LMFDB - Embedded newform 459.2.l.a.325.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(298,459)] 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("459.298"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.l (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,-16,0,0,0,0,0,-48,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			325.9
Character	$\chi$	$=$	459.325
Dual form			459.2.l.a.298.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.899127 + 0.899127i) q^{2} -0.383141i q^{4} +(-0.719544 - 1.73713i) q^{5} +(0.0885100 - 0.213682i) q^{7} +(2.14275 - 2.14275i) q^{8} +(0.914941 - 2.20886i) q^{10} +(-3.16414 - 1.31063i) q^{11} -5.14809i q^{13} +(0.271709 - 0.112546i) q^{14} +3.08692 q^{16} +(-3.84181 - 1.49682i) q^{17} +(5.06448 + 5.06448i) q^{19} +(-0.665566 + 0.275686i) q^{20} +(-1.66654 - 4.02339i) q^{22} +(2.21359 + 0.916899i) q^{23} +(1.03565 - 1.03565i) q^{25} +(4.62878 - 4.62878i) q^{26} +(-0.0818703 - 0.0339118i) q^{28} +(1.80460 + 4.35669i) q^{29} +(4.29431 - 1.77876i) q^{31} +(-1.50996 - 1.50996i) q^{32} +(-2.10845 - 4.80011i) q^{34} -0.434881 q^{35} +(-3.90224 + 1.61636i) q^{37} +9.10722i q^{38} +(-5.26403 - 2.18043i) q^{40} +(0.0604469 - 0.145932i) q^{41} +(6.35460 - 6.35460i) q^{43} +(-0.502156 + 1.21231i) q^{44} +(1.16589 + 2.81471i) q^{46} +8.05136i q^{47} +(4.91192 + 4.91192i) q^{49} +1.86236 q^{50} -1.97244 q^{52} +(-0.969947 - 0.969947i) q^{53} +6.43958i q^{55} +(-0.268212 - 0.647521i) q^{56} +(-2.29465 + 5.53978i) q^{58} +(-4.57543 + 4.57543i) q^{59} +(-4.97123 + 12.0016i) q^{61} +(5.46046 + 2.26180i) q^{62} -8.88913i q^{64} +(-8.94290 + 3.70427i) q^{65} +0.781257 q^{67} +(-0.573493 + 1.47195i) q^{68} +(-0.391013 - 0.391013i) q^{70} +(7.27435 - 3.01313i) q^{71} +(-1.13792 - 2.74719i) q^{73} +(-4.96192 - 2.05530i) q^{74} +(1.94041 - 1.94041i) q^{76} +(-0.560116 + 0.560116i) q^{77} +(-10.2276 - 4.23640i) q^{79} +(-2.22117 - 5.36239i) q^{80} +(0.185561 - 0.0768618i) q^{82} +(2.36509 + 2.36509i) q^{83} +(0.164176 + 7.75076i) q^{85} +11.4272 q^{86} +(-9.58830 + 3.97160i) q^{88} -16.6262i q^{89} +(-1.10005 - 0.455657i) q^{91} +(0.351301 - 0.848116i) q^{92} +(-7.23920 + 7.23920i) q^{94} +(5.15355 - 12.4418i) q^{95} +(5.98350 + 14.4454i) q^{97} +8.83288i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{10} - 48 q^{16} - 16 q^{19} - 24 q^{22} + 16 q^{25} + 24 q^{28} - 40 q^{31} + 64 q^{34} + 48 q^{37} - 48 q^{40} - 8 q^{43} + 24 q^{46} - 16 q^{49} + 32 q^{52} + 64 q^{58} - 24 q^{61} - 32 q^{67}+ \cdots - 88 q^{97}+O(q^{100}) $ 48 * q - 16 * q^10 - 48 * q^16 - 16 * q^19 - 24 * q^22 + 16 * q^25 + 24 * q^28 - 40 * q^31 + 64 * q^34 + 48 * q^37 - 48 * q^40 - 8 * q^43 + 24 * q^46 - 16 * q^49 + 32 * q^52 + 64 * q^58 - 24 * q^61 - 32 * q^67 + 96 * q^70 + 48 * q^73 + 96 * q^76 - 48 * q^79 + 112 * q^82 - 56 * q^85 - 160 * q^88 - 80 * q^91 - 40 * q^94 - 88 * q^97

Character values

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

$n$	$137$	$190$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.899127	+	0.899127i	0.635779	+	0.635779i	0.949511	−	0.313733i	$-0.101580\pi$
$2$	0.899127	+	0.899127i	0.635779	+	0.635779i	−0.313733	+	0.949511i	$0.601580\pi$
$3$		0			0
$3$		0			0
$4$		−	0.383141i		−	0.191570i
$5$	−0.719544	−	1.73713i	−0.321790	−	0.776869i	−0.999150	−	0.0412178i	$-0.986876\pi$
$5$	−0.719544	−	1.73713i	−0.321790	−	0.776869i	0.677360	−	0.735651i	$-0.263124\pi$
$6$		0			0
$7$	0.0885100	−	0.213682i	0.0334536	−	0.0807642i	−0.906270	−	0.422700i	$-0.861082\pi$
$7$	0.0885100	−	0.213682i	0.0334536	−	0.0807642i	0.939723	+	0.341936i	$0.111082\pi$
$8$	2.14275	−	2.14275i	0.757575	−	0.757575i
$9$		0			0
$10$	0.914941	−	2.20886i	0.289330	−	0.698504i
$11$	−3.16414	−	1.31063i	−0.954024	−	0.395170i	−0.149282	−	0.988795i	$-0.547696\pi$
$11$	−3.16414	−	1.31063i	−0.954024	−	0.395170i	−0.804742	+	0.593625i	$0.797696\pi$
$12$		0			0
$13$		−	5.14809i		−	1.42782i	−0.700236	−	0.713911i	$-0.746922\pi$
$13$		−	5.14809i		−	1.42782i	0.700236	−	0.713911i	$-0.253078\pi$
$14$	0.271709	−	0.112546i	0.0726173	−	0.0300791i
$15$		0			0
$16$	3.08692			0.771730
$17$	−3.84181	−	1.49682i	−0.931776	−	0.363032i
$17$	−3.84181	−	1.49682i	−0.931776	−	0.363032i
$18$		0			0
$19$	5.06448	+	5.06448i	1.16187	+	1.16187i	0.984066	+	0.177805i	$0.0568996\pi$
$19$	5.06448	+	5.06448i	1.16187	+	1.16187i	0.177805	+	0.984066i	$0.443100\pi$
$20$	−0.665566	+	0.275686i	−0.148825	+	0.0616454i
$21$		0			0
$22$	−1.66654	−	4.02339i	−0.355308	−	0.857789i
$23$	2.21359	+	0.916899i	0.461565	+	0.191187i	0.601334	−	0.798998i	$-0.294636\pi$
$23$	2.21359	+	0.916899i	0.461565	+	0.191187i	−0.139769	+	0.990184i	$0.544636\pi$
$24$		0			0
$25$	1.03565	−	1.03565i	0.207130	−	0.207130i
$26$	4.62878	−	4.62878i	0.907779	−	0.907779i
$27$		0			0
$28$	−0.0818703	−	0.0339118i	−0.0154720	−	0.00640873i
$29$	1.80460	+	4.35669i	0.335105	+	0.809016i	0.998171	+	0.0604547i	$0.0192551\pi$
$29$	1.80460	+	4.35669i	0.335105	+	0.809016i	−0.663065	+	0.748561i	$0.730745\pi$
$30$		0			0
$31$	4.29431	−	1.77876i	0.771281	−	0.319475i	0.0378896	−	0.999282i	$-0.487936\pi$
$31$	4.29431	−	1.77876i	0.771281	−	0.319475i	0.733391	+	0.679807i	$0.237936\pi$
$32$	−1.50996	−	1.50996i	−0.266925	−	0.266925i
$33$		0			0
$34$	−2.10845	−	4.80011i	−0.361595	−	0.823212i
$35$	−0.434881			−0.0735083
$36$		0			0
$37$	−3.90224	+	1.61636i	−0.641524	+	0.265728i	−0.679641	−	0.733545i	$-0.737864\pi$
$37$	−3.90224	+	1.61636i	−0.641524	+	0.265728i	0.0381162	+	0.999273i	$0.487864\pi$
$38$			9.10722i			1.47739i
$39$		0			0
$40$	−5.26403	−	2.18043i	−0.832317	−	0.344757i
$41$	0.0604469	−	0.145932i	0.00944023	−	0.0227907i	−0.919089	−	0.394050i	$-0.871074\pi$
$41$	0.0604469	−	0.145932i	0.00944023	−	0.0227907i	0.928529	+	0.371259i	$0.121074\pi$
$42$		0			0
$43$	6.35460	−	6.35460i	0.969068	−	0.969068i	−0.0304678	−	0.999536i	$-0.509700\pi$
$43$	6.35460	−	6.35460i	0.969068	−	0.969068i	0.999536	+	0.0304678i	$0.00969970\pi$
$44$	−0.502156	+	1.21231i	−0.0757028	+	0.182763i
$45$		0			0
$46$	1.16589	+	2.81471i	0.171901	+	0.415006i
$47$			8.05136i			1.17441i	0.809437	+	0.587206i	$0.199772\pi$
$47$			8.05136i			1.17441i	−0.809437	+	0.587206i	$0.800228\pi$
$48$		0			0
$49$	4.91192	+	4.91192i	0.701703	+	0.701703i
$50$	1.86236			0.263378
$51$		0			0
$52$	−1.97244			−0.273528
$53$	−0.969947	−	0.969947i	−0.133232	−	0.133232i	0.637346	−	0.770578i	$-0.280032\pi$
$53$	−0.969947	−	0.969947i	−0.133232	−	0.133232i	−0.770578	+	0.637346i	$0.780032\pi$
$54$		0			0
$55$			6.43958i			0.868313i
$56$	−0.268212	−	0.647521i	−0.0358413	−	0.0865287i
$57$		0			0
$58$	−2.29465	+	5.53978i	−0.301302	+	0.727408i
$59$	−4.57543	+	4.57543i	−0.595670	+	0.595670i	−0.939157	−	0.343487i	$-0.888392\pi$
$59$	−4.57543	+	4.57543i	−0.595670	+	0.595670i	0.343487	+	0.939157i	$0.388392\pi$
$60$		0			0
$61$	−4.97123	+	12.0016i	−0.636501	+	1.53665i	0.194809	+	0.980841i	$0.437591\pi$
$61$	−4.97123	+	12.0016i	−0.636501	+	1.53665i	−0.831310	+	0.555808i	$0.812409\pi$
$62$	5.46046	+	2.26180i	0.693479	+	0.287249i
$63$		0			0
$64$		−	8.88913i		−	1.11114i
$65$	−8.94290	+	3.70427i	−1.10923	+	0.459458i
$66$		0			0
$67$	0.781257			0.0954458			0.0477229	−	0.998861i	$-0.484804\pi$
$67$	0.781257			0.0954458			0.0477229	+	0.998861i	$0.484804\pi$
$68$	−0.573493	+	1.47195i	−0.0695463	+	0.178501i
$69$		0			0
$70$	−0.391013	−	0.391013i	−0.0467350	−	0.0467350i
$71$	7.27435	−	3.01313i	0.863306	−	0.357593i	0.0933065	−	0.995637i	$-0.470256\pi$
$71$	7.27435	−	3.01313i	0.863306	−	0.357593i	0.770000	+	0.638044i	$0.220256\pi$
$72$		0			0
$73$	−1.13792	−	2.74719i	−0.133184	−	0.321535i	0.843192	−	0.537612i	$-0.180674\pi$
$73$	−1.13792	−	2.74719i	−0.133184	−	0.321535i	−0.976376	+	0.216078i	$0.930674\pi$
$74$	−4.96192	−	2.05530i	−0.576812	−	0.238923i
$75$		0			0
$76$	1.94041	−	1.94041i	0.222580	−	0.222580i
$77$	−0.560116	+	0.560116i	−0.0638312	+	0.0638312i
$78$		0			0
$79$	−10.2276	−	4.23640i	−1.15069	−	0.476632i	−0.275926	−	0.961179i	$-0.588985\pi$
$79$	−10.2276	−	4.23640i	−1.15069	−	0.476632i	−0.874765	+	0.484547i	$0.838985\pi$
$80$	−2.22117	−	5.36239i	−0.248335	−	0.599534i
$81$		0			0
$82$	0.185561	−	0.0768618i	0.0204918	−	0.00848796i
$83$	2.36509	+	2.36509i	0.259602	+	0.259602i	0.824892	−	0.565290i	$-0.191236\pi$
$83$	2.36509	+	2.36509i	0.259602	+	0.259602i	−0.565290	+	0.824892i	$0.691236\pi$
$84$		0			0
$85$	0.164176	+	7.75076i	0.0178074	+	0.840688i
$86$	11.4272			1.23223
$87$		0			0
$88$	−9.58830	+	3.97160i	−1.02212	+	0.423374i
$89$		−	16.6262i		−	1.76237i	−0.472767	−	0.881187i	$-0.656745\pi$
$89$		−	16.6262i		−	1.76237i	0.472767	−	0.881187i	$-0.343255\pi$
$90$		0			0
$91$	−1.10005	−	0.455657i	−0.115317	−	0.0477659i
$92$	0.351301	−	0.848116i	0.0366257	−	0.0884222i
$93$		0			0
$94$	−7.23920	+	7.23920i	−0.746666	+	0.746666i
$95$	5.15355	−	12.4418i	0.528743	−	1.27650i
$96$		0			0
$97$	5.98350	+	14.4454i	0.607532	+	1.46671i	0.865675	+	0.500606i	$0.166890\pi$
$97$	5.98350	+	14.4454i	0.607532	+	1.46671i	−0.258143	+	0.966107i	$0.583110\pi$
$98$			8.83288i			0.892256i
$99$		0			0
$100$	−0.396799	−	0.396799i	−0.0396799	−	0.0396799i
$101$	−0.195673			−0.0194702			−0.00973509	−	0.999953i	$-0.503099\pi$
$101$	−0.195673			−0.0194702			−0.00973509	+	0.999953i	$0.503099\pi$
$102$		0			0
$103$	−0.355474			−0.0350259			−0.0175129	−	0.999847i	$-0.505575\pi$
$103$	−0.355474			−0.0350259			−0.0175129	+	0.999847i	$0.505575\pi$
$104$	−11.0310	−	11.0310i	−1.08168	−	1.08168i
$105$		0			0
$106$		−	1.74421i		−	0.169413i
$107$	−3.85168	−	9.29878i	−0.372356	−	0.898947i	−0.993350	−	0.115132i	$-0.963271\pi$
$107$	−3.85168	−	9.29878i	−0.372356	−	0.898947i	0.620994	−	0.783815i	$-0.286729\pi$
$108$		0			0
$109$	−3.93930	+	9.51031i	−0.377317	+	0.910923i	0.615150	+	0.788410i	$0.289095\pi$
$109$	−3.93930	+	9.51031i	−0.377317	+	0.910923i	−0.992467	+	0.122513i	$0.960905\pi$
$110$	−5.79001	+	5.79001i	−0.552055	+	0.552055i
$111$		0			0
$112$	0.273224	−	0.659620i	0.0258172	−	0.0623282i
$113$	13.4701	+	5.57948i	1.26716	+	0.524874i	0.912099	−	0.409971i	$-0.134461\pi$
$113$	13.4701	+	5.57948i	1.26716	+	0.524874i	0.355058	+	0.934844i	$0.384461\pi$
$114$		0			0
$115$		−	4.50505i		−	0.420098i
$116$	1.66922	−	0.691415i	0.154984	−	0.0641963i
$117$		0			0
$118$	−8.22779			−0.757429
$119$	−0.659883	+	0.688443i	−0.0604914	+	0.0631095i
$120$		0			0
$121$	0.515857	+	0.515857i	0.0468961	+	0.0468961i
$122$	−15.2607	+	6.32121i	−1.38164	+	0.572295i
$123$		0			0
$124$	−0.681516	−	1.64532i	−0.0612019	−	0.147754i
$125$	−11.2299	−	4.65158i	−1.00443	−	0.416050i
$126$		0			0
$127$	2.16672	−	2.16672i	0.192265	−	0.192265i	−0.604409	−	0.796674i	$-0.706591\pi$
$127$	2.16672	−	2.16672i	0.192265	−	0.192265i	0.796674	+	0.604409i	$0.206591\pi$
$128$	4.97254	−	4.97254i	0.439515	−	0.439515i
$129$		0			0
$130$	−11.3714	−	4.71020i	−0.997340	−	0.413112i
$131$	2.87069	+	6.93045i	0.250813	+	0.605516i	0.998270	−	0.0587940i	$-0.0187255\pi$
$131$	2.87069	+	6.93045i	0.250813	+	0.605516i	−0.747457	+	0.664310i	$0.768726\pi$
$132$		0			0
$133$	1.53044	−	0.633931i	0.132706	−	0.0549688i
$134$	0.702450	+	0.702450i	0.0606824	+	0.0606824i
$135$		0			0
$136$	−11.4393	+	5.02472i	−0.980915	+	0.430866i
$137$	9.35686			0.799411			0.399705	−	0.916644i	$-0.369112\pi$
$137$	9.35686			0.799411			0.399705	+	0.916644i	$0.369112\pi$
$138$		0			0
$139$	4.68934	−	1.94239i	0.397745	−	0.164751i	−0.174840	−	0.984597i	$-0.555941\pi$
$139$	4.68934	−	1.94239i	0.397745	−	0.164751i	0.572585	+	0.819846i	$0.305941\pi$
$140$			0.166621i			0.0140820i
$141$		0			0
$142$	9.24975	+	3.83137i	0.776222	+	0.321522i
$143$	−6.74723	+	16.2893i	−0.564232	+	1.36218i
$144$		0			0
$145$	6.26965	−	6.26965i	0.520666	−	0.520666i
$146$	1.44694	−	3.49321i	0.119749	−	0.289100i
$147$		0			0
$148$	0.619294	+	1.49511i	0.0509056	+	0.122897i
$149$		−	3.54068i		−	0.290063i	−0.989427	−	0.145032i	$-0.953672\pi$
$149$		−	3.54068i		−	0.290063i	0.989427	−	0.145032i	$-0.0463284\pi$
$150$		0			0
$151$	8.80774	+	8.80774i	0.716764	+	0.716764i	0.967941	−	0.251177i	$-0.0808176\pi$
$151$	8.80774	+	8.80774i	0.716764	+	0.716764i	−0.251177	+	0.967941i	$0.580818\pi$
$152$	21.7038			1.76041
$153$		0			0
$154$	−1.00723			−0.0811650
$155$	−6.17988	−	6.17988i	−0.496380	−	0.496380i
$156$		0			0
$157$			11.6965i			0.933485i	0.884393	+	0.466742i	$0.154572\pi$
$157$			11.6965i			0.933485i	−0.884393	+	0.466742i	$0.845428\pi$
$158$	−5.38682	−	13.0049i	−0.428553	−	1.03462i
$159$		0			0
$160$	−1.53652	+	3.70948i	−0.121472	+	0.293260i
$161$	0.391850	−	0.391850i	0.0308821	−	0.0308821i
$162$		0			0
$163$	6.01281	−	14.5162i	0.470959	−	1.13700i	−0.492781	−	0.870154i	$-0.664019\pi$
$163$	6.01281	−	14.5162i	0.470959	−	1.13700i	0.963740	−	0.266843i	$-0.0859805\pi$
$164$	−0.0559124	−	0.0231597i	−0.00436603	−	0.00180847i
$165$		0			0
$166$			4.25303i			0.330099i
$167$	4.78041	−	1.98011i	0.369919	−	0.153226i	−0.189976	−	0.981789i	$-0.560841\pi$
$167$	4.78041	−	1.98011i	0.369919	−	0.153226i	0.559896	+	0.828563i	$0.310841\pi$
$168$		0			0
$169$	−13.5028			−1.03868
$170$	−6.82131	+	7.11654i	−0.523170	+	0.545814i
$171$		0			0
$172$	−2.43471	−	2.43471i	−0.185645	−	0.185645i
$173$	16.7704	−	6.94651i	1.27503	−	0.528133i	0.360538	−	0.932745i	$-0.382593\pi$
$173$	16.7704	−	6.94651i	1.27503	−	0.528133i	0.914489	+	0.404612i	$0.132593\pi$
$174$		0			0
$175$	−0.129634	−	0.312965i	−0.00979944	−	0.0236579i
$176$	−9.76745	−	4.04581i	−0.736249	−	0.304965i
$177$		0			0
$178$	14.9491	−	14.9491i	1.12048	−	1.12048i
$179$	6.23840	−	6.23840i	0.466280	−	0.466280i	−0.434427	−	0.900707i	$-0.643049\pi$
$179$	6.23840	−	6.23840i	0.466280	−	0.466280i	0.900707	+	0.434427i	$0.143049\pi$
$180$		0			0
$181$	−21.4082	−	8.86758i	−1.59126	−	0.659122i	−0.601116	−	0.799162i	$-0.705277\pi$
$181$	−21.4082	−	8.86758i	−1.59126	−	0.659122i	−0.990146	+	0.140040i	$0.955277\pi$
$182$	−0.579394	−	1.39878i	−0.0429476	−	0.103685i
$183$		0			0
$184$	6.70784	−	2.77848i	0.494509	−	0.204832i
$185$	5.61567	+	5.61567i	0.412872	+	0.412872i
$186$		0			0
$187$	10.1943	+	9.77135i	0.745478	+	0.714552i
$188$	3.08481			0.224983
$189$		0			0
$190$	15.8204	−	6.55304i	1.14774	−	0.475407i
$191$			25.4613i			1.84231i	0.389191	+	0.921157i	$0.372755\pi$
$191$			25.4613i			1.84231i	−0.389191	+	0.921157i	$0.627245\pi$
$192$		0			0
$193$	7.53364	+	3.12053i	0.542283	+	0.224621i	0.636973	−	0.770886i	$-0.280186\pi$
$193$	7.53364	+	3.12053i	0.542283	+	0.224621i	−0.0946904	+	0.995507i	$0.530186\pi$
$194$	−7.60837	+	18.3682i	−0.546249	+	1.31876i
$195$		0			0
$196$	1.88196	−	1.88196i	0.134426	−	0.134426i
$197$	−5.46613	+	13.1964i	−0.389446	+	0.940206i	0.600611	+	0.799541i	$0.294924\pi$
$197$	−5.46613	+	13.1964i	−0.389446	+	0.940206i	−0.990057	+	0.140665i	$0.955076\pi$
$198$		0			0
$199$	0.206050	+	0.497449i	0.0146065	+	0.0352632i	0.931015	−	0.364982i	$-0.118925\pi$
$199$	0.206050	+	0.497449i	0.0146065	+	0.0352632i	−0.916408	+	0.400245i	$0.868925\pi$
$200$		−	4.43827i		−	0.313833i
$201$		0			0
$202$	−0.175935	−	0.175935i	−0.0123787	−	0.0123787i
$203$	1.09067			0.0765501
$204$		0			0
$205$	−0.296997			−0.0207432
$206$	−0.319616	−	0.319616i	−0.0222687	−	0.0222687i
$207$		0			0
$208$		−	15.8917i		−	1.10189i
$209$	−9.38706	−	22.6624i	−0.649316	−	1.56759i
$210$		0			0
$211$	−1.30732	+	3.15616i	−0.0899999	+	0.217279i	−0.962470	−	0.271389i	$-0.912517\pi$
$211$	−1.30732	+	3.15616i	−0.0899999	+	0.217279i	0.872470	+	0.488668i	$0.162517\pi$
$212$	−0.371626	+	0.371626i	−0.0255234	+	0.0255234i
$213$		0			0
$214$	4.89763	−	11.8239i	0.334795	−	0.808268i
$215$	−15.6112	−	6.46637i	−1.06468	−	0.441003i
$216$		0			0
$217$		−	1.07506i		−	0.0729795i
$218$	−12.0929	+	5.00905i	−0.819035	+	0.339256i
$219$		0			0
$220$	2.46727			0.166343
$221$	−7.70576	+	19.7780i	−0.518346	+	1.33041i
$222$		0			0
$223$	−14.2750	−	14.2750i	−0.955925	−	0.955925i	0.0431441	−	0.999069i	$-0.486263\pi$
$223$	−14.2750	−	14.2750i	−0.955925	−	0.955925i	−0.999069	+	0.0431441i	$0.986263\pi$
$224$	−0.456297	+	0.189005i	−0.0304877	+	0.0126284i
$225$		0			0
$226$	7.09464	+	17.1280i	0.471928	+	1.13934i
$227$	−1.33180	−	0.551651i	−0.0883949	−	0.0366144i	0.338048	−	0.941129i	$-0.390233\pi$
$227$	−1.33180	−	0.551651i	−0.0883949	−	0.0366144i	−0.426443	+	0.904515i	$0.640233\pi$
$228$		0			0
$229$	7.44196	−	7.44196i	0.491779	−	0.491779i	−0.417088	−	0.908866i	$-0.636949\pi$
$229$	7.44196	−	7.44196i	0.491779	−	0.491779i	0.908866	+	0.417088i	$0.136949\pi$
$230$	4.05061	−	4.05061i	0.267089	−	0.267089i
$231$		0			0
$232$	13.2021	+	5.46848i	0.866758	+	0.359023i
$233$	5.14541	+	12.4221i	0.337087	+	0.813801i	0.997993	+	0.0633314i	$0.0201725\pi$
$233$	5.14541	+	12.4221i	0.337087	+	0.813801i	−0.660905	+	0.750469i	$0.729828\pi$
$234$		0			0
$235$	13.9863	−	5.79331i	0.912364	−	0.377914i
$236$	1.75303	+	1.75303i	0.114113	+	0.114113i
$237$		0			0
$238$	−1.21232	+	0.0256792i	−0.0785828	+	0.00166453i
$239$	17.3220			1.12047			0.560233	−	0.828335i	$-0.310712\pi$
$239$	17.3220			1.12047			0.560233	+	0.828335i	$0.310712\pi$
$240$		0			0
$241$	−13.7074	+	5.67780i	−0.882972	+	0.365739i	−0.777649	−	0.628699i	$-0.783588\pi$
$241$	−13.7074	+	5.67780i	−0.882972	+	0.365739i	−0.105324	+	0.994438i	$0.533588\pi$
$242$			0.927643i			0.0596311i
$243$		0			0
$244$	4.59831	+	1.90468i	0.294377	+	0.121935i
$245$	4.99831	−	12.0670i	0.319331	−	0.770932i
$246$		0			0
$247$	26.0724	−	26.0724i	1.65894	−	1.65894i
$248$	5.39018	−	13.0130i	0.342277	−	0.826329i
$249$		0			0
$250$	−5.91476	−	14.2795i	−0.374082	−	0.903114i
$251$			28.1651i			1.77776i	0.458136	+	0.888882i	$0.348517\pi$
$251$			28.1651i			1.77776i	−0.458136	+	0.888882i	$0.651483\pi$
$252$		0			0
$253$	−5.80239	−	5.80239i	−0.364793	−	0.364793i
$254$	3.89631			0.244476
$255$		0			0
$256$	−8.83636			−0.552273
$257$	3.14970	+	3.14970i	0.196473	+	0.196473i	0.798486	−	0.602013i	$-0.205635\pi$
$257$	3.14970	+	3.14970i	0.196473	+	0.196473i	−0.602013	+	0.798486i	$0.705635\pi$
$258$		0			0
$259$			0.976903i			0.0607018i
$260$	1.41926	+	3.42639i	0.0880186	+	0.212496i
$261$		0			0
$262$	−3.65024	+	8.81246i	−0.225513	+	0.544436i
$263$	12.3171	−	12.3171i	0.759503	−	0.759503i	−0.216729	−	0.976232i	$-0.569539\pi$
$263$	12.3171	−	12.3171i	0.759503	−	0.759503i	0.976232	+	0.216729i	$0.0695387\pi$
$264$		0			0
$265$	−0.987006	+	2.38284i	−0.0606313	+	0.146377i
$266$	1.94605	+	0.806080i	0.119320	+	0.0494239i
$267$		0			0
$268$		−	0.299332i		−	0.0182846i
$269$	−20.0339	+	8.29832i	−1.22149	+	0.505958i	−0.897883	−	0.440234i	$-0.854896\pi$
$269$	−20.0339	+	8.29832i	−1.22149	+	0.505958i	−0.323607	+	0.946192i	$0.604896\pi$
$270$		0			0
$271$	27.4783			1.66919			0.834593	−	0.550866i	$-0.185703\pi$
$271$	27.4783			1.66919			0.834593	+	0.550866i	$0.185703\pi$
$272$	−11.8594	−	4.62057i	−0.719080	−	0.280163i
$273$		0			0
$274$	8.41301	+	8.41301i	0.508248	+	0.508248i
$275$	−4.63429	+	1.91959i	−0.279458	+	0.115755i
$276$		0			0
$277$	−9.75322	−	23.5463i	−0.586014	−	1.41476i	−0.887284	−	0.461224i	$-0.847410\pi$
$277$	−9.75322	−	23.5463i	−0.586014	−	1.41476i	0.301270	−	0.953539i	$-0.402590\pi$
$278$	5.96277	+	2.46986i	0.357623	+	0.148132i
$279$		0			0
$280$	−0.931839	+	0.931839i	−0.0556881	+	0.0556881i
$281$	15.2659	−	15.2659i	0.910690	−	0.910690i	−0.0856363	−	0.996326i	$-0.527292\pi$
$281$	15.2659	−	15.2659i	0.910690	−	0.910690i	0.996326	+	0.0856363i	$0.0272923\pi$
$282$		0			0
$283$	−7.99214	−	3.31045i	−0.475084	−	0.196786i	0.132276	−	0.991213i	$-0.457771\pi$
$283$	−7.99214	−	3.31045i	−0.475084	−	0.196786i	−0.607360	+	0.794427i	$0.707771\pi$
$284$	−1.15445	−	2.78710i	−0.0685042	−	0.165384i
$285$		0			0
$286$	−20.7127	+	8.57950i	−1.22477	+	0.507316i
$287$	−0.0258329	−	0.0258329i	−0.00152487	−	0.00152487i
$288$		0			0
$289$	12.5191	+	11.5010i	0.736415	+	0.676530i
$290$	11.2744			0.662057
$291$		0			0
$292$	−1.05256	+	0.435985i	−0.0615965	+	0.0255141i
$293$			15.4778i			0.904222i	0.891962	+	0.452111i	$0.149329\pi$
$293$			15.4778i			0.904222i	−0.891962	+	0.452111i	$0.850671\pi$
$294$		0			0
$295$	11.2404	+	4.65591i	0.654439	+	0.271077i
$296$	−4.89806	+	11.8250i	−0.284694	+	0.687312i
$297$		0			0
$298$	3.18352	−	3.18352i	0.184416	−	0.184416i
$299$	4.72027	−	11.3957i	0.272980	−	0.659033i
$300$		0			0
$301$	−0.795419	−	1.92031i	−0.0458472	−	0.110685i
$302$			15.8386i			0.911407i
$303$		0			0
$304$	15.6336	+	15.6336i	0.896651	+	0.896651i
$305$	24.4254			1.39860
$306$		0			0
$307$	−31.1421			−1.77737			−0.888687	−	0.458514i	$-0.848382\pi$
$307$	−31.1421			−1.77737			−0.888687	+	0.458514i	$0.848382\pi$
$308$	0.214603	+	0.214603i	0.0122282	+	0.0122282i
$309$		0			0
$310$		−	11.1130i		−	0.631176i
$311$	−11.3142	−	27.3149i	−0.641570	−	1.54889i	−0.824561	−	0.565773i	$-0.808578\pi$
$311$	−11.3142	−	27.3149i	−0.641570	−	1.54889i	0.182990	−	0.983115i	$-0.441422\pi$
$312$		0			0
$313$	5.14187	−	12.4136i	0.290636	−	0.701657i	−0.709359	−	0.704847i	$-0.751016\pi$
$313$	5.14187	−	12.4136i	0.290636	−	0.701657i	0.999995	+	0.00319046i	$0.00101556\pi$
$314$	−10.5167	+	10.5167i	−0.593490	+	0.593490i
$315$		0			0
$316$	−1.62314	+	3.91860i	−0.0913086	+	0.220438i
$317$	−0.376787	−	0.156070i	−0.0211625	−	0.00876578i	0.372077	−	0.928202i	$-0.378646\pi$
$317$	−0.376787	−	0.156070i	−0.0211625	−	0.00876578i	−0.393240	+	0.919436i	$0.628646\pi$
$318$		0			0
$319$		−	16.1503i		−	0.904244i
$320$	−15.4416	+	6.39612i	−0.863211	+	0.357554i
$321$		0			0
$322$	0.704645			0.0392684
$323$	−11.8762	−	27.0374i	−0.660807	−	1.50440i
$324$		0			0
$325$	−5.33161	−	5.33161i	−0.295745	−	0.295745i
$326$	18.4582	−	7.64563i	1.02230	−	0.423452i
$327$		0			0
$328$	−0.183172	−	0.442217i	−0.0101140	−	0.0244174i
$329$	1.72043	+	0.712626i	0.0948505	+	0.0392884i
$330$		0			0
$331$	5.83848	−	5.83848i	0.320912	−	0.320912i	−0.528205	−	0.849117i	$-0.677135\pi$
$331$	5.83848	−	5.83848i	0.320912	−	0.320912i	0.849117	+	0.528205i	$0.177135\pi$
$332$	0.906161	−	0.906161i	0.0497321	−	0.0497321i
$333$		0			0
$334$	6.07857	+	2.51783i	0.332605	+	0.137769i
$335$	−0.562149	−	1.35715i	−0.0307135	−	0.0741489i
$336$		0			0
$337$	−21.9004	+	9.07145i	−1.19299	+	0.494154i	−0.888728	−	0.458434i	$-0.848410\pi$
$337$	−21.9004	+	9.07145i	−1.19299	+	0.494154i	−0.304264	+	0.952588i	$0.598410\pi$
$338$	−12.1407	−	12.1407i	−0.660368	−	0.660368i
$339$		0			0
$340$	2.96963	−	0.0629025i	0.161051	−	0.00341137i
$341$	−15.9191			−0.862067
$342$		0			0
$343$	2.98012	−	1.23441i	0.160911	−	0.0666516i
$344$		−	27.2326i		−	1.46828i
$345$		0			0
$346$	21.3245	+	8.83289i	1.14641	+	0.474859i
$347$	11.3866	−	27.4896i	0.611262	−	1.47572i	−0.250352	−	0.968155i	$-0.580547\pi$
$347$	11.3866	−	27.4896i	0.611262	−	1.47572i	0.861615	−	0.507563i	$-0.169453\pi$
$348$		0			0
$349$	−13.1320	+	13.1320i	−0.702939	+	0.702939i	−0.965040	−	0.262102i	$-0.915584\pi$
$349$	−13.1320	+	13.1320i	−0.702939	+	0.702939i	0.262102	+	0.965040i	$0.415584\pi$
$350$	0.164838	−	0.397953i	0.00881094	−	0.0212715i
$351$		0			0
$352$	2.79872	+	6.75671i	0.149172	+	0.360134i
$353$			32.4661i			1.72800i	0.503494	+	0.863999i	$0.332047\pi$
$353$			32.4661i			1.72800i	−0.503494	+	0.863999i	$0.667953\pi$
$354$		0			0
$355$	−10.4684	−	10.4684i	−0.555606	−	0.555606i
$356$	−6.37018			−0.337619
$357$		0			0
$358$	11.2182			0.592902
$359$	−21.8909	−	21.8909i	−1.15536	−	1.15536i	−0.985462	−	0.169896i	$-0.945657\pi$
$359$	−21.8909	−	21.8909i	−1.15536	−	1.15536i	−0.169896	−	0.985462i	$-0.554343\pi$
$360$		0			0
$361$			32.2978i			1.69989i
$362$	−11.2756	−	27.2218i	−0.592635	−	1.43075i
$363$		0			0
$364$	−0.174581	+	0.421475i	−0.00915052	+	0.0220913i
$365$	−3.95345	+	3.95345i	−0.206933	+	0.206933i
$366$		0			0
$367$	−1.43044	+	3.45339i	−0.0746684	+	0.180265i	−0.956807	−	0.290725i	$-0.906103\pi$
$367$	−1.43044	+	3.45339i	−0.0746684	+	0.180265i	0.882138	+	0.470991i	$0.156103\pi$
$368$	6.83318	+	2.83039i	0.356204	+	0.147545i
$369$		0			0
$370$			10.0984i			0.524991i
$371$	−0.293110	+	0.121410i	−0.0152175	+	0.00630331i
$372$		0			0
$373$	−14.3295			−0.741954			−0.370977	−	0.928642i	$-0.620977\pi$
$373$	−14.3295			−0.741954			−0.370977	+	0.928642i	$0.620977\pi$
$374$	0.380249	+	17.9516i	0.0196622	+	0.928256i
$375$		0			0
$376$	17.2520	+	17.2520i	0.889706	+	0.889706i
$377$	22.4286	−	9.29023i	1.15513	−	0.478471i
$378$		0			0
$379$	6.25632	+	15.1041i	0.321366	+	0.775845i	0.999175	+	0.0406077i	$0.0129294\pi$
$379$	6.25632	+	15.1041i	0.321366	+	0.775845i	−0.677810	+	0.735238i	$0.737071\pi$
$380$	−4.76695	−	1.97454i	−0.244539	−	0.101292i
$381$		0			0
$382$	−22.8929	+	22.8929i	−1.17130	+	1.17130i
$383$	8.08546	−	8.08546i	0.413148	−	0.413148i	−0.469686	−	0.882834i	$-0.655633\pi$
$383$	8.08546	−	8.08546i	0.413148	−	0.413148i	0.882834	+	0.469686i	$0.155633\pi$
$384$		0			0
$385$	1.37602	+	0.569968i	0.0701287	+	0.0290482i
$386$	3.96794	+	9.57945i	0.201963	+	0.487581i
$387$		0			0
$388$	5.53464	−	2.29252i	0.280979	−	0.116385i
$389$	−25.6389	−	25.6389i	−1.29994	−	1.29994i	−0.928426	−	0.371517i	$-0.878838\pi$
$389$	−25.6389	−	25.6389i	−1.29994	−	1.29994i	−0.371517	−	0.928426i	$-0.621162\pi$
$390$		0			0
$391$	−7.13176	−	6.83590i	−0.360669	−	0.345706i
$392$	21.0500			1.06319
$393$		0			0
$394$	−16.7800	+	6.95051i	−0.845364	+	0.350161i
$395$			20.8149i			1.04731i
$396$		0			0
$397$	−19.5851	−	8.11239i	−0.982946	−	0.407149i	−0.167430	−	0.985884i	$-0.553547\pi$
$397$	−19.5851	−	8.11239i	−0.982946	−	0.407149i	−0.815516	+	0.578735i	$0.803547\pi$
$398$	−0.262005	+	0.632535i	−0.0131331	+	0.0317061i
$399$		0			0
$400$	3.19697	−	3.19697i	0.159848	−	0.159848i
$401$	−2.96415	+	7.15609i	−0.148023	+	0.357358i	−0.980448	−	0.196779i	$-0.936952\pi$
$401$	−2.96415	+	7.15609i	−0.148023	+	0.357358i	0.832425	+	0.554137i	$0.186952\pi$
$402$		0			0
$403$	−9.15721	−	22.1075i	−0.456153	−	1.10125i
$404$			0.0749703i			0.00372991i
$405$		0			0
$406$	0.980652	+	0.980652i	0.0486689	+	0.0486689i
$407$	14.4657			0.717037
$408$		0			0
$409$	−18.6180			−0.920599			−0.460300	−	0.887764i	$-0.652258\pi$
$409$	−18.6180			−0.920599			−0.460300	+	0.887764i	$0.652258\pi$
$410$	−0.267038	−	0.267038i	−0.0131881	−	0.0131881i
$411$		0			0
$412$			0.136197i			0.00670992i
$413$	0.572716	+	1.38266i	0.0281815	+	0.0680362i
$414$		0			0
$415$	2.40669	−	5.81025i	0.118140	−	0.285214i
$416$	−7.77339	+	7.77339i	−0.381122	+	0.381122i
$417$		0			0
$418$	11.9362	−	28.8165i	0.583818	−	1.40946i
$419$	28.5967	+	11.8452i	1.39704	+	0.578673i	0.948982	−	0.315330i	$-0.102115\pi$
$419$	28.5967	+	11.8452i	1.39704	+	0.578673i	0.448059	+	0.894004i	$0.352115\pi$
$420$		0			0
$421$			12.6804i			0.618004i	0.951061	+	0.309002i	$0.0999950\pi$
$421$			12.6804i			0.618004i	−0.951061	+	0.309002i	$0.900005\pi$
$422$	−4.01324	+	1.66234i	−0.195361	+	0.0809213i
$423$		0			0
$424$	−4.15670			−0.201867
$425$	−5.52895	+	2.42859i	−0.268194	+	0.117804i
$426$		0			0
$427$	2.12453	+	2.12453i	0.102813	+	0.102813i
$428$	−3.56274	+	1.47574i	−0.172212	+	0.0713324i
$429$		0			0
$430$	−8.22236	−	19.8505i	−0.396518	−	0.957278i
$431$	−4.05249	−	1.67860i	−0.195202	−	0.0808552i	0.282941	−	0.959137i	$-0.408690\pi$
$431$	−4.05249	−	1.67860i	−0.195202	−	0.0808552i	−0.478143	+	0.878282i	$0.658690\pi$
$432$		0			0
$433$	−16.7791	+	16.7791i	−0.806350	+	0.806350i	−0.984079	−	0.177730i	$-0.943125\pi$
$433$	−16.7791	+	16.7791i	−0.806350	+	0.806350i	0.177730	+	0.984079i	$0.443125\pi$
$434$	0.966611	−	0.966611i	0.0463988	−	0.0463988i
$435$		0			0
$436$	3.64379	+	1.50931i	0.174506	+	0.0722827i
$437$	6.56706	+	15.8543i	0.314145	+	0.758413i
$438$		0			0
$439$	−14.8642	+	6.15697i	−0.709432	+	0.293856i	−0.708069	−	0.706143i	$-0.750434\pi$
$439$	−14.8642	+	6.15697i	−0.709432	+	0.293856i	−0.00136242	+	0.999999i	$0.500434\pi$
$440$	13.7984	+	13.7984i	0.657813	+	0.657813i
$441$		0			0
$442$	−24.7114	+	10.8545i	−1.17540	+	0.516294i
$443$	−1.22288			−0.0581009			−0.0290505	−	0.999578i	$-0.509248\pi$
$443$	−1.22288			−0.0581009			−0.0290505	+	0.999578i	$0.509248\pi$
$444$		0			0
$445$	−28.8819	+	11.9633i	−1.36913	+	0.567114i
$446$		−	25.6701i		−	1.21551i
$447$		0			0
$448$	−1.89945	−	0.786777i	−0.0897405	−	0.0371717i
$449$	−8.98146	+	21.6832i	−0.423862	+	1.02329i	0.557336	+	0.830287i	$0.311823\pi$
$449$	−8.98146	+	21.6832i	−0.423862	+	1.02329i	−0.981198	+	0.193005i	$0.938177\pi$
$450$		0			0
$451$	−0.382525	+	0.382525i	−0.0180124	+	0.0180124i
$452$	2.13773	−	5.16093i	0.100550	−	0.242750i
$453$		0			0
$454$	−0.701456	−	1.69346i	−0.0329210	−	0.0794782i
$455$			2.23880i			0.104957i
$456$		0			0
$457$	27.3129	+	27.3129i	1.27764	+	1.27764i	0.941983	+	0.335661i	$0.108960\pi$
$457$	27.3129	+	27.3129i	1.27764	+	1.27764i	0.335661	+	0.941983i	$0.391040\pi$
$458$	13.3825			0.625325
$459$		0			0
$460$	−1.72607			−0.0804783
$461$	12.6806	+	12.6806i	0.590595	+	0.590595i	0.937792	−	0.347197i	$-0.112867\pi$
$461$	12.6806	+	12.6806i	0.590595	+	0.590595i	−0.347197	+	0.937792i	$0.612867\pi$
$462$		0			0
$463$		−	9.71279i		−	0.451392i	−0.974198	−	0.225696i	$-0.927534\pi$
$463$		−	9.71279i		−	0.451392i	0.974198	−	0.225696i	$-0.0724656\pi$
$464$	5.57065	+	13.4487i	0.258611	+	0.624342i
$465$		0			0
$466$	−6.54269	+	15.7955i	−0.303084	+	0.731710i
$467$	−23.7764	+	23.7764i	−1.10024	+	1.10024i	−0.105858	+	0.994381i	$0.533759\pi$
$467$	−23.7764	+	23.7764i	−1.10024	+	1.10024i	−0.994381	+	0.105858i	$0.966241\pi$
$468$		0			0
$469$	0.0691491	−	0.166941i	0.00319301	−	0.00770861i
$470$	17.7844	+	7.36653i	0.820332	+	0.339792i
$471$		0			0
$472$			19.6080i			0.902530i
$473$	−28.4354	+	11.7783i	−1.30746	+	0.541568i
$474$		0			0
$475$	10.4900			0.481316
$476$	0.263771	+	0.252828i	0.0120899	+	0.0115884i
$477$		0			0
$478$	15.5747	+	15.5747i	0.712368	+	0.712368i
$479$	−27.0470	+	11.2032i	−1.23581	+	0.511889i	−0.902402	−	0.430894i	$-0.858198\pi$
$479$	−27.0470	+	11.2032i	−1.23581	+	0.511889i	−0.333406	+	0.942783i	$0.608198\pi$
$480$		0			0
$481$	8.32117	+	20.0891i	0.379412	+	0.915983i
$482$	−17.4298	−	7.21965i	−0.793905	−	0.328846i
$483$		0			0
$484$	0.197646	−	0.197646i	0.00898391	−	0.00898391i
$485$	20.7883	−	20.7883i	0.943946	−	0.943946i
$486$		0			0
$487$	25.2643	+	10.4648i	1.14483	+	0.474206i	0.872798	−	0.488081i	$-0.162303\pi$
$487$	25.2643	+	10.4648i	1.14483	+	0.474206i	0.272036	+	0.962287i	$0.412303\pi$
$488$	15.0643	+	36.3685i	0.681930	+	1.64633i
$489$		0			0
$490$	15.3439	−	6.35565i	0.693166	−	0.287119i
$491$	0.573616	+	0.573616i	0.0258869	+	0.0258869i	0.719932	−	0.694045i	$-0.244173\pi$
$491$	0.573616	+	0.573616i	0.0258869	+	0.0258869i	−0.694045	+	0.719932i	$0.744173\pi$
$492$		0			0
$493$	−0.411749	−	19.4387i	−0.0185443	−	0.875476i
$494$	46.8847			2.10944
$495$		0			0
$496$	13.2562	−	5.49090i	0.595221	−	0.246548i
$497$		−	1.82109i		−	0.0816871i
$498$		0			0
$499$	−26.3669	−	10.9215i	−1.18034	−	0.488914i	−0.295745	−	0.955267i	$-0.595568\pi$
$499$	−26.3669	−	10.9215i	−1.18034	−	0.488914i	−0.884599	+	0.466353i	$0.845568\pi$
$500$	−1.78221	+	4.30264i	−0.0797029	+	0.192420i
$501$		0			0
$502$	−25.3240	+	25.3240i	−1.13027	+	1.13027i
$503$	−2.96369	+	7.15498i	−0.132144	+	0.319025i	−0.976077	−	0.217424i	$-0.930235\pi$
$503$	−2.96369	+	7.15498i	−0.132144	+	0.319025i	0.843933	+	0.536449i	$0.180235\pi$
$504$		0			0
$505$	0.140795	+	0.339910i	0.00626530	+	0.0151258i
$506$		−	10.4342i		−	0.463856i
$507$		0			0
$508$	−0.830157	−	0.830157i	−0.0368323	−	0.0368323i
$509$	−24.2954			−1.07687			−0.538437	−	0.842666i	$-0.680985\pi$
$509$	−24.2954			−1.07687			−0.538437	+	0.842666i	$0.680985\pi$
$510$		0			0
$511$	−0.687744			−0.0304240
$512$	−17.8901	−	17.8901i	−0.790638	−	0.790638i
$513$		0			0
$514$			5.66396i			0.249827i
$515$	0.255779	+	0.617505i	0.0112710	+	0.0272105i
$516$		0			0
$517$	10.5524	−	25.4756i	0.464092	−	1.12042i
$518$	−0.878360	+	0.878360i	−0.0385929	+	0.0385929i
$519$		0			0
$520$	−11.2251	+	27.0997i	−0.492251	+	1.18840i
$521$	−35.3917	−	14.6597i	−1.55054	−	0.642254i	−0.567126	−	0.823631i	$-0.691945\pi$
$521$	−35.3917	−	14.6597i	−1.55054	−	0.642254i	−0.983414	+	0.181377i	$0.941945\pi$
$522$		0			0
$523$		−	34.6641i		−	1.51576i	−0.652397	−	0.757878i	$-0.726236\pi$
$523$		−	34.6641i		−	1.51576i	0.652397	−	0.757878i	$-0.273764\pi$
$524$	2.65534	−	1.09988i	0.115999	−	0.0480483i
$525$		0			0
$526$	22.1492			0.965752
$527$	−19.1604	+	0.405854i	−0.834641	+	0.0176793i
$528$		0			0
$529$	−12.2042	−	12.2042i	−0.530617	−	0.530617i
$530$	−3.02992	+	1.25504i	−0.131611	+	0.0545153i
$531$		0			0
$532$	−0.242885	−	0.586376i	−0.0105304	−	0.0254226i
$533$	−0.751270	−	0.311186i	−0.0325411	−	0.0134790i
$534$		0			0
$535$	−13.3818	+	13.3818i	−0.578544	+	0.578544i
$536$	1.67404	−	1.67404i	0.0723074	−	0.0723074i
$537$		0			0
$538$	−25.4743	−	10.5518i	−1.09827	−	0.454920i
$539$	−9.10430	−	21.9797i	−0.392150	−	0.946733i
$540$		0			0
$541$	4.39249	−	1.81943i	0.188848	−	0.0782234i	−0.286256	−	0.958153i	$-0.592411\pi$
$541$	4.39249	−	1.81943i	0.188848	−	0.0782234i	0.475103	+	0.879930i	$0.342411\pi$
$542$	24.7065	+	24.7065i	1.06123	+	1.06123i
$543$		0			0
$544$	3.54084	+	8.06111i	0.151812	+	0.345617i
$545$	19.3552			0.829084
$546$		0			0
$547$	17.9566	−	7.43786i	0.767768	−	0.318020i	0.0357998	−	0.999359i	$-0.488602\pi$
$547$	17.9566	−	7.43786i	0.767768	−	0.318020i	0.731968	+	0.681339i	$0.238602\pi$
$548$		−	3.58499i		−	0.153143i
$549$		0			0
$550$	−5.89277	−	2.44087i	−0.251269	−	0.104079i
$551$	−12.9250	+	31.2037i	−0.550623	+	1.32932i
$552$		0			0
$553$	−1.81048	+	1.81048i	−0.0769896	+	0.0769896i
$554$	12.4018	−	29.9405i	0.526901	−	1.27205i
$555$		0			0
$556$	−0.744208	−	1.79668i	−0.0315615	−	0.0761961i
$557$		−	9.95386i		−	0.421759i	−0.977512	−	0.210879i	$-0.932367\pi$
$557$		−	9.95386i		−	0.421759i	0.977512	−	0.210879i	$-0.0676327\pi$
$558$		0			0
$559$	−32.7140	−	32.7140i	−1.38366	−	1.38366i
$560$	−1.34244			−0.0567286
$561$		0			0
$562$	27.4521			1.15800
$563$	5.03524	+	5.03524i	0.212210	+	0.212210i	0.805206	−	0.592996i	$-0.202055\pi$
$563$	5.03524	+	5.03524i	0.212210	+	0.212210i	−0.592996	+	0.805206i	$0.702055\pi$
$564$		0			0
$565$		−	27.4140i		−	1.15331i
$566$	−4.20943	−	10.1625i	−0.176936	−	0.427161i
$567$		0			0
$568$	9.13070	−	22.0435i	0.383116	−	0.924923i
$569$	17.3432	−	17.3432i	0.727065	−	0.727065i	−0.242969	−	0.970034i	$-0.578121\pi$
$569$	17.3432	−	17.3432i	0.727065	−	0.727065i	0.970034	+	0.242969i	$0.0781215\pi$
$570$		0			0
$571$	−13.5010	+	32.5943i	−0.564999	+	1.36403i	0.340726	+	0.940163i	$0.389327\pi$
$571$	−13.5010	+	32.5943i	−0.564999	+	1.36403i	−0.905725	+	0.423866i	$0.860673\pi$
$572$	6.24108	+	2.58514i	0.260953	+	0.108090i
$573$		0			0
$574$		−	0.0464541i		−	0.00193895i
$575$	3.24209	−	1.34292i	0.135204	−	0.0560035i
$576$		0			0
$577$	−3.41354			−0.142108			−0.0710538	−	0.997472i	$-0.522636\pi$
$577$	−3.41354			−0.142108			−0.0710538	+	0.997472i	$0.522636\pi$
$578$	0.915346	+	21.5971i	0.0380734	+	0.898321i
$579$		0			0
$580$	−2.40216	−	2.40216i	−0.0997442	−	0.0997442i
$581$	0.714711	−	0.296043i	0.0296512	−	0.0122819i
$582$		0			0
$583$	1.79781	+	4.34029i	0.0744575	+	0.179756i
$584$	−8.32482	−	3.44825i	−0.344484	−	0.142690i
$585$		0			0
$586$	−13.9165	+	13.9165i	−0.574885	+	0.574885i
$587$	−11.6891	+	11.6891i	−0.482459	+	0.482459i	−0.905916	−	0.423457i	$-0.860816\pi$
$587$	−11.6891	+	11.6891i	−0.482459	+	0.482459i	0.423457	+	0.905916i	$0.360816\pi$
$588$		0			0
$589$	30.7569	+	12.7399i	1.26732	+	0.524940i
$590$	5.92025	+	14.2928i	0.243733	+	0.588424i
$591$		0			0
$592$	−12.0459	+	4.98958i	−0.495084	+	0.205070i
$593$	5.78039	+	5.78039i	0.237372	+	0.237372i	0.815761	−	0.578389i	$-0.196318\pi$
$593$	5.78039	+	5.78039i	0.237372	+	0.237372i	−0.578389	+	0.815761i	$0.696318\pi$
$594$		0			0
$595$	1.67073	+	0.650939i	0.0684933	+	0.0266859i
$596$	−1.35658			−0.0555676
$597$		0			0
$598$	14.4904	−	6.00210i	0.592555	−	0.245444i
$599$			31.5073i			1.28735i	0.765298	+	0.643676i	$0.222592\pi$
$599$			31.5073i			1.28735i	−0.765298	+	0.643676i	$0.777408\pi$
$600$		0			0
$601$	4.07121	+	1.68635i	0.166068	+	0.0687876i	0.464169	−	0.885747i	$-0.346353\pi$
$601$	4.07121	+	1.68635i	0.166068	+	0.0687876i	−0.298101	+	0.954534i	$0.596353\pi$
$602$	1.01142	−	2.44179i	0.0412224	−	0.0995198i
$603$		0			0
$604$	3.37461	−	3.37461i	0.137311	−	0.137311i
$605$	0.524931	−	1.26729i	0.0213415	−	0.0515228i
$606$		0			0
$607$	14.2244	+	34.3407i	0.577350	+	1.39385i	0.895183	+	0.445699i	$0.147045\pi$
$607$	14.2244	+	34.3407i	0.577350	+	1.39385i	−0.317834	+	0.948147i	$0.602955\pi$
$608$		−	15.2943i		−	0.620265i
$609$		0			0
$610$	21.9616	+	21.9616i	0.889197	+	0.889197i
$611$	41.4491			1.67685
$612$		0			0
$613$	1.50892			0.0609449			0.0304724	−	0.999536i	$-0.490299\pi$
$613$	1.50892			0.0609449			0.0304724	+	0.999536i	$0.490299\pi$
$614$	−28.0007	−	28.0007i	−1.13002	−	1.13002i
$615$		0			0
$616$			2.40037i			0.0967138i
$617$	−15.8882	−	38.3575i	−0.639636	−	1.54422i	−0.827166	−	0.561958i	$-0.810048\pi$
$617$	−15.8882	−	38.3575i	−0.639636	−	1.54422i	0.187530	−	0.982259i	$-0.439952\pi$
$618$		0			0
$619$	12.4230	−	29.9919i	0.499324	−	1.20547i	−0.450525	−	0.892764i	$-0.648763\pi$
$619$	12.4230	−	29.9919i	0.499324	−	1.20547i	0.949848	−	0.312710i	$-0.101237\pi$
$620$	−2.36777	+	2.36777i	−0.0950917	+	0.0950917i
$621$		0			0
$622$	14.3867	−	34.7325i	0.576853	−	1.39265i
$623$	−3.55272	−	1.47159i	−0.142337	−	0.0589579i
$624$		0			0
$625$			15.5317i			0.621269i
$626$	15.7846	−	6.53819i	0.630879	−	0.261318i
$627$		0			0
$628$	4.48142			0.178828
$629$	17.4111	−	0.368800i	0.694225	−	0.0147050i
$630$		0			0
$631$	−8.22064	−	8.22064i	−0.327259	−	0.327259i	0.524284	−	0.851543i	$-0.324333\pi$
$631$	−8.22064	−	8.22064i	−0.327259	−	0.327259i	−0.851543	+	0.524284i	$0.824333\pi$
$632$	−30.9926	+	12.8376i	−1.23282	+	0.510651i
$633$		0			0
$634$	−0.198452	−	0.479106i	−0.00788155	−	0.0190277i
$635$	−5.32292	−	2.20483i	−0.211234	−	0.0874959i
$636$		0			0
$637$	25.2870	−	25.2870i	1.00191	−	1.00191i
$638$	14.5212	−	14.5212i	0.574900	−	0.574900i
$639$		0			0
$640$	−12.2159	−	5.06000i	−0.482877	−	0.200014i
$641$	−5.45090	−	13.1596i	−0.215298	−	0.519775i	0.778924	−	0.627118i	$-0.215766\pi$
$641$	−5.45090	−	13.1596i	−0.215298	−	0.519775i	−0.994222	+	0.107343i	$0.965766\pi$
$642$		0			0
$643$	24.4163	−	10.1136i	0.962886	−	0.398840i	0.154827	−	0.987942i	$-0.450518\pi$
$643$	24.4163	−	10.1136i	0.962886	−	0.398840i	0.808059	+	0.589101i	$0.200518\pi$
$644$	−0.150134	−	0.150134i	−0.00591609	−	0.00591609i
$645$		0			0
$646$	13.6319	−	34.9882i	0.536339	−	1.37659i
$647$	−9.88070			−0.388451			−0.194225	−	0.980957i	$-0.562219\pi$
$647$	−9.88070			−0.388451			−0.194225	+	0.980957i	$0.562219\pi$
$648$		0			0
$649$	20.4740	−	8.48061i	0.803675	−	0.332893i
$650$		−	9.58759i		−	0.376056i
$651$		0			0
$652$	−5.56175	−	2.30375i	−0.217815	−	0.0902219i
$653$	0.789779	−	1.90670i	0.0309065	−	0.0746148i	−0.907673	−	0.419679i	$-0.862143\pi$
$653$	0.789779	−	1.90670i	0.0309065	−	0.0746148i	0.938579	+	0.345064i	$0.112143\pi$
$654$		0			0
$655$	9.97352	−	9.97352i	0.389698	−	0.389698i
$656$	0.186595	−	0.450480i	0.00728531	−	0.0175883i
$657$		0			0
$658$	0.906146	+	2.18763i	0.0353252	+	0.0852827i
$659$			21.3928i			0.833343i	0.909057	+	0.416672i	$0.136804\pi$
$659$			21.3928i			0.833343i	−0.909057	+	0.416672i	$0.863196\pi$
$660$		0			0
$661$	−17.1745	−	17.1745i	−0.668009	−	0.668009i	0.289246	−	0.957255i	$-0.406595\pi$
$661$	−17.1745	−	17.1745i	−0.668009	−	0.668009i	−0.957255	+	0.289246i	$0.906595\pi$
$662$	10.4991			0.408058
$663$		0			0
$664$	10.1356			0.393336
$665$	−2.20244	−	2.20244i	−0.0854071	−	0.0854071i
$666$		0			0
$667$			11.2985i			0.437481i
$668$	−0.758661	−	1.83157i	−0.0293535	−	0.0708656i
$669$		0			0
$670$	0.714805	−	1.72569i	0.0276153	−	0.0666693i
$671$	31.4594	−	31.4594i	1.21447	−	1.21447i
$672$		0			0
$673$	−13.4885	+	32.5641i	−0.519943	+	1.25525i	0.417995	+	0.908449i	$0.362733\pi$
$673$	−13.4885	+	32.5641i	−0.519943	+	1.25525i	−0.937938	+	0.346804i	$0.887267\pi$
$674$	−27.8477	−	11.5349i	−1.07265	−	0.444307i
$675$		0			0
$676$			5.17347i			0.198980i
$677$	1.28360	−	0.531685i	0.0493328	−	0.0204343i	−0.357881	−	0.933767i	$-0.616501\pi$
$677$	1.28360	−	0.531685i	0.0493328	−	0.0204343i	0.407213	+	0.913333i	$0.366501\pi$
$678$		0			0
$679$	3.61633			0.138782
$680$	16.9597	+	16.2561i	0.650375	+	0.623394i
$681$		0			0
$682$	−14.3133	−	14.3133i	−0.548084	−	0.548084i
$683$	29.4135	−	12.1835i	1.12548	−	0.466187i	0.259235	−	0.965814i	$-0.416530\pi$
$683$	29.4135	−	12.1835i	1.12548	−	0.466187i	0.866241	+	0.499627i	$0.166530\pi$
$684$		0			0
$685$	−6.73267	−	16.2541i	−0.257242	−	0.621037i
$686$	3.78939	+	1.56962i	0.144680	+	0.0599283i
$687$		0			0
$688$	19.6162	−	19.6162i	0.747859	−	0.747859i
$689$	−4.99337	+	4.99337i	−0.190232	+	0.190232i
$690$		0			0
$691$	16.1938	+	6.70768i	0.616041	+	0.255172i	0.668809	−	0.743434i	$-0.266804\pi$
$691$	16.1938	+	6.70768i	0.616041	+	0.255172i	−0.0527683	+	0.998607i	$0.516804\pi$
$692$	−2.66149	−	6.42540i	−0.101175	−	0.244257i
$693$		0			0
$694$	34.9546	−	14.4787i	1.32686	−	0.549602i
$695$	−6.74837	−	6.74837i	−0.255980	−	0.255980i
$696$		0			0
$697$	−0.450660	+	0.470165i	−0.0170700	+	0.0178088i
$698$	−23.6146			−0.893827
$699$		0			0
$700$	−0.119910	+	0.0496682i	−0.00453216	+	0.00187728i
$701$		−	26.4148i		−	0.997674i	−0.866696	−	0.498837i	$-0.833761\pi$
$701$		−	26.4148i		−	0.997674i	0.866696	−	0.498837i	$-0.166239\pi$
$702$		0			0
$703$	−27.9488	−	11.5768i	−1.05411	−	0.436627i
$704$	−11.6504	+	28.1265i	−0.439089	+	1.06006i
$705$		0			0
$706$	−29.1912	+	29.1912i	−1.09862	+	1.09862i
$707$	−0.0173190	+	0.0418118i	−0.000651348	+	0.00157249i
$708$		0			0
$709$	4.34914	+	10.4998i	0.163335	+	0.394327i	0.984264	−	0.176704i	$-0.0565436\pi$
$709$	4.34914	+	10.4998i	0.163335	+	0.394327i	−0.820929	+	0.571031i	$0.806544\pi$
$710$		−	18.8249i		−	0.706485i
$711$		0			0
$712$	−35.6258	−	35.6258i	−1.33513	−	1.33513i
$713$	11.1368			0.417076
$714$		0			0
$715$	33.1515			1.23980
$716$	−2.39018	−	2.39018i	−0.0893254	−	0.0893254i
$717$		0			0
$718$		−	39.3654i		−	1.46910i
$719$	5.88854	+	14.2162i	0.219605	+	0.530174i	0.994835	−	0.101505i	$-0.0323659\pi$
$719$	5.88854	+	14.2162i	0.219605	+	0.530174i	−0.775230	+	0.631679i	$0.782366\pi$
$720$		0			0
$721$	−0.0314630	+	0.0759584i	−0.00117174	+	0.00282884i
$722$	−29.0399	+	29.0399i	−1.08075	+	1.08075i
$723$		0			0
$724$	−3.39753	+	8.20237i	−0.126268	+	0.304839i
$725$	6.38093	+	2.64307i	0.236982	+	0.0981611i
$726$		0			0
$727$			43.0876i			1.59803i	0.601311	+	0.799015i	$0.294645\pi$
$727$			43.0876i			1.59803i	−0.601311	+	0.799015i	$0.705355\pi$
$728$	−3.33349	+	1.38078i	−0.123548	+	0.0511751i
$729$		0			0
$730$	−7.10931			−0.263127
$731$	−33.9249	+	14.9015i	−1.25476	+	0.551152i
$732$		0			0
$733$	−17.0745	−	17.0745i	−0.630663	−	0.630663i	0.317572	−	0.948234i	$-0.397133\pi$
$733$	−17.0745	−	17.0745i	−0.630663	−	0.630663i	−0.948234	+	0.317572i	$0.897133\pi$
$734$	−4.39118	+	1.81889i	−0.162082	+	0.0671364i
$735$		0			0
$736$	−1.95795	−	4.72691i	−0.0721709	−	0.174236i
$737$	−2.47201	−	1.02394i	−0.0910576	−	0.0377173i
$738$		0			0
$739$	−0.704902	+	0.704902i	−0.0259302	+	0.0259302i	−0.719953	−	0.694023i	$-0.755837\pi$
$739$	−0.704902	+	0.704902i	−0.0259302	+	0.0259302i	0.694023	+	0.719953i	$0.255837\pi$
$740$	2.15159	−	2.15159i	0.0790940	−	0.0790940i
$741$		0			0
$742$	−0.372707	−	0.154380i	−0.0136825	−	0.00566747i
$743$	−12.4696	−	30.1042i	−0.457463	−	1.10441i	−0.969421	−	0.245404i	$-0.921079\pi$
$743$	−12.4696	−	30.1042i	−0.457463	−	1.10441i	0.511957	−	0.859011i	$-0.328921\pi$
$744$		0			0
$745$	−6.15062	+	2.54767i	−0.225341	+	0.0933394i
$746$	−12.8841	−	12.8841i	−0.471719	−	0.471719i
$747$		0			0
$748$	3.74380	−	3.90583i	0.136887	−	0.142811i
$749$	−2.32790			−0.0850594
$750$		0			0
$751$	32.3860	−	13.4147i	1.18178	−	0.489510i	0.296711	−	0.954967i	$-0.404110\pi$
$751$	32.3860	−	13.4147i	1.18178	−	0.489510i	0.885070	+	0.465457i	$0.154110\pi$
$752$			24.8539i			0.906330i
$753$		0			0
$754$	28.5192	+	11.8131i	1.03861	+	0.430206i
$755$	8.96266	−	21.6378i	0.326185	−	0.787479i
$756$		0			0
$757$	−5.04978	+	5.04978i	−0.183538	+	0.183538i	−0.792895	−	0.609358i	$-0.791427\pi$
$757$	−5.04978	+	5.04978i	−0.183538	+	0.183538i	0.609358	+	0.792895i	$0.291427\pi$
$758$	−7.95527	+	19.2057i	−0.288949	+	0.697584i
$759$		0			0
$760$	−15.6168	−	37.7023i	−0.566481	−	1.36761i
$761$			13.7182i			0.497283i	0.968596	+	0.248641i	$0.0799840\pi$
$761$			13.7182i			0.497283i	−0.968596	+	0.248641i	$0.920016\pi$
$762$		0			0
$763$	1.68352	+	1.68352i	0.0609474	+	0.0609474i
$764$	9.75526			0.352933
$765$		0			0
$766$	14.5397			0.525341
$767$	23.5547	+	23.5547i	0.850511	+	0.850511i
$768$		0			0
$769$			15.2265i			0.549081i	0.961576	+	0.274540i	$0.0885257\pi$
$769$			15.2265i			0.549081i	−0.961576	+	0.274540i	$0.911474\pi$
$770$	0.724747	+	1.74969i	0.0261181	+	0.0630546i
$771$		0			0
$772$	1.19560	−	2.88644i	0.0430307	−	0.103885i
$773$	16.1436	−	16.1436i	0.580645	−	0.580645i	−0.354435	−	0.935080i	$-0.615327\pi$
$773$	16.1436	−	16.1436i	0.580645	−	0.580645i	0.935080	+	0.354435i	$0.115327\pi$
$774$		0			0
$775$	2.60523	−	6.28957i	0.0935824	−	0.225928i
$776$	43.7741	+	18.1318i	1.57140	+	0.650894i
$777$		0			0
$778$		−	46.1052i		−	1.65295i
$779$	1.04520	−	0.432936i	0.0374482	−	0.0155115i
$780$		0			0
$781$	−26.9662			−0.964925
$782$	−0.266017	−	12.5587i	−0.00951276	−	0.449098i
$783$		0			0
$784$	15.1627	+	15.1627i	0.541526	+	0.541526i
$785$	20.3184	−	8.41616i	0.725195	−	0.300386i
$786$		0			0
$787$	1.04824	+	2.53067i	0.0373656	+	0.0902085i	0.941461	−	0.337123i	$-0.109454\pi$
$787$	1.04824	+	2.53067i	0.0373656	+	0.0902085i	−0.904095	+	0.427331i	$0.859454\pi$
$788$	5.05608	+	2.09430i	0.180116	+	0.0746063i
$789$		0			0
$790$	−18.7153	+	18.7153i	−0.665859	+	0.665859i
$791$	2.38447	−	2.38447i	0.0847820	−	0.0847820i
$792$		0			0
$793$	61.7854	+	25.5923i	2.19406	+	0.908810i
$794$	−10.3154	−	24.9035i	−0.366079	−	0.883793i
$795$		0			0
$796$	0.190593	−	0.0789462i	0.00675539	−	0.00279817i
$797$	−4.10012	−	4.10012i	−0.145234	−	0.145234i	0.630751	−	0.775985i	$-0.282747\pi$
$797$	−4.10012	−	4.10012i	−0.145234	−	0.145234i	−0.775985	+	0.630751i	$0.782747\pi$
$798$		0			0
$799$	12.0515	−	30.9318i	0.426350	−	1.09429i
$800$	−3.12757			−0.110576
$801$		0			0
$802$	−9.09939	+	3.76909i	−0.321310	+	0.133091i
$803$			10.1839i			0.359382i
$804$		0			0
$805$	−0.962648	−	0.398742i	−0.0339289	−	0.0140538i
$806$	11.6439	−	28.1109i	0.410140	−	0.990165i
$807$		0			0
$808$	−0.419277	+	0.419277i	−0.0147501	+	0.0147501i
$809$	7.39678	−	17.8574i	0.260057	−	0.627833i	−0.738885	−	0.673832i	$-0.764647\pi$
$809$	7.39678	−	17.8574i	0.260057	−	0.627833i	0.998941	+	0.0459992i	$0.0146472\pi$
$810$		0			0
$811$	2.80344	+	6.76811i	0.0984421	+	0.237660i	0.965427	−	0.260675i	$-0.0839450\pi$
$811$	2.80344	+	6.76811i	0.0984421	+	0.237660i	−0.866985	+	0.498335i	$0.833945\pi$
$812$		−	0.417880i		−	0.0146647i
$813$		0			0
$814$	13.0065	+	13.0065i	0.455877	+	0.455877i
$815$	−29.5430			−1.03485
$816$		0			0
$817$	64.3655			2.25186
$818$	−16.7399	−	16.7399i	−0.585298	−	0.585298i
$819$		0			0
$820$			0.113792i			0.00397378i
$821$	−1.98807	−	4.79963i	−0.0693842	−	0.167508i	0.885383	−	0.464862i	$-0.153896\pi$
$821$	−1.98807	−	4.79963i	−0.0693842	−	0.167508i	−0.954767	+	0.297354i	$0.903896\pi$
$822$		0			0
$823$	−8.80390	+	21.2545i	−0.306885	+	0.740885i	0.692918	+	0.721016i	$0.256325\pi$
$823$	−8.80390	+	21.2545i	−0.306885	+	0.740885i	−0.999803	+	0.0198685i	$0.993675\pi$
$824$	−0.761690	+	0.761690i	−0.0265347	+	0.0265347i
$825$		0			0
$826$	−0.728242	+	1.75813i	−0.0253388	+	0.0611732i
$827$	16.6002	+	6.87603i	0.577245	+	0.239103i	0.652153	−	0.758088i	$-0.273866\pi$
$827$	16.6002	+	6.87603i	0.577245	+	0.239103i	−0.0749073	+	0.997191i	$0.523866\pi$
$828$		0			0
$829$			9.11808i			0.316684i	0.987384	+	0.158342i	$0.0506148\pi$
$829$			9.11808i			0.316684i	−0.987384	+	0.158342i	$0.949385\pi$
$830$	7.38807	−	3.06024i	0.256444	−	0.106222i
$831$		0			0
$832$	−45.7620			−1.58651
$833$	−11.5184	−	26.2230i	−0.399089	−	0.908571i
$834$		0			0
$835$	−6.87943	−	6.87943i	−0.238072	−	0.238072i
$836$	−8.68288	+	3.59656i	−0.300304	+	0.124390i
$837$		0			0
$838$	15.0618	+	36.3624i	0.520301	+	1.25612i
$839$	22.9904	+	9.52294i	0.793717	+	0.328768i	0.742437	−	0.669916i	$-0.233670\pi$
$839$	22.9904	+	9.52294i	0.793717	+	0.328768i	0.0512799	+	0.998684i	$0.483670\pi$
$840$		0			0
$841$	4.78196	−	4.78196i	0.164895	−	0.164895i
$842$	−11.4013	+	11.4013i	−0.392914	+	0.392914i
$843$		0			0
$844$	1.20925	+	0.500889i	0.0416242	+	0.0172413i
$845$	9.71584	+	23.4561i	0.334235	+	0.806915i
$846$		0			0
$847$	0.155888	−	0.0645709i	0.00535638	−	0.00221868i
$848$	−2.99415	−	2.99415i	−0.102820	−	0.102820i
$849$		0			0
$850$	−7.15484	−	2.78762i	−0.245409	−	0.0956146i
$851$	−10.1200			−0.346909
$852$		0			0
$853$	−53.3267	+	22.0886i	−1.82587	+	0.756300i	−0.854205	+	0.519936i	$0.825956\pi$
$853$	−53.3267	+	22.0886i	−1.82587	+	0.756300i	−0.971664	+	0.236364i	$0.924044\pi$
$854$			3.82044i			0.130733i
$855$		0			0
$856$	−28.1781	−	11.6718i	−0.963108	−	0.398932i
$857$	4.66282	−	11.2570i	0.159279	−	0.384533i	−0.824013	−	0.566572i	$-0.808269\pi$
$857$	4.66282	−	11.2570i	0.159279	−	0.384533i	0.983291	+	0.182038i	$0.0582695\pi$
$858$		0			0
$859$	−23.1913	+	23.1913i	−0.791276	+	0.791276i	−0.981702	−	0.190426i	$-0.939013\pi$
$859$	−23.1913	+	23.1913i	−0.791276	+	0.791276i	0.190426	+	0.981702i	$0.439013\pi$
$860$	−2.47753	+	5.98129i	−0.0844831	+	0.203960i
$861$		0			0
$862$	−2.13443	−	5.15298i	−0.0726991	−	0.175511i
$863$			34.6709i			1.18021i	0.807326	+	0.590106i	$0.200914\pi$
$863$			34.6709i			1.18021i	−0.807326	+	0.590106i	$0.799086\pi$
$864$		0			0
$865$	−24.1340	−	24.1340i	−0.820581	−	0.820581i
$866$	−30.1730			−1.02532
$867$		0			0
$868$	−0.411897			−0.0139807
$869$	26.8091	+	26.8091i	0.909437	+	0.909437i
$870$		0			0
$871$		−	4.02198i		−	0.136280i
$872$	11.9373	+	28.8191i	0.404247	+	0.975938i
$873$		0			0
$874$	−8.35040	+	20.1596i	−0.282456	+	0.681910i
$875$	−1.98792	+	1.98792i	−0.0672040	+	0.0672040i
$876$		0			0
$877$	11.8544	−	28.6190i	0.400294	−	0.966395i	−0.587300	−	0.809369i	$-0.699809\pi$
$877$	11.8544	−	28.6190i	0.400294	−	0.966395i	0.987594	−	0.157026i	$-0.0501907\pi$
$878$	−18.9008	−	7.82895i	−0.637869	−	0.264214i
$879$		0			0
$880$			19.8785i			0.670104i
$881$	−30.8849	+	12.7929i	−1.04054	+	0.431005i	−0.836505	−	0.547960i	$-0.815405\pi$
$881$	−30.8849	+	12.7929i	−1.04054	+	0.431005i	−0.204032	+	0.978964i	$0.565405\pi$
$882$		0			0
$883$	18.2136			0.612938			0.306469	−	0.951881i	$-0.400852\pi$
$883$	18.2136			0.612938			0.306469	+	0.951881i	$0.400852\pi$
$884$	7.57775	+	2.95239i	0.254867	+	0.0992997i
$885$		0			0
$886$	−1.09953	−	1.09953i	−0.0369393	−	0.0369393i
$887$	51.9613	−	21.5231i	1.74469	−	0.722675i	0.746322	−	0.665585i	$-0.231818\pi$
$887$	51.9613	−	21.5231i	1.74469	−	0.722675i	0.998369	−	0.0570891i	$-0.0181819\pi$
$888$		0			0
$889$	−0.271212	−	0.654765i	−0.00909617	−	0.0219601i
$890$	−36.7250	−	15.2120i	−1.23103	−	0.509908i
$891$		0			0
$892$	−5.46933	+	5.46933i	−0.183127	+	0.183127i
$893$	−40.7759	+	40.7759i	−1.36451	+	1.36451i
$894$		0			0
$895$	−15.3257	−	6.34812i	−0.512282	−	0.212194i
$896$	−0.622424	−	1.50266i	−0.0207937	−	0.0502005i
$897$		0			0
$898$	−27.5714	+	11.4205i	−0.920070	+	0.381105i
$899$	15.4990	+	15.4990i	0.516921	+	0.516921i
$900$		0			0
$901$	2.27452	+	5.17819i	0.0757751	+	0.172511i
$902$	−0.687878			−0.0229038
$903$		0			0
$904$	40.8184	−	16.9075i	1.35760	−	0.562336i
$905$			43.5695i			1.44830i
$906$		0			0
$907$	8.79621	+	3.64351i	0.292073	+	0.120981i	0.523909	−	0.851774i	$-0.324473\pi$
$907$	8.79621	+	3.64351i	0.292073	+	0.120981i	−0.231836	+	0.972755i	$0.574473\pi$
$908$	−0.211360	+	0.510268i	−0.00701422	+	0.0169338i
$909$		0			0
$910$	−2.01297	+	2.01297i	−0.0667293	+	0.0667293i
$911$	−5.72937	+	13.8319i	−0.189822	+	0.458272i	−0.989925	−	0.141591i	$-0.954778\pi$
$911$	−5.72937	+	13.8319i	−0.189822	+	0.458272i	0.800103	+	0.599863i	$0.204778\pi$
$912$		0			0
$913$	−4.38371	−	10.5832i	−0.145080	−	0.350253i
$914$			49.1155i			1.62460i
$915$		0			0
$916$	−2.85132	−	2.85132i	−0.0942102	−	0.0942102i
$917$	1.73500			0.0572946
$918$		0			0
$919$	−12.5474			−0.413900			−0.206950	−	0.978352i	$-0.566354\pi$
$919$	−12.5474			−0.413900			−0.206950	+	0.978352i	$0.566354\pi$
$920$	−9.65317	−	9.65317i	−0.318256	−	0.318256i
$921$		0			0
$922$			22.8030i			0.750975i
$923$	−15.5119	−	37.4490i	−0.510579	−	1.23265i
$924$		0			0
$925$	−2.36737	+	5.71534i	−0.0778386	+	0.187919i
$926$	8.73304	−	8.73304i	0.286985	−	0.286985i
$927$		0			0
$928$	3.85354	−	9.30328i	0.126499	−	0.305395i
$929$	−1.63949	−	0.679101i	−0.0537901	−	0.0222806i	0.355626	−	0.934628i	$-0.384268\pi$
$929$	−1.63949	−	0.679101i	−0.0537901	−	0.0222806i	−0.409416	+	0.912348i	$0.634268\pi$
$930$		0			0
$931$			49.7526i			1.63058i
$932$	4.75942	−	1.97142i	0.155900	−	0.0645759i
$933$		0			0
$934$	−42.7560			−1.39902
$935$	9.63891	−	24.7397i	0.315226	−	0.809074i
$936$		0			0
$937$	18.7440	+	18.7440i	0.612341	+	0.612341i	0.943556	−	0.331214i	$-0.107458\pi$
$937$	18.7440	+	18.7440i	0.612341	+	0.612341i	−0.331214	+	0.943556i	$0.607458\pi$
$938$	0.212275	−	0.0879271i	0.00693102	−	0.00287092i
$939$		0			0
$940$	−2.21965	−	5.35871i	−0.0723971	−	0.174782i
$941$	30.4275	+	12.6035i	0.991910	+	0.410862i	0.818824	−	0.574044i	$-0.194626\pi$
$941$	30.4275	+	12.6035i	0.991910	+	0.410862i	0.173085	+	0.984907i	$0.444626\pi$
$942$		0			0
$943$	0.267609	−	0.267609i	0.00871456	−	0.00871456i
$944$	−14.1240	+	14.1240i	−0.459697	+	0.459697i
$945$		0			0
$946$	−36.1572	−	14.9768i	−1.17557	−	0.486938i
$947$	3.13524	+	7.56914i	0.101882	+	0.245964i	0.966598	−	0.256296i	$-0.0825021\pi$
$947$	3.13524	+	7.56914i	0.101882	+	0.245964i	−0.864717	+	0.502260i	$0.832502\pi$
$948$		0			0
$949$	−14.1428	+	5.85813i	−0.459094	+	0.190163i
$950$	9.43188	+	9.43188i	0.306011	+	0.306011i
$951$		0			0
$952$	0.0611971	+	2.88912i	0.00198341	+	0.0936369i
$953$	−17.5763			−0.569353			−0.284676	−	0.958624i	$-0.591886\pi$
$953$	−17.5763			−0.569353			−0.284676	+	0.958624i	$0.591886\pi$
$954$		0			0
$955$	44.2296	−	18.3205i	1.43124	−	0.592838i
$956$		−	6.63675i		−	0.214648i
$957$		0			0
$958$	−34.3918	−	14.2456i	−1.11115	−	0.460253i
$959$	0.828176	−	1.99939i	0.0267432	−	0.0645638i
$960$		0			0
$961$	−6.64322	+	6.64322i	−0.214297	+	0.214297i
$962$	−10.5808	+	25.5444i	−0.341140	+	0.823585i
$963$		0			0
$964$	2.17540	+	5.25187i	0.0700648	+	0.169151i
$965$		−	15.3323i		−	0.493564i
$966$		0			0
$967$	−29.1425	−	29.1425i	−0.937159	−	0.937159i	0.0609800	−	0.998139i	$-0.480577\pi$
$967$	−29.1425	−	29.1425i	−0.937159	−	0.937159i	−0.998139	+	0.0609800i	$0.980577\pi$
$968$	2.21070			0.0710547
$969$		0			0
$970$	37.3826			1.20028
$971$	41.3050	+	41.3050i	1.32554	+	1.32554i	0.909217	+	0.416323i	$0.136681\pi$
$971$	41.3050	+	41.3050i	1.32554	+	1.32554i	0.416323	+	0.909217i	$0.363319\pi$
$972$		0			0
$973$		−	1.17395i		−	0.0376351i
$974$	13.3066	+	32.1250i	0.426371	+	1.02935i
$975$		0			0
$976$	−15.3458	+	37.0481i	−0.491207	+	1.18588i
$977$	−33.8659	+	33.8659i	−1.08347	+	1.08347i	−0.0872814	+	0.996184i	$0.527818\pi$
$977$	−33.8659	+	33.8659i	−1.08347	+	1.08347i	−0.996184	+	0.0872814i	$0.972182\pi$
$978$		0			0
$979$	−21.7908	+	52.6077i	−0.696437	+	1.68135i
$980$	−4.62336	−	1.91506i	−0.147688	−	0.0611743i
$981$		0			0
$982$			1.03151i			0.0329167i
$983$	5.15743	−	2.13628i	0.164496	−	0.0681366i	−0.298916	−	0.954279i	$-0.596625\pi$
$983$	5.15743	−	2.13628i	0.164496	−	0.0681366i	0.463412	+	0.886143i	$0.346625\pi$
$984$		0			0
$985$	26.8570			0.855736
$986$	17.1077	−	17.8481i	0.544819	−	0.568399i
$987$		0			0
$988$	−9.98938	−	9.98938i	−0.317805	−	0.317805i
$989$	19.8930	−	8.23996i	0.632561	−	0.262015i
$990$		0			0
$991$	23.0317	+	55.6036i	0.731628	+	1.76631i	0.637097	+	0.770783i	$0.280135\pi$
$991$	23.0317	+	55.6036i	0.731628	+	1.76631i	0.0945302	+	0.995522i	$0.469865\pi$
$992$	−9.17008	−	3.79837i	−0.291150	−	0.120598i
$993$		0			0
$994$	1.63739	−	1.63739i	0.0519349	−	0.0519349i
$995$	0.715873	−	0.715873i	0.0226947	−	0.0226947i
$996$		0			0
$997$	35.0330	+	14.5112i	1.10951	+	0.459573i	0.860768	−	0.508998i	$-0.169984\pi$
$997$	35.0330	+	14.5112i	1.10951	+	0.459573i	0.248739	+	0.968571i	$0.419984\pi$
$998$	−13.8873	−	33.5270i	−0.439596	−	1.06128i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.l.a.325.9	yes	48
3.2	odd	2	inner	459.2.l.a.325.4	yes	48
17.3	odd	16		7803.2.a.cg.1.17		24
17.9	even	8	inner	459.2.l.a.298.9	yes	48
17.14	odd	16		7803.2.a.cd.1.17		24
51.14	even	16		7803.2.a.cg.1.8		24
51.20	even	16		7803.2.a.cd.1.8		24
51.26	odd	8	inner	459.2.l.a.298.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.l.a.298.4	✓	48	51.26	odd	8	inner
459.2.l.a.298.9	yes	48	17.9	even	8	inner
459.2.l.a.325.4	yes	48	3.2	odd	2	inner
459.2.l.a.325.9	yes	48	1.1	even	1	trivial
7803.2.a.cd.1.8		24	51.20	even	16
7803.2.a.cd.1.17		24	17.14	odd	16
7803.2.a.cg.1.8		24	51.14	even	16
7803.2.a.cg.1.17		24	17.3	odd	16

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.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.899127 + 0.899127i) q^{2} -0.383141i q^{4} +(-0.719544 - 1.73713i) q^{5} +(0.0885100 - 0.213682i) q^{7} +(2.14275 - 2.14275i) q^{8} +(0.914941 - 2.20886i) q^{10} +(-3.16414 - 1.31063i) q^{11} -5.14809i q^{13} +(0.271709 - 0.112546i) q^{14} +3.08692 q^{16} +(-3.84181 - 1.49682i) q^{17} +(5.06448 + 5.06448i) q^{19} +(-0.665566 + 0.275686i) q^{20} +(-1.66654 - 4.02339i) q^{22} +(2.21359 + 0.916899i) q^{23} +(1.03565 - 1.03565i) q^{25} +(4.62878 - 4.62878i) q^{26} +(-0.0818703 - 0.0339118i) q^{28} +(1.80460 + 4.35669i) q^{29} +(4.29431 - 1.77876i) q^{31} +(-1.50996 - 1.50996i) q^{32} +(-2.10845 - 4.80011i) q^{34} -0.434881 q^{35} +(-3.90224 + 1.61636i) q^{37} +9.10722i q^{38} +(-5.26403 - 2.18043i) q^{40} +(0.0604469 - 0.145932i) q^{41} +(6.35460 - 6.35460i) q^{43} +(-0.502156 + 1.21231i) q^{44} +(1.16589 + 2.81471i) q^{46} +8.05136i q^{47} +(4.91192 + 4.91192i) q^{49} +1.86236 q^{50} -1.97244 q^{52} +(-0.969947 - 0.969947i) q^{53} +6.43958i q^{55} +(-0.268212 - 0.647521i) q^{56} +(-2.29465 + 5.53978i) q^{58} +(-4.57543 + 4.57543i) q^{59} +(-4.97123 + 12.0016i) q^{61} +(5.46046 + 2.26180i) q^{62} -8.88913i q^{64} +(-8.94290 + 3.70427i) q^{65} +0.781257 q^{67} +(-0.573493 + 1.47195i) q^{68} +(-0.391013 - 0.391013i) q^{70} +(7.27435 - 3.01313i) q^{71} +(-1.13792 - 2.74719i) q^{73} +(-4.96192 - 2.05530i) q^{74} +(1.94041 - 1.94041i) q^{76} +(-0.560116 + 0.560116i) q^{77} +(-10.2276 - 4.23640i) q^{79} +(-2.22117 - 5.36239i) q^{80} +(0.185561 - 0.0768618i) q^{82} +(2.36509 + 2.36509i) q^{83} +(0.164176 + 7.75076i) q^{85} +11.4272 q^{86} +(-9.58830 + 3.97160i) q^{88} -16.6262i q^{89} +(-1.10005 - 0.455657i) q^{91} +(0.351301 - 0.848116i) q^{92} +(-7.23920 + 7.23920i) q^{94} +(5.15355 - 12.4418i) q^{95} +(5.98350 + 14.4454i) q^{97} +8.83288i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{10} - 48 q^{16} - 16 q^{19} - 24 q^{22} + 16 q^{25} + 24 q^{28} - 40 q^{31} + 64 q^{34} + 48 q^{37} - 48 q^{40} - 8 q^{43} + 24 q^{46} - 16 q^{49} + 32 q^{52} + 64 q^{58} - 24 q^{61} - 32 q^{67}+ \cdots - 88 q^{97}+O(q^{100}) \) 48 * q - 16 * q^10 - 48 * q^16 - 16 * q^19 - 24 * q^22 + 16 * q^25 + 24 * q^28 - 40 * q^31 + 64 * q^34 + 48 * q^37 - 48 * q^40 - 8 * q^43 + 24 * q^46 - 16 * q^49 + 32 * q^52 + 64 * q^58 - 24 * q^61 - 32 * q^67 + 96 * q^70 + 48 * q^73 + 96 * q^76 - 48 * q^79 + 112 * q^82 - 56 * q^85 - 160 * q^88 - 80 * q^91 - 40 * q^94 - 88 * q^97

Introduction

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