i) q^{86} +(0.0759202 - 0.131498i) q^{88} +2.18327 q^{89} -2.44784 q^{91} +(1.62930 - 2.82203i) q^{92} +(-4.04427 - 7.00489i) q^{94} +(7.71913 + 13.3699i) q^{95} +(2.42861 - 4.20648i) q^{97} +7.32894 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 3 q^{4} + q^{5} + 3 q^{7} + 6 q^{8} - 22 q^{10} + 3 q^{11} + 9 q^{13} + 5 q^{14} + 3 q^{16} + 8 q^{17} - 14 q^{19} + 5 q^{20} + 3 q^{22} + 10 q^{23} + 9 q^{25} - 22 q^{26} - 38 q^{28} - 15 q^{29}+ \cdots + 30 q^{98}+O(q^{100}) $ 8 * q - q^2 - 3 * q^4 + q^5 + 3 * q^7 + 6 * q^8 - 22 * q^10 + 3 * q^11 + 9 * q^13 + 5 * q^14 + 3 * q^16 + 8 * q^17 - 14 * q^19 + 5 * q^20 + 3 * q^22 + 10 * q^23 + 9 * q^25 - 22 * q^26 - 38 * q^28 - 15 * q^29 + 15 * q^31 - 2 * q^32 - q^34 + 10 * q^35 - 24 * q^37 - 20 * q^38 + 3 * q^40 - 6 * q^41 + 18 * q^43 - 24 * q^44 + 8 * q^46 + 12 * q^47 + 9 * q^49 - 2 * q^50 + 4 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^56 + 9 * q^58 - 5 * q^61 - 16 * q^62 - 22 * q^64 - 11 * q^65 + 6 * q^67 - 3 * q^68 - 25 * q^70 + 50 * q^71 + 8 * q^73 + 44 * q^74 - 6 * q^76 - 12 * q^77 + 8 * q^79 - 16 * q^80 - 18 * q^82 - 7 * q^83 + q^85 - 34 * q^86 + 27 * q^88 + 28 * q^89 + 8 * q^91 - 19 * q^92 - 12 * q^94 + 20 * q^95 + 16 * q^97 + 30 * q^98

Character values

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

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

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 $

$2$	0.974693	−	1.68822i	0.689212	−	1.19375i	−0.282881	−	0.959155i	$-0.591290\pi$
$2$	0.974693	−	1.68822i	0.689212	−	1.19375i	0.972093	−	0.234596i	$-0.0753766\pi$
$3$		0			0
$3$		0			0
$4$	−0.900054	−	1.55894i	−0.450027	−	0.779470i
$5$	−0.974693	−	1.68822i	−0.435896	−	0.754994i	0.561472	−	0.827496i	$-0.310235\pi$
$5$	−0.974693	−	1.68822i	−0.435896	−	0.754994i	−0.997368	+	0.0725014i	$0.976902\pi$
$6$		0			0
$7$	0.900054	−	1.55894i	0.340188	−	0.589224i	−0.644279	−	0.764790i	$-0.722842\pi$
$7$	0.900054	−	1.55894i	0.340188	−	0.589224i	0.984468	+	0.175567i	$0.0561758\pi$
$8$	0.389667			0.137768
$9$		0			0
$10$	−3.80011			−1.20170
$11$	0.194834	−	0.337462i	0.0587445	−	0.101748i	−0.835158	−	0.550011i	$-0.814624\pi$
$11$	0.194834	−	0.337462i	0.0587445	−	0.101748i	0.893902	+	0.448262i	$0.147957\pi$
$12$		0			0
$13$	−0.679914	−	1.17765i	−0.188574	−	0.326620i	0.756201	−	0.654339i	$-0.227053\pi$
$13$	−0.679914	−	1.17765i	−0.188574	−	0.326620i	−0.944775	+	0.327719i	$0.893720\pi$
$14$	−1.75455	−	3.03897i	−0.468924	−	0.812200i
$15$		0			0
$16$	2.17991	−	3.77572i	0.544978	−	0.943930i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$		0			0
$19$	−7.91955			−1.81687			−0.908434	−	0.418028i	$-0.862722\pi$
$19$	−7.91955			−1.81687			−0.908434	+	0.418028i	$0.862722\pi$
$20$	−1.75455	+	3.03897i	−0.392330	+	0.679535i
$21$		0			0
$22$	−0.379806	−	0.657843i	−0.0809749	−	0.140253i
$23$	0.905113	+	1.56770i	0.188729	+	0.326888i	0.944827	−	0.327570i	$-0.106230\pi$
$23$	0.905113	+	1.56770i	0.188729	+	0.326888i	−0.756098	+	0.654459i	$0.772897\pi$
$24$		0			0
$25$	0.599946	−	1.03914i	0.119989	−	0.207827i
$26$	−2.65083			−0.519870
$27$		0			0
$28$	−3.24039			−0.612376
$29$	−2.26947	+	3.93084i	−0.421431	+	0.729939i	−0.996080	−	0.0884608i	$-0.971805\pi$
$29$	−2.26947	+	3.93084i	−0.421431	+	0.729939i	0.574649	+	0.818400i	$0.305139\pi$
$30$		0			0
$31$	2.40005	+	4.15702i	0.431062	+	0.746622i	0.996965	−	0.0778501i	$-0.0248055\pi$
$31$	2.40005	+	4.15702i	0.431062	+	0.746622i	−0.565903	+	0.824472i	$0.691472\pi$
$32$	−3.85983	−	6.68542i	−0.682328	−	1.18183i
$33$		0			0
$34$	0.974693	−	1.68822i	0.167159	−	0.289527i
$35$	−3.50911			−0.593147
$36$		0			0
$37$	7.20799			1.18499			0.592493	−	0.805576i	$-0.298144\pi$
$37$	7.20799			1.18499			0.592493	+	0.805576i	$0.298144\pi$
$38$	−7.71913	+	13.3699i	−1.25221	+	2.16889i
$39$		0			0
$40$	−0.379806	−	0.657843i	−0.0600526	−	0.104014i
$41$	1.00533	+	1.74128i	0.157006	+	0.271942i	0.933788	−	0.357828i	$-0.116482\pi$
$41$	1.00533	+	1.74128i	0.157006	+	0.271942i	−0.776782	+	0.629770i	$0.783149\pi$
$42$		0			0
$43$	6.28844	−	10.8919i	0.958978	−	1.66100i	0.233988	−	0.972239i	$-0.424822\pi$
$43$	6.28844	−	10.8919i	0.958978	−	1.66100i	0.724990	−	0.688759i	$-0.241844\pi$
$44$	−0.701443			−0.105746
$45$		0			0
$46$	3.52883			0.520297
$47$	2.07464	−	3.59338i	0.302617	−	0.524148i	−0.674111	−	0.738630i	$-0.735473\pi$
$47$	2.07464	−	3.59338i	0.302617	−	0.524148i	0.976728	+	0.214482i	$0.0688063\pi$
$48$		0			0
$49$	1.87981	+	3.25592i	0.268544	+	0.465131i
$50$	−1.16953	−	2.02568i	−0.165396	−	0.286474i
$51$		0			0
$52$	−1.22392	+	2.11989i	−0.169727	+	0.293976i
$53$	2.08855			0.286884			0.143442	−	0.989659i	$-0.454183\pi$
$53$	2.08855			0.286884			0.143442	+	0.989659i	$0.454183\pi$
$54$		0			0
$55$	−0.759612			−0.102426
$56$	0.350721	−	0.607467i	0.0468671	−	0.0811762i
$57$		0			0
$58$	4.42408	+	7.66273i	0.580910	+	1.00617i
$59$	5.80921	+	10.0619i	0.756295	+	1.30994i	0.944728	+	0.327856i	$0.106326\pi$
$59$	5.80921	+	10.0619i	0.756295	+	1.30994i	−0.188433	+	0.982086i	$0.560341\pi$
$60$		0			0
$61$	−4.74444	+	8.21760i	−0.607463	+	1.05216i	0.384194	+	0.923252i	$0.374479\pi$
$61$	−4.74444	+	8.21760i	−0.607463	+	1.05216i	−0.991657	+	0.128904i	$0.958854\pi$
$62$	9.35727			1.18837
$63$		0			0
$64$	−6.32894			−0.791117
$65$	−1.32541	+	2.29569i	−0.164397	+	0.284745i
$66$		0			0
$67$	1.81555	+	3.14463i	0.221805	+	0.384178i	0.955356	−	0.295457i	$-0.0954718\pi$
$67$	1.81555	+	3.14463i	0.221805	+	0.384178i	−0.733551	+	0.679634i	$0.762138\pi$
$68$	−0.900054	−	1.55894i	−0.109148	−	0.189049i
$69$		0			0
$70$	−3.42030	+	5.92414i	−0.408804	+	0.708070i
$71$	14.5198			1.72318			0.861589	−	0.507606i	$-0.169469\pi$
$71$	14.5198			1.72318			0.861589	+	0.507606i	$0.169469\pi$
$72$		0			0
$73$	0.111884			0.0130950			0.00654749	−	0.999979i	$-0.497916\pi$
$73$	0.111884			0.0130950			0.00654749	+	0.999979i	$0.497916\pi$
$74$	7.02558	−	12.1687i	0.816707	−	1.41458i
$75$		0			0
$76$	7.12802	+	12.3461i	0.817640	+	1.41619i
$77$	−0.350721	−	0.607467i	−0.0399684	−	0.0692273i
$78$		0			0
$79$	−5.36841	+	9.29835i	−0.603993	+	1.04615i	0.388217	+	0.921568i	$0.373091\pi$
$79$	−5.36841	+	9.29835i	−0.603993	+	1.04615i	−0.992210	+	0.124579i	$0.960242\pi$
$80$	−8.49899			−0.950216
$81$		0			0
$82$	3.91955			0.432842
$83$	−2.10527	+	3.64644i	−0.231084	+	0.400249i	−0.958127	−	0.286342i	$-0.907561\pi$
$83$	−2.10527	+	3.64644i	−0.231084	+	0.400249i	0.727043	+	0.686591i	$0.240894\pi$
$84$		0			0
$85$	−0.974693	−	1.68822i	−0.105720	−	0.183113i
$86$	−12.2586	−	21.2325i	−1.32188	−	2.28956i
$87$		0			0
$88$	0.0759202	−	0.131498i	0.00809312	−	0.0140177i
$89$	2.18327			0.231426			0.115713	−	0.993283i	$-0.463085\pi$
$89$	2.18327			0.231426			0.115713	+	0.993283i	$0.463085\pi$
$90$		0			0
$91$	−2.44784			−0.256603
$92$	1.62930	−	2.82203i	0.169866	−	0.294217i
$93$		0			0
$94$	−4.04427	−	7.00489i	−0.417135	−	0.722499i
$95$	7.71913	+	13.3699i	0.791966	+	1.37173i
$96$		0			0
$97$	2.42861	−	4.20648i	0.246588	−	0.427103i	−0.715989	−	0.698112i	$-0.754024\pi$
$97$	2.42861	−	4.20648i	0.246588	−	0.427103i	0.962577	+	0.271008i	$0.0873571\pi$
$98$	7.32894			0.740334
$99$		0			0
$100$	−2.15994			−0.215994
$101$	6.67486	−	11.5612i	0.664173	−	1.15038i	−0.315336	−	0.948980i	$-0.602117\pi$
$101$	6.67486	−	11.5612i	0.664173	−	1.15038i	0.979509	−	0.201401i	$-0.0645495\pi$
$102$		0			0
$103$	−3.54832	−	6.14587i	−0.349626	−	0.605571i	0.636557	−	0.771230i	$-0.280358\pi$
$103$	−3.54832	−	6.14587i	−0.349626	−	0.605571i	−0.986183	+	0.165659i	$0.947025\pi$
$104$	−0.264940	−	0.458889i	−0.0259795	−	0.0449978i
$105$		0			0
$106$	2.03569	−	3.52592i	0.197724	−	0.342468i
$107$	−15.9058			−1.53767			−0.768837	−	0.639445i	$-0.779164\pi$
$107$	−15.9058			−1.53767			−0.768837	+	0.639445i	$0.779164\pi$
$108$		0			0
$109$	−7.21705			−0.691268			−0.345634	−	0.938369i	$-0.612336\pi$
$109$	−7.21705			−0.691268			−0.345634	+	0.938369i	$0.612336\pi$
$110$	−0.740388	+	1.28239i	−0.0705933	+	0.122271i
$111$		0			0
$112$	−3.92408	−	6.79671i	−0.370791	−	0.642228i
$113$	9.30948	+	16.1245i	0.875763	+	1.51687i	0.855948	+	0.517062i	$0.172974\pi$
$113$	9.30948	+	16.1245i	0.875763	+	1.51687i	0.0198143	+	0.999804i	$0.493692\pi$
$114$		0			0
$115$	1.76441	−	3.05606i	0.164532	−	0.284979i
$116$	8.17059			0.758620
$117$		0			0
$118$	22.6488			2.08499
$119$	0.900054	−	1.55894i	0.0825078	−	0.142908i
$120$		0			0
$121$	5.42408	+	9.39478i	0.493098	+	0.854071i
$122$	9.24874	+	16.0193i	0.837342	+	1.45032i
$123$		0			0
$124$	4.32036	−	7.48308i	0.387979	−	0.672000i
$125$	−12.0860			−1.08100
$126$		0			0
$127$	−16.4175			−1.45682			−0.728408	−	0.685144i	$-0.759739\pi$
$127$	−16.4175			−1.45682			−0.728408	+	0.685144i	$0.759739\pi$
$128$	1.55088	−	2.68621i	0.137080	−	0.237430i
$129$		0			0
$130$	2.58375	+	4.47518i	0.226609	+	0.392499i
$131$	−1.74624	−	3.02458i	−0.152570	−	0.264259i	0.779602	−	0.626276i	$-0.215422\pi$
$131$	−1.74624	−	3.02458i	−0.152570	−	0.264259i	−0.932172	+	0.362017i	$0.882088\pi$
$132$		0			0
$133$	−7.12802	+	12.3461i	−0.618078	+	1.07054i
$134$	7.07843			0.611483
$135$		0			0
$136$	0.389667			0.0334137
$137$	9.27885	−	16.0714i	0.792746	−	1.37308i	−0.131515	−	0.991314i	$-0.541984\pi$
$137$	9.27885	−	16.0714i	0.792746	−	1.37308i	0.924261	−	0.381761i	$-0.124682\pi$
$138$		0			0
$139$	−4.86814	−	8.43186i	−0.412910	−	0.715181i	0.582296	−	0.812977i	$-0.302154\pi$
$139$	−4.86814	−	8.43186i	−0.412910	−	0.715181i	−0.995207	+	0.0977953i	$0.968821\pi$
$140$	3.15838	+	5.47048i	0.266932	+	0.462340i
$141$		0			0
$142$	14.1523	−	24.5125i	1.18764	−	2.05705i
$143$	−0.529880			−0.0443108
$144$		0			0
$145$	8.84816			0.734800
$146$	0.109052	−	0.188884i	0.00902522	−	0.0156321i
$147$		0			0
$148$	−6.48758	−	11.2368i	−0.533276	−	0.923660i
$149$	−9.85504	−	17.0694i	−0.807356	−	1.39838i	−0.914689	−	0.404159i	$-0.867564\pi$
$149$	−9.85504	−	17.0694i	−0.807356	−	1.39838i	0.107333	−	0.994223i	$-0.465769\pi$
$150$		0			0
$151$	0.120194	−	0.208182i	0.00978126	−	0.0169416i	−0.861093	−	0.508447i	$-0.830220\pi$
$151$	0.120194	−	0.208182i	0.00978126	−	0.0169416i	0.870875	+	0.491505i	$0.163553\pi$
$152$	−3.08599			−0.250307
$153$		0			0
$154$	−1.36738			−0.110187
$155$	4.67863	−	8.10363i	0.375797	−	0.650899i
$156$		0			0
$157$	11.1083	+	19.2402i	0.886540	+	1.53553i	0.843939	+	0.536440i	$0.180231\pi$
$157$	11.1083	+	19.2402i	0.886540	+	1.53553i	0.0426010	+	0.999092i	$0.486436\pi$
$158$	10.4651	+	18.1261i	0.832559	+	1.44203i
$159$		0			0
$160$	−7.52430	+	13.0325i	−0.594848	+	1.03031i
$161$	3.25860			0.256814
$162$		0			0
$163$	−11.9743			−0.937901			−0.468950	−	0.883225i	$-0.655368\pi$
$163$	−11.9743			−0.937901			−0.468950	+	0.883225i	$0.655368\pi$
$164$	1.80970	−	3.13449i	0.141314	−	0.244763i
$165$		0			0
$166$	4.10399	+	7.10833i	0.318532	+	0.551713i
$167$	5.90943	+	10.2354i	0.457285	+	0.792042i	0.998816	−	0.0486392i	$-0.0154885\pi$
$167$	5.90943	+	10.2354i	0.457285	+	0.792042i	−0.541531	+	0.840681i	$0.682155\pi$
$168$		0			0
$169$	5.57543	−	9.65694i	0.428880	−	0.742841i
$170$	−3.80011			−0.291455
$171$		0			0
$172$	−22.6397			−1.72626
$173$	−2.52558	+	4.37443i	−0.192016	+	0.332582i	−0.945918	−	0.324405i	$-0.894836\pi$
$173$	−2.52558	+	4.37443i	−0.192016	+	0.332582i	0.753902	+	0.656987i	$0.228169\pi$
$174$		0			0
$175$	−1.07997	−	1.87056i	−0.0816379	−	0.141401i
$176$	−0.849440	−	1.47127i	−0.0640290	−	0.110901i
$177$		0			0
$178$	2.12802	−	3.68584i	0.159502	−	0.276265i
$179$	−1.64881			−0.123238			−0.0616188	−	0.998100i	$-0.519626\pi$
$179$	−1.64881			−0.123238			−0.0616188	+	0.998100i	$0.519626\pi$
$180$		0			0
$181$	8.87905			0.659975			0.329987	−	0.943985i	$-0.392956\pi$
$181$	8.87905			0.659975			0.329987	+	0.943985i	$0.392956\pi$
$182$	−2.38589	+	4.13248i	−0.176854	+	0.306320i
$183$		0			0
$184$	0.352693	+	0.610881i	0.0260008	+	0.0450348i
$185$	−7.02558	−	12.1687i	−0.516531	−	0.894657i
$186$		0			0
$187$	0.194834	−	0.337462i	0.0142476	−	0.0246776i
$188$	−7.46915			−0.544744
$189$		0			0
$190$	30.0951			2.18333
$191$	−5.86489	+	10.1583i	−0.424368	+	0.735027i	−0.996361	−	0.0852312i	$-0.972837\pi$
$191$	−5.86489	+	10.1583i	−0.424368	+	0.735027i	0.571993	+	0.820259i	$0.306170\pi$
$192$		0			0
$193$	2.75961	+	4.77979i	0.198641	+	0.344057i	0.948088	−	0.318008i	$-0.103014\pi$
$193$	2.75961	+	4.77979i	0.198641	+	0.344057i	−0.749447	+	0.662064i	$0.769680\pi$
$194$	−4.73430	−	8.20006i	−0.339903	−	0.588730i
$195$		0			0
$196$	3.38385	−	5.86101i	0.241704	−	0.418643i
$197$	−13.3832			−0.953511			−0.476755	−	0.879036i	$-0.658187\pi$
$197$	−13.3832			−0.953511			−0.476755	+	0.879036i	$0.658187\pi$
$198$		0			0
$199$	−23.5917			−1.67237			−0.836185	−	0.548447i	$-0.815219\pi$
$199$	−23.5917			−1.67237			−0.836185	+	0.548447i	$0.815219\pi$
$200$	0.233779	−	0.404917i	0.0165307	−	0.0286320i
$201$		0			0
$202$	−13.0119	−	22.5372i	−0.915512	−	1.58571i
$203$	4.08530	+	7.07594i	0.286732	+	0.496634i
$204$		0			0
$205$	1.95977	−	3.39443i	0.136877	−	0.237077i
$206$	−13.8341			−0.963867
$207$		0			0
$208$	−5.92861			−0.411075
$209$	−1.54299	+	2.67254i	−0.106731	+	0.184864i
$210$		0			0
$211$	2.50858	+	4.34499i	0.172698	+	0.299121i	0.939362	−	0.342927i	$-0.111418\pi$
$211$	2.50858	+	4.34499i	0.172698	+	0.299121i	−0.766664	+	0.642048i	$0.778085\pi$
$212$	−1.87981	−	3.25592i	−0.129106	−	0.223617i
$213$		0			0
$214$	−15.5033	+	26.8525i	−1.05978	+	1.83560i
$215$	−24.5172			−1.67206
$216$		0			0
$217$	8.64071			0.586570
$218$	−7.03441	+	12.1840i	−0.476431	+	0.825202i
$219$		0			0
$220$	0.683691	+	1.18419i	0.0460945	+	0.0798380i
$221$	−0.679914	−	1.17765i	−0.0457359	−	0.0792170i
$222$		0			0
$223$	−9.01118	+	15.6078i	−0.603433	+	1.04518i	0.388864	+	0.921295i	$0.372868\pi$
$223$	−9.01118	+	15.6078i	−0.603433	+	1.04518i	−0.992297	+	0.123882i	$0.960466\pi$
$224$	−13.8962			−0.928480
$225$		0			0
$226$	36.2956			2.41435
$227$	−8.79404	+	15.2317i	−0.583681	+	1.01096i	0.411358	+	0.911474i	$0.365055\pi$
$227$	−8.79404	+	15.2317i	−0.583681	+	1.01096i	−0.995038	+	0.0994908i	$0.968279\pi$
$228$		0			0
$229$	−0.431700	−	0.747727i	−0.0285275	−	0.0494112i	0.851409	−	0.524502i	$-0.175748\pi$
$229$	−0.431700	−	0.747727i	−0.0285275	−	0.0494112i	−0.879937	+	0.475091i	$0.842415\pi$
$230$	−3.43953	−	5.95743i	−0.226796	−	0.392821i
$231$		0			0
$232$	−0.884339	+	1.53172i	−0.0580597	+	0.100562i
$233$	16.6249			1.08914			0.544568	−	0.838717i	$-0.316694\pi$
$233$	16.6249			1.08914			0.544568	+	0.838717i	$0.316694\pi$
$234$		0			0
$235$	−8.08855			−0.527639
$236$	10.4572	−	18.1124i	0.680707	−	1.17902i
$237$		0			0
$238$	−1.75455	−	3.03897i	−0.113731	−	0.196987i
$239$	−8.27912	−	14.3399i	−0.535532	−	0.927568i	−0.999137	−	0.0415264i	$-0.986778\pi$
$239$	−8.27912	−	14.3399i	−0.535532	−	0.927568i	0.463606	−	0.886042i	$-0.346555\pi$
$240$		0			0
$241$	−7.06116	+	12.2303i	−0.454850	+	0.787823i	−0.998680	−	0.0513728i	$-0.983640\pi$
$241$	−7.06116	+	12.2303i	−0.454850	+	0.787823i	0.543830	+	0.839195i	$0.316974\pi$
$242$	21.1473			1.35940
$243$		0			0
$244$	17.0810			1.09350
$245$	3.66447	−	6.34705i	0.234114	−	0.405498i
$246$		0			0
$247$	5.38461	+	9.32642i	0.342614	+	0.593426i
$248$	0.935222	+	1.61985i	0.0593866	+	0.102861i
$249$		0			0
$250$	−11.7801	+	20.4038i	−0.745041	+	1.29045i
$251$	−6.28790			−0.396889			−0.198444	−	0.980112i	$-0.563589\pi$
$251$	−6.28790			−0.396889			−0.198444	+	0.980112i	$0.563589\pi$
$252$		0			0
$253$	0.705385			0.0443472
$254$	−16.0020	+	27.7163i	−1.00406	+	1.73908i
$255$		0			0
$256$	−9.35221	−	16.1985i	−0.584513	−	1.01241i
$257$	−4.60127	−	7.96963i	−0.287019	−	0.497132i	0.686078	−	0.727528i	$-0.259331\pi$
$257$	−4.60127	−	7.96963i	−0.287019	−	0.497132i	−0.973097	+	0.230397i	$0.925998\pi$
$258$		0			0
$259$	6.48758	−	11.2368i	0.403118	−	0.698222i
$260$	4.77178			0.295933
$261$		0			0
$262$	−6.80820			−0.420612
$263$	−11.2205	+	19.4344i	−0.691883	+	1.19838i	0.279338	+	0.960193i	$0.409885\pi$
$263$	−11.2205	+	19.4344i	−0.691883	+	1.19838i	−0.971220	+	0.238183i	$0.923448\pi$
$264$		0			0
$265$	−2.03569	−	3.52592i	−0.125052	−	0.216596i
$266$	13.8953	+	24.0673i	0.851973	+	1.47566i
$267$		0			0
$268$	3.26819	−	5.66067i	0.199637	−	0.345781i
$269$	2.85669			0.174175			0.0870876	−	0.996201i	$-0.472244\pi$
$269$	2.85669			0.174175			0.0870876	+	0.996201i	$0.472244\pi$
$270$		0			0
$271$	−19.8653			−1.20673			−0.603366	−	0.797464i	$-0.706174\pi$
$271$	−19.8653			−1.20673			−0.603366	+	0.797464i	$0.706174\pi$
$272$	2.17991	−	3.77572i	0.132177	−	0.228937i
$273$		0			0
$274$	−18.0881	−	31.3294i	−1.09274	−	1.89268i
$275$	−0.233779	−	0.404917i	−0.0140974	−	0.0244174i
$276$		0			0
$277$	11.2399	−	19.4681i	0.675340	−	1.16972i	−0.301029	−	0.953615i	$-0.597330\pi$
$277$	11.2399	−	19.4681i	0.675340	−	1.16972i	0.976369	−	0.216109i	$-0.0693366\pi$
$278$	−18.9798			−1.13833
$279$		0			0
$280$	−1.36738			−0.0817168
$281$	1.17512	−	2.03538i	0.0701021	−	0.121420i	−0.828844	−	0.559480i	$-0.811001\pi$
$281$	1.17512	−	2.03538i	0.0701021	−	0.121420i	0.898946	+	0.438060i	$0.144334\pi$
$282$		0			0
$283$	2.66447	+	4.61499i	0.158386	+	0.274333i	0.934287	−	0.356522i	$-0.116038\pi$
$283$	2.66447	+	4.61499i	0.158386	+	0.274333i	−0.775901	+	0.630855i	$0.782704\pi$
$284$	−13.0686	−	22.6354i	−0.775477	−	1.34317i
$285$		0			0
$286$	−0.516470	+	0.894553i	−0.0305395	+	0.0528960i
$287$	3.61940			0.213646
$288$		0			0
$289$	1.00000			0.0588235
$290$	8.62424	−	14.9376i	0.506433	−	0.877168i
$291$		0			0
$292$	−0.100701	−	0.174420i	−0.00589309	−	0.0102071i
$293$	−1.51183	−	2.61857i	−0.0883222	−	0.152979i	0.818480	−	0.574535i	$-0.194817\pi$
$293$	−1.51183	−	2.61857i	−0.0883222	−	0.152979i	−0.906802	+	0.421557i	$0.861484\pi$
$294$		0			0
$295$	11.3244	−	19.6144i	0.659332	−	1.14200i
$296$	2.80871			0.163253
$297$		0			0
$298$	−38.4226			−2.22576
$299$	1.23080	−	2.13180i	0.0711788	−	0.123285i
$300$		0			0
$301$	−11.3199	−	19.6066i	−0.652466	−	1.13011i
$302$	−0.234305	−	0.405828i	−0.0134827	−	0.0233528i
$303$		0			0
$304$	−17.2639	+	29.9020i	−0.990154	+	1.71500i
$305$	18.4975			1.05916
$306$		0			0
$307$	28.1214			1.60497			0.802485	−	0.596672i	$-0.203511\pi$
$307$	28.1214			1.60497			0.802485	+	0.596672i	$0.203511\pi$
$308$	−0.631336	+	1.09351i	−0.0359737	+	0.0623083i
$309$		0			0
$310$	−9.12046	−	15.7971i	−0.518008	−	0.897215i
$311$	−9.13916	−	15.8295i	−0.518234	−	0.897608i	−0.999776	−	0.0211847i	$-0.993256\pi$
$311$	−9.13916	−	15.8295i	−0.518234	−	0.897608i	0.481541	−	0.876423i	$-0.340077\pi$
$312$		0			0
$313$	9.50809	−	16.4685i	0.537429	−	0.930855i	−0.461612	−	0.887082i	$-0.652729\pi$
$313$	9.50809	−	16.4685i	0.537429	−	0.930855i	0.999042	−	0.0437730i	$-0.0139378\pi$
$314$	43.3088			2.44406
$315$		0			0
$316$	19.3274			1.08725
$317$	3.04155	−	5.26812i	0.170830	−	0.295887i	−0.767880	−	0.640594i	$-0.778688\pi$
$317$	3.04155	−	5.26812i	0.170830	−	0.295887i	0.938710	+	0.344707i	$0.112022\pi$
$318$		0			0
$319$	0.884339	+	1.53172i	0.0495135	+	0.0857598i
$320$	6.16877	+	10.6846i	0.344845	+	0.597289i
$321$		0			0
$322$	3.17614	−	5.50123i	0.176999	−	0.306571i
$323$	−7.91955			−0.440655
$324$		0			0
$325$	−1.63165			−0.0905074
$326$	−11.6713	+	20.2153i	−0.646413	+	1.11962i
$327$		0			0
$328$	0.391743	+	0.678519i	0.0216304	+	0.0374650i
$329$	−3.73457	−	6.46847i	−0.205894	−	0.356618i
$330$		0			0
$331$	−1.80416	+	3.12489i	−0.0991653	+	0.171759i	−0.911339	−	0.411656i	$-0.864951\pi$
$331$	−1.80416	+	3.12489i	−0.0991653	+	0.171759i	0.812174	+	0.583415i	$0.198284\pi$
$332$	7.57944			0.415976
$333$		0			0
$334$	23.0395			1.26067
$335$	3.53922	−	6.13010i	0.193368	−	0.334923i
$336$		0			0
$337$	−0.773480	−	1.33971i	−0.0421341	−	0.0729785i	0.844189	−	0.536045i	$-0.180082\pi$
$337$	−0.773480	−	1.33971i	−0.0421341	−	0.0729785i	−0.886323	+	0.463067i	$0.846749\pi$
$338$	−10.8687	−	18.8251i	−0.591178	−	1.02395i
$339$		0			0
$340$	−1.75455	+	3.03897i	−0.0951540	+	0.164812i
$341$	1.87044			0.101290
$342$		0			0
$343$	19.3685			1.04580
$344$	2.45040	−	4.24421i	0.132117	−	0.228833i
$345$		0			0
$346$	4.92332	+	8.52745i	0.264680	+	0.458438i
$347$	16.6333	+	28.8098i	0.892925	+	1.54659i	0.836352	+	0.548193i	$0.184684\pi$
$347$	16.6333	+	28.8098i	0.892925	+	1.54659i	0.0565729	+	0.998398i	$0.481983\pi$
$348$		0			0
$349$	−8.23963	+	14.2715i	−0.441057	+	0.763934i	−0.997768	−	0.0667725i	$-0.978730\pi$
$349$	−8.23963	+	14.2715i	−0.441057	+	0.763934i	0.556711	+	0.830706i	$0.312063\pi$
$350$	−4.21055			−0.225063
$351$		0			0
$352$	−3.00809			−0.160332
$353$	2.10580	−	3.64735i	0.112080	−	0.194129i	−0.804528	−	0.593914i	$-0.797582\pi$
$353$	2.10580	−	3.64735i	0.112080	−	0.194129i	0.916609	+	0.399785i	$0.130915\pi$
$354$		0			0
$355$	−14.1523	−	24.5125i	−0.751127	−	1.30099i
$356$	−1.96506	−	3.40359i	−0.104148	−	0.180390i
$357$		0			0
$358$	−1.60708	+	2.78355i	−0.0849369	+	0.147115i
$359$	−14.6145			−0.771323			−0.385662	−	0.922640i	$-0.626027\pi$
$359$	−14.6145			−0.771323			−0.385662	+	0.922640i	$0.626027\pi$
$360$		0			0
$361$	43.7192			2.30101
$362$	8.65435	−	14.9898i	0.454863	−	0.787845i
$363$		0			0
$364$	2.20318	+	3.81603i	0.115478	+	0.200014i
$365$	−0.109052	−	0.188884i	−0.00570805	−	0.00988663i
$366$		0			0
$367$	1.57970	−	2.73612i	0.0824596	−	0.142824i	−0.821846	−	0.569709i	$-0.807056\pi$
$367$	1.57970	−	2.73612i	0.0824596	−	0.142824i	0.904306	+	0.426885i	$0.140389\pi$
$368$	7.89227			0.411413
$369$		0			0
$370$	−27.3911			−1.42400
$371$	1.87981	−	3.25592i	0.0975947	−	0.169039i
$372$		0			0
$373$	−0.306973	−	0.531693i	−0.0158945	−	0.0275300i	0.857969	−	0.513702i	$-0.171726\pi$
$373$	−0.306973	−	0.531693i	−0.0158945	−	0.0275300i	−0.873863	+	0.486172i	$0.838393\pi$
$374$	−0.379806	−	0.657843i	−0.0196393	−	0.0340163i
$375$		0			0
$376$	0.808419	−	1.40022i	0.0416910	−	0.0722109i
$377$	6.17218			0.317884
$378$		0			0
$379$	4.19989			0.215734			0.107867	−	0.994165i	$-0.465598\pi$
$379$	4.19989			0.215734			0.107867	+	0.994165i	$0.465598\pi$
$380$	13.8953	−	24.0673i	0.712812	−	1.23463i
$381$		0			0
$382$	11.4329	+	19.8024i	0.584960	+	1.01318i
$383$	−17.0708	−	29.5675i	−0.872277	−	1.51083i	−0.859635	−	0.510908i	$-0.829309\pi$
$383$	−17.0708	−	29.5675i	−0.872277	−	1.51083i	−0.0126415	−	0.999920i	$-0.504024\pi$
$384$		0			0
$385$	−0.683691	+	1.18419i	−0.0348441	+	0.0603518i
$386$	10.7591			0.547624
$387$		0			0
$388$	−8.74353			−0.443885
$389$	−8.77401	+	15.1970i	−0.444860	+	0.770520i	−0.998042	−	0.0625403i	$-0.980080\pi$
$389$	−8.77401	+	15.1970i	−0.444860	+	0.770520i	0.553183	+	0.833060i	$0.313413\pi$
$390$		0			0
$391$	0.905113	+	1.56770i	0.0457735	+	0.0792820i
$392$	0.732498	+	1.26872i	0.0369968	+	0.0640803i
$393$		0			0
$394$	−13.0445	+	22.5937i	−0.657171	+	1.13825i
$395$	20.9302			1.05311
$396$		0			0
$397$	−22.4827			−1.12837			−0.564187	−	0.825647i	$-0.690810\pi$
$397$	−22.4827			−1.12837			−0.564187	+	0.825647i	$0.690810\pi$
$398$	−22.9947	+	39.8279i	−1.15262	+	1.99639i
$399$		0			0
$400$	−2.61566	−	4.53046i	−0.130783	−	0.226523i
$401$	3.95392	+	6.84839i	0.197449	+	0.341992i	0.947701	−	0.319160i	$-0.103401\pi$
$401$	3.95392	+	6.84839i	0.197449	+	0.341992i	−0.750251	+	0.661153i	$0.770068\pi$
$402$		0			0
$403$	3.26366	−	5.65282i	0.162574	−	0.281587i
$404$	−24.0309			−1.19558
$405$		0			0
$406$	15.9276			0.790476
$407$	1.40436	−	2.43242i	0.0696114	−	0.120571i
$408$		0			0
$409$	−9.53234	−	16.5105i	−0.471344	−	0.816391i	0.528119	−	0.849170i	$-0.322898\pi$
$409$	−9.53234	−	16.5105i	−0.471344	−	0.816391i	−0.999463	+	0.0327792i	$0.989564\pi$
$410$	−3.82036	−	6.61705i	−0.188674	−	0.326793i
$411$		0			0
$412$	−6.38736	+	11.0632i	−0.314683	+	0.545046i
$413$	20.9144			1.02913
$414$		0			0
$415$	8.20799			0.402914
$416$	−5.24870	+	9.09101i	−0.257339	+	0.445724i
$417$		0			0
$418$	3.00789	+	5.20982i	0.147121	+	0.254821i
$419$	−4.55233	−	7.88486i	−0.222396	−	0.385201i	0.733139	−	0.680079i	$-0.238054\pi$
$419$	−4.55233	−	7.88486i	−0.222396	−	0.385201i	−0.955535	+	0.294878i	$0.904721\pi$
$420$		0			0
$421$	11.3322	−	19.6280i	0.552299	−	0.956610i	−0.445809	−	0.895128i	$-0.647084\pi$
$421$	11.3322	−	19.6280i	0.552299	−	0.956610i	0.998108	−	0.0614820i	$-0.0195827\pi$
$422$	9.78039			0.476102
$423$		0			0
$424$	0.813838			0.0395235
$425$	0.599946	−	1.03914i	0.0291017	−	0.0504056i
$426$		0			0
$427$	8.54050	+	14.7926i	0.413304	+	0.715863i
$428$	14.3161	+	24.7962i	0.691994	+	1.19857i
$429$		0			0
$430$	−23.8968	+	41.3904i	−1.15240	+	1.99602i
$431$	14.8259			0.714139			0.357069	−	0.934078i	$-0.383776\pi$
$431$	14.8259			0.714139			0.357069	+	0.934078i	$0.383776\pi$
$432$		0			0
$433$	1.76633			0.0848842			0.0424421	−	0.999099i	$-0.486486\pi$
$433$	1.76633			0.0848842			0.0424421	+	0.999099i	$0.486486\pi$
$434$	8.42204	−	14.5874i	0.404271	−	0.700218i
$435$		0			0
$436$	6.49574	+	11.2509i	0.311089	+	0.538823i
$437$	−7.16808	−	12.4155i	−0.342896	−	0.593913i
$438$		0			0
$439$	−0.416945	+	0.722170i	−0.0198997	+	0.0344673i	−0.875804	−	0.482667i	$-0.839668\pi$
$439$	−0.416945	+	0.722170i	−0.0198997	+	0.0344673i	0.855904	+	0.517135i	$0.173001\pi$
$440$	−0.295996			−0.0141110
$441$		0			0
$442$	−2.65083			−0.126087
$443$	−11.2371	+	19.4632i	−0.533889	+	0.924724i	0.465327	+	0.885139i	$0.345937\pi$
$443$	−11.2371	+	19.4632i	−0.533889	+	0.924724i	−0.999216	+	0.0395846i	$0.987397\pi$
$444$		0			0
$445$	−2.12802	−	3.68584i	−0.100878	−	0.174725i
$446$	17.5663	+	30.4257i	0.831787	+	1.44070i
$447$		0			0
$448$	−5.69638	+	9.86643i	−0.269129	+	0.466145i
$449$	23.4874			1.10844			0.554219	−	0.832371i	$-0.313017\pi$
$449$	23.4874			1.10844			0.554219	+	0.832371i	$0.313017\pi$
$450$		0			0
$451$	0.783487			0.0368929
$452$	16.7581	−	29.0258i	0.788234	−	1.36526i
$453$		0			0
$454$	17.1430	+	29.6925i	0.804560	+	1.39354i
$455$	2.38589	+	4.13248i	0.111852	+	0.193734i
$456$		0			0
$457$	−6.56857	+	11.3771i	−0.307265	+	0.532198i	−0.977763	−	0.209713i	$-0.932747\pi$
$457$	−6.56857	+	11.3771i	−0.307265	+	0.532198i	0.670498	+	0.741911i	$0.266080\pi$
$458$	−1.68310			−0.0786461
$459$		0			0
$460$	−6.35227			−0.296176
$461$	7.45471	−	12.9119i	0.347201	−	0.601369i	−0.638550	−	0.769580i	$-0.720466\pi$
$461$	7.45471	−	12.9119i	0.347201	−	0.601369i	0.985751	+	0.168211i	$0.0537989\pi$
$462$		0			0
$463$	16.4684	+	28.5240i	0.765349	+	1.32562i	0.940062	+	0.341004i	$0.110767\pi$
$463$	16.4684	+	28.5240i	0.765349	+	1.32562i	−0.174712	+	0.984620i	$0.555900\pi$
$464$	9.89451	+	17.1378i	0.459341	+	0.795602i
$465$		0			0
$466$	16.2042	−	28.0665i	0.750645	−	1.30016i
$467$	−21.3041			−0.985836			−0.492918	−	0.870076i	$-0.664070\pi$
$467$	−21.3041			−0.985836			−0.492918	+	0.870076i	$0.664070\pi$
$468$		0			0
$469$	6.53638			0.301822
$470$	−7.88385	+	13.6552i	−0.363655	+	0.629869i
$471$		0			0
$472$	2.26366	+	3.92077i	0.104193	+	0.180468i
$473$	−2.45040	−	4.24421i	−0.112669	−	0.195149i
$474$		0			0
$475$	−4.75130	+	8.22949i	−0.218005	+	0.377595i
$476$	−3.24039			−0.148523
$477$		0			0
$478$	−32.2784			−1.47638
$479$	6.11487	−	10.5913i	0.279395	−	0.483927i	−0.691839	−	0.722052i	$-0.743199\pi$
$479$	6.11487	−	10.5913i	0.279395	−	0.483927i	0.971235	+	0.238125i	$0.0765327\pi$
$480$		0			0
$481$	−4.90081	−	8.48845i	−0.223458	−	0.387040i
$482$	13.7649	+	23.8416i	0.626976	+	1.08595i
$483$		0			0
$484$	9.76393	−	16.9116i	0.443815	−	0.768710i
$485$	−9.46861			−0.429947
$486$		0			0
$487$	1.97774			0.0896201			0.0448100	−	0.998996i	$-0.485732\pi$
$487$	1.97774			0.0896201			0.0448100	+	0.998996i	$0.485732\pi$
$488$	−1.84875	+	3.20213i	−0.0836890	+	0.144954i
$489$		0			0
$490$	−7.14346	−	12.3728i	−0.322709	−	0.558948i
$491$	−8.47730	−	14.6831i	−0.382575	−	0.662639i	0.608855	−	0.793282i	$-0.291629\pi$
$491$	−8.47730	−	14.6831i	−0.382575	−	0.662639i	−0.991430	+	0.130643i	$0.958296\pi$
$492$		0			0
$493$	−2.26947	+	3.93084i	−0.102212	+	0.177036i
$494$	20.9934			0.944536
$495$		0			0
$496$	20.9276			0.939679
$497$	13.0686	−	22.6354i	0.586205	−	1.01534i
$498$		0			0
$499$	11.0609	+	19.1581i	0.495156	+	0.857636i	0.999984	−	0.00558426i	$-0.00177754\pi$
$499$	11.0609	+	19.1581i	0.495156	+	0.857636i	−0.504828	+	0.863220i	$0.668444\pi$
$500$	10.8780	+	18.8413i	0.486481	+	0.842609i
$501$		0			0
$502$	−6.12877	+	10.6153i	−0.273541	+	0.473786i
$503$	3.44784			0.153731			0.0768657	−	0.997041i	$-0.475509\pi$
$503$	3.44784			0.153731			0.0768657	+	0.997041i	$0.475509\pi$
$504$		0			0
$505$	−26.0237			−1.15804
$506$	0.687534	−	1.19084i	0.0305646	−	0.0529395i
$507$		0			0
$508$	14.7766	+	25.5939i	0.655607	+	1.13554i
$509$	4.93421	+	8.54630i	0.218705	+	0.378808i	0.954412	−	0.298491i	$-0.0964834\pi$
$509$	4.93421	+	8.54630i	0.218705	+	0.378808i	−0.735707	+	0.677300i	$0.763150\pi$
$510$		0			0
$511$	0.100701	−	0.174420i	0.00445476	−	0.00771587i
$512$	−30.2586			−1.33725
$513$		0			0
$514$	−17.9393			−0.791268
$515$	−6.91705	+	11.9807i	−0.304802	+	0.527932i
$516$		0			0
$517$	−0.808419	−	1.40022i	−0.0355542	−	0.0615817i
$518$	−12.6468	−	21.9049i	−0.555668	−	0.962446i
$519$		0			0
$520$	−0.516470	+	0.894553i	−0.0226487	+	0.0392287i
$521$	−9.13811			−0.400348			−0.200174	−	0.979760i	$-0.564151\pi$
$521$	−9.13811			−0.400348			−0.200174	+	0.979760i	$0.564151\pi$
$522$		0			0
$523$	−21.7036			−0.949031			−0.474515	−	0.880247i	$-0.657377\pi$
$523$	−21.7036			−0.949031			−0.474515	+	0.880247i	$0.657377\pi$
$524$	−3.14342	+	5.44457i	−0.137321	+	0.237847i
$525$		0			0
$526$	21.8730	+	37.8851i	0.953708	+	1.65187i
$527$	2.40005	+	4.15702i	0.104548	+	0.181082i
$528$		0			0
$529$	9.86154	−	17.0807i	0.428763	−	0.742639i
$530$	−7.93671			−0.344749
$531$		0			0
$532$	25.6624			1.11261
$533$	1.36707	−	2.36784i	0.0592145	−	0.102563i
$534$		0			0
$535$	15.5033	+	26.8525i	0.670266	+	1.16093i
$536$	0.707461	+	1.22536i	0.0305577	+	0.0529274i
$537$		0			0
$538$	2.78439	−	4.82271i	0.120044	−	0.207922i
$539$	1.46500			0.0631019
$540$		0			0
$541$	26.5284			1.14054			0.570272	−	0.821456i	$-0.306838\pi$
$541$	26.5284			1.14054			0.570272	+	0.821456i	$0.306838\pi$
$542$	−19.3626	+	33.5370i	−0.831695	+	1.44054i
$543$		0			0
$544$	−3.85983	−	6.68542i	−0.165489	−	0.286635i
$545$	7.03441	+	12.1840i	0.301321	+	0.521904i
$546$		0			0
$547$	−0.356201	+	0.616958i	−0.0152300	+	0.0263792i	−0.873540	−	0.486752i	$-0.838181\pi$
$547$	−0.356201	+	0.616958i	−0.0152300	+	0.0263792i	0.858310	+	0.513132i	$0.171515\pi$
$548$	−33.4059			−1.42703
$549$		0			0
$550$	−0.911452			−0.0388644
$551$	17.9732	−	31.1305i	0.765684	−	1.32620i
$552$		0			0
$553$	9.66371	+	16.7380i	0.410943	+	0.711774i
$554$	−21.9109	−	37.9508i	−0.930906	−	1.61238i
$555$		0			0
$556$	−8.76317	+	15.1783i	−0.371641	+	0.643702i
$557$	−4.23942			−0.179630			−0.0898149	−	0.995958i	$-0.528628\pi$
$557$	−4.23942			−0.179630			−0.0898149	+	0.995958i	$0.528628\pi$
$558$		0			0
$559$	−17.1024			−0.723354
$560$	−7.64955	+	13.2494i	−0.323252	+	0.559890i
$561$		0			0
$562$	−2.29077	−	3.96773i	−0.0966304	−	0.167369i
$563$	0.720882	+	1.24860i	0.0303815	+	0.0526224i	0.880816	−	0.473458i	$-0.156994\pi$
$563$	0.720882	+	1.24860i	0.0303815	+	0.0526224i	−0.850435	+	0.526080i	$0.823661\pi$
$564$		0			0
$565$	18.1478	−	31.4329i	0.763483	−	1.32239i
$566$	10.3882			0.436647
$567$		0			0
$568$	5.65787			0.237399
$569$	−14.6505	+	25.3754i	−0.614181	+	1.06379i	0.376346	+	0.926479i	$0.377180\pi$
$569$	−14.6505	+	25.3754i	−0.614181	+	1.06379i	−0.990528	+	0.137314i	$0.956153\pi$
$570$		0			0
$571$	−21.2171	−	36.7491i	−0.887908	−	1.53790i	−0.842344	−	0.538941i	$-0.818825\pi$
$571$	−21.2171	−	36.7491i	−0.887908	−	1.53790i	−0.0455647	−	0.998961i	$-0.514509\pi$
$572$	0.476920	+	0.826051i	0.0199410	+	0.0345389i
$573$		0			0
$574$	3.52780	−	6.11034i	0.147248	−	0.255040i
$575$	2.17207			0.0905818
$576$		0			0
$577$	18.9824			0.790248			0.395124	−	0.918628i	$-0.370702\pi$
$577$	18.9824			0.790248			0.395124	+	0.918628i	$0.370702\pi$
$578$	0.974693	−	1.68822i	0.0405419	−	0.0702206i
$579$		0			0
$580$	−7.96382	−	13.7937i	−0.330680	−	0.572754i
$581$	3.78972	+	6.56399i	0.157224	+	0.272320i
$582$		0			0
$583$	0.406919	−	0.704805i	0.0168529	−	0.0291900i
$584$	0.0435973			0.00180407
$585$		0			0
$586$	−5.89429			−0.243491
$587$	−15.7450	+	27.2711i	−0.649864	+	1.12560i	0.333291	+	0.942824i	$0.391841\pi$
$587$	−15.7450	+	27.2711i	−0.649864	+	1.12560i	−0.983155	+	0.182774i	$0.941492\pi$
$588$		0			0
$589$	−19.0073	−	32.9217i	−0.783184	−	1.35651i
$590$	−22.0756	−	38.2361i	−0.908840	−	1.57416i
$591$		0			0
$592$	15.7128	−	27.2153i	0.645792	−	1.11854i
$593$	15.1442			0.621896			0.310948	−	0.950427i	$-0.399354\pi$
$593$	15.1442			0.621896			0.310948	+	0.950427i	$0.399354\pi$
$594$		0			0
$595$	−3.50911			−0.143859
$596$	−17.7401	+	30.7268i	−0.726664	+	1.25862i
$597$		0			0
$598$	−2.39930	−	4.15571i	−0.0981146	−	0.169940i
$599$	−3.48678	−	6.03928i	−0.142466	−	0.246758i	0.785959	−	0.618279i	$-0.212170\pi$
$599$	−3.48678	−	6.03928i	−0.142466	−	0.246758i	−0.928425	+	0.371521i	$0.878837\pi$
$600$		0			0
$601$	−16.7131	+	28.9479i	−0.681740	+	1.18081i	0.292710	+	0.956201i	$0.405443\pi$
$601$	−16.7131	+	28.9479i	−0.681740	+	1.18081i	−0.974449	+	0.224607i	$0.927890\pi$
$602$	−44.1336			−1.79875
$603$		0			0
$604$	−0.432725			−0.0176073
$605$	10.5736	−	18.3141i	0.429879	−	0.744572i
$606$		0			0
$607$	6.17629	+	10.6976i	0.250688	+	0.434204i	0.963715	−	0.266932i	$-0.0860099\pi$
$607$	6.17629	+	10.6976i	0.250688	+	0.434204i	−0.713028	+	0.701136i	$0.752677\pi$
$608$	30.5681	+	52.9455i	1.23970	+	2.14722i
$609$		0			0
$610$	18.0294	−	31.2278i	0.729988	−	1.26438i
$611$	−5.64230			−0.228263
$612$		0			0
$613$	17.6107			0.711288			0.355644	−	0.934622i	$-0.384262\pi$
$613$	17.6107			0.711288			0.355644	+	0.934622i	$0.384262\pi$
$614$	27.4097	−	47.4750i	1.10617	−	1.91593i
$615$		0			0
$616$	−0.136665	−	0.236710i	−0.00550637	−	0.00953731i
$617$	16.4613	+	28.5117i	0.662705	+	1.14784i	0.979902	+	0.199480i	$0.0639251\pi$
$617$	16.4613	+	28.5117i	0.662705	+	1.14784i	−0.317197	+	0.948360i	$0.602742\pi$
$618$		0			0
$619$	5.40047	−	9.35390i	0.217063	−	0.375965i	−0.736846	−	0.676061i	$-0.763685\pi$
$619$	5.40047	−	9.35390i	0.217063	−	0.375965i	0.953909	+	0.300096i	$0.0970188\pi$
$620$	−16.8441			−0.676475
$621$		0			0
$622$	−35.6315			−1.42869
$623$	1.96506	−	3.40359i	0.0787285	−	0.136362i
$624$		0			0
$625$	8.78040	+	15.2081i	0.351216	+	0.608324i
$626$	−18.5350	−	32.1035i	−0.740806	−	1.28311i
$627$		0			0
$628$	19.9962	−	34.6344i	0.797934	−	1.38206i
$629$	7.20799			0.287401
$630$		0			0
$631$	−13.3668			−0.532126			−0.266063	−	0.963956i	$-0.585723\pi$
$631$	−13.3668			−0.532126			−0.266063	+	0.963956i	$0.585723\pi$
$632$	−2.09189	+	3.62326i	−0.0832110	+	0.144126i
$633$		0			0
$634$	−5.92915	−	10.2696i	−0.235477	−	0.407858i
$635$	16.0020	+	27.7163i	0.635020	+	1.09989i
$636$		0			0
$637$	2.55621	−	4.42749i	0.101281	−	0.175423i
$638$	3.44784			0.136501
$639$		0			0
$640$	−6.04654			−0.239011
$641$	13.9580	−	24.1760i	0.551308	−	0.954894i	−0.446872	−	0.894598i	$-0.647462\pi$
$641$	13.9580	−	24.1760i	0.551308	−	0.954894i	0.998181	−	0.0602960i	$-0.0192045\pi$
$642$		0			0
$643$	−20.8497	−	36.1127i	−0.822230	−	1.42414i	−0.904018	−	0.427495i	$-0.859396\pi$
$643$	−20.8497	−	36.1127i	−0.822230	−	1.42414i	0.0817875	−	0.996650i	$-0.473937\pi$
$644$	−2.93292	−	5.07996i	−0.115573	−	0.200178i
$645$		0			0
$646$	−7.71913	+	13.3699i	−0.303705	+	0.526033i
$647$	−0.889627			−0.0349748			−0.0174874	−	0.999847i	$-0.505567\pi$
$647$	−0.889627			−0.0349748			−0.0174874	+	0.999847i	$0.505567\pi$
$648$		0			0
$649$	4.52732			0.177713
$650$	−1.59035	+	2.75457i	−0.0623788	+	0.108043i
$651$		0			0
$652$	10.7775	+	18.6672i	0.422081	+	0.731065i
$653$	−23.6265	−	40.9223i	−0.924577	−	1.60141i	−0.792240	−	0.610210i	$-0.791085\pi$
$653$	−23.6265	−	40.9223i	−0.924577	−	1.60141i	−0.132338	−	0.991205i	$-0.542248\pi$
$654$		0			0
$655$	−3.40410	+	5.89608i	−0.133009	+	0.230379i
$656$	8.76612			0.342259
$657$		0			0
$658$	−14.5603			−0.567618
$659$	12.7791	−	22.1341i	0.497804	−	0.862221i	−0.502193	−	0.864756i	$-0.667473\pi$
$659$	12.7791	−	22.1341i	0.497804	−	0.862221i	0.999997	+	0.00253413i	$0.000806640\pi$
$660$		0			0
$661$	−9.35152	−	16.1973i	−0.363732	−	0.630002i	0.624840	−	0.780753i	$-0.285164\pi$
$661$	−9.35152	−	16.1973i	−0.363732	−	0.630002i	−0.988572	+	0.150751i	$0.951831\pi$
$662$	3.51700	+	6.09162i	0.136692	+	0.236757i
$663$		0			0
$664$	−0.820356	+	1.42090i	−0.0318360	+	0.0551415i
$665$	27.7905			1.07767
$666$		0			0
$667$	−8.21651			−0.318145
$668$	10.6376	−	18.4249i	0.411582	−	0.712880i
$669$		0			0
$670$	−6.89930	−	11.9499i	−0.266543	−	0.461666i
$671$	1.84875	+	3.20213i	0.0713702	+	0.123617i
$672$		0			0
$673$	5.44460	−	9.43032i	0.209874	−	0.363512i	−0.741801	−	0.670620i	$-0.766028\pi$
$673$	5.44460	−	9.43032i	0.209874	−	0.363512i	0.951675	+	0.307108i	$0.0993613\pi$
$674$	−3.01562			−0.116157
$675$		0			0
$676$	−20.0728			−0.772030
$677$	−18.6000	+	32.2161i	−0.714856	+	1.23817i	0.248160	+	0.968719i	$0.420174\pi$
$677$	−18.6000	+	32.2161i	−0.714856	+	1.23817i	−0.963015	+	0.269447i	$0.913159\pi$
$678$		0			0
$679$	−4.37176	−	7.57212i	−0.167773	−	0.290591i
$680$	−0.379806	−	0.657843i	−0.0145649	−	0.0252271i
$681$		0			0
$682$	1.82311	−	3.15772i	0.0698104	−	0.120915i
$683$	0.232833			0.00890910			0.00445455	−	0.999990i	$-0.498582\pi$
$683$	0.232833			0.00890910			0.00445455	+	0.999990i	$0.498582\pi$
$684$		0			0
$685$	−36.1761			−1.38222
$686$	18.8783	−	32.6982i	0.720777	−	1.24842i
$687$		0			0
$688$	−27.4165	−	47.4868i	−1.04524	−	1.81042i
$689$	−1.42003	−	2.45957i	−0.0540989	−	0.0937021i
$690$		0			0
$691$	16.2391	−	28.1270i	0.617766	−	1.07000i	−0.372126	−	0.928182i	$-0.621371\pi$
$691$	16.2391	−	28.1270i	0.617766	−	1.07000i	0.989892	−	0.141820i	$-0.0452956\pi$
$692$	9.09262			0.345650
$693$		0			0
$694$	64.8496			2.46166
$695$	−9.48988	+	16.4370i	−0.359972	+	0.623489i
$696$		0			0
$697$	1.00533	+	1.74128i	0.0380795	+	0.0659557i
$698$	16.0622	+	27.8206i	0.607964	+	1.05303i
$699$		0			0
$700$	−1.94406	+	3.36721i	−0.0734785	+	0.127268i
$701$	−20.1974			−0.762846			−0.381423	−	0.924401i	$-0.624566\pi$
$701$	−20.1974			−0.762846			−0.381423	+	0.924401i	$0.624566\pi$
$702$		0			0
$703$	−57.0840			−2.15296
$704$	−1.23309	+	2.13577i	−0.0464738	+	0.0804950i
$705$		0			0
$706$	−4.10502	−	7.11010i	−0.154494	−	0.267592i
$707$	−12.0155	−	20.8114i	−0.451888	−	0.782693i
$708$		0			0
$709$	7.25253	−	12.5618i	0.272375	−	0.471766i	−0.697095	−	0.716979i	$-0.745524\pi$
$709$	7.25253	−	12.5618i	0.272375	−	0.471766i	0.969469	+	0.245212i	$0.0788577\pi$
$710$	−55.1767			−2.07074
$711$		0			0
$712$	0.850749			0.0318832
$713$	−4.34464	+	7.52513i	−0.162708	+	0.281818i
$714$		0			0
$715$	0.516470	+	0.894553i	0.0193149	+	0.0334544i
$716$	1.48402	+	2.57039i	0.0554602	+	0.0960600i
$717$		0			0
$718$	−14.2446	+	24.6724i	−0.531605	+	0.920767i
$719$	−6.75756			−0.252015			−0.126007	−	0.992029i	$-0.540216\pi$
$719$	−6.75756			−0.252015			−0.126007	+	0.992029i	$0.540216\pi$
$720$		0			0
$721$	−12.7747			−0.475756
$722$	42.6128	−	73.8076i	1.58589	−	2.74683i
$723$		0			0
$724$	−7.99162	−	13.8419i	−0.297006	−	0.514430i
$725$	2.72312	+	4.71659i	0.101134	+	0.175170i
$726$		0			0
$727$	1.51895	−	2.63090i	0.0563349	−	0.0975749i	−0.836483	−	0.547993i	$-0.815392\pi$
$727$	1.51895	−	2.63090i	0.0563349	−	0.0975749i	0.892818	+	0.450419i	$0.148725\pi$
$728$	−0.953841			−0.0353517
$729$		0			0
$730$	−0.425169			−0.0157362
$731$	6.28844	−	10.8919i	0.232586	−	0.402851i
$732$		0			0
$733$	−5.39655	−	9.34709i	−0.199326	−	0.345243i	0.748984	−	0.662588i	$-0.230542\pi$
$733$	−5.39655	−	9.34709i	−0.199326	−	0.345243i	−0.948310	+	0.317345i	$0.897209\pi$
$734$	−3.07944	−	5.33375i	−0.113664	−	0.196872i
$735$		0			0
$736$	6.98716	−	12.1021i	0.257550	−	0.446090i
$737$	1.41492			0.0521193
$738$		0			0
$739$	8.83251			0.324909			0.162455	−	0.986716i	$-0.448059\pi$
$739$	8.83251			0.324909			0.162455	+	0.986716i	$0.448059\pi$
$740$	−12.6468	+	21.9049i	−0.464905	+	0.805240i
$741$		0			0
$742$	−3.66447	−	6.34705i	−0.134527	−	0.233007i
$743$	−7.09840	−	12.2948i	−0.260415	−	0.451052i	0.705937	−	0.708274i	$-0.250526\pi$
$743$	−7.09840	−	12.2948i	−0.260415	−	0.451052i	−0.966352	+	0.257223i	$0.917193\pi$
$744$		0			0
$745$	−19.2113	+	33.2749i	−0.703847	+	1.21910i
$746$	−1.19682			−0.0438186
$747$		0			0
$748$	−0.701443			−0.0256473
$749$	−14.3161	+	24.7962i	−0.523099	+	0.906033i
$750$		0			0
$751$	−10.9724	−	19.0048i	−0.400389	−	0.693493i	0.593384	−	0.804919i	$-0.297792\pi$
$751$	−10.9724	−	19.0048i	−0.400389	−	0.693493i	−0.993773	+	0.111426i	$0.964458\pi$
$752$	−9.04507	−	15.6665i	−0.329840	−	0.571299i
$753$		0			0
$754$	6.01598	−	10.4200i	0.219089	−	0.379474i
$755$	−0.468610			−0.0170545
$756$		0			0
$757$	4.01608			0.145967			0.0729835	−	0.997333i	$-0.476748\pi$
$757$	4.01608			0.145967			0.0729835	+	0.997333i	$0.476748\pi$
$758$	4.09361	−	7.09033i	0.148686	−	0.257533i
$759$		0			0
$760$	3.00789	+	5.20982i	0.109108	+	0.188980i
$761$	3.57309	+	6.18877i	0.129524	+	0.224343i	0.923492	−	0.383617i	$-0.125322\pi$
$761$	3.57309	+	6.18877i	0.129524	+	0.224343i	−0.793968	+	0.607960i	$0.791988\pi$
$762$		0			0
$763$	−6.49574	+	11.2509i	−0.235161	+	0.407312i
$764$	21.1149			0.763909
$765$		0			0
$766$	−66.5552			−2.40474
$767$	7.89953	−	13.6824i	0.285235	−	0.494042i
$768$		0			0
$769$	10.7733	+	18.6598i	0.388494	+	0.672891i	0.992247	−	0.124280i	$-0.0396621\pi$
$769$	10.7733	+	18.6598i	0.388494	+	0.672891i	−0.603753	+	0.797171i	$0.706329\pi$
$770$	1.33278	+	2.30844i	0.0480300	+	0.0831904i
$771$		0			0
$772$	4.96760	−	8.60413i	0.178788	−	0.309670i
$773$	−53.7951			−1.93488			−0.967438	−	0.253108i	$-0.918547\pi$
$773$	−53.7951			−1.93488			−0.967438	+	0.253108i	$0.918547\pi$
$774$		0			0
$775$	5.75961			0.206891
$776$	0.946350	−	1.63913i	0.0339720	−	0.0588412i
$777$		0			0
$778$	17.1039	+	29.6249i	0.613206	+	1.06210i
$779$	−7.96174	−	13.7901i	−0.285259	−	0.494083i
$780$		0			0
$781$	2.82894	−	4.89986i	0.101227	−	0.175331i
$782$	3.52883			0.126191
$783$		0			0
$784$	16.3913			0.585402
$785$	21.6544	−	37.5065i	0.772878	−	1.33866i
$786$		0			0
$787$	26.0812	+	45.1740i	0.929694	+	1.61028i	0.783832	+	0.620973i	$0.213262\pi$
$787$	26.0812	+	45.1740i	0.929694	+	1.61028i	0.145862	+	0.989305i	$0.453404\pi$
$788$	12.0456	+	20.8635i	0.429106	+	0.743233i
$789$		0			0
$790$	20.4005	−	35.3348i	0.725818	−	1.25715i
$791$	33.5161			1.19170
$792$		0			0
$793$	12.9032			0.458207
$794$	−21.9137	+	37.9557i	−0.777689	+	1.34700i
$795$		0			0
$796$	21.2338	+	36.7780i	0.752612	+	1.30356i
$797$	9.69738	+	16.7964i	0.343499	+	0.594958i	0.985080	−	0.172098i	$-0.0550545\pi$
$797$	9.69738	+	16.7964i	0.343499	+	0.594958i	−0.641581	+	0.767055i	$0.721721\pi$
$798$		0			0
$799$	2.07464	−	3.59338i	0.0733955	−	0.127125i
$800$	−9.26275			−0.327488
$801$		0			0
$802$	15.4154			0.544338
$803$	0.0217987	−	0.0377564i	0.000769258	−	0.00133239i
$804$		0			0
$805$	−3.17614	−	5.50123i	−0.111944	−	0.193893i
$806$	−6.36213	−	11.0195i	−0.224097	−	0.388147i
$807$		0			0
$808$	2.60097	−	4.50501i	0.0915018	−	0.158486i
$809$	−55.0196			−1.93439			−0.967193	−	0.254041i	$-0.918240\pi$
$809$	−55.0196			−1.93439			−0.967193	+	0.254041i	$0.918240\pi$
$810$		0			0
$811$	20.8406			0.731813			0.365906	−	0.930652i	$-0.380759\pi$
$811$	20.8406			0.731813			0.365906	+	0.930652i	$0.380759\pi$
$812$	7.35397	−	12.7375i	0.258074	−	0.446997i
$813$		0			0
$814$	−2.73764	−	4.74172i	−0.0959541	−	0.166197i
$815$	11.6713	+	20.2153i	0.408827	+	0.708109i
$816$		0			0
$817$	−49.8016	+	86.2589i	−1.74234	+	3.01782i
$818$	−37.1644			−1.29942
$819$		0			0
$820$	−7.05561			−0.246392
$821$	−19.5068	+	33.7868i	−0.680793	+	1.17917i	0.293946	+	0.955822i	$0.405031\pi$
$821$	−19.5068	+	33.7868i	−0.680793	+	1.17917i	−0.974739	+	0.223346i	$0.928302\pi$
$822$		0			0
$823$	20.0081	+	34.6550i	0.697438	+	1.20800i	0.969352	+	0.245677i	$0.0790102\pi$
$823$	20.0081	+	34.6550i	0.697438	+	1.20800i	−0.271913	+	0.962322i	$0.587656\pi$
$824$	−1.38266	−	2.39484i	−0.0481674	−	0.0834283i
$825$		0			0
$826$	20.3851	−	35.3081i	0.709290	−	1.22853i
$827$	16.0203			0.557081			0.278540	−	0.960424i	$-0.410149\pi$
$827$	16.0203			0.557081			0.278540	+	0.960424i	$0.410149\pi$
$828$		0			0
$829$	6.90636			0.239868			0.119934	−	0.992782i	$-0.461732\pi$
$829$	6.90636			0.239868			0.119934	+	0.992782i	$0.461732\pi$
$830$	8.00027	−	13.8569i	0.277693	−	0.480979i
$831$		0			0
$832$	4.30313	+	7.45324i	0.149184	+	0.258395i
$833$	1.87981	+	3.25592i	0.0651314	+	0.112811i
$834$		0			0
$835$	11.5198	−	19.9528i	0.398658	−	0.690496i
$836$	5.55511			0.192127
$837$		0			0
$838$	−17.7485			−0.613112
$839$	−21.0977	+	36.5423i	−0.728374	+	1.26158i	0.229196	+	0.973380i	$0.426390\pi$
$839$	−21.0977	+	36.5423i	−0.728374	+	1.26158i	−0.957570	+	0.288200i	$0.906943\pi$
$840$		0			0
$841$	4.19899	+	7.27286i	0.144793	+	0.250788i
$842$	−22.0909	−	38.2626i	−0.761302	−	1.31861i
$843$		0			0
$844$	4.51572	−	7.82145i	0.155437	−	0.269225i
$845$	−21.7374			−0.747788
$846$		0			0
$847$	19.5279			0.670985
$848$	4.55285	−	7.88578i	0.156346	−	0.270799i
$849$		0			0
$850$	−1.16953	−	2.02568i	−0.0401144	−	0.0694802i
$851$	6.52404	+	11.3000i	0.223641	+	0.387358i
$852$		0			0
$853$	−9.64812	+	16.7110i	−0.330345	+	0.572175i	−0.982580	−	0.185843i	$-0.940499\pi$
$853$	−9.64812	+	16.7110i	−0.330345	+	0.572175i	0.652234	+	0.758017i	$0.273832\pi$
$854$	33.2975			1.13942
$855$		0			0
$856$	−6.19797			−0.211842
$857$	3.97730	−	6.88888i	0.135862	−	0.235320i	−0.790065	−	0.613024i	$-0.789953\pi$
$857$	3.97730	−	6.88888i	0.135862	−	0.235320i	0.925926	+	0.377704i	$0.123286\pi$
$858$		0			0
$859$	8.64400	+	14.9719i	0.294930	+	0.510833i	0.974969	−	0.222343i	$-0.0713705\pi$
$859$	8.64400	+	14.9719i	0.294930	+	0.510833i	−0.680039	+	0.733176i	$0.738037\pi$
$860$	22.0668	+	38.2208i	0.752472	+	1.30332i
$861$		0			0
$862$	14.4507	−	25.0294i	0.492193	−	0.852503i
$863$	54.8726			1.86788			0.933942	−	0.357425i	$-0.116345\pi$
$863$	54.8726			1.86788			0.933942	+	0.357425i	$0.116345\pi$
$864$		0			0
$865$	9.84665			0.334796
$866$	1.72163	−	2.98194i	0.0585032	−	0.101331i
$867$		0			0
$868$	−7.77711	−	13.4703i	−0.263972	−	0.457213i
$869$	2.09189	+	3.62326i	0.0709626	+	0.122911i
$870$		0			0
$871$	2.46884	−	4.27616i	0.0836534	−	0.144892i
$872$	−2.81225			−0.0952347
$873$		0			0
$874$	−27.9467			−0.945312
$875$	−10.8780	+	18.8413i	−0.367745	+	0.636953i
$876$		0			0
$877$	9.89319	+	17.1355i	0.334069	+	0.578625i	0.983306	−	0.181962i	$-0.0582447\pi$
$877$	9.89319	+	17.1355i	0.334069	+	0.578625i	−0.649236	+	0.760587i	$0.724911\pi$
$878$	0.812787	+	1.40779i	0.0274302	+	0.0475105i
$879$		0			0
$880$	−1.65589	+	2.86808i	−0.0558200	+	0.0966830i
$881$	23.1023			0.778336			0.389168	−	0.921167i	$-0.372763\pi$
$881$	23.1023			0.778336			0.389168	+	0.921167i	$0.372763\pi$
$882$		0			0
$883$	−57.1266			−1.92246			−0.961231	−	0.275745i	$-0.911076\pi$
$883$	−57.1266			−1.92246			−0.961231	+	0.275745i	$0.911076\pi$
$884$	−1.22392	+	2.11989i	−0.0411648	+	0.0712996i
$885$		0			0
$886$	21.9054	+	37.9413i	0.735926	+	1.27466i
$887$	−10.2591	−	17.7694i	−0.344468	−	0.596636i	0.640789	−	0.767717i	$-0.278607\pi$
$887$	−10.2591	−	17.7694i	−0.344468	−	0.596636i	−0.985257	+	0.171081i	$0.945274\pi$
$888$		0			0
$889$	−14.7766	+	25.5939i	−0.495592	+	0.858390i
$890$	−8.29666			−0.278105
$891$		0			0
$892$	32.4422			1.08625
$893$	−16.4302	+	28.4579i	−0.549816	+	0.952309i
$894$		0			0
$895$	1.60708	+	2.78355i	0.0537188	+	0.0930437i
$896$	−2.79176	−	4.83546i	−0.0932661	−	0.161542i
$897$		0			0
$898$	22.8930	−	39.6518i	0.763948	−	1.32320i
$899$	−21.7874			−0.726651
$900$		0			0
$901$	2.08855			0.0695796
$902$	0.763659	−	1.32270i	0.0254271	−	0.0440410i
$903$		0			0
$904$	3.62760	+	6.28319i	0.120652	+	0.208976i
$905$	−8.65435	−	14.9898i	−0.287680	−	0.498277i
$906$		0			0
$907$	−18.6947	+	32.3801i	−0.620746	+	1.07516i	0.368601	+	0.929588i	$0.379837\pi$
$907$	−18.6947	+	32.3801i	−0.620746	+	1.07516i	−0.989347	+	0.145576i	$0.953497\pi$
$908$	31.6604			1.05069
$909$		0			0
$910$	9.30204			0.308360
$911$	−12.6231	+	21.8639i	−0.418223	+	0.724383i	−0.995761	−	0.0919807i	$-0.970680\pi$
$911$	−12.6231	+	21.8639i	−0.418223	+	0.724383i	0.577538	+	0.816364i	$0.304014\pi$
$912$		0			0
$913$	0.820356	+	1.42090i	0.0271498	+	0.0470249i
$914$	12.8047	+	22.1784i	0.423541	+	0.733595i
$915$		0			0
$916$	−0.777107	+	1.34599i	−0.0256763	+	0.0444727i
$917$	−6.28685			−0.207610
$918$		0			0
$919$	26.0729			0.860065			0.430032	−	0.902813i	$-0.358502\pi$
$919$	26.0729			0.860065			0.430032	+	0.902813i	$0.358502\pi$
$920$	0.687534	−	1.19084i	0.0226673	−	0.0392610i
$921$		0			0
$922$	−14.5321	−	25.1704i	−0.478590	−	0.828942i
$923$	−9.87219	−	17.0991i	−0.324947	−	0.562825i
$924$		0			0
$925$	4.32440	−	7.49009i	0.142186	−	0.246273i
$926$	64.2064			2.10995
$927$		0			0
$928$	35.0391			1.15021
$929$	−6.47773	+	11.2198i	−0.212527	+	0.368108i	−0.952505	−	0.304523i	$-0.901503\pi$
$929$	−6.47773	+	11.2198i	−0.212527	+	0.368108i	0.739977	+	0.672632i	$0.234836\pi$
$930$		0			0
$931$	−14.8872	−	25.7854i	−0.487909	−	0.845083i
$932$	−14.9633	−	25.9173i	−0.490140	−	0.848948i
$933$		0			0
$934$	−20.7650	+	35.9660i	−0.679450	+	1.17684i
$935$	−0.759612			−0.0248420
$936$		0			0
$937$	42.1013			1.37539			0.687695	−	0.726000i	$-0.258623\pi$
$937$	42.1013			1.37539			0.687695	+	0.726000i	$0.258623\pi$
$938$	6.37097	−	11.0348i	0.208020	−	0.360300i
$939$		0			0
$940$	7.28013	+	12.6096i	0.237452	+	0.411278i
$941$	19.7050	+	34.1301i	0.642365	+	1.11261i	0.984903	+	0.173105i	$0.0553799\pi$
$941$	19.7050	+	34.1301i	0.642365	+	1.11261i	−0.342539	+	0.939504i	$0.611287\pi$
$942$		0			0
$943$	−1.81987	+	3.15211i	−0.0592631	+	0.102647i
$944$	50.6543			1.64866
$945$		0			0
$946$	−9.55354			−0.310613
$947$	5.38902	−	9.33405i	0.175120	−	0.303316i	−0.765083	−	0.643932i	$-0.777302\pi$
$947$	5.38902	−	9.33405i	0.175120	−	0.303316i	0.940203	+	0.340616i	$0.110635\pi$
$948$		0			0
$949$	−0.0760711	−	0.131759i	−0.00246937	−	0.00427708i
$950$	9.26212	+	16.0425i	0.300503	+	0.520486i
$951$		0			0
$952$	0.350721	−	0.607467i	0.0113669	−	0.0196881i
$953$	−18.9985			−0.615421			−0.307711	−	0.951480i	$-0.599563\pi$
$953$	−18.9985			−0.615421			−0.307711	+	0.951480i	$0.599563\pi$
$954$		0			0
$955$	22.8659			0.739922
$956$	−14.9033	+	25.8133i	−0.482007	+	0.834861i
$957$		0			0
$958$	−11.9202	−	20.6465i	−0.385125	−	0.667057i
$959$	−16.7029	−	28.9303i	−0.539366	−	0.934209i
$960$		0			0
$961$	3.97948	−	6.89267i	0.128370	−	0.222344i
$962$	−19.1071			−0.616039
$963$		0			0
$964$	25.4217			0.818778
$965$	5.37955	−	9.31765i	0.173174	−	0.299946i
$966$		0			0
$967$	4.10735	+	7.11414i	0.132083	+	0.228775i	0.924480	−	0.381232i	$-0.124500\pi$
$967$	4.10735	+	7.11414i	0.132083	+	0.228775i	−0.792396	+	0.610007i	$0.791167\pi$
$968$	2.11359	+	3.66084i	0.0679332	+	0.117664i
$969$		0			0
$970$	−9.22899	+	15.9851i	−0.296325	+	0.513250i
$971$	−10.0253			−0.321726			−0.160863	−	0.986977i	$-0.551428\pi$
$971$	−10.0253			−0.321726			−0.160863	+	0.986977i	$0.551428\pi$
$972$		0			0
$973$	−17.5263			−0.561869
$974$	1.92769	−	3.33886i	0.0617673	−	0.106984i
$975$		0			0
$976$	20.6849	+	35.8273i	0.662108	+	1.14681i
$977$	20.3751	+	35.2907i	0.651857	+	1.12905i	0.982672	+	0.185354i	$0.0593432\pi$
$977$	20.3751	+	35.2907i	0.651857	+	1.12905i	−0.330815	+	0.943696i	$0.607324\pi$
$978$		0			0
$979$	0.425374	−	0.736770i	0.0135950	−	0.0235473i
$980$	−13.1929			−0.421431
$981$		0			0
$982$	−33.0511			−1.05470
$983$	1.42616	−	2.47017i	0.0454873	−	0.0787863i	−0.842385	−	0.538876i	$-0.818849\pi$
$983$	1.42616	−	2.47017i	0.0454873	−	0.0787863i	0.887873	+	0.460089i	$0.152183\pi$
$984$		0			0
$985$	13.0445	+	22.5937i	0.415632	+	0.719895i
$986$	4.42408	+	7.66273i	0.140891	+	0.244031i
$987$		0			0
$988$	9.69288	−	16.7886i	0.308371	−	0.534115i
$989$	22.7670			0.723948
$990$		0			0
$991$	−30.4975			−0.968785			−0.484393	−	0.874851i	$-0.660959\pi$
$991$	−30.4975			−0.968785			−0.484393	+	0.874851i	$0.660959\pi$
$992$	18.5276	−	32.0907i	0.588252	−	1.01888i
$993$		0			0
$994$	−25.4757	−	44.1252i	−0.808040	−	1.39957i
$995$	22.9947	+	39.8279i	0.728980	+	1.26263i
$996$		0			0
$997$	−6.62706	+	11.4784i	−0.209881	+	0.363525i	−0.951677	−	0.307101i	$-0.900641\pi$
$997$	−6.62706	+	11.4784i	−0.209881	+	0.363525i	0.741796	+	0.670626i	$0.233974\pi$
$998$	43.1241			1.36507
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.e.b.154.4		8
3.2	odd	2		153.2.e.b.52.1	✓	8
9.2	odd	6		1377.2.a.e.1.4		4
9.4	even	3	inner	459.2.e.b.307.4		8
9.5	odd	6		153.2.e.b.103.1	yes	8
9.7	even	3		1377.2.a.f.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.e.b.52.1	✓	8	3.2	odd	2
153.2.e.b.103.1	yes	8	9.5	odd	6
459.2.e.b.154.4		8	1.1	even	1	trivial
459.2.e.b.307.4		8	9.4	even	3	inner
1377.2.a.e.1.4		4	9.2	odd	6
1377.2.a.f.1.1		4	9.7	even	3

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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.974693 - 1.68822i) q^{2} +(-0.900054 - 1.55894i) q^{4} +(-0.974693 - 1.68822i) q^{5} +(0.900054 - 1.55894i) q^{7} +0.389667 q^{8} -3.80011 q^{10} +(0.194834 - 0.337462i) q^{11} +(-0.679914 - 1.17765i) q^{13} +(-1.75455 - 3.03897i) q^{14} +(2.17991 - 3.77572i) q^{16} +1.00000 q^{17} -7.91955 q^{19} +(-1.75455 + 3.03897i) q^{20} +(-0.379806 - 0.657843i) q^{22} +(0.905113 + 1.56770i) q^{23} +(0.599946 - 1.03914i) q^{25} -2.65083 q^{26} -3.24039 q^{28} +(-2.26947 + 3.93084i) q^{29} +(2.40005 + 4.15702i) q^{31} +(-3.85983 - 6.68542i) q^{32} +(0.974693 - 1.68822i) q^{34} -3.50911 q^{35} +7.20799 q^{37} +(-7.71913 + 13.3699i) q^{38} +(-0.379806 - 0.657843i) q^{40} +(1.00533 + 1.74128i) q^{41} +(6.28844 - 10.8919i) q^{43} -0.701443 q^{44} +3.52883 q^{46} +(2.07464 - 3.59338i) q^{47} +(1.87981 + 3.25592i) q^{49} +(-1.16953 - 2.02568i) q^{50} +(-1.22392 + 2.11989i) q^{52} +2.08855 q^{53} -0.759612 q^{55} +(0.350721 - 0.607467i) q^{56} +(4.42408 + 7.66273i) q^{58} +(5.80921 + 10.0619i) q^{59} +(-4.74444 + 8.21760i) q^{61} +9.35727 q^{62} -6.32894 q^{64} +(-1.32541 + 2.29569i) q^{65} +(1.81555 + 3.14463i) q^{67} +(-0.900054 - 1.55894i) q^{68} +(-3.42030 + 5.92414i) q^{70} +14.5198 q^{71} +0.111884 q^{73} +(7.02558 - 12.1687i) q^{74} +(7.12802 + 12.3461i) q^{76} +(-0.350721 - 0.607467i) q^{77} +(-5.36841 + 9.29835i) q^{79} -8.49899 q^{80} +3.91955 q^{82} +(-2.10527 + 3.64644i) q^{83} +(-0.974693 - 1.68822i) q^{85} +(-12.2586 - 21.2325i) q^{86} +(0.0759202 - 0.131498i) q^{88} +2.18327 q^{89} -2.44784 q^{91} +(1.62930 - 2.82203i) q^{92} +(-4.04427 - 7.00489i) q^{94} +(7.71913 + 13.3699i) q^{95} +(2.42861 - 4.20648i) q^{97} +7.32894 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 3 q^{4} + q^{5} + 3 q^{7} + 6 q^{8} - 22 q^{10} + 3 q^{11} + 9 q^{13} + 5 q^{14} + 3 q^{16} + 8 q^{17} - 14 q^{19} + 5 q^{20} + 3 q^{22} + 10 q^{23} + 9 q^{25} - 22 q^{26} - 38 q^{28} - 15 q^{29}+ \cdots + 30 q^{98}+O(q^{100}) \) 8 * q - q^2 - 3 * q^4 + q^5 + 3 * q^7 + 6 * q^8 - 22 * q^10 + 3 * q^11 + 9 * q^13 + 5 * q^14 + 3 * q^16 + 8 * q^17 - 14 * q^19 + 5 * q^20 + 3 * q^22 + 10 * q^23 + 9 * q^25 - 22 * q^26 - 38 * q^28 - 15 * q^29 + 15 * q^31 - 2 * q^32 - q^34 + 10 * q^35 - 24 * q^37 - 20 * q^38 + 3 * q^40 - 6 * q^41 + 18 * q^43 - 24 * q^44 + 8 * q^46 + 12 * q^47 + 9 * q^49 - 2 * q^50 + 4 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^56 + 9 * q^58 - 5 * q^61 - 16 * q^62 - 22 * q^64 - 11 * q^65 + 6 * q^67 - 3 * q^68 - 25 * q^70 + 50 * q^71 + 8 * q^73 + 44 * q^74 - 6 * q^76 - 12 * q^77 + 8 * q^79 - 16 * q^80 - 18 * q^82 - 7 * q^83 + q^85 - 34 * q^86 + 27 * q^88 + 28 * q^89 + 8 * q^91 - 19 * q^92 - 12 * q^94 + 20 * q^95 + 16 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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