LMFDB - Embedded newform 351.2.e.c.118.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(118,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.118"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12] 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 3 x^{10} - x^{9} - 2 x^{8} + 9 x^{7} + 24 x^{6} + 27 x^{5} - 18 x^{4} - 27 x^{3} + \cdots + 729 $ x^12 - x^11 - 3x^10 - x^9 - 2x^8 + 9x^7 + 24x^6 + 27x^5 - 18x^4 - 27x^3 - 243x^2 - 243*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.4
Root			$1.70010 - 0.331167i$ of defining polynomial
Character	$\chi$	$=$	351.118
Dual form			351.2.e.c.235.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.129090 - 0.223591i) q^{2} +(0.966671 - 1.67432i) q^{4} +(1.73641 - 3.00755i) q^{5} +(2.21165 + 3.83070i) q^{7} -1.01551 q^{8} -0.896615 q^{10} +(0.0632497 + 0.109552i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.571006 - 0.989012i) q^{14} +(-1.80225 - 3.12159i) q^{16} -0.346319 q^{17} -0.863955 q^{19} +(-3.35707 - 5.81462i) q^{20} +(0.0163299 - 0.0282841i) q^{22} +(-4.05879 + 7.03003i) q^{23} +(-3.53023 - 6.11454i) q^{25} -0.258181 q^{26} +8.55177 q^{28} +(-1.25024 - 2.16549i) q^{29} +(3.01390 - 5.22023i) q^{31} +(-1.48082 + 2.56485i) q^{32} +(0.0447064 + 0.0774338i) q^{34} +15.3613 q^{35} -2.44616 q^{37} +(0.111528 + 0.193173i) q^{38} +(-1.76335 + 3.05421i) q^{40} +(2.36645 - 4.09881i) q^{41} +(3.36581 + 5.82976i) q^{43} +0.244567 q^{44} +2.09580 q^{46} +(0.107498 + 0.186192i) q^{47} +(-6.28282 + 10.8822i) q^{49} +(-0.911438 + 1.57866i) q^{50} +(-0.966671 - 1.67432i) q^{52} +4.02070 q^{53} +0.439310 q^{55} +(-2.24596 - 3.89012i) q^{56} +(-0.322789 + 0.559087i) q^{58} +(-6.87049 + 11.9000i) q^{59} +(1.36331 + 2.36132i) q^{61} -1.55626 q^{62} -6.44436 q^{64} +(-1.73641 - 3.00755i) q^{65} +(-2.00833 + 3.47853i) q^{67} +(-0.334776 + 0.579850i) q^{68} +(-1.98300 - 3.43466i) q^{70} -8.55239 q^{71} -9.17500 q^{73} +(0.315775 + 0.546939i) q^{74} +(-0.835161 + 1.44654i) q^{76} +(-0.279773 + 0.484581i) q^{77} +(-0.216092 - 0.374282i) q^{79} -12.5178 q^{80} -1.22194 q^{82} +(-0.520310 - 0.901203i) q^{83} +(-0.601351 + 1.04157i) q^{85} +(0.868988 - 1.50513i) q^{86} +(-0.0642309 - 0.111251i) q^{88} +10.8984 q^{89} +4.42331 q^{91} +(7.84703 + 13.5915i) q^{92} +(0.0277539 - 0.0480712i) q^{94} +(-1.50018 + 2.59839i) q^{95} +(-0.0894355 - 0.154907i) q^{97} +3.24421 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + 12 q^{8} - 12 q^{10} - 7 q^{11} + 6 q^{13} - 13 q^{14} - 6 q^{16} + 28 q^{17} - 6 q^{19} - 17 q^{20} + 3 q^{22} - 17 q^{23} - 3 q^{25} - 4 q^{26} + 30 q^{28} - 14 q^{29}+ \cdots + 34 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + 12 * q^8 - 12 * q^10 - 7 * q^11 + 6 * q^13 - 13 * q^14 - 6 * q^16 + 28 * q^17 - 6 * q^19 - 17 * q^20 + 3 * q^22 - 17 * q^23 - 3 * q^25 - 4 * q^26 + 30 * q^28 - 14 * q^29 - 6 * q^31 - 9 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 + 4 * q^38 + 6 * q^40 + 4 * q^41 + 3 * q^43 + 26 * q^44 - 9 * q^47 + 21 * q^50 + 6 * q^52 + 56 * q^53 + 30 * q^55 - 16 * q^56 - 18 * q^58 - 17 * q^59 + 6 * q^61 - 8 * q^62 - 60 * q^64 + 3 * q^65 + 12 * q^67 - 22 * q^68 - 9 * q^70 - 2 * q^71 - 18 * q^73 + 27 * q^74 + 3 * q^76 - 15 * q^77 + 6 * q^79 - 48 * q^80 + 54 * q^82 - 28 * q^83 - 27 * q^85 + 6 * q^86 + 9 * q^88 - 18 * q^89 - 44 * q^92 + 24 * q^94 - 32 * q^95 + 34 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.129090	−	0.223591i	−0.0912807	−	0.158103i	0.816770	−	0.576964i	$-0.195763\pi$
$2$	−0.129090	−	0.223591i	−0.0912807	−	0.158103i	−0.908050	+	0.418861i	$0.862429\pi$
$3$		0			0
$3$		0			0
$4$	0.966671	−	1.67432i	0.483336	−	0.837162i
$5$	1.73641	−	3.00755i	0.776546	−	1.34502i	−0.157376	−	0.987539i	$-0.550303\pi$
$5$	1.73641	−	3.00755i	0.776546	−	1.34502i	0.933922	−	0.357478i	$-0.116363\pi$
$6$		0			0
$7$	2.21165	+	3.83070i	0.835927	+	1.44787i	0.893274	+	0.449513i	$0.148402\pi$
$7$	2.21165	+	3.83070i	0.835927	+	1.44787i	−0.0573473	+	0.998354i	$0.518264\pi$
$8$	−1.01551			−0.359038
$9$		0			0
$10$	−0.896615			−0.283534
$11$	0.0632497	+	0.109552i	0.0190705	+	0.0330311i	0.875403	−	0.483394i	$-0.160596\pi$
$11$	0.0632497	+	0.109552i	0.0190705	+	0.0330311i	−0.856333	+	0.516425i	$0.827263\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	0.571006	−	0.989012i	0.152608	−	0.264325i
$15$		0			0
$16$	−1.80225	−	3.12159i	−0.450562	−	0.780397i
$17$	−0.346319			−0.0839947			−0.0419973	−	0.999118i	$-0.513372\pi$
$17$	−0.346319			−0.0839947			−0.0419973	+	0.999118i	$0.513372\pi$
$18$		0			0
$19$	−0.863955			−0.198205			−0.0991024	−	0.995077i	$-0.531597\pi$
$19$	−0.863955			−0.198205			−0.0991024	+	0.995077i	$0.531597\pi$
$20$	−3.35707	−	5.81462i	−0.750665	−	1.30019i
$21$		0			0
$22$	0.0163299	−	0.0282841i	0.00348154	−	0.00603020i
$23$	−4.05879	+	7.03003i	−0.846316	+	1.46586i	0.0381573	+	0.999272i	$0.487851\pi$
$23$	−4.05879	+	7.03003i	−0.846316	+	1.46586i	−0.884473	+	0.466591i	$0.845482\pi$
$24$		0			0
$25$	−3.53023	−	6.11454i	−0.706047	−	1.22291i
$26$	−0.258181			−0.0506334
$27$		0			0
$28$	8.55177			1.61613
$29$	−1.25024	−	2.16549i	−0.232165	−	0.402121i	0.726280	−	0.687399i	$-0.241247\pi$
$29$	−1.25024	−	2.16549i	−0.232165	−	0.402121i	−0.958445	+	0.285278i	$0.907914\pi$
$30$		0			0
$31$	3.01390	−	5.22023i	0.541313	−	0.937582i	−0.457516	−	0.889201i	$-0.651261\pi$
$31$	3.01390	−	5.22023i	0.541313	−	0.937582i	0.998829	−	0.0483803i	$-0.0154059\pi$
$32$	−1.48082	+	2.56485i	−0.261774	+	0.453406i
$33$		0			0
$34$	0.0447064	+	0.0774338i	0.00766709	+	0.0132798i
$35$	15.3613			2.59654
$36$		0			0
$37$	−2.44616			−0.402146			−0.201073	−	0.979576i	$-0.564443\pi$
$37$	−2.44616			−0.402146			−0.201073	+	0.979576i	$0.564443\pi$
$38$	0.111528	+	0.193173i	0.0180923	+	0.0313367i
$39$		0			0
$40$	−1.76335	+	3.05421i	−0.278810	+	0.482912i
$41$	2.36645	−	4.09881i	0.369577	−	0.640127i	−0.619922	−	0.784663i	$-0.712836\pi$
$41$	2.36645	−	4.09881i	0.369577	−	0.640127i	0.989499	+	0.144537i	$0.0461692\pi$
$42$		0			0
$43$	3.36581	+	5.82976i	0.513281	+	0.889030i	0.999881	+	0.0154046i	$0.00490364\pi$
$43$	3.36581	+	5.82976i	0.513281	+	0.889030i	−0.486600	+	0.873625i	$0.661763\pi$
$44$	0.244567			0.0368698
$45$		0			0
$46$	2.09580			0.309009
$47$	0.107498	+	0.186192i	0.0156802	+	0.0271589i	0.873759	−	0.486359i	$-0.161675\pi$
$47$	0.107498	+	0.186192i	0.0156802	+	0.0271589i	−0.858079	+	0.513518i	$0.828342\pi$
$48$		0			0
$49$	−6.28282	+	10.8822i	−0.897546	+	1.55460i
$50$	−0.911438	+	1.57866i	−0.128897	+	0.223256i
$51$		0			0
$52$	−0.966671	−	1.67432i	−0.134053	−	0.232187i
$53$	4.02070			0.552285			0.276142	−	0.961117i	$-0.410944\pi$
$53$	4.02070			0.552285			0.276142	+	0.961117i	$0.410944\pi$
$54$		0			0
$55$	0.439310			0.0592365
$56$	−2.24596	−	3.89012i	−0.300130	−	0.519840i
$57$		0			0
$58$	−0.322789	+	0.559087i	−0.0423843	+	0.0734117i
$59$	−6.87049	+	11.9000i	−0.894461	+	1.54925i	−0.0599909	+	0.998199i	$0.519107\pi$
$59$	−6.87049	+	11.9000i	−0.894461	+	1.54925i	−0.834470	+	0.551053i	$0.814226\pi$
$60$		0			0
$61$	1.36331	+	2.36132i	0.174554	+	0.302336i	0.940007	−	0.341156i	$-0.110818\pi$
$61$	1.36331	+	2.36132i	0.174554	+	0.302336i	−0.765453	+	0.643492i	$0.777485\pi$
$62$	−1.55626			−0.197646
$63$		0			0
$64$	−6.44436			−0.805545
$65$	−1.73641	−	3.00755i	−0.215375	−	0.373041i
$66$		0			0
$67$	−2.00833	+	3.47853i	−0.245356	+	0.424970i	−0.962232	−	0.272232i	$-0.912238\pi$
$67$	−2.00833	+	3.47853i	−0.245356	+	0.424970i	0.716875	+	0.697201i	$0.245572\pi$
$68$	−0.334776	+	0.579850i	−0.0405976	+	0.0703171i
$69$		0			0
$70$	−1.98300	−	3.43466i	−0.237014	−	0.410520i
$71$	−8.55239			−1.01498			−0.507491	−	0.861657i	$-0.669427\pi$
$71$	−8.55239			−1.01498			−0.507491	+	0.861657i	$0.669427\pi$
$72$		0			0
$73$	−9.17500			−1.07385			−0.536926	−	0.843629i	$-0.680415\pi$
$73$	−9.17500			−1.07385			−0.536926	+	0.843629i	$0.680415\pi$
$74$	0.315775	+	0.546939i	0.0367081	+	0.0635803i
$75$		0			0
$76$	−0.835161	+	1.44654i	−0.0957995	+	0.165930i
$77$	−0.279773	+	0.484581i	−0.0318831	+	0.0552231i
$78$		0			0
$79$	−0.216092	−	0.374282i	−0.0243122	−	0.0421100i	0.853613	−	0.520907i	$-0.174406\pi$
$79$	−0.216092	−	0.374282i	−0.0243122	−	0.0421100i	−0.877926	+	0.478797i	$0.841073\pi$
$80$	−12.5178			−1.39953
$81$		0			0
$82$	−1.22194			−0.134941
$83$	−0.520310	−	0.901203i	−0.0571114	−	0.0989198i	0.836056	−	0.548644i	$-0.184856\pi$
$83$	−0.520310	−	0.901203i	−0.0571114	−	0.0989198i	−0.893168	+	0.449724i	$0.851522\pi$
$84$		0			0
$85$	−0.601351	+	1.04157i	−0.0652257	+	0.112974i
$86$	0.868988	−	1.50513i	0.0937053	−	0.162302i
$87$		0			0
$88$	−0.0642309	−	0.111251i	−0.00684704	−	0.0118594i
$89$	10.8984			1.15523			0.577614	−	0.816310i	$-0.303984\pi$
$89$	10.8984			1.15523			0.577614	+	0.816310i	$0.303984\pi$
$90$		0			0
$91$	4.42331			0.463689
$92$	7.84703	+	13.5915i	0.818109	+	1.41701i
$93$		0			0
$94$	0.0277539	−	0.0480712i	0.00286260	−	0.00495817i
$95$	−1.50018	+	2.59839i	−0.153915	+	0.266589i
$96$		0			0
$97$	−0.0894355	−	0.154907i	−0.00908080	−	0.0157284i	0.861449	−	0.507844i	$-0.169557\pi$
$97$	−0.0894355	−	0.154907i	−0.00908080	−	0.0157284i	−0.870530	+	0.492115i	$0.836224\pi$
$98$	3.24421			0.327715
$99$		0			0
$100$	−13.6503			−1.36503
$101$	6.46044	+	11.1898i	0.642838	+	1.11343i	0.984796	+	0.173713i	$0.0555766\pi$
$101$	6.46044	+	11.1898i	0.642838	+	1.11343i	−0.341958	+	0.939715i	$0.611090\pi$
$102$		0			0
$103$	3.06676	−	5.31178i	0.302177	−	0.523385i	−0.674452	−	0.738319i	$-0.735620\pi$
$103$	3.06676	−	5.31178i	0.302177	−	0.523385i	0.976629	+	0.214933i	$0.0689535\pi$
$104$	−0.507757	+	0.879460i	−0.0497896	+	0.0862382i
$105$		0			0
$106$	−0.519033	−	0.898991i	−0.0504129	−	0.0873178i
$107$	15.9671			1.54360			0.771801	−	0.635864i	$-0.219356\pi$
$107$	15.9671			1.54360			0.771801	+	0.635864i	$0.219356\pi$
$108$		0			0
$109$	−3.73167			−0.357429			−0.178715	−	0.983901i	$-0.557194\pi$
$109$	−3.73167			−0.357429			−0.178715	+	0.983901i	$0.557194\pi$
$110$	−0.0567106	−	0.0982257i	−0.00540715	−	0.00936545i
$111$		0			0
$112$	7.97190	−	13.8077i	0.753274	−	1.30471i
$113$	−7.85519	+	13.6056i	−0.738954	+	1.27991i	0.214013	+	0.976831i	$0.431347\pi$
$113$	−7.85519	+	13.6056i	−0.738954	+	1.27991i	−0.952967	+	0.303075i	$0.901987\pi$
$114$		0			0
$115$	14.0954	+	24.4140i	1.31441	+	2.27662i
$116$	−4.83430			−0.448854
$117$		0			0
$118$	3.54765			0.326588
$119$	−0.765937	−	1.32664i	−0.0702134	−	0.121613i
$120$		0			0
$121$	5.49200	−	9.51242i	0.499273	−	0.864766i
$122$	0.351980	−	0.609647i	0.0318668	−	0.0551949i
$123$		0			0
$124$	−5.82691	−	10.0925i	−0.523272	−	0.906333i
$125$	−7.15563			−0.640019
$126$		0			0
$127$	14.0100			1.24319			0.621594	−	0.783340i	$-0.286486\pi$
$127$	14.0100			1.24319			0.621594	+	0.783340i	$0.286486\pi$
$128$	3.79354	+	6.57061i	0.335305	+	0.580765i
$129$		0			0
$130$	−0.448307	+	0.776491i	−0.0393192	+	0.0681028i
$131$	2.92767	−	5.07088i	0.255792	−	0.443045i	−0.709318	−	0.704888i	$-0.750997\pi$
$131$	2.92767	−	5.07088i	0.255792	−	0.443045i	0.965110	+	0.261844i	$0.0843305\pi$
$132$		0			0
$133$	−1.91077	−	3.30955i	−0.165685	−	0.286974i
$134$	1.03702			0.0895852
$135$		0			0
$136$	0.351691			0.0301573
$137$	−8.47896	−	14.6860i	−0.724406	−	1.25471i	−0.959218	−	0.282667i	$-0.908781\pi$
$137$	−8.47896	−	14.6860i	−0.724406	−	1.25471i	0.234812	−	0.972041i	$-0.424553\pi$
$138$		0			0
$139$	−5.36604	+	9.29425i	−0.455142	+	0.788328i	−0.998696	−	0.0510454i	$-0.983745\pi$
$139$	−5.36604	+	9.29425i	−0.455142	+	0.788328i	0.543555	+	0.839374i	$0.317078\pi$
$140$	14.8494	−	25.7199i	1.25500	−	2.17373i
$141$		0			0
$142$	1.10403	+	1.91224i	0.0926483	+	0.160472i
$143$	0.126499			0.0105784
$144$		0			0
$145$	−8.68375			−0.721146
$146$	1.18440	+	2.05145i	0.0980220	+	0.169779i
$147$		0			0
$148$	−2.36463	+	4.09566i	−0.194371	+	0.336661i
$149$	2.98801	−	5.17539i	0.244787	−	0.423984i	−0.717284	−	0.696781i	$-0.754615\pi$
$149$	2.98801	−	5.17539i	0.244787	−	0.423984i	0.962072	+	0.272796i	$0.0879485\pi$
$150$		0			0
$151$	−9.59560	−	16.6201i	−0.780879	−	1.35252i	−0.931430	−	0.363920i	$-0.881438\pi$
$151$	−9.59560	−	16.6201i	−0.780879	−	1.35252i	0.150551	−	0.988602i	$-0.451895\pi$
$152$	0.877358			0.0711631
$153$		0			0
$154$	0.144464			0.0116412
$155$	−10.4667	−	18.1289i	−0.840709	−	1.45615i
$156$		0			0
$157$	−9.50028	+	16.4550i	−0.758205	+	1.31325i	0.185560	+	0.982633i	$0.440590\pi$
$157$	−9.50028	+	16.4550i	−0.758205	+	1.31325i	−0.943765	+	0.330617i	$0.892743\pi$
$158$	−0.0557907	+	0.0966323i	−0.00443847	+	0.00768765i
$159$		0			0
$160$	5.14262	+	8.90727i	0.406560	+	0.704182i
$161$	−35.9065			−2.82983
$162$		0			0
$163$	4.70788			0.368750			0.184375	−	0.982856i	$-0.440974\pi$
$163$	4.70788			0.368750			0.184375	+	0.982856i	$0.440974\pi$
$164$	−4.57516	−	7.92440i	−0.357260	−	0.618792i
$165$		0			0
$166$	−0.134334	+	0.232673i	−0.0104263	+	0.0180589i
$167$	8.06308	−	13.9657i	0.623940	−	1.08070i	−0.364805	−	0.931084i	$-0.618864\pi$
$167$	8.06308	−	13.9657i	0.623940	−	1.08070i	0.988745	−	0.149612i	$-0.0478023\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	0.310515			0.0238154
$171$		0			0
$172$	13.0145			0.992349
$173$	5.96073	+	10.3243i	0.453186	+	0.784940i	0.998582	−	0.0532379i	$-0.0169542\pi$
$173$	5.96073	+	10.3243i	0.453186	+	0.784940i	−0.545396	+	0.838178i	$0.683621\pi$
$174$		0			0
$175$	15.6153	−	27.0465i	1.18041	−	2.04452i
$176$	0.227984	−	0.394879i	0.0171849	−	0.0297651i
$177$		0			0
$178$	−1.40688	−	2.43678i	−0.105450	−	0.182645i
$179$	3.82703			0.286046			0.143023	−	0.989719i	$-0.454318\pi$
$179$	3.82703			0.286046			0.143023	+	0.989719i	$0.454318\pi$
$180$		0			0
$181$	11.3406			0.842940			0.421470	−	0.906842i	$-0.361514\pi$
$181$	11.3406			0.842940			0.421470	+	0.906842i	$0.361514\pi$
$182$	−0.571006	−	0.989012i	−0.0423258	−	0.0733104i
$183$		0			0
$184$	4.12175	−	7.13909i	0.303860	−	0.526301i
$185$	−4.24753	+	7.35693i	−0.312284	+	0.540892i
$186$		0			0
$187$	−0.0219046	−	0.0379398i	−0.00160182	−	0.00277444i
$188$	0.415661			0.0303152
$189$		0			0
$190$	0.774635			0.0561979
$191$	3.19558	+	5.53491i	0.231224	+	0.400492i	0.958169	−	0.286204i	$-0.0923935\pi$
$191$	3.19558	+	5.53491i	0.231224	+	0.400492i	−0.726944	+	0.686696i	$0.759060\pi$
$192$		0			0
$193$	−6.14567	+	10.6446i	−0.442375	+	0.766215i	−0.997865	−	0.0653075i	$-0.979197\pi$
$193$	−6.14567	+	10.6446i	−0.442375	+	0.766215i	0.555491	+	0.831523i	$0.312531\pi$
$194$	−0.0230905	+	0.0399940i	−0.00165780	+	0.00287140i
$195$		0			0
$196$	12.1469	+	21.0390i	0.867632	+	1.50278i
$197$	6.01862			0.428809			0.214404	−	0.976745i	$-0.431219\pi$
$197$	6.01862			0.428809			0.214404	+	0.976745i	$0.431219\pi$
$198$		0			0
$199$	−11.0716			−0.784846			−0.392423	−	0.919785i	$-0.628363\pi$
$199$	−11.0716			−0.784846			−0.392423	+	0.919785i	$0.628363\pi$
$200$	3.58500	+	6.20940i	0.253498	+	0.439071i
$201$		0			0
$202$	1.66796	−	2.88900i	0.117357	−	0.203269i
$203$	5.53022	−	9.57862i	0.388145	−	0.672287i
$204$		0			0
$205$	−8.21825	−	14.2344i	−0.573987	−	0.994175i
$206$	−1.58355			−0.110331
$207$		0			0
$208$	−3.60450			−0.249927
$209$	−0.0546449	−	0.0946478i	−0.00377987	−	0.00654692i
$210$		0			0
$211$	−5.03787	+	8.72584i	−0.346821	+	0.600712i	−0.985683	−	0.168610i	$-0.946072\pi$
$211$	−5.03787	+	8.72584i	−0.346821	+	0.600712i	0.638862	+	0.769321i	$0.279406\pi$
$212$	3.88669	−	6.73195i	0.266939	−	0.462352i
$213$		0			0
$214$	−2.06120	−	3.57011i	−0.140901	−	0.244048i
$215$	23.3777			1.59435
$216$		0			0
$217$	26.6628			1.80999
$218$	0.481722	+	0.834368i	0.0326264	+	0.0565105i
$219$		0			0
$220$	0.424668	−	0.735547i	0.0286311	−	0.0495905i
$221$	−0.173159	+	0.299921i	−0.0116480	+	0.0201749i
$222$		0			0
$223$	−8.78466	−	15.2155i	−0.588264	−	1.01890i	−0.994460	−	0.105117i	$-0.966478\pi$
$223$	−8.78466	−	15.2155i	−0.588264	−	1.01890i	0.406196	−	0.913786i	$-0.366855\pi$
$224$	−13.1002			−0.875297
$225$		0			0
$226$	4.05612			0.269809
$227$	−11.6006	−	20.0928i	−0.769958	−	1.33361i	−0.937585	−	0.347756i	$-0.886944\pi$
$227$	−11.6006	−	20.0928i	−0.769958	−	1.33361i	0.167627	−	0.985850i	$-0.446390\pi$
$228$		0			0
$229$	4.57963	−	7.93215i	0.302630	−	0.524171i	−0.674101	−	0.738640i	$-0.735469\pi$
$229$	4.57963	−	7.93215i	0.302630	−	0.524171i	0.976731	+	0.214468i	$0.0688019\pi$
$230$	3.63917	−	6.30323i	0.239960	−	0.415623i
$231$		0			0
$232$	1.26964	+	2.19908i	0.0833560	+	0.144377i
$233$	−20.1888			−1.32261			−0.661307	−	0.750116i	$-0.729998\pi$
$233$	−20.1888			−1.32261			−0.661307	+	0.750116i	$0.729998\pi$
$234$		0			0
$235$	0.746643			0.0487056
$236$	13.2830	+	23.0068i	0.864650	+	1.49762i
$237$		0			0
$238$	−0.197750	+	0.342513i	−0.0128182	+	0.0222018i
$239$	3.84883	−	6.66638i	0.248960	−	0.431212i	−0.714277	−	0.699863i	$-0.753244\pi$
$239$	3.84883	−	6.66638i	0.248960	−	0.431212i	0.963238	+	0.268651i	$0.0865778\pi$
$240$		0			0
$241$	−1.55399	−	2.69159i	−0.100101	−	0.173381i	0.811625	−	0.584179i	$-0.198583\pi$
$241$	−1.55399	−	2.69159i	−0.100101	−	0.173381i	−0.911726	+	0.410798i	$0.865250\pi$
$242$	−2.83586			−0.182296
$243$		0			0
$244$	5.27149			0.337472
$245$	21.8191	+	37.7918i	1.39397	+	2.41443i
$246$		0			0
$247$	−0.431977	+	0.748207i	−0.0274861	+	0.0476073i
$248$	−3.06066	+	5.30122i	−0.194352	+	0.336628i
$249$		0			0
$250$	0.923722	+	1.59993i	0.0584213	+	0.101189i
$251$	−9.63549			−0.608187			−0.304093	−	0.952642i	$-0.598354\pi$
$251$	−9.63549			−0.608187			−0.304093	+	0.952642i	$0.598354\pi$
$252$		0			0
$253$	−1.02687			−0.0645587
$254$	−1.80856	−	3.13251i	−0.113479	−	0.196551i
$255$		0			0
$256$	−5.46494	+	9.46556i	−0.341559	+	0.591597i
$257$	2.12898	−	3.68750i	0.132802	−	0.230020i	−0.791954	−	0.610581i	$-0.790936\pi$
$257$	2.12898	−	3.68750i	0.132802	−	0.230020i	0.924756	+	0.380561i	$0.124269\pi$
$258$		0			0
$259$	−5.41005	−	9.37048i	−0.336164	−	0.582253i
$260$	−6.71415			−0.416394
$261$		0			0
$262$	−1.51174			−0.0933954
$263$	−9.94611	−	17.2272i	−0.613303	−	1.06227i	−0.990680	−	0.136213i	$-0.956507\pi$
$263$	−9.94611	−	17.2272i	−0.613303	−	1.06227i	0.377376	−	0.926060i	$-0.376826\pi$
$264$		0			0
$265$	6.98157	−	12.0924i	0.428875	−	0.742832i
$266$	−0.493324	+	0.854462i	−0.0302476	+	0.0523904i
$267$		0			0
$268$	3.88279	+	6.72519i	0.237179	+	0.410806i
$269$	−5.80864			−0.354159			−0.177080	−	0.984197i	$-0.556665\pi$
$269$	−5.80864			−0.354159			−0.177080	+	0.984197i	$0.556665\pi$
$270$		0			0
$271$	−18.1178			−1.10058			−0.550290	−	0.834974i	$-0.685483\pi$
$271$	−18.1178			−1.10058			−0.550290	+	0.834974i	$0.685483\pi$
$272$	0.624153	+	1.08106i	0.0378448	+	0.0655492i
$273$		0			0
$274$	−2.18910	+	3.79164i	−0.132249	+	0.229061i
$275$	0.446573	−	0.773486i	0.0269293	−	0.0466430i
$276$		0			0
$277$	−5.60978	−	9.71642i	−0.337059	−	0.583803i	0.646819	−	0.762643i	$-0.276099\pi$
$277$	−5.60978	−	9.71642i	−0.337059	−	0.583803i	−0.983878	+	0.178840i	$0.942766\pi$
$278$	2.77082			0.166183
$279$		0			0
$280$	−15.5996			−0.932257
$281$	−4.51700	−	7.82368i	−0.269462	−	0.466721i	0.699261	−	0.714866i	$-0.253512\pi$
$281$	−4.51700	−	7.82368i	−0.269462	−	0.466721i	−0.968723	+	0.248145i	$0.920179\pi$
$282$		0			0
$283$	9.31076	−	16.1267i	0.553467	−	0.958633i	−0.444554	−	0.895752i	$-0.646638\pi$
$283$	9.31076	−	16.1267i	0.553467	−	0.958633i	0.998021	−	0.0628813i	$-0.0200289\pi$
$284$	−8.26735	+	14.3195i	−0.490577	+	0.849705i
$285$		0			0
$286$	−0.0163299	−	0.0282841i	−0.000965605	−	0.00167248i
$287$	20.9351			1.23576
$288$		0			0
$289$	−16.8801			−0.992945
$290$	1.12099	+	1.94161i	0.0658267	+	0.114015i
$291$		0			0
$292$	−8.86921	+	15.3619i	−0.519031	+	0.898989i
$293$	−1.75915	+	3.04694i	−0.102771	+	0.178004i	−0.912825	−	0.408350i	$-0.866104\pi$
$293$	−1.75915	+	3.04694i	−0.102771	+	0.178004i	0.810054	+	0.586355i	$0.199437\pi$
$294$		0			0
$295$	23.8599	+	41.3266i	1.38918	+	2.40613i
$296$	2.48410			0.144386
$297$		0			0
$298$	−1.54289			−0.0893774
$299$	4.05879	+	7.03003i	0.234726	+	0.406557i
$300$		0			0
$301$	−14.8880	+	25.7868i	−0.858131	+	1.48633i
$302$	−2.47740	+	4.29098i	−0.142558	+	0.246918i
$303$		0			0
$304$	1.55706	+	2.69691i	0.0893037	+	0.154678i
$305$	9.46905			0.542196
$306$		0			0
$307$	15.8342			0.903707			0.451853	−	0.892092i	$-0.350763\pi$
$307$	15.8342			0.903707			0.451853	+	0.892092i	$0.350763\pi$
$308$	0.540897	+	0.936861i	0.0308205	+	0.0533826i
$309$		0			0
$310$	−2.70231	+	4.68054i	−0.153481	+	0.265837i
$311$	−8.04473	+	13.9339i	−0.456175	+	0.790117i	−0.998755	−	0.0498865i	$-0.984114\pi$
$311$	−8.04473	+	13.9339i	−0.456175	+	0.790117i	0.542580	+	0.840004i	$0.317447\pi$
$312$		0			0
$313$	−2.23621	−	3.87323i	−0.126398	−	0.218928i	0.795880	−	0.605454i	$-0.207008\pi$
$313$	−2.23621	−	3.87323i	−0.126398	−	0.218928i	−0.922279	+	0.386526i	$0.873675\pi$
$314$	4.90558			0.276838
$315$		0			0
$316$	−0.835558			−0.0470038
$317$	6.48094	+	11.2253i	0.364006	+	0.630477i	0.988616	−	0.150460i	$-0.0480754\pi$
$317$	6.48094	+	11.2253i	0.364006	+	0.630477i	−0.624610	+	0.780937i	$0.714742\pi$
$318$		0			0
$319$	0.158155	−	0.273933i	0.00885500	−	0.0153373i
$320$	−11.1900	+	19.3817i	−0.625543	+	1.08347i
$321$		0			0
$322$	4.63519	+	8.02838i	0.258309	+	0.447404i
$323$	0.299204			0.0166481
$324$		0			0
$325$	−7.06047			−0.391644
$326$	−0.607743	−	1.05264i	−0.0336597	−	0.0583004i
$327$		0			0
$328$	−2.40316	+	4.16240i	−0.132692	+	0.229830i
$329$	−0.475497	+	0.823585i	−0.0262150	+	0.0454057i
$330$		0			0
$331$	−7.08304	−	12.2682i	−0.389319	−	0.674320i	0.603039	−	0.797712i	$-0.293956\pi$
$331$	−7.08304	−	12.2682i	−0.389319	−	0.674320i	−0.992358	+	0.123391i	$0.960623\pi$
$332$	−2.01187			−0.110416
$333$		0			0
$334$	−4.16346			−0.227815
$335$	6.97456	+	12.0803i	0.381061	+	0.660017i
$336$		0			0
$337$	13.0374	−	22.5815i	0.710194	−	1.23009i	−0.254590	−	0.967049i	$-0.581941\pi$
$337$	13.0374	−	22.5815i	0.710194	−	1.23009i	0.964784	−	0.263043i	$-0.0847260\pi$
$338$	−0.129090	+	0.223591i	−0.00702159	+	0.0121617i
$339$		0			0
$340$	1.16262	+	2.01371i	0.0630518	+	0.109209i
$341$	0.762514			0.0412925
$342$		0			0
$343$	−24.6186			−1.32928
$344$	−3.41803	−	5.92020i	−0.184288	−	0.319196i
$345$		0			0
$346$	1.53894	−	2.66553i	0.0827342	−	0.143300i
$347$	12.5166	−	21.6793i	0.671924	−	1.16381i	−0.305433	−	0.952213i	$-0.598801\pi$
$347$	12.5166	−	21.6793i	0.671924	−	1.16381i	0.977358	−	0.211594i	$-0.0678654\pi$
$348$		0			0
$349$	−5.96790	−	10.3367i	−0.319454	−	0.553311i	0.660920	−	0.750456i	$-0.270166\pi$
$349$	−5.96790	−	10.3367i	−0.319454	−	0.553311i	−0.980374	+	0.197145i	$0.936833\pi$
$350$	−8.06314			−0.430993
$351$		0			0
$352$	−0.374646			−0.0199687
$353$	−7.42385	−	12.8585i	−0.395132	−	0.684388i	0.597986	−	0.801506i	$-0.295968\pi$
$353$	−7.42385	−	12.8585i	−0.395132	−	0.684388i	−0.993118	+	0.117118i	$0.962634\pi$
$354$		0			0
$355$	−14.8505	+	25.7217i	−0.788180	+	1.36517i
$356$	10.5352	−	18.2475i	0.558363	−	0.967113i
$357$		0			0
$358$	−0.494033	−	0.855690i	−0.0261105	−	0.0452246i
$359$	−35.0911			−1.85204			−0.926019	−	0.377477i	$-0.876792\pi$
$359$	−35.0911			−1.85204			−0.926019	+	0.377477i	$0.876792\pi$
$360$		0			0
$361$	−18.2536			−0.960715
$362$	−1.46396	−	2.53566i	−0.0769442	−	0.133271i
$363$		0			0
$364$	4.27588	−	7.40605i	0.224117	−	0.388182i
$365$	−15.9316	+	27.5943i	−0.833896	+	1.44435i
$366$		0			0
$367$	6.82647	+	11.8238i	0.356339	+	0.617197i	0.987346	−	0.158580i	$-0.0506916\pi$
$367$	6.82647	+	11.8238i	0.356339	+	0.617197i	−0.631007	+	0.775777i	$0.717358\pi$
$368$	29.2598			1.52527
$369$		0			0
$370$	2.19326			0.114022
$371$	8.89239	+	15.4021i	0.461670	+	0.799635i
$372$		0			0
$373$	8.89873	−	15.4130i	0.460759	−	0.798057i	−0.538240	−	0.842791i	$-0.680911\pi$
$373$	8.89873	−	15.4130i	0.460759	−	0.798057i	0.998999	+	0.0447342i	$0.0142441\pi$
$374$	−0.00565534	+	0.00979533i	−0.000292431	+	0.000506505i
$375$		0			0
$376$	−0.109166	−	0.189081i	−0.00562979	−	0.00975109i
$377$	−2.50049			−0.128782
$378$		0			0
$379$	21.8610			1.12292			0.561461	−	0.827503i	$-0.310240\pi$
$379$	21.8610			1.12292			0.561461	+	0.827503i	$0.310240\pi$
$380$	2.90036	+	5.02357i	0.148785	+	0.257704i
$381$		0			0
$382$	0.825038	−	1.42901i	0.0422126	−	0.0731144i
$383$	−4.25617	+	7.37190i	−0.217480	+	0.376687i	−0.954037	−	0.299689i	$-0.903117\pi$
$383$	−4.25617	+	7.37190i	−0.217480	+	0.376687i	0.736557	+	0.676376i	$0.236450\pi$
$384$		0			0
$385$	0.971601	+	1.68286i	0.0495174	+	0.0857666i
$386$	3.17338			0.161521
$387$		0			0
$388$	−0.345819			−0.0175563
$389$	−6.27691	−	10.8719i	−0.318252	−	0.551229i	0.661871	−	0.749618i	$-0.269763\pi$
$389$	−6.27691	−	10.8719i	−0.318252	−	0.551229i	−0.980123	+	0.198389i	$0.936429\pi$
$390$		0			0
$391$	1.40564	−	2.43463i	0.0710860	−	0.123125i
$392$	6.38029	−	11.0510i	0.322253	−	0.558159i
$393$		0			0
$394$	−0.776946	−	1.34571i	−0.0391420	−	0.0677959i
$395$	−1.50089			−0.0755182
$396$		0			0
$397$	5.98359			0.300308			0.150154	−	0.988663i	$-0.452023\pi$
$397$	5.98359			0.300308			0.150154	+	0.988663i	$0.452023\pi$
$398$	1.42924	+	2.47551i	0.0716413	+	0.124086i
$399$		0			0
$400$	−12.7247	+	22.0399i	−0.636236	+	1.10199i
$401$	11.2778	−	19.5337i	0.563185	−	0.975466i	−0.434031	−	0.900898i	$-0.642909\pi$
$401$	11.2778	−	19.5337i	0.563185	−	0.975466i	0.997216	−	0.0745676i	$-0.0237577\pi$
$402$		0			0
$403$	−3.01390	−	5.22023i	−0.150133	−	0.260038i
$404$	24.9805			1.24283
$405$		0			0
$406$	−2.85559			−0.141721
$407$	−0.154719	−	0.267981i	−0.00766912	−	0.0132833i
$408$		0			0
$409$	−1.36458	+	2.36351i	−0.0674739	+	0.116868i	−0.897789	−	0.440426i	$-0.854827\pi$
$409$	−1.36458	+	2.36351i	−0.0674739	+	0.116868i	0.830315	+	0.557295i	$0.188161\pi$
$410$	−2.12179	+	3.67505i	−0.104788	+	0.181498i
$411$		0			0
$412$	−5.92909	−	10.2695i	−0.292105	−	0.505941i
$413$	−60.7805			−2.99082
$414$		0			0
$415$	−3.61388			−0.177398
$416$	1.48082	+	2.56485i	0.0726031	+	0.125752i
$417$		0			0
$418$	−0.0141083	+	0.0244362i	−0.000690058	+	0.00119521i
$419$	−16.2360	+	28.1216i	−0.793180	+	1.37383i	0.130809	+	0.991408i	$0.458243\pi$
$419$	−16.2360	+	28.1216i	−0.793180	+	1.37383i	−0.923989	+	0.382420i	$0.875091\pi$
$420$		0			0
$421$	−6.69111	−	11.5894i	−0.326105	−	0.564830i	0.655630	−	0.755082i	$-0.272403\pi$
$421$	−6.69111	−	11.5894i	−0.326105	−	0.564830i	−0.981735	+	0.190252i	$0.939070\pi$
$422$	2.60136			0.126632
$423$		0			0
$424$	−4.08307			−0.198291
$425$	1.22259	+	2.11758i	0.0593041	+	0.102718i
$426$		0			0
$427$	−6.03033	+	10.4448i	−0.291828	+	0.505461i
$428$	15.4350	−	26.7342i	0.746078	−	1.29225i
$429$		0			0
$430$	−3.01784	−	5.22705i	−0.145533	−	0.252071i
$431$	14.6522			0.705772			0.352886	−	0.935666i	$-0.385200\pi$
$431$	14.6522			0.705772			0.352886	+	0.935666i	$0.385200\pi$
$432$		0			0
$433$	6.62721			0.318483			0.159242	−	0.987240i	$-0.449095\pi$
$433$	6.62721			0.318483			0.159242	+	0.987240i	$0.449095\pi$
$434$	−3.44192	−	5.96157i	−0.165217	−	0.286165i
$435$		0			0
$436$	−3.60730	+	6.24802i	−0.172758	+	0.299226i
$437$	3.50661	−	6.07363i	0.167744	−	0.290541i
$438$		0			0
$439$	15.9958	+	27.7055i	0.763438	+	1.32231i	0.941069	+	0.338216i	$0.109823\pi$
$439$	15.9958	+	27.7055i	0.763438	+	1.32231i	−0.177631	+	0.984097i	$0.556843\pi$
$440$	−0.446125			−0.0212682
$441$		0			0
$442$	0.0894128			0.00425293
$443$	−10.5559	−	18.2834i	−0.501527	−	0.868670i	−0.999998	−	0.00176387i	$-0.999439\pi$
$443$	−10.5559	−	18.2834i	−0.501527	−	0.868670i	0.498472	−	0.866906i	$-0.333895\pi$
$444$		0			0
$445$	18.9241	−	32.7775i	0.897087	−	1.55380i
$446$	−2.26803	+	3.92834i	−0.107394	+	0.186012i
$447$		0			0
$448$	−14.2527	−	24.6864i	−0.673377	−	1.16632i
$449$	7.87220			0.371512			0.185756	−	0.982596i	$-0.440527\pi$
$449$	7.87220			0.371512			0.185756	+	0.982596i	$0.440527\pi$
$450$		0			0
$451$	0.598709			0.0281921
$452$	15.1868	+	26.3043i	0.714326	+	1.23725i
$453$		0			0
$454$	−2.99505	+	5.18758i	−0.140565	+	0.243465i
$455$	7.68067	−	13.3033i	0.360075	−	0.623669i
$456$		0			0
$457$	12.6044	+	21.8315i	0.589609	+	1.02123i	0.994283	+	0.106773i	$0.0340517\pi$
$457$	12.6044	+	21.8315i	0.589609	+	1.02123i	−0.404674	+	0.914461i	$0.632615\pi$
$458$	−2.36474			−0.110497
$459$		0			0
$460$	54.5026			2.54120
$461$	5.65188	+	9.78934i	0.263234	+	0.455935i	0.967099	−	0.254398i	$-0.0818775\pi$
$461$	5.65188	+	9.78934i	0.263234	+	0.455935i	−0.703865	+	0.710333i	$0.748544\pi$
$462$		0			0
$463$	−15.1397	+	26.2227i	−0.703602	+	1.21867i	0.263592	+	0.964634i	$0.415093\pi$
$463$	−15.1397	+	26.2227i	−0.703602	+	1.21867i	−0.967194	+	0.254040i	$0.918241\pi$
$464$	−4.50651	+	7.80550i	−0.209209	+	0.362361i
$465$		0			0
$466$	2.60618	+	4.51404i	0.120729	+	0.209109i
$467$	30.8192			1.42614			0.713070	−	0.701093i	$-0.247304\pi$
$467$	30.8192			1.42614			0.713070	+	0.701093i	$0.247304\pi$
$468$		0			0
$469$	−17.7669			−0.820400
$470$	−0.0963843	−	0.166943i	−0.00444588	−	0.00770049i
$471$		0			0
$472$	6.97707	−	12.0846i	0.321146	−	0.556241i
$473$	−0.425773	+	0.737461i	−0.0195771	+	0.0339085i
$474$		0			0
$475$	3.04996	+	5.28269i	0.139942	+	0.242386i
$476$	−2.96164			−0.135746
$477$		0			0
$478$	−1.98739			−0.0909011
$479$	−6.39593	−	11.0781i	−0.292237	−	0.506170i	0.682101	−	0.731258i	$-0.261066\pi$
$479$	−6.39593	−	11.0781i	−0.292237	−	0.506170i	−0.974338	+	0.225088i	$0.927733\pi$
$480$		0			0
$481$	−1.22308	+	2.11843i	−0.0557675	+	0.0965922i
$482$	−0.401210	+	0.694917i	−0.0182746	+	0.0316526i
$483$		0			0
$484$	−10.6179	−	18.3908i	−0.482633	−	0.835944i
$485$	−0.621187			−0.0282066
$486$		0			0
$487$	7.29411			0.330528			0.165264	−	0.986249i	$-0.447152\pi$
$487$	7.29411			0.330528			0.165264	+	0.986249i	$0.447152\pi$
$488$	−1.38446	−	2.39795i	−0.0626715	−	0.108550i
$489$		0			0
$490$	5.63327	−	9.75711i	0.254485	−	0.440782i
$491$	2.41978	−	4.19118i	0.109203	−	0.189146i	−0.806244	−	0.591582i	$-0.798503\pi$
$491$	2.41978	−	4.19118i	0.109203	−	0.189146i	0.915448	+	0.402437i	$0.131837\pi$
$492$		0			0
$493$	0.432983	+	0.749949i	0.0195006	+	0.0337760i
$494$	0.223057			0.0100358
$495$		0			0
$496$	−21.7272			−0.975581
$497$	−18.9149	−	32.7616i	−0.848451	−	1.46956i
$498$		0			0
$499$	1.05749	−	1.83163i	0.0473398	−	0.0819949i	−0.841385	−	0.540437i	$-0.818259\pi$
$499$	1.05749	−	1.83163i	0.0473398	−	0.0819949i	0.888724	+	0.458442i	$0.151592\pi$
$500$	−6.91714	+	11.9808i	−0.309344	+	0.535799i
$501$		0			0
$502$	1.24385	+	2.15441i	0.0555157	+	0.0961560i
$503$	−2.80951			−0.125270			−0.0626349	−	0.998037i	$-0.519950\pi$
$503$	−2.80951			−0.125270			−0.0626349	+	0.998037i	$0.519950\pi$
$504$		0			0
$505$	44.8719			1.99677
$506$	0.132559	+	0.229599i	0.00589296	+	0.0102069i
$507$		0			0
$508$	13.5431	−	23.4573i	0.600877	−	1.04075i
$509$	−8.57868	+	14.8587i	−0.380243	+	0.658601i	−0.991097	−	0.133143i	$-0.957493\pi$
$509$	−8.57868	+	14.8587i	−0.380243	+	0.658601i	0.610853	+	0.791744i	$0.290826\pi$
$510$		0			0
$511$	−20.2919	−	35.1466i	−0.897662	−	1.55480i
$512$	17.9961			0.795321
$513$		0			0
$514$	−1.09932			−0.0484890
$515$	−10.6503	−	18.4468i	−0.469308	−	0.812865i
$516$		0			0
$517$	−0.0135984	+	0.0235532i	−0.000598059	+	0.00103587i
$518$	−1.39677	+	2.41928i	−0.0613706	+	0.106297i
$519$		0			0
$520$	1.76335	+	3.05421i	0.0773279	+	0.133936i
$521$	38.3213			1.67889			0.839444	−	0.543447i	$-0.182881\pi$
$521$	38.3213			1.67889			0.839444	+	0.543447i	$0.182881\pi$
$522$		0			0
$523$	2.55236			0.111607			0.0558034	−	0.998442i	$-0.482228\pi$
$523$	2.55236			0.111607			0.0558034	+	0.998442i	$0.482228\pi$
$524$	−5.66019	−	9.80374i	−0.247267	−	0.428279i
$525$		0			0
$526$	−2.56789	+	4.44772i	−0.111965	+	0.193930i
$527$	−1.04377	+	1.80787i	−0.0454674	+	0.0787518i
$528$		0			0
$529$	−21.4475	−	37.1482i	−0.932502	−	1.61514i
$530$	−3.60501			−0.156592
$531$		0			0
$532$	−7.38834			−0.320325
$533$	−2.36645	−	4.09881i	−0.102502	−	0.177539i
$534$		0			0
$535$	27.7255	−	48.0220i	1.19868	−	2.07617i
$536$	2.03948	−	3.53249i	0.0880923	−	0.152580i
$537$		0			0
$538$	0.749840	+	1.29876i	0.0323279	+	0.0559935i
$539$	−1.58955			−0.0684667
$540$		0			0
$541$	36.7134			1.57843			0.789216	−	0.614115i	$-0.210487\pi$
$541$	36.7134			1.57843			0.789216	+	0.614115i	$0.210487\pi$
$542$	2.33884	+	4.05098i	0.100462	+	0.174005i
$543$		0			0
$544$	0.512836	−	0.888257i	0.0219876	−	0.0380837i
$545$	−6.47970	+	11.2232i	−0.277560	+	0.480748i
$546$		0			0
$547$	3.05186	+	5.28597i	0.130488	+	0.226012i	0.923865	−	0.382719i	$-0.125012\pi$
$547$	3.05186	+	5.28597i	0.130488	+	0.226012i	−0.793377	+	0.608731i	$0.791679\pi$
$548$	−32.7855			−1.40053
$549$		0			0
$550$	−0.230593			−0.00983251
$551$	1.08016	+	1.87088i	0.0460162	+	0.0797023i
$552$		0			0
$553$	0.955840	−	1.65556i	0.0406464	−	0.0704017i
$554$	−1.44834	+	2.50859i	−0.0615339	+	0.106580i
$555$		0			0
$556$	10.3744	+	17.9690i	0.439972	+	0.762054i
$557$	−13.9705			−0.591948			−0.295974	−	0.955196i	$-0.595644\pi$
$557$	−13.9705			−0.591948			−0.295974	+	0.955196i	$0.595644\pi$
$558$		0			0
$559$	6.73162			0.284717
$560$	−27.6850	−	47.9518i	−1.16990	−	2.02633i
$561$		0			0
$562$	−1.16620	+	2.01992i	−0.0491933	+	0.0852053i
$563$	−7.16514	+	12.4104i	−0.301975	+	0.523035i	−0.976583	−	0.215140i	$-0.930979\pi$
$563$	−7.16514	+	12.4104i	−0.301975	+	0.523035i	0.674609	+	0.738176i	$0.264312\pi$
$564$		0			0
$565$	27.2796	+	47.2497i	1.14766	+	1.98781i
$566$	−4.80772			−0.202083
$567$		0			0
$568$	8.68507			0.364417
$569$	−8.61432	−	14.9204i	−0.361131	−	0.625497i	0.627016	−	0.779006i	$-0.284276\pi$
$569$	−8.61432	−	14.9204i	−0.361131	−	0.625497i	−0.988147	+	0.153509i	$0.950943\pi$
$570$		0			0
$571$	2.40564	−	4.16669i	0.100673	−	0.174371i	−0.811289	−	0.584645i	$-0.801234\pi$
$571$	2.40564	−	4.16669i	0.100673	−	0.174371i	0.911962	+	0.410275i	$0.134567\pi$
$572$	0.122283	−	0.211801i	0.00511293	−	0.00885585i
$573$		0			0
$574$	−2.70251	−	4.68089i	−0.112801	−	0.195377i
$575$	57.3139			2.39015
$576$		0			0
$577$	−34.1265			−1.42071			−0.710353	−	0.703845i	$-0.751465\pi$
$577$	−34.1265			−1.42071			−0.710353	+	0.703845i	$0.751465\pi$
$578$	2.17905	+	3.77423i	0.0906367	+	0.156987i
$579$		0			0
$580$	−8.39433	+	14.5394i	−0.348556	+	0.603716i
$581$	2.30149	−	3.98630i	0.0954819	−	0.165379i
$582$		0			0
$583$	0.254308	+	0.440474i	0.0105324	+	0.0182426i
$584$	9.31734			0.385554
$585$		0			0
$586$	0.908359			0.0375240
$587$	−5.05262	−	8.75140i	−0.208544	−	0.361209i	0.742712	−	0.669611i	$-0.233539\pi$
$587$	−5.05262	−	8.75140i	−0.208544	−	0.361209i	−0.951256	+	0.308402i	$0.900206\pi$
$588$		0			0
$589$	−2.60388	+	4.51005i	−0.107291	+	0.185833i
$590$	6.16018	−	10.6697i	0.253611	−	0.439266i
$591$		0			0
$592$	4.40858	+	7.63589i	0.181192	+	0.313833i
$593$	38.0081			1.56081			0.780403	−	0.625277i	$-0.215014\pi$
$593$	38.0081			1.56081			0.780403	+	0.625277i	$0.215014\pi$
$594$		0			0
$595$	−5.31992			−0.218096
$596$	−5.77685	−	10.0058i	−0.236629	−	0.409853i
$597$		0			0
$598$	1.04790	−	1.81502i	0.0428519	−	0.0742216i
$599$	−14.6376	+	25.3531i	−0.598078	+	1.03590i	0.395027	+	0.918670i	$0.370735\pi$
$599$	−14.6376	+	25.3531i	−0.598078	+	1.03590i	−0.993105	+	0.117231i	$0.962598\pi$
$600$		0			0
$601$	22.8635	+	39.6007i	0.932621	+	1.61535i	0.778823	+	0.627244i	$0.215817\pi$
$601$	22.8635	+	39.6007i	0.932621	+	1.61535i	0.153798	+	0.988102i	$0.450849\pi$
$602$	7.68760			0.313323
$603$		0			0
$604$	−37.1032			−1.50971
$605$	−19.0727	−	33.0349i	−0.775416	−	1.34306i
$606$		0			0
$607$	−19.4032	+	33.6074i	−0.787552	+	1.36408i	0.139910	+	0.990164i	$0.455319\pi$
$607$	−19.4032	+	33.6074i	−0.787552	+	1.36408i	−0.927462	+	0.373916i	$0.878015\pi$
$608$	1.27936	−	2.21592i	0.0518849	−	0.0898674i
$609$		0			0
$610$	−1.22236	−	2.11719i	−0.0494920	−	0.0857227i
$611$	0.214996			0.00869781
$612$		0			0
$613$	−36.9472			−1.49228			−0.746142	−	0.665787i	$-0.768096\pi$
$613$	−36.9472			−1.49228			−0.746142	+	0.665787i	$0.768096\pi$
$614$	−2.04405	−	3.54039i	−0.0824910	−	0.142879i
$615$		0			0
$616$	0.284113	−	0.492098i	0.0114472	−	0.0198272i
$617$	3.13825	−	5.43561i	0.126341	−	0.218830i	−0.795915	−	0.605408i	$-0.793010\pi$
$617$	3.13825	−	5.43561i	0.126341	−	0.218830i	0.922256	+	0.386579i	$0.126343\pi$
$618$		0			0
$619$	−7.04204	−	12.1972i	−0.283043	−	0.490246i	0.689089	−	0.724676i	$-0.258011\pi$
$619$	−7.04204	−	12.1972i	−0.283043	−	0.490246i	−0.972133	+	0.234431i	$0.924677\pi$
$620$	−40.4716			−1.62538
$621$		0			0
$622$	4.15399			0.166560
$623$	24.1035	+	41.7485i	0.965686	+	1.67262i
$624$		0			0
$625$	5.22607	−	9.05182i	0.209043	−	0.362073i
$626$	−0.577347	+	0.999994i	−0.0230754	+	0.0399678i
$627$		0			0
$628$	18.3673	+	31.8131i	0.732935	+	1.26948i
$629$	0.847150			0.0337781
$630$		0			0
$631$	7.83048			0.311727			0.155863	−	0.987779i	$-0.450184\pi$
$631$	7.83048			0.311727			0.155863	+	0.987779i	$0.450184\pi$
$632$	0.219444	+	0.380088i	0.00872901	+	0.0151191i
$633$		0			0
$634$	1.67325	−	2.89816i	0.0664534	−	0.115101i
$635$	24.3271	−	42.1358i	0.965392	−	1.67211i
$636$		0			0
$637$	6.28282	+	10.8822i	0.248935	+	0.431167i
$638$	−0.0816653			−0.00323316
$639$		0			0
$640$	26.3486			1.04152
$641$	−15.7922	−	27.3529i	−0.623754	−	1.08037i	−0.988780	−	0.149376i	$-0.952273\pi$
$641$	−15.7922	−	27.3529i	−0.623754	−	1.08037i	0.365026	−	0.930997i	$-0.381060\pi$
$642$		0			0
$643$	−15.7929	+	27.3540i	−0.622809	+	1.07874i	0.366151	+	0.930556i	$0.380675\pi$
$643$	−15.7929	+	27.3540i	−0.622809	+	1.07874i	−0.988960	+	0.148182i	$0.952658\pi$
$644$	−34.7098	+	60.1192i	−1.36776	+	2.36903i
$645$		0			0
$646$	−0.0386243	−	0.0668993i	−0.00151965	−	0.00263212i
$647$	33.6109			1.32138			0.660691	−	0.750658i	$-0.270263\pi$
$647$	33.6109			1.32138			0.660691	+	0.750658i	$0.270263\pi$
$648$		0			0
$649$	−1.73823			−0.0682313
$650$	0.911438	+	1.57866i	0.0357495	+	0.0619200i
$651$		0			0
$652$	4.55098	−	7.88252i	0.178230	−	0.308703i
$653$	11.3303	−	19.6246i	0.443389	−	0.767972i	−0.554550	−	0.832151i	$-0.687110\pi$
$653$	11.3303	−	19.6246i	0.443389	−	0.767972i	0.997938	+	0.0641790i	$0.0204429\pi$
$654$		0			0
$655$	−10.1673	−	17.6102i	−0.397268	−	0.688089i
$656$	−17.0597			−0.666071
$657$		0			0
$658$	0.245528			0.00957169
$659$	7.75617	+	13.4341i	0.302137	+	0.523317i	0.976620	−	0.214973i	$-0.0689665\pi$
$659$	7.75617	+	13.4341i	0.302137	+	0.523317i	−0.674482	+	0.738291i	$0.735633\pi$
$660$		0			0
$661$	13.8979	−	24.0719i	0.540566	−	0.936287i	−0.458306	−	0.888795i	$-0.651544\pi$
$661$	13.8979	−	24.0719i	0.540566	−	0.936287i	0.998872	−	0.0474928i	$-0.0151231\pi$
$662$	−1.82870	+	3.16741i	−0.0710746	+	0.123105i
$663$		0			0
$664$	0.528381	+	0.915183i	0.0205052	+	0.0355160i
$665$	−13.2715			−0.514647
$666$		0			0
$667$	20.2979			0.785939
$668$	−15.5887	−	27.0004i	−0.603145	−	1.04468i
$669$		0			0
$670$	1.80070	−	3.11890i	0.0695670	−	0.120494i
$671$	−0.172458	+	0.298706i	−0.00665766	+	0.0115314i
$672$		0			0
$673$	−18.1337	−	31.4085i	−0.699004	−	1.21071i	−0.968812	−	0.247796i	$-0.920294\pi$
$673$	−18.1337	−	31.4085i	−0.699004	−	1.21071i	0.269809	−	0.962914i	$-0.413040\pi$
$674$	−6.73202			−0.259308
$675$		0			0
$676$	−1.93334			−0.0743593
$677$	2.57859	+	4.46625i	0.0991033	+	0.171652i	0.911314	−	0.411713i	$-0.135069\pi$
$677$	2.57859	+	4.46625i	0.0991033	+	0.171652i	−0.812210	+	0.583365i	$0.801736\pi$
$678$		0			0
$679$	0.395601	−	0.685201i	0.0151818	−	0.0262956i
$680$	0.610680	−	1.05773i	0.0234185	−	0.0405621i
$681$		0			0
$682$	−0.0984332	−	0.170491i	−0.00376920	−	0.00652845i
$683$	8.03083			0.307291			0.153646	−	0.988126i	$-0.450899\pi$
$683$	8.03083			0.307291			0.153646	+	0.988126i	$0.450899\pi$
$684$		0			0
$685$	−58.8917			−2.25014
$686$	3.17802	+	5.50449i	0.121337	+	0.210163i
$687$		0			0
$688$	12.1321	−	21.0134i	0.462531	−	0.801127i
$689$	2.01035	−	3.48202i	0.0765881	−	0.132655i
$690$		0			0
$691$	11.1712	+	19.3491i	0.424973	+	0.736075i	0.996418	−	0.0845656i	$-0.0269503\pi$
$691$	11.1712	+	19.3491i	0.424973	+	0.736075i	−0.571445	+	0.820640i	$0.693617\pi$
$692$	23.0482			0.876163
$693$		0			0
$694$	−6.46307			−0.245335
$695$	18.6353	+	32.2773i	0.706877	+	1.22435i
$696$		0			0
$697$	−0.819546	+	1.41950i	−0.0310425	+	0.0537672i
$698$	−1.54080	+	2.66874i	−0.0583200	+	0.101013i
$699$		0			0
$700$	−30.1897	−	52.2902i	−1.14106	−	1.97638i
$701$	17.7526			0.670507			0.335253	−	0.942128i	$-0.391178\pi$
$701$	17.7526			0.670507			0.335253	+	0.942128i	$0.391178\pi$
$702$		0			0
$703$	2.11337			0.0797072
$704$	−0.407604	−	0.705991i	−0.0153622	−	0.0266080i
$705$		0			0
$706$	−1.91669	+	3.31981i	−0.0721357	+	0.124943i
$707$	−28.5765	+	49.4960i	−1.07473	+	1.86149i
$708$		0			0
$709$	−9.36197	−	16.2154i	−0.351596	−	0.608983i	0.634933	−	0.772567i	$-0.281028\pi$
$709$	−9.36197	−	16.2154i	−0.351596	−	0.608983i	−0.986529	+	0.163585i	$0.947694\pi$
$710$	7.66820			0.287782
$711$		0			0
$712$	−11.0675			−0.414771
$713$	24.4656	+	42.3757i	0.916244	+	1.58698i
$714$		0			0
$715$	0.219655	−	0.380453i	0.00821462	−	0.0142281i
$716$	3.69948	−	6.40769i	0.138256	−	0.239467i
$717$		0			0
$718$	4.52992	+	7.84606i	0.169055	+	0.292812i
$719$	−25.9370			−0.967287			−0.483643	−	0.875265i	$-0.660687\pi$
$719$	−25.9370			−0.967287			−0.483643	+	0.875265i	$0.660687\pi$
$720$		0			0
$721$	27.1304			1.01039
$722$	2.35636	+	4.08134i	0.0876947	+	0.151892i
$723$		0			0
$724$	10.9626	−	18.9878i	0.407423	−	0.705678i
$725$	−8.82731	+	15.2894i	−0.327838	+	0.567832i
$726$		0			0
$727$	18.6904	+	32.3727i	0.693189	+	1.20064i	0.970788	+	0.239941i	$0.0771280\pi$
$727$	18.6904	+	32.3727i	0.693189	+	1.20064i	−0.277599	+	0.960697i	$0.589539\pi$
$728$	−4.49193			−0.166482
$729$		0			0
$730$	8.22644			0.304474
$731$	−1.16564	−	2.01895i	−0.0431129	−	0.0746737i
$732$		0			0
$733$	−15.5642	+	26.9579i	−0.574875	+	0.995713i	0.421180	+	0.906977i	$0.361616\pi$
$733$	−15.5642	+	26.9579i	−0.574875	+	0.995713i	−0.996055	+	0.0887358i	$0.971717\pi$
$734$	1.76246	−	3.05268i	0.0650537	−	0.112676i
$735$		0			0
$736$	−12.0207	−	20.8204i	−0.443088	−	0.767450i
$737$	−0.508105			−0.0187163
$738$		0			0
$739$	23.1713			0.852369			0.426184	−	0.904636i	$-0.359858\pi$
$739$	23.1713			0.852369			0.426184	+	0.904636i	$0.359858\pi$
$740$	8.21193	+	14.2235i	0.301876	+	0.522865i
$741$		0			0
$742$	2.29584	−	3.97652i	0.0842830	−	0.145982i
$743$	7.95031	−	13.7703i	0.291669	−	0.505185i	−0.682536	−	0.730852i	$-0.739123\pi$
$743$	7.95031	−	13.7703i	0.291669	−	0.505185i	0.974204	+	0.225667i	$0.0724562\pi$
$744$		0			0
$745$	−10.3768	−	17.9732i	−0.380177	−	0.658486i
$746$	−4.59496			−0.168233
$747$		0			0
$748$	−0.0846981			−0.00309687
$749$	35.3138	+	61.1653i	1.29034	+	2.23493i
$750$		0			0
$751$	4.97369	−	8.61468i	0.181492	−	0.314354i	−0.760897	−	0.648873i	$-0.775241\pi$
$751$	4.97369	−	8.61468i	0.181492	−	0.314354i	0.942389	+	0.334519i	$0.108574\pi$
$752$	0.387477	−	0.671129i	0.0141298	−	0.0244736i
$753$		0			0
$754$	0.322789	+	0.559087i	0.0117553	+	0.0203608i
$755$	−66.6476			−2.42555
$756$		0			0
$757$	−43.8603			−1.59413			−0.797064	−	0.603894i	$-0.793615\pi$
$757$	−43.8603			−1.59413			−0.797064	+	0.603894i	$0.793615\pi$
$758$	−2.82204	−	4.88791i	−0.102501	−	0.177537i
$759$		0			0
$760$	1.52345	−	2.63870i	0.0552614	−	0.0957156i
$761$	23.8404	−	41.2927i	0.864213	−	1.49686i	−0.00361442	−	0.999993i	$-0.501151\pi$
$761$	23.8404	−	41.2927i	0.864213	−	1.49686i	0.867827	−	0.496867i	$-0.165516\pi$
$762$		0			0
$763$	−8.25316	−	14.2949i	−0.298784	−	0.517510i
$764$	12.3563			0.447036
$765$		0			0
$766$	2.19772			0.0794069
$767$	6.87049	+	11.9000i	0.248079	+	0.429685i
$768$		0			0
$769$	−7.85242	+	13.6008i	−0.283165	+	0.490457i	−0.972163	−	0.234307i	$-0.924718\pi$
$769$	−7.85242	+	13.6008i	−0.283165	+	0.490457i	0.688997	+	0.724764i	$0.258051\pi$
$770$	0.250849	−	0.434482i	0.00903996	−	0.0156577i
$771$		0			0
$772$	11.8817	+	20.5797i	0.427631	+	0.740678i
$773$	11.8142			0.424929			0.212464	−	0.977169i	$-0.431851\pi$
$773$	11.8142			0.424929			0.212464	+	0.977169i	$0.431851\pi$
$774$		0			0
$775$	−42.5591			−1.52877
$776$	0.0908229	+	0.157310i	0.00326035	+	0.00564710i
$777$		0			0
$778$	−1.62058	+	2.80692i	−0.0581005	+	0.100633i
$779$	−2.04451	+	3.54119i	−0.0732520	+	0.126876i
$780$		0			0
$781$	−0.540937	−	0.936930i	−0.0193562	−	0.0335260i
$782$	−0.725816			−0.0259551
$783$		0			0
$784$	45.2929			1.61760
$785$	32.9928	+	57.1451i	1.17756	+	2.03960i
$786$		0			0
$787$	−7.21696	+	12.5001i	−0.257257	+	0.445582i	−0.965506	−	0.260381i	$-0.916152\pi$
$787$	−7.21696	+	12.5001i	−0.257257	+	0.445582i	0.708249	+	0.705962i	$0.249485\pi$
$788$	5.81803	−	10.0771i	0.207259	−	0.358983i
$789$		0			0
$790$	0.193751	+	0.335586i	0.00689335	+	0.0119396i
$791$	−69.4918			−2.47084
$792$		0			0
$793$	2.72662			0.0968250
$794$	−0.772423	−	1.33788i	−0.0274123	−	0.0474795i
$795$		0			0
$796$	−10.7026	+	18.5375i	−0.379344	+	0.657043i
$797$	−16.5103	+	28.5967i	−0.584826	+	1.01295i	0.410071	+	0.912054i	$0.365504\pi$
$797$	−16.5103	+	28.5967i	−0.584826	+	1.01295i	−0.994897	+	0.100895i	$0.967829\pi$
$798$		0			0
$799$	−0.0372286	−	0.0644818i	−0.00131705	−	0.00228120i
$800$	20.9106			0.739300
$801$		0			0
$802$	−5.82341			−0.205632
$803$	−0.580316	−	1.00514i	−0.0204789	−	0.0354705i
$804$		0			0
$805$	−62.3485	+	107.991i	−2.19749	+	3.80617i
$806$	−0.778132	+	1.34776i	−0.0274085	+	0.0474730i
$807$		0			0
$808$	−6.56067	−	11.3634i	−0.230803	−	0.399763i
$809$	−33.4952			−1.17763			−0.588815	−	0.808268i	$-0.700405\pi$
$809$	−33.4952			−1.17763			−0.588815	+	0.808268i	$0.700405\pi$
$810$		0			0
$811$	4.18463			0.146942			0.0734710	−	0.997297i	$-0.476592\pi$
$811$	4.18463			0.146942			0.0734710	+	0.997297i	$0.476592\pi$
$812$	−10.6918	−	18.5188i	−0.375209	−	0.649881i
$813$		0			0
$814$	−0.0399454	+	0.0691874i	−0.00140008	+	0.00242502i
$815$	8.17481	−	14.1592i	0.286351	−	0.495975i
$816$		0			0
$817$	−2.90791	−	5.03665i	−0.101735	−	0.176210i
$818$	0.704614			0.0246363
$819$		0			0
$820$	−31.7774			−1.10971
$821$	19.0814	+	33.0499i	0.665944	+	1.15345i	0.979028	+	0.203724i	$0.0653044\pi$
$821$	19.0814	+	33.0499i	0.665944	+	1.15345i	−0.313084	+	0.949725i	$0.601362\pi$
$822$		0			0
$823$	−22.2367	+	38.5150i	−0.775121	+	1.34255i	0.159605	+	0.987181i	$0.448978\pi$
$823$	−22.2367	+	38.5150i	−0.775121	+	1.34255i	−0.934726	+	0.355368i	$0.884355\pi$
$824$	−3.11433	+	5.39418i	−0.108493	+	0.187915i
$825$		0			0
$826$	7.84618	+	13.5900i	0.273004	+	0.472856i
$827$	38.7632			1.34793			0.673964	−	0.738764i	$-0.264590\pi$
$827$	38.7632			1.34793			0.673964	+	0.738764i	$0.264590\pi$
$828$		0			0
$829$	−8.74501			−0.303727			−0.151863	−	0.988402i	$-0.548527\pi$
$829$	−8.74501			−0.303727			−0.151863	+	0.988402i	$0.548527\pi$
$830$	0.466517	+	0.808032i	0.0161930	+	0.0280472i
$831$		0			0
$832$	−3.22218	+	5.58098i	−0.111709	+	0.193486i
$833$	2.17586	−	3.76870i	0.0753891	−	0.130578i
$834$		0			0
$835$	−28.0016	−	48.5002i	−0.969036	−	1.67842i
$836$	−0.211295			−0.00730778
$837$		0			0
$838$	8.38364			0.289608
$839$	−17.5080	−	30.3247i	−0.604442	−	1.04692i	−0.992139	−	0.125138i	$-0.960063\pi$
$839$	−17.5080	−	30.3247i	−0.604442	−	1.04692i	0.387697	−	0.921787i	$-0.373271\pi$
$840$		0			0
$841$	11.3738	−	19.7000i	0.392199	−	0.679309i
$842$	−1.72752	+	2.99215i	−0.0595342	+	0.103116i
$843$		0			0
$844$	9.73992	+	16.8700i	0.335262	+	0.580691i
$845$	−3.47282			−0.119469
$846$		0			0
$847$	48.5856			1.66942
$848$	−7.24630	−	12.5510i	−0.248839	−	0.431002i
$849$		0			0
$850$	0.315648	−	0.546719i	0.0108266	−	0.0187523i
$851$	9.92843	−	17.1965i	0.340342	−	0.589490i
$852$		0			0
$853$	15.2934	+	26.4889i	0.523635	+	0.906963i	0.999622	+	0.0275101i	$0.00875785\pi$
$853$	15.2934	+	26.4889i	0.523635	+	0.906963i	−0.475986	+	0.879453i	$0.657909\pi$
$854$	3.11383			0.106553
$855$		0			0
$856$	−16.2148			−0.554212
$857$	−16.5262	−	28.6243i	−0.564526	−	0.977787i	−0.997094	−	0.0761860i	$-0.975726\pi$
$857$	−16.5262	−	28.6243i	−0.564526	−	0.977787i	0.432568	−	0.901601i	$-0.357608\pi$
$858$		0			0
$859$	2.95877	−	5.12474i	0.100952	−	0.174854i	−0.811125	−	0.584873i	$-0.801144\pi$
$859$	2.95877	−	5.12474i	0.100952	−	0.174854i	0.912077	+	0.410019i	$0.134478\pi$
$860$	22.5986	−	39.1419i	0.770604	−	1.33473i
$861$		0			0
$862$	−1.89146	−	3.27610i	−0.0644233	−	0.111584i
$863$	−23.2448			−0.791262			−0.395631	−	0.918410i	$-0.629474\pi$
$863$	−23.2448			−0.791262			−0.395631	+	0.918410i	$0.629474\pi$
$864$		0			0
$865$	41.4010			1.40768
$866$	−0.855509	−	1.48178i	−0.0290714	−	0.0503531i
$867$		0			0
$868$	25.7742	−	44.6422i	0.874834	−	1.51526i
$869$	0.0273355	−	0.0473464i	0.000927292	−	0.00160612i
$870$		0			0
$871$	2.00833	+	3.47853i	0.0680496	+	0.117865i
$872$	3.78956			0.128331
$873$		0			0
$874$	−1.81068			−0.0612471
$875$	−15.8258	−	27.4110i	−0.535009	−	0.926662i
$876$		0			0
$877$	4.42022	−	7.65604i	0.149260	−	0.258526i	−0.781694	−	0.623662i	$-0.785644\pi$
$877$	4.42022	−	7.65604i	0.149260	−	0.258526i	0.930954	+	0.365136i	$0.118978\pi$
$878$	4.12981	−	7.15303i	0.139374	−	0.241403i
$879$		0			0
$880$	−0.791746	−	1.37134i	−0.0266897	−	0.0462280i
$881$	−9.48167			−0.319445			−0.159723	−	0.987162i	$-0.551060\pi$
$881$	−9.48167			−0.319445			−0.159723	+	0.987162i	$0.551060\pi$
$882$		0			0
$883$	−13.6316			−0.458739			−0.229369	−	0.973339i	$-0.573666\pi$
$883$	−13.6316			−0.458739			−0.229369	+	0.973339i	$0.573666\pi$
$884$	0.334776	+	0.579850i	0.0112598	+	0.0195025i
$885$		0			0
$886$	−2.72533	+	4.72042i	−0.0915594	+	0.158586i
$887$	−25.0936	+	43.4634i	−0.842560	+	1.45936i	0.0451636	+	0.998980i	$0.485619\pi$
$887$	−25.0936	+	43.4634i	−0.842560	+	1.45936i	−0.887724	+	0.460377i	$0.847714\pi$
$888$		0			0
$889$	30.9853	+	53.6681i	1.03921	+	1.79997i
$890$	−9.77167			−0.327547
$891$		0			0
$892$	−33.9675			−1.13732
$893$	−0.0928735	−	0.160862i	−0.00310789	−	0.00538303i
$894$		0			0
$895$	6.64530	−	11.5100i	0.222128	−	0.384737i
$896$	−16.7800	+	29.0638i	−0.560581	+	0.970954i
$897$		0			0
$898$	−1.01623	−	1.76015i	−0.0339119	−	0.0587371i
$899$	−15.0725			−0.502695
$900$		0			0
$901$	−1.39244			−0.0463890
$902$	−0.0772876	−	0.133866i	−0.00257339	−	0.00445725i
$903$		0			0
$904$	7.97705	−	13.8167i	0.265313	−	0.459535i
$905$	19.6919	−	34.1074i	0.654582	−	1.13377i
$906$		0			0
$907$	−27.6176	−	47.8351i	−0.917028	−	1.58834i	−0.803905	−	0.594758i	$-0.797248\pi$
$907$	−27.6176	−	47.8351i	−0.917028	−	1.58834i	−0.113124	−	0.993581i	$-0.536086\pi$
$908$	−44.8558			−1.48859
$909$		0			0
$910$	−3.96600			−0.131472
$911$	1.94875	+	3.37533i	0.0645649	+	0.111830i	0.896501	−	0.443042i	$-0.146101\pi$
$911$	1.94875	+	3.37533i	0.0645649	+	0.111830i	−0.831936	+	0.554872i	$0.812767\pi$
$912$		0			0
$913$	0.0658189	−	0.114002i	0.00217829	−	0.00377290i
$914$	3.25422	−	5.63647i	0.107640	−	0.186438i
$915$		0			0
$916$	−8.85399	−	15.3356i	−0.292544	−	0.506701i
$917$	25.9000			0.855293
$918$		0			0
$919$	47.2360			1.55817			0.779087	−	0.626916i	$-0.215683\pi$
$919$	47.2360			1.55817			0.779087	+	0.626916i	$0.215683\pi$
$920$	−14.3141	−	24.7928i	−0.471922	−	0.817393i
$921$		0			0
$922$	1.45921	−	2.52742i	0.0480564	−	0.0832361i
$923$	−4.27620	+	7.40659i	−0.140753	+	0.243791i
$924$		0			0
$925$	8.63550	+	14.9571i	0.283934	+	0.491787i
$926$	7.81756			0.256901
$927$		0			0
$928$	7.40555			0.243099
$929$	20.7302	+	35.9057i	0.680136	+	1.17803i	0.974939	+	0.222472i	$0.0714124\pi$
$929$	20.7302	+	35.9057i	0.680136	+	1.17803i	−0.294804	+	0.955558i	$0.595254\pi$
$930$		0			0
$931$	5.42808	−	9.40171i	0.177898	−	0.308128i
$932$	−19.5159	+	33.8026i	−0.639266	+	1.10724i
$933$		0			0
$934$	−3.97846	−	6.89089i	−0.130179	−	0.225477i
$935$	−0.152141			−0.00497555
$936$		0			0
$937$	40.5189			1.32369			0.661847	−	0.749639i	$-0.269773\pi$
$937$	40.5189			1.32369			0.661847	+	0.749639i	$0.269773\pi$
$938$	2.29354	+	3.97252i	0.0748866	+	0.129707i
$939$		0			0
$940$	0.721758	−	1.25012i	0.0235411	−	0.0407745i
$941$	26.3131	−	45.5757i	0.857783	−	1.48572i	−0.0162551	−	0.999868i	$-0.505174\pi$
$941$	26.3131	−	45.5757i	0.857783	−	1.48572i	0.874039	−	0.485857i	$-0.161492\pi$
$942$		0			0
$943$	19.2098	+	33.2724i	0.625558	+	1.08350i
$944$	49.5293			1.61204
$945$		0			0
$946$	0.219853			0.00714804
$947$	−29.4464	−	51.0027i	−0.956880	−	1.65737i	−0.730006	−	0.683441i	$-0.760483\pi$
$947$	−29.4464	−	51.0027i	−0.956880	−	1.65737i	−0.226875	−	0.973924i	$-0.572851\pi$
$948$		0			0
$949$	−4.58750	+	7.94578i	−0.148917	+	0.257931i
$950$	0.787442	−	1.36389i	0.0255480	−	0.0442504i
$951$		0			0
$952$	0.777819	+	1.34722i	0.0252093	+	0.0436637i
$953$	48.3782			1.56712			0.783562	−	0.621313i	$-0.213400\pi$
$953$	48.3782			1.56712			0.783562	+	0.621313i	$0.213400\pi$
$954$		0			0
$955$	22.1954			0.718225
$956$	−7.44112	−	12.8884i	−0.240663	−	0.416840i
$957$		0			0
$958$	−1.65131	+	2.86014i	−0.0533513	+	0.0924071i
$959$	37.5050	−	64.9606i	1.21110	−	2.09769i
$960$		0			0
$961$	−2.66723	−	4.61978i	−0.0860396	−	0.149025i
$962$	0.631550			0.0203620
$963$		0			0
$964$	−6.00879			−0.193530
$965$	21.3428	+	36.9668i	0.687048	+	1.19000i
$966$		0			0
$967$	3.33999	−	5.78503i	0.107407	−	0.186034i	−0.807312	−	0.590125i	$-0.799079\pi$
$967$	3.33999	−	5.78503i	0.107407	−	0.186034i	0.914719	+	0.404091i	$0.132412\pi$
$968$	−5.57720	+	9.65999i	−0.179258	+	0.310484i
$969$		0			0
$970$	0.0801892	+	0.138892i	0.00257472	+	0.00445955i
$971$	10.4893			0.336618			0.168309	−	0.985734i	$-0.446169\pi$
$971$	10.4893			0.336618			0.168309	+	0.985734i	$0.446169\pi$
$972$		0			0
$973$	−47.4713			−1.52186
$974$	−0.941599	−	1.63090i	−0.0301708	−	0.0522573i
$975$		0			0
$976$	4.91405	−	8.51138i	0.157295	−	0.272443i
$977$	14.5581	−	25.2153i	0.465754	−	0.806709i	−0.533482	−	0.845812i	$-0.679117\pi$
$977$	14.5581	−	25.2153i	0.465754	−	0.806709i	0.999235	+	0.0391027i	$0.0124499\pi$
$978$		0			0
$979$	0.689321	+	1.19394i	0.0220308	+	0.0381584i
$980$	84.3676			2.69503
$981$		0			0
$982$	−1.24948			−0.0398726
$983$	26.9267	+	46.6385i	0.858829	+	1.48754i	0.873047	+	0.487637i	$0.162141\pi$
$983$	26.9267	+	46.6385i	0.858829	+	1.48754i	−0.0142175	+	0.999899i	$0.504526\pi$
$984$		0			0
$985$	10.4508	−	18.1013i	0.332990	−	0.576755i
$986$	0.111788	−	0.193622i	0.00356005	−	0.00616619i
$987$		0			0
$988$	0.835161	+	1.44654i	0.0265700	+	0.0460206i
$989$	−54.6445			−1.73759
$990$		0			0
$991$	−16.0335			−0.509322			−0.254661	−	0.967030i	$-0.581964\pi$
$991$	−16.0335			−0.509322			−0.254661	+	0.967030i	$0.581964\pi$
$992$	8.92609	+	15.4604i	0.283404	+	0.490870i
$993$		0			0
$994$	−4.88347	+	8.45842i	−0.154894	+	0.268285i
$995$	−19.2249	+	33.2984i	−0.609469	+	1.05563i
$996$		0			0
$997$	17.0632	+	29.5544i	0.540397	+	0.935996i	0.998881	+	0.0472930i	$0.0150595\pi$
$997$	17.0632	+	29.5544i	0.540397	+	0.935996i	−0.458484	+	0.888703i	$0.651607\pi$
$998$	−0.546048			−0.0172848
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.e.c.118.4		12
3.2	odd	2		117.2.e.c.40.3	✓	12
9.2	odd	6		117.2.e.c.79.3	yes	12
9.4	even	3		1053.2.a.m.1.3		6
9.5	odd	6		1053.2.a.l.1.4		6
9.7	even	3	inner	351.2.e.c.235.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.c.40.3	✓	12	3.2	odd	2
117.2.e.c.79.3	yes	12	9.2	odd	6
351.2.e.c.118.4		12	1.1	even	1	trivial
351.2.e.c.235.4		12	9.7	even	3	inner
1053.2.a.l.1.4		6	9.5	odd	6
1053.2.a.m.1.3		6	9.4	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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.129090 - 0.223591i) q^{2} +(0.966671 - 1.67432i) q^{4} +(1.73641 - 3.00755i) q^{5} +(2.21165 + 3.83070i) q^{7} -1.01551 q^{8} -0.896615 q^{10} +(0.0632497 + 0.109552i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.571006 - 0.989012i) q^{14} +(-1.80225 - 3.12159i) q^{16} -0.346319 q^{17} -0.863955 q^{19} +(-3.35707 - 5.81462i) q^{20} +(0.0163299 - 0.0282841i) q^{22} +(-4.05879 + 7.03003i) q^{23} +(-3.53023 - 6.11454i) q^{25} -0.258181 q^{26} +8.55177 q^{28} +(-1.25024 - 2.16549i) q^{29} +(3.01390 - 5.22023i) q^{31} +(-1.48082 + 2.56485i) q^{32} +(0.0447064 + 0.0774338i) q^{34} +15.3613 q^{35} -2.44616 q^{37} +(0.111528 + 0.193173i) q^{38} +(-1.76335 + 3.05421i) q^{40} +(2.36645 - 4.09881i) q^{41} +(3.36581 + 5.82976i) q^{43} +0.244567 q^{44} +2.09580 q^{46} +(0.107498 + 0.186192i) q^{47} +(-6.28282 + 10.8822i) q^{49} +(-0.911438 + 1.57866i) q^{50} +(-0.966671 - 1.67432i) q^{52} +4.02070 q^{53} +0.439310 q^{55} +(-2.24596 - 3.89012i) q^{56} +(-0.322789 + 0.559087i) q^{58} +(-6.87049 + 11.9000i) q^{59} +(1.36331 + 2.36132i) q^{61} -1.55626 q^{62} -6.44436 q^{64} +(-1.73641 - 3.00755i) q^{65} +(-2.00833 + 3.47853i) q^{67} +(-0.334776 + 0.579850i) q^{68} +(-1.98300 - 3.43466i) q^{70} -8.55239 q^{71} -9.17500 q^{73} +(0.315775 + 0.546939i) q^{74} +(-0.835161 + 1.44654i) q^{76} +(-0.279773 + 0.484581i) q^{77} +(-0.216092 - 0.374282i) q^{79} -12.5178 q^{80} -1.22194 q^{82} +(-0.520310 - 0.901203i) q^{83} +(-0.601351 + 1.04157i) q^{85} +(0.868988 - 1.50513i) q^{86} +(-0.0642309 - 0.111251i) q^{88} +10.8984 q^{89} +4.42331 q^{91} +(7.84703 + 13.5915i) q^{92} +(0.0277539 - 0.0480712i) q^{94} +(-1.50018 + 2.59839i) q^{95} +(-0.0894355 - 0.154907i) q^{97} +3.24421 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + 12 q^{8} - 12 q^{10} - 7 q^{11} + 6 q^{13} - 13 q^{14} - 6 q^{16} + 28 q^{17} - 6 q^{19} - 17 q^{20} + 3 q^{22} - 17 q^{23} - 3 q^{25} - 4 q^{26} + 30 q^{28} - 14 q^{29}+ \cdots + 34 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + 12 * q^8 - 12 * q^10 - 7 * q^11 + 6 * q^13 - 13 * q^14 - 6 * q^16 + 28 * q^17 - 6 * q^19 - 17 * q^20 + 3 * q^22 - 17 * q^23 - 3 * q^25 - 4 * q^26 + 30 * q^28 - 14 * q^29 - 6 * q^31 - 9 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 + 4 * q^38 + 6 * q^40 + 4 * q^41 + 3 * q^43 + 26 * q^44 - 9 * q^47 + 21 * q^50 + 6 * q^52 + 56 * q^53 + 30 * q^55 - 16 * q^56 - 18 * q^58 - 17 * q^59 + 6 * q^61 - 8 * q^62 - 60 * q^64 + 3 * q^65 + 12 * q^67 - 22 * q^68 - 9 * q^70 - 2 * q^71 - 18 * q^73 + 27 * q^74 + 3 * q^76 - 15 * q^77 + 6 * q^79 - 48 * q^80 + 54 * q^82 - 28 * q^83 - 27 * q^85 + 6 * q^86 + 9 * q^88 - 18 * q^89 - 44 * q^92 + 24 * q^94 - 32 * q^95 + 34 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more