LMFDB - Embedded newform 351.2.h.a.334.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(289,351)] 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([4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.289"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			334.7
Character	$\chi$	$=$	351.334
Dual form			351.2.h.a.289.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.163365 q^{2} -1.97331 q^{4} +(1.55806 - 2.69863i) q^{5} +(0.0682144 - 0.118151i) q^{7} -0.649100 q^{8} +(0.254532 - 0.440862i) q^{10} -4.17771 q^{11} +(0.300890 - 3.59297i) q^{13} +(0.0111438 - 0.0193017i) q^{14} +3.84058 q^{16} +(-2.67892 - 4.64002i) q^{17} +(-0.154748 - 0.268032i) q^{19} +(-3.07453 + 5.32524i) q^{20} -0.682491 q^{22} +(-0.961735 - 1.66577i) q^{23} +(-2.35507 - 4.07910i) q^{25} +(0.0491549 - 0.586967i) q^{26} +(-0.134608 + 0.233148i) q^{28} +2.75870 q^{29} +(2.28432 - 3.95657i) q^{31} +1.92562 q^{32} +(-0.437642 - 0.758018i) q^{34} +(-0.212564 - 0.368171i) q^{35} +(4.48902 - 7.77522i) q^{37} +(-0.0252804 - 0.0437870i) q^{38} +(-1.01133 + 1.75168i) q^{40} +(3.56877 + 6.18129i) q^{41} +(-5.32209 + 9.21812i) q^{43} +8.24392 q^{44} +(-0.157114 - 0.272129i) q^{46} +(0.663436 + 1.14910i) q^{47} +(3.49069 + 6.04606i) q^{49} +(-0.384737 - 0.666383i) q^{50} +(-0.593749 + 7.09006i) q^{52} -7.10873 q^{53} +(-6.50910 + 11.2741i) q^{55} +(-0.0442780 + 0.0766917i) q^{56} +0.450675 q^{58} +4.80940 q^{59} +(3.61647 - 6.26392i) q^{61} +(0.373179 - 0.646365i) q^{62} -7.36659 q^{64} +(-9.22731 - 6.41004i) q^{65} +(6.53369 + 11.3167i) q^{67} +(5.28634 + 9.15621i) q^{68} +(-0.0347255 - 0.0601463i) q^{70} +(-2.24787 - 3.89343i) q^{71} +1.18478 q^{73} +(0.733350 - 1.27020i) q^{74} +(0.305366 + 0.528910i) q^{76} +(-0.284980 + 0.493599i) q^{77} +(-1.41978 - 2.45913i) q^{79} +(5.98384 - 10.3643i) q^{80} +(0.583013 + 1.00981i) q^{82} +(5.19008 + 8.98948i) q^{83} -16.6956 q^{85} +(-0.869443 + 1.50592i) q^{86} +2.71175 q^{88} +(-6.17396 + 10.6936i) q^{89} +(-0.403988 - 0.280643i) q^{91} +(1.89780 + 3.28709i) q^{92} +(0.108382 + 0.187723i) q^{94} -0.964425 q^{95} +(8.05756 - 13.9561i) q^{97} +(0.570257 + 0.987715i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 18 q^{4} + 2 q^{5} + 3 q^{7} + 18 q^{8} - 6 q^{11} - 2 q^{14} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 11 q^{20} - 18 q^{22} - 17 q^{23} - 6 q^{25} + 12 q^{26} + 24 q^{29} - 6 q^{31} + 38 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 18 * q^4 + 2 * q^5 + 3 * q^7 + 18 * q^8 - 6 * q^11 - 2 * q^14 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 11 * q^20 - 18 * q^22 - 17 * q^23 - 6 * q^25 + 12 * q^26 + 24 * q^29 - 6 * q^31 + 38 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 - 5 * q^41 - 3 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 + 3 * q^49 + 20 * q^50 - 24 * q^52 + 20 * q^53 + 3 * q^55 - 40 * q^56 + 18 * q^58 - 38 * q^59 - 6 * q^61 - 19 * q^62 - 42 * q^64 + 2 * q^65 - 6 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 - 29 * q^74 - 15 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 - 78 * q^88 + q^89 - 6 * q^91 + 10 * q^92 - 9 * q^94 + 100 * q^95 + 24 * q^97 + 61 * q^98

Character values

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

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.163365			0.115517			0.0577583	−	0.998331i	$-0.481605\pi$
$2$	0.163365			0.115517			0.0577583	+	0.998331i	$0.481605\pi$
$3$		0			0
$3$		0			0
$4$	−1.97331			−0.986656
$5$	1.55806	−	2.69863i	0.696783	−	1.20686i	−0.272792	−	0.962073i	$-0.587947\pi$
$5$	1.55806	−	2.69863i	0.696783	−	1.20686i	0.969576	−	0.244791i	$-0.0787195\pi$
$6$		0			0
$7$	0.0682144	−	0.118151i	0.0257826	−	0.0446568i	−0.852846	−	0.522162i	$-0.825126\pi$
$7$	0.0682144	−	0.118151i	0.0257826	−	0.0446568i	0.878629	+	0.477505i	$0.158459\pi$
$8$	−0.649100			−0.229492
$9$		0			0
$10$	0.254532	−	0.440862i	0.0804900	−	0.139413i
$11$	−4.17771			−1.25963			−0.629813	−	0.776747i	$-0.716868\pi$
$11$	−4.17771			−1.25963			−0.629813	+	0.776747i	$0.716868\pi$
$12$		0			0
$13$	0.300890	−	3.59297i	0.0834518	−	0.996512i
$13$	0.300890	−	3.59297i	0.0834518	−	0.996512i
$14$	0.0111438	−	0.0193017i	0.00297832	−	0.00515860i
$15$		0			0
$16$	3.84058			0.960146
$17$	−2.67892	−	4.64002i	−0.649733	−	1.12537i	−0.983186	−	0.182604i	$-0.941547\pi$
$17$	−2.67892	−	4.64002i	−0.649733	−	1.12537i	0.333453	−	0.942767i	$-0.391786\pi$
$18$		0			0
$19$	−0.154748	−	0.268032i	−0.0355017	−	0.0614907i	0.847729	−	0.530430i	$-0.177970\pi$
$19$	−0.154748	−	0.268032i	−0.0355017	−	0.0614907i	−0.883230	+	0.468939i	$0.844636\pi$
$20$	−3.07453	+	5.32524i	−0.687486	+	1.19076i
$21$		0			0
$22$	−0.682491			−0.145508
$23$	−0.961735	−	1.66577i	−0.200536	−	0.347338i	0.748166	−	0.663512i	$-0.230935\pi$
$23$	−0.961735	−	1.66577i	−0.200536	−	0.347338i	−0.948701	+	0.316174i	$0.897602\pi$
$24$		0			0
$25$	−2.35507	−	4.07910i	−0.471014	−	0.815821i
$26$	0.0491549	−	0.586967i	0.00964007	−	0.115114i
$27$		0			0
$28$	−0.134608	+	0.233148i	−0.0254386	+	0.0440609i
$29$	2.75870			0.512278			0.256139	−	0.966640i	$-0.417550\pi$
$29$	2.75870			0.512278			0.256139	+	0.966640i	$0.417550\pi$
$30$		0			0
$31$	2.28432	−	3.95657i	0.410277	−	0.710620i	−0.584643	−	0.811291i	$-0.698765\pi$
$31$	2.28432	−	3.95657i	0.410277	−	0.710620i	0.994920	+	0.100670i	$0.0320988\pi$
$32$	1.92562			0.340404
$33$		0			0
$34$	−0.437642	−	0.758018i	−0.0750550	−	0.129999i
$35$	−0.212564	−	0.368171i	−0.0359298	−	0.0622322i
$36$		0			0
$37$	4.48902	−	7.77522i	0.737991	−	1.27824i	−0.215408	−	0.976524i	$-0.569108\pi$
$37$	4.48902	−	7.77522i	0.737991	−	1.27824i	0.953399	−	0.301713i	$-0.0975586\pi$
$38$	−0.0252804	−	0.0437870i	−0.00410103	−	0.00710319i
$39$		0			0
$40$	−1.01133	+	1.75168i	−0.159906	+	0.276965i
$41$	3.56877	+	6.18129i	0.557349	+	0.965356i	0.997717	+	0.0675387i	$0.0215146\pi$
$41$	3.56877	+	6.18129i	0.557349	+	0.965356i	−0.440368	+	0.897817i	$0.645152\pi$
$42$		0			0
$43$	−5.32209	+	9.21812i	−0.811610	+	1.40575i	0.100126	+	0.994975i	$0.468075\pi$
$43$	−5.32209	+	9.21812i	−0.811610	+	1.40575i	−0.911736	+	0.410776i	$0.865258\pi$
$44$	8.24392			1.24282
$45$		0			0
$46$	−0.157114	−	0.272129i	−0.0231652	−	0.0401233i
$47$	0.663436	+	1.14910i	0.0967720	+	0.167614i	0.910347	−	0.413846i	$-0.135815\pi$
$47$	0.663436	+	1.14910i	0.0967720	+	0.167614i	−0.813575	+	0.581460i	$0.802482\pi$
$48$		0			0
$49$	3.49069	+	6.04606i	0.498671	+	0.863723i
$50$	−0.384737	−	0.666383i	−0.0544100	−	0.0942408i
$51$		0			0
$52$	−0.593749	+	7.09006i	−0.0823382	+	0.983214i
$53$	−7.10873			−0.976459			−0.488230	−	0.872715i	$-0.662357\pi$
$53$	−7.10873			−0.976459			−0.488230	+	0.872715i	$0.662357\pi$
$54$		0			0
$55$	−6.50910	+	11.2741i	−0.877687	+	1.52020i
$56$	−0.0442780	+	0.0766917i	−0.00591689	+	0.0102484i
$57$		0			0
$58$	0.450675			0.0591765
$59$	4.80940			0.626131			0.313066	−	0.949732i	$-0.398644\pi$
$59$	4.80940			0.626131			0.313066	+	0.949732i	$0.398644\pi$
$60$		0			0
$61$	3.61647	−	6.26392i	0.463042	−	0.802012i	−0.536069	−	0.844174i	$-0.680091\pi$
$61$	3.61647	−	6.26392i	0.463042	−	0.802012i	0.999111	+	0.0421621i	$0.0134246\pi$
$62$	0.373179	−	0.646365i	0.0473938	−	0.0820884i
$63$		0			0
$64$	−7.36659			−0.920823
$65$	−9.22731	−	6.41004i	−1.14451	−	0.795068i
$66$		0			0
$67$	6.53369	+	11.3167i	0.798218	+	1.38255i	0.920776	+	0.390092i	$0.127557\pi$
$67$	6.53369	+	11.3167i	0.798218	+	1.38255i	−0.122558	+	0.992461i	$0.539110\pi$
$68$	5.28634	+	9.15621i	0.641063	+	1.11035i
$69$		0			0
$70$	−0.0347255	−	0.0601463i	−0.00415049	−	0.00718885i
$71$	−2.24787	−	3.89343i	−0.266773	−	0.462065i	0.701253	−	0.712912i	$-0.252624\pi$
$71$	−2.24787	−	3.89343i	−0.266773	−	0.462065i	−0.968027	+	0.250847i	$0.919291\pi$
$72$		0			0
$73$	1.18478			0.138668			0.0693340	−	0.997594i	$-0.477913\pi$
$73$	1.18478			0.138668			0.0693340	+	0.997594i	$0.477913\pi$
$74$	0.733350	−	1.27020i	0.0852502	−	0.147658i
$75$		0			0
$76$	0.305366	+	0.528910i	0.0350279	+	0.0606702i
$77$	−0.284980	+	0.493599i	−0.0324764	+	0.0562509i
$78$		0			0
$79$	−1.41978	−	2.45913i	−0.159737	−	0.276673i	0.775037	−	0.631916i	$-0.217731\pi$
$79$	−1.41978	−	2.45913i	−0.159737	−	0.276673i	−0.934774	+	0.355243i	$0.884398\pi$
$80$	5.98384	−	10.3643i	0.669014	−	1.15877i
$81$		0			0
$82$	0.583013	+	1.00981i	0.0643830	+	0.111515i
$83$	5.19008	+	8.98948i	0.569685	+	0.986724i	0.996597	+	0.0824302i	$0.0262682\pi$
$83$	5.19008	+	8.98948i	0.569685	+	0.986724i	−0.426912	+	0.904293i	$0.640399\pi$
$84$		0			0
$85$	−16.6956			−1.81089
$86$	−0.869443	+	1.50592i	−0.0937545	+	0.162387i
$87$		0			0
$88$	2.71175			0.289074
$89$	−6.17396	+	10.6936i	−0.654439	+	1.13352i	0.327595	+	0.944818i	$0.393762\pi$
$89$	−6.17396	+	10.6936i	−0.654439	+	1.13352i	−0.982034	+	0.188703i	$0.939572\pi$
$90$		0			0
$91$	−0.403988	−	0.280643i	−0.0423494	−	0.0294194i
$92$	1.89780	+	3.28709i	0.197860	+	0.342703i
$93$		0			0
$94$	0.108382	+	0.187723i	0.0111788	+	0.0193622i
$95$	−0.964425			−0.0989479
$96$		0			0
$97$	8.05756	−	13.9561i	0.818121	−	1.41703i	−0.0889443	−	0.996037i	$-0.528349\pi$
$97$	8.05756	−	13.9561i	0.818121	−	1.41703i	0.907065	−	0.420990i	$-0.138317\pi$
$98$	0.570257	+	0.987715i	0.0576047	+	0.0997743i
$99$		0			0
$100$	4.64729	+	8.04935i	0.464729	+	0.804935i
$101$	17.4488			1.73622			0.868110	−	0.496373i	$-0.165335\pi$
$101$	17.4488			1.73622			0.868110	+	0.496373i	$0.165335\pi$
$102$		0			0
$103$	7.28512	−	12.6182i	0.717824	−	1.24331i	−0.244036	−	0.969766i	$-0.578471\pi$
$103$	7.28512	−	12.6182i	0.717824	−	1.24331i	0.961860	−	0.273542i	$-0.0881953\pi$
$104$	−0.195308	+	2.33220i	−0.0191515	+	0.228691i
$105$		0			0
$106$	−1.16132			−0.112797
$107$	2.71632	−	4.70481i	0.262597	−	0.454831i	−0.704334	−	0.709868i	$-0.748754\pi$
$107$	2.71632	−	4.70481i	0.262597	−	0.454831i	0.966931	+	0.255037i	$0.0820877\pi$
$108$		0			0
$109$	−3.10914			−0.297802			−0.148901	−	0.988852i	$-0.547574\pi$
$109$	−3.10914			−0.297802			−0.148901	+	0.988852i	$0.547574\pi$
$110$	−1.06336	+	1.84179i	−0.101387	+	0.175608i
$111$		0			0
$112$	0.261983	−	0.453768i	0.0247551	−	0.0428770i
$113$	−7.02864			−0.661198			−0.330599	−	0.943771i	$-0.607251\pi$
$113$	−7.02864			−0.661198			−0.330599	+	0.943771i	$0.607251\pi$
$114$		0			0
$115$	−5.99374			−0.558919
$116$	−5.44377			−0.505442
$117$		0			0
$118$	0.785689			0.0723285
$119$	−0.730963			−0.0670073
$120$		0			0
$121$	6.45323			0.586658
$122$	0.590805	−	1.02331i	0.0534890	−	0.0926457i
$123$		0			0
$124$	−4.50768	+	7.80754i	−0.404802	+	0.701138i
$125$	0.903222			0.0807866
$126$		0			0
$127$	0.669477	−	1.15957i	0.0594065	−	0.102895i	−0.834793	−	0.550564i	$-0.814413\pi$
$127$	0.669477	−	1.15957i	0.0594065	−	0.102895i	0.894199	+	0.447669i	$0.147746\pi$
$128$	−5.05468			−0.446775
$129$		0			0
$130$	−1.50742	−	1.04718i	−0.132209	−	0.0918435i
$131$	6.59535	−	11.4235i	0.576238	−	0.998074i	−0.419668	−	0.907678i	$-0.637853\pi$
$131$	6.59535	−	11.4235i	0.576238	−	0.998074i	0.995906	−	0.0903959i	$-0.0288132\pi$
$132$		0			0
$133$	−0.0422242			−0.00366130
$134$	1.06738	+	1.84875i	0.0922074	+	0.159708i
$135$		0			0
$136$	1.73889	+	3.01184i	0.149108	+	0.258263i
$137$	−4.14439	+	7.17829i	−0.354079	+	0.613283i	−0.986960	−	0.160966i	$-0.948539\pi$
$137$	−4.14439	+	7.17829i	−0.354079	+	0.613283i	0.632881	+	0.774249i	$0.281872\pi$
$138$		0			0
$139$	−6.15797			−0.522313			−0.261156	−	0.965297i	$-0.584104\pi$
$139$	−6.15797			−0.522313			−0.261156	+	0.965297i	$0.584104\pi$
$140$	0.419454	+	0.726516i	0.0354503	+	0.0614018i
$141$		0			0
$142$	−0.367224	−	0.636050i	−0.0308167	−	0.0533761i
$143$	−1.25703	+	15.0104i	−0.105118	+	1.25523i
$144$		0			0
$145$	4.29821	−	7.44471i	0.356947	−	0.618250i
$146$	0.193552			0.0160185
$147$		0			0
$148$	−8.85824	+	15.3429i	−0.728143	+	1.26118i
$149$	3.97159			0.325365			0.162683	−	0.986678i	$-0.447985\pi$
$149$	3.97159			0.325365			0.162683	+	0.986678i	$0.447985\pi$
$150$		0			0
$151$	4.38546	+	7.59584i	0.356884	+	0.618141i	0.987438	−	0.158004i	$-0.0505059\pi$
$151$	4.38546	+	7.59584i	0.356884	+	0.618141i	−0.630555	+	0.776145i	$0.717173\pi$
$152$	0.100447	+	0.173979i	0.00814734	+	0.0141116i
$153$		0			0
$154$	−0.0465557	+	0.0806369i	−0.00375157	+	0.00649791i
$155$	−7.11821	−	12.3291i	−0.571748	−	0.990297i
$156$		0			0
$157$	6.29755	−	10.9077i	0.502599	−	0.870527i	−0.497397	−	0.867523i	$-0.665711\pi$
$157$	6.29755	−	10.9077i	0.502599	−	0.870527i	0.999995	−	0.00300365i	$-0.000956092\pi$
$158$	−0.231942	−	0.401735i	−0.0184523	−	0.0319604i
$159$		0			0
$160$	3.00022	−	5.19653i	0.237188	−	0.410822i
$161$	−0.262417			−0.0206813
$162$		0			0
$163$	1.05864	+	1.83361i	0.0829188	+	0.143620i	0.904502	−	0.426468i	$-0.140242\pi$
$163$	1.05864	+	1.83361i	0.0829188	+	0.143620i	−0.821584	+	0.570088i	$0.806909\pi$
$164$	−7.04230	−	12.1976i	−0.549911	−	0.952474i
$165$		0			0
$166$	0.847878	+	1.46857i	0.0658081	+	0.113983i
$167$	−4.66281	−	8.07622i	−0.360819	−	0.624956i	0.627277	−	0.778796i	$-0.284169\pi$
$167$	−4.66281	−	8.07622i	−0.360819	−	0.624956i	−0.988096	+	0.153840i	$0.950836\pi$
$168$		0			0
$169$	−12.8189	−	2.16218i	−0.986072	−	0.166321i
$170$	−2.72748			−0.209188
$171$		0			0
$172$	10.5021	−	18.1902i	0.800780	−	1.38699i
$173$	−4.27403	+	7.40284i	−0.324948	+	0.562827i	−0.981502	−	0.191452i	$-0.938680\pi$
$173$	−4.27403	+	7.40284i	−0.324948	+	0.562827i	0.656553	+	0.754279i	$0.272014\pi$
$174$		0			0
$175$	−0.642599			−0.0485759
$176$	−16.0448			−1.20942
$177$		0			0
$178$	−1.00861	+	1.74696i	−0.0755985	+	0.130941i
$179$	−1.59537	+	2.76327i	−0.119244	+	0.206536i	−0.919468	−	0.393164i	$-0.871380\pi$
$179$	−1.59537	+	2.76327i	−0.119244	+	0.206536i	0.800224	+	0.599701i	$0.204714\pi$
$180$		0			0
$181$	−1.50392			−0.111786			−0.0558928	−	0.998437i	$-0.517801\pi$
$181$	−1.50392			−0.111786			−0.0558928	+	0.998437i	$0.517801\pi$
$182$	−0.0659975	−	0.0458472i	−0.00489206	−	0.00339842i
$183$		0			0
$184$	0.624262	+	1.08125i	0.0460212	+	0.0797111i
$185$	−13.9883	−	24.2284i	−1.02844	−	1.78131i
$186$		0			0
$187$	11.1917	+	19.3847i	0.818421	+	1.41755i
$188$	−1.30917	−	2.26754i	−0.0954807	−	0.165377i
$189$		0			0
$190$	−0.157553			−0.0114301
$191$	10.0559	−	17.4174i	0.727621	−	1.26028i	−0.230264	−	0.973128i	$-0.573959\pi$
$191$	10.0559	−	17.4174i	0.727621	−	1.26028i	0.957886	−	0.287149i	$-0.0927076\pi$
$192$		0			0
$193$	−3.94854	−	6.83908i	−0.284222	−	0.492287i	0.688198	−	0.725523i	$-0.258402\pi$
$193$	−3.94854	−	6.83908i	−0.284222	−	0.492287i	−0.972420	+	0.233235i	$0.925069\pi$
$194$	1.31632	−	2.27994i	0.0945065	−	0.163690i
$195$		0			0
$196$	−6.88823	−	11.9308i	−0.492016	−	0.852197i
$197$	11.6325	−	20.1482i	0.828785	−	1.43550i	−0.0702072	−	0.997532i	$-0.522366\pi$
$197$	11.6325	−	20.1482i	0.828785	−	1.43550i	0.898992	−	0.437965i	$-0.144301\pi$
$198$		0			0
$199$	−4.59323	−	7.95571i	−0.325605	−	0.563965i	0.656029	−	0.754735i	$-0.272235\pi$
$199$	−4.59323	−	7.95571i	−0.325605	−	0.563965i	−0.981635	+	0.190770i	$0.938901\pi$
$200$	1.52868	+	2.64775i	0.108094	+	0.187224i
$201$		0			0
$202$	2.85052			0.200562
$203$	0.188183	−	0.325942i	0.0132079	−	0.0228767i
$204$		0			0
$205$	22.2414			1.55340
$206$	1.19013	−	2.06137i	0.0829206	−	0.143623i
$207$		0			0
$208$	1.15559	−	13.7991i	0.0801259	−	0.956797i
$209$	0.646493	+	1.11976i	0.0447188	+	0.0774553i
$210$		0			0
$211$	−6.24157	−	10.8107i	−0.429687	−	0.744241i	0.567158	−	0.823609i	$-0.308043\pi$
$211$	−6.24157	−	10.8107i	−0.429687	−	0.744241i	−0.996845	+	0.0793686i	$0.974710\pi$
$212$	14.0277			0.963429
$213$		0			0
$214$	0.443752	−	0.768602i	0.0303343	−	0.0525405i
$215$	16.5842	+	28.7247i	1.13103	+	1.95901i
$216$		0			0
$217$	−0.311647	−	0.539789i	−0.0211560	−	0.0366433i
$218$	−0.507925			−0.0344010
$219$		0			0
$220$	12.8445	−	22.2473i	0.865975	−	1.49991i
$221$	−17.4775	+	8.22915i	−1.17567	+	0.553553i
$222$		0			0
$223$	−9.88798			−0.662148			−0.331074	−	0.943605i	$-0.607411\pi$
$223$	−9.88798			−0.662148			−0.331074	+	0.943605i	$0.607411\pi$
$224$	0.131355	−	0.227513i	0.00877651	−	0.0152014i
$225$		0			0
$226$	−1.14823			−0.0763794
$227$	5.01892	−	8.69303i	0.333118	−	0.576977i	−0.650004	−	0.759931i	$-0.725233\pi$
$227$	5.01892	−	8.69303i	0.333118	−	0.576977i	0.983121	+	0.182954i	$0.0585661\pi$
$228$		0			0
$229$	−2.85730	+	4.94899i	−0.188816	+	0.327039i	−0.944856	−	0.327487i	$-0.893798\pi$
$229$	−2.85730	+	4.94899i	−0.188816	+	0.327039i	0.756040	+	0.654526i	$0.227132\pi$
$230$	−0.979168			−0.0645644
$231$		0			0
$232$	−1.79067			−0.117563
$233$	−20.4987			−1.34292			−0.671458	−	0.741043i	$-0.734331\pi$
$233$	−20.4987			−1.34292			−0.671458	+	0.741043i	$0.734331\pi$
$234$		0			0
$235$	4.13468			0.269717
$236$	−9.49046			−0.617776
$237$		0			0
$238$	−0.119414			−0.00774045
$239$	−14.9837	+	25.9525i	−0.969212	+	1.67872i	−0.271368	+	0.962476i	$0.587476\pi$
$239$	−14.9837	+	25.9525i	−0.969212	+	1.67872i	−0.697845	+	0.716249i	$0.745857\pi$
$240$		0			0
$241$	−7.66471	+	13.2757i	−0.493727	+	0.855161i	−0.999974	−	0.00722792i	$-0.997699\pi$
$241$	−7.66471	+	13.2757i	−0.493727	+	0.855161i	0.506247	+	0.862389i	$0.331033\pi$
$242$	1.05423			0.0677687
$243$		0			0
$244$	−7.13643	+	12.3607i	−0.456863	+	0.791310i
$245$	21.7548			1.38986
$246$		0			0
$247$	−1.00959	+	0.475358i	−0.0642389	+	0.0302463i
$248$	−1.48276	+	2.56821i	−0.0941551	+	0.163081i
$249$		0			0
$250$	0.147555			0.00933219
$251$	10.1509	+	17.5818i	0.640718	+	1.10976i	0.985273	+	0.170990i	$0.0546964\pi$
$251$	10.1509	+	17.5818i	0.640718	+	1.10976i	−0.344555	+	0.938766i	$0.611970\pi$
$252$		0			0
$253$	4.01785	+	6.95911i	0.252600	+	0.437516i
$254$	0.109369	−	0.189433i	0.00686243	−	0.0118861i
$255$		0			0
$256$	13.9074			0.869214
$257$	−13.9975	−	24.2444i	−0.873140	−	1.51232i	−0.858731	−	0.512427i	$-0.828747\pi$
$257$	−13.9975	−	24.2444i	−0.873140	−	1.51232i	−0.0144089	−	0.999896i	$-0.504587\pi$
$258$		0			0
$259$	−0.612432	−	1.06076i	−0.0380547	−	0.0659126i
$260$	18.2084	+	12.6490i	1.12923	+	0.784459i
$261$		0			0
$262$	1.07745	−	1.86620i	0.0665650	−	0.115294i
$263$	2.63843			0.162693			0.0813464	−	0.996686i	$-0.474078\pi$
$263$	2.63843			0.162693			0.0813464	+	0.996686i	$0.474078\pi$
$264$		0			0
$265$	−11.0758	+	19.1838i	−0.680381	+	1.17845i
$266$	−0.00689796			−0.000422941
$267$		0			0
$268$	−12.8930	−	22.3314i	−0.787566	−	1.36410i
$269$	1.95848	+	3.39219i	0.119411	+	0.206826i	0.919534	−	0.393010i	$-0.128566\pi$
$269$	1.95848	+	3.39219i	0.119411	+	0.206826i	−0.800124	+	0.599835i	$0.795233\pi$
$270$		0			0
$271$	−9.54824	+	16.5380i	−0.580015	+	1.00461i	0.415462	+	0.909610i	$0.363620\pi$
$271$	−9.54824	+	16.5380i	−0.580015	+	1.00461i	−0.995477	+	0.0950042i	$0.969714\pi$
$272$	−10.2886	−	17.8204i	−0.623839	−	1.08052i
$273$		0			0
$274$	−0.677048	+	1.17268i	−0.0409020	+	0.0708443i
$275$	9.83880	+	17.0413i	0.593302	+	1.02763i
$276$		0			0
$277$	1.48070	−	2.56464i	0.0889664	−	0.154094i	−0.818108	−	0.575064i	$-0.804977\pi$
$277$	1.48070	−	2.56464i	0.0889664	−	0.154094i	0.907074	+	0.420970i	$0.138310\pi$
$278$	−1.00600			−0.0603358
$279$		0			0
$280$	0.137975	+	0.238980i	0.00824559	+	0.0142818i
$281$	2.16169	+	3.74415i	0.128955	+	0.223357i	0.923272	−	0.384147i	$-0.125504\pi$
$281$	2.16169	+	3.74415i	0.128955	+	0.223357i	−0.794317	+	0.607504i	$0.792171\pi$
$282$		0			0
$283$	10.8996	+	18.8787i	0.647916	+	1.12222i	0.983620	+	0.180256i	$0.0576926\pi$
$283$	10.8996	+	18.8787i	0.647916	+	1.12222i	−0.335704	+	0.941968i	$0.608974\pi$
$284$	4.43575	+	7.68295i	0.263213	+	0.455899i
$285$		0			0
$286$	−0.205355	+	2.45217i	−0.0121429	+	0.145000i
$287$	0.973766			0.0574796
$288$		0			0
$289$	−5.85322	+	10.1381i	−0.344307	+	0.596357i
$290$	0.702177	−	1.21621i	0.0412332	−	0.0714181i
$291$		0			0
$292$	−2.33794			−0.136818
$293$	10.6414			0.621679			0.310839	−	0.950462i	$-0.399390\pi$
$293$	10.6414			0.621679			0.310839	+	0.950462i	$0.399390\pi$
$294$		0			0
$295$	7.49332	−	12.9788i	0.436278	−	0.755655i
$296$	−2.91383	+	5.04690i	−0.169363	+	0.293345i
$297$		0			0
$298$	0.648819			0.0375851
$299$	−6.27446	+	2.95427i	−0.362861	+	0.170850i
$300$		0			0
$301$	0.726086	+	1.25762i	0.0418509	+	0.0724878i
$302$	0.716431	+	1.24089i	0.0412260	+	0.0714055i
$303$		0			0
$304$	−0.594323	−	1.02940i	−0.0340868	−	0.0590400i
$305$	−11.2693	−	19.5191i	−0.645280	−	1.11766i
$306$		0			0
$307$	10.9099			0.622662			0.311331	−	0.950302i	$-0.399225\pi$
$307$	10.9099			0.622662			0.311331	+	0.950302i	$0.399225\pi$
$308$	0.562354	−	0.974025i	0.0320431	−	0.0555002i
$309$		0			0
$310$	−1.16287	−	2.01414i	−0.0660464	−	0.114396i
$311$	0.145889	−	0.252687i	0.00827259	−	0.0143285i	−0.861859	−	0.507147i	$-0.830700\pi$
$311$	0.145889	−	0.252687i	0.00827259	−	0.0143285i	0.870132	+	0.492819i	$0.164033\pi$
$312$		0			0
$313$	4.12641	+	7.14715i	0.233239	+	0.403981i	0.958759	−	0.284219i	$-0.0917344\pi$
$313$	4.12641	+	7.14715i	0.233239	+	0.403981i	−0.725521	+	0.688200i	$0.758401\pi$
$314$	1.02880	−	1.78193i	0.0580585	−	0.100560i
$315$		0			0
$316$	2.80166	+	4.85262i	0.157606	+	0.272981i
$317$	7.08881	+	12.2782i	0.398147	+	0.689611i	0.993497	−	0.113855i	$-0.0363200\pi$
$317$	7.08881	+	12.2782i	0.398147	+	0.689611i	−0.595350	+	0.803466i	$0.702987\pi$
$318$		0			0
$319$	−11.5250			−0.645278
$320$	−11.4776	+	19.8797i	−0.641615	+	1.11131i
$321$		0			0
$322$	−0.0428697			−0.00238903
$323$	−0.829116	+	1.43607i	−0.0461332	+	0.0799051i
$324$		0			0
$325$	−15.3647	+	7.23435i	−0.852282	+	0.401290i
$326$	0.172944	+	0.299548i	0.00957849	+	0.0165904i
$327$		0			0
$328$	−2.31649	−	4.01228i	−0.127907	−	0.221541i
$329$	0.181023			0.00998014
$330$		0			0
$331$	−5.75482	+	9.96765i	−0.316314	+	0.547872i	−0.979716	−	0.200392i	$-0.935779\pi$
$331$	−5.75482	+	9.96765i	−0.316314	+	0.547872i	0.663402	+	0.748263i	$0.269112\pi$
$332$	−10.2416	−	17.7390i	−0.562083	−	0.973557i
$333$		0			0
$334$	−0.761740	−	1.31937i	−0.0416805	−	0.0721928i
$335$	40.7194			2.22474
$336$		0			0
$337$	−6.72098	+	11.6411i	−0.366115	+	0.634130i	−0.988954	−	0.148220i	$-0.952646\pi$
$337$	−6.72098	+	11.6411i	−0.366115	+	0.634130i	0.622839	+	0.782350i	$0.285979\pi$
$338$	−2.09417	−	0.353224i	−0.113908	−	0.0192129i
$339$		0			0
$340$	32.9457			1.78673
$341$	−9.54324	+	16.5294i	−0.516795	+	0.895116i
$342$		0			0
$343$	1.90746			0.102993
$344$	3.45457	−	5.98349i	0.186258	−	0.322608i
$345$		0			0
$346$	−0.698227	+	1.20937i	−0.0375369	+	0.0650159i
$347$	8.51438			0.457076			0.228538	−	0.973535i	$-0.426606\pi$
$347$	8.51438			0.457076			0.228538	+	0.973535i	$0.426606\pi$
$348$		0			0
$349$	−10.5936			−0.567064			−0.283532	−	0.958963i	$-0.591506\pi$
$349$	−10.5936			−0.567064			−0.283532	+	0.958963i	$0.591506\pi$
$350$	−0.104978			−0.00561132
$351$		0			0
$352$	−8.04467			−0.428782
$353$	1.69055			0.0899790			0.0449895	−	0.998987i	$-0.485675\pi$
$353$	1.69055			0.0899790			0.0449895	+	0.998987i	$0.485675\pi$
$354$		0			0
$355$	−14.0092			−0.743533
$356$	12.1832	−	21.1018i	0.645706	−	1.11840i
$357$		0			0
$358$	−0.260628	+	0.451421i	−0.0137746	+	0.0238584i
$359$	31.9604			1.68680			0.843402	−	0.537282i	$-0.180549\pi$
$359$	31.9604			1.68680			0.843402	+	0.537282i	$0.180549\pi$
$360$		0			0
$361$	9.45211	−	16.3715i	0.497479	−	0.861659i
$362$	−0.245688			−0.0129131
$363$		0			0
$364$	0.797194	+	0.553796i	0.0417843	+	0.0290268i
$365$	1.84595	−	3.19728i	0.0966216	−	0.167353i
$366$		0			0
$367$	18.8213			0.982465			0.491232	−	0.871029i	$-0.336547\pi$
$367$	18.8213			0.982465			0.491232	+	0.871029i	$0.336547\pi$
$368$	−3.69362	−	6.39754i	−0.192543	−	0.333495i
$369$		0			0
$370$	−2.28520	−	3.95808i	−0.118802	−	0.205771i
$371$	−0.484918	+	0.839902i	−0.0251757	+	0.0436055i
$372$		0			0
$373$	14.5944			0.755671			0.377835	−	0.925873i	$-0.376669\pi$
$373$	14.5944			0.755671			0.377835	+	0.925873i	$0.376669\pi$
$374$	1.82834	+	3.16678i	0.0945412	+	0.163750i
$375$		0			0
$376$	−0.430636	−	0.745884i	−0.0222084	−	0.0384660i
$377$	0.830064	−	9.91194i	0.0427505	−	0.510491i
$378$		0			0
$379$	−9.71303	+	16.8235i	−0.498925	+	0.864164i	−0.999999	−	0.00124079i	$-0.999605\pi$
$379$	−9.71303	+	16.8235i	−0.498925	+	0.864164i	0.501074	+	0.865404i	$0.332938\pi$
$380$	1.90311			0.0976275
$381$		0			0
$382$	1.64279	−	2.84539i	0.0840523	−	0.145583i
$383$	8.25957			0.422044			0.211022	−	0.977481i	$-0.432321\pi$
$383$	8.25957			0.422044			0.211022	+	0.977481i	$0.432321\pi$
$384$		0			0
$385$	0.888028	+	1.53811i	0.0452581	+	0.0783893i
$386$	−0.645054	−	1.11727i	−0.0328324	−	0.0568674i
$387$		0			0
$388$	−15.9001	+	27.5397i	−0.807204	+	1.39812i
$389$	−3.64491	−	6.31318i	−0.184805	−	0.320091i	0.758706	−	0.651433i	$-0.225832\pi$
$389$	−3.64491	−	6.31318i	−0.184805	−	0.320091i	−0.943511	+	0.331342i	$0.892499\pi$
$390$		0			0
$391$	−5.15282	+	8.92494i	−0.260589	+	0.451354i
$392$	−2.26581	−	3.92450i	−0.114441	−	0.198217i
$393$		0			0
$394$	1.90035	−	3.29151i	0.0957384	−	0.165824i
$395$	−8.84837			−0.445210
$396$		0			0
$397$	−4.03967	−	6.99691i	−0.202745	−	0.351165i	0.746667	−	0.665198i	$-0.231653\pi$
$397$	−4.03967	−	6.99691i	−0.202745	−	0.351165i	−0.949412	+	0.314033i	$0.898320\pi$
$398$	−0.750373	−	1.29968i	−0.0376128	−	0.0651473i
$399$		0			0
$400$	−9.04485	−	15.6661i	−0.452243	−	0.783307i
$401$	−0.0564213	−	0.0977246i	−0.00281755	−	0.00488013i	0.864613	−	0.502438i	$-0.167564\pi$
$401$	−0.0564213	−	0.0977246i	−0.00281755	−	0.00488013i	−0.867431	+	0.497558i	$0.834230\pi$
$402$		0			0
$403$	−13.5285	−	9.39801i	−0.673903	−	0.468148i
$404$	−34.4319			−1.71305
$405$		0			0
$406$	0.0307425	−	0.0532476i	0.00152573	−	0.00264263i
$407$	−18.7538	+	32.4826i	−0.929592	+	1.61010i
$408$		0			0
$409$	25.5211			1.26194			0.630969	−	0.775808i	$-0.282657\pi$
$409$	25.5211			1.26194			0.630969	+	0.775808i	$0.282657\pi$
$410$	3.63346			0.179444
$411$		0			0
$412$	−14.3758	+	24.8996i	−0.708246	+	1.22672i
$413$	0.328071	−	0.568235i	0.0161433	−	0.0279610i
$414$		0			0
$415$	32.3457			1.58779
$416$	0.579399	−	6.91870i	0.0284074	−	0.339217i
$417$		0			0
$418$	0.105614	+	0.182929i	0.00516576	+	0.00894737i
$419$	7.80239	+	13.5141i	0.381171	+	0.660208i	0.991230	−	0.132148i	$-0.0421874\pi$
$419$	7.80239	+	13.5141i	0.381171	+	0.660208i	−0.610059	+	0.792356i	$0.708854\pi$
$420$		0			0
$421$	−4.15567	−	7.19784i	−0.202535	−	0.350801i	0.746809	−	0.665038i	$-0.231585\pi$
$421$	−4.15567	−	7.19784i	−0.202535	−	0.350801i	−0.949345	+	0.314237i	$0.898251\pi$
$422$	−1.01965	−	1.76609i	−0.0496360	−	0.0859721i
$423$		0			0
$424$	4.61428			0.224089
$425$	−12.6181	+	21.8552i	−0.612068	+	1.06013i
$426$		0			0
$427$	−0.493391	−	0.854578i	−0.0238769	−	0.0413559i
$428$	−5.36015	+	9.28406i	−0.259093	+	0.448762i
$429$		0			0
$430$	2.70928	+	4.69261i	0.130653	+	0.226298i
$431$	−9.43395	+	16.3401i	−0.454417	+	0.787074i	−0.998655	−	0.0518573i	$-0.983486\pi$
$431$	−9.43395	+	16.3401i	−0.454417	+	0.787074i	0.544237	+	0.838932i	$0.316819\pi$
$432$		0			0
$433$	−5.44393	−	9.42916i	−0.261619	−	0.453137i	0.705054	−	0.709154i	$-0.250923\pi$
$433$	−5.44393	−	9.42916i	−0.261619	−	0.453137i	−0.966672	+	0.256017i	$0.917590\pi$
$434$	−0.0509123	−	0.0881827i	−0.00244387	−	0.00423291i
$435$		0			0
$436$	6.13531			0.293828
$437$	−0.297653	+	0.515551i	−0.0142387	+	0.0246621i
$438$		0			0
$439$	−35.3376			−1.68657			−0.843285	−	0.537466i	$-0.819382\pi$
$439$	−35.3376			−1.68657			−0.843285	+	0.537466i	$0.819382\pi$
$440$	4.22506	−	7.31802i	0.201422	−	0.348873i
$441$		0			0
$442$	−2.85522	+	1.34436i	−0.135809	+	0.0639445i
$443$	−4.71029	−	8.15846i	−0.223793	−	0.387620i	0.732164	−	0.681129i	$-0.238511\pi$
$443$	−4.71029	−	8.15846i	−0.223793	−	0.387620i	−0.955957	+	0.293508i	$0.905177\pi$
$444$		0			0
$445$	19.2388	+	33.3225i	0.912004	+	1.57964i
$446$	−1.61535			−0.0764891
$447$		0			0
$448$	−0.502507	+	0.870368i	−0.0237412	+	0.0411210i
$449$	10.8122	+	18.7273i	0.510259	+	0.883795i	0.999929	+	0.0118874i	$0.00378395\pi$
$449$	10.8122	+	18.7273i	0.510259	+	0.883795i	−0.489670	+	0.871908i	$0.662883\pi$
$450$		0			0
$451$	−14.9093	−	25.8236i	−0.702051	−	1.21599i
$452$	13.8697			0.652375
$453$		0			0
$454$	0.819917	−	1.42014i	0.0384806	−	0.0666503i
$455$	−1.38679	+	0.652957i	−0.0650136	+	0.0306111i
$456$		0			0
$457$	21.9147			1.02512			0.512562	−	0.858650i	$-0.328696\pi$
$457$	21.9147			1.02512			0.512562	+	0.858650i	$0.328696\pi$
$458$	−0.466784	+	0.808493i	−0.0218114	+	0.0377784i
$459$		0			0
$460$	11.8275			0.551461
$461$	−16.2574	+	28.1586i	−0.757182	+	1.31148i	0.187101	+	0.982341i	$0.440091\pi$
$461$	−16.2574	+	28.1586i	−0.757182	+	1.31148i	−0.944282	+	0.329136i	$0.893242\pi$
$462$		0			0
$463$	5.55585	−	9.62301i	0.258202	−	0.447219i	−0.707558	−	0.706655i	$-0.750203\pi$
$463$	5.55585	−	9.62301i	0.258202	−	0.447219i	0.965760	+	0.259436i	$0.0835366\pi$
$464$	10.5950			0.491861
$465$		0			0
$466$	−3.34877			−0.155129
$467$	22.2399			1.02914			0.514571	−	0.857448i	$-0.327951\pi$
$467$	22.2399			1.02914			0.514571	+	0.857448i	$0.327951\pi$
$468$		0			0
$469$	1.78277			0.0823206
$470$	0.675462			0.0311567
$471$		0			0
$472$	−3.12179			−0.143692
$473$	22.2341	−	38.5106i	1.02233	−	1.77072i
$474$		0			0
$475$	−0.728886	+	1.26247i	−0.0334436	+	0.0579260i
$476$	1.44242			0.0661131
$477$		0			0
$478$	−2.44781	+	4.23973i	−0.111960	+	0.193921i
$479$	−20.0436			−0.915814			−0.457907	−	0.889000i	$-0.651401\pi$
$479$	−20.0436			−0.915814			−0.457907	+	0.889000i	$0.651401\pi$
$480$		0			0
$481$	−26.5854	−	18.4684i	−1.21219	−	0.842088i
$482$	−1.25215	+	2.16878i	−0.0570337	+	0.0987852i
$483$		0			0
$484$	−12.7342			−0.578829
$485$	−25.1082	−	43.4887i	−1.14011	−	1.97472i
$486$		0			0
$487$	−0.356440	−	0.617373i	−0.0161519	−	0.0279758i	0.857837	−	0.513923i	$-0.171808\pi$
$487$	−0.356440	−	0.617373i	−0.0161519	−	0.0279758i	−0.873988	+	0.485947i	$0.838475\pi$
$488$	−2.34745	+	4.06591i	−0.106264	+	0.184055i
$489$		0			0
$490$	3.55397			0.160552
$491$	−5.09385	−	8.82281i	−0.229882	−	0.398168i	0.727891	−	0.685693i	$-0.240501\pi$
$491$	−5.09385	−	8.82281i	−0.229882	−	0.398168i	−0.957773	+	0.287525i	$0.907167\pi$
$492$		0			0
$493$	−7.39033	−	12.8004i	−0.332844	−	0.576502i
$494$	−0.164932	+	0.0776569i	−0.00742065	+	0.00349395i
$495$		0			0
$496$	8.77314	−	15.1955i	0.393925	−	0.682299i
$497$	−0.613349			−0.0275124
$498$		0			0
$499$	19.9631	−	34.5772i	0.893673	−	1.54789i	0.0582348	−	0.998303i	$-0.481453\pi$
$499$	19.9631	−	34.5772i	0.893673	−	1.54789i	0.835438	−	0.549584i	$-0.185214\pi$
$500$	−1.78234			−0.0797086
$501$		0			0
$502$	1.65830	+	2.87226i	0.0740135	+	0.128195i
$503$	−11.9792	−	20.7485i	−0.534125	−	0.925132i	−0.999205	−	0.0398630i	$-0.987308\pi$
$503$	−11.9792	−	20.7485i	−0.534125	−	0.925132i	0.465080	−	0.885269i	$-0.346025\pi$
$504$		0			0
$505$	27.1862	−	47.0878i	1.20977	−	2.09538i
$506$	0.656376	+	1.13688i	0.0291795	+	0.0505403i
$507$		0			0
$508$	−1.32109	+	2.28819i	−0.0586137	+	0.101522i
$509$	7.55690	+	13.0889i	0.334954	+	0.580157i	0.983476	−	0.181039i	$-0.0579460\pi$
$509$	7.55690	+	13.0889i	0.334954	+	0.580157i	−0.648522	+	0.761196i	$0.724613\pi$
$510$		0			0
$511$	0.0808190	−	0.139983i	0.00357522	−	0.00619247i
$512$	12.3813			0.547183
$513$		0			0
$514$	−2.28670	−	3.96068i	−0.100862	−	0.174698i
$515$	−22.7012	−	39.3197i	−1.00034	−	1.73263i
$516$		0			0
$517$	−2.77164	−	4.80062i	−0.121897	−	0.211131i
$518$	−0.100050	−	0.173292i	−0.00439594	−	0.00761400i
$519$		0			0
$520$	5.98945	+	4.16076i	0.262655	+	0.182461i
$521$	19.9265			0.872994			0.436497	−	0.899706i	$-0.356219\pi$
$521$	19.9265			0.872994			0.436497	+	0.899706i	$0.356219\pi$
$522$		0			0
$523$	7.52452	−	13.0328i	0.329024	−	0.569887i	−0.653294	−	0.757104i	$-0.726614\pi$
$523$	7.52452	−	13.0328i	0.329024	−	0.569887i	0.982319	+	0.187217i	$0.0599469\pi$
$524$	−13.0147	+	22.5421i	−0.568549	+	0.984755i
$525$		0			0
$526$	0.431028			0.0187937
$527$	−24.4781			−1.06628
$528$		0			0
$529$	9.65013	−	16.7145i	0.419571	−	0.726718i
$530$	−1.80940	+	3.13397i	−0.0785952	+	0.136131i
$531$		0			0
$532$	0.0833215			0.00361245
$533$	23.2830	−	10.9626i	1.00850	−	0.474844i
$534$		0			0
$535$	−8.46436	−	14.6607i	−0.365946	−	0.633838i
$536$	−4.24102	−	7.34567i	−0.183184	−	0.317285i
$537$		0			0
$538$	0.319948	+	0.554166i	0.0137939	+	0.0238918i
$539$	−14.5831	−	25.2587i	−0.628138	−	1.08797i
$540$		0			0
$541$	−34.9072			−1.50078			−0.750389	−	0.660997i	$-0.770134\pi$
$541$	−34.9072			−1.50078			−0.750389	+	0.660997i	$0.770134\pi$
$542$	−1.55985	+	2.70174i	−0.0670013	+	0.116050i
$543$		0			0
$544$	−5.15858	−	8.93491i	−0.221172	−	0.383081i
$545$	−4.84421	+	8.39042i	−0.207503	+	0.359406i
$546$		0			0
$547$	6.34298	+	10.9864i	0.271206	+	0.469743i	0.969171	−	0.246389i	$-0.0792441\pi$
$547$	6.34298	+	10.9864i	0.271206	+	0.469743i	−0.697965	+	0.716132i	$0.745911\pi$
$548$	8.17817	−	14.1650i	0.349354	−	0.605099i
$549$		0			0
$550$	1.60732	+	2.78395i	0.0685362	+	0.118708i
$551$	−0.426904	−	0.739419i	−0.0181867	−	0.0315003i
$552$		0			0
$553$	−0.387397			−0.0164738
$554$	0.241894	−	0.418973i	0.0102771	−	0.0178005i
$555$		0			0
$556$	12.1516			0.515343
$557$	3.74325	−	6.48350i	0.158607	−	0.274715i	−0.775760	−	0.631028i	$-0.782633\pi$
$557$	3.74325	−	6.48350i	0.158607	−	0.274715i	0.934366	+	0.356314i	$0.115967\pi$
$558$		0			0
$559$	31.5191	+	21.8958i	1.33312	+	0.926092i
$560$	−0.816368	−	1.41399i	−0.0344978	−	0.0597520i
$561$		0			0
$562$	0.353144	+	0.611664i	0.0148965	+	0.0258015i
$563$	18.5788			0.783003			0.391501	−	0.920178i	$-0.371956\pi$
$563$	18.5788			0.783003			0.391501	+	0.920178i	$0.371956\pi$
$564$		0			0
$565$	−10.9510	+	18.9677i	−0.460712	+	0.797977i
$566$	1.78062	+	3.08412i	0.0748450	+	0.129635i
$567$		0			0
$568$	1.45909	+	2.52723i	0.0612222	+	0.106040i
$569$	−26.1468			−1.09613			−0.548066	−	0.836435i	$-0.684636\pi$
$569$	−26.1468			−1.09613			−0.548066	+	0.836435i	$0.684636\pi$
$570$		0			0
$571$	−13.5880	+	23.5351i	−0.568640	+	0.984913i	0.428061	+	0.903750i	$0.359197\pi$
$571$	−13.5880	+	23.5351i	−0.568640	+	0.984913i	−0.996701	+	0.0811634i	$0.974136\pi$
$572$	2.48051	−	29.6202i	0.103715	−	1.23848i
$573$		0			0
$574$	0.159079			0.00663985
$575$	−4.52991	+	7.84603i	−0.188910	+	0.327202i
$576$		0			0
$577$	6.97981			0.290573			0.145287	−	0.989390i	$-0.453590\pi$
$577$	6.97981			0.290573			0.145287	+	0.989390i	$0.453590\pi$
$578$	−0.956211	+	1.65621i	−0.0397731	+	0.0688891i
$579$		0			0
$580$	−8.48170	+	14.6907i	−0.352183	+	0.610000i
$581$	1.41615			0.0587519
$582$		0			0
$583$	29.6982			1.22997
$584$	−0.769041			−0.0318232
$585$		0			0
$586$	1.73844			0.0718142
$587$	−45.7017			−1.88631			−0.943155	−	0.332353i	$-0.892157\pi$
$587$	−45.7017			−1.88631			−0.943155	+	0.332353i	$0.892157\pi$
$588$		0			0
$589$	−1.41398			−0.0582620
$590$	1.22415	−	2.12028i	0.0503973	−	0.0872907i
$591$		0			0
$592$	17.2405	−	29.8614i	0.708579	−	1.22729i
$593$	18.9869			0.779700			0.389850	−	0.920878i	$-0.372527\pi$
$593$	18.9869			0.779700			0.389850	+	0.920878i	$0.372527\pi$
$594$		0			0
$595$	−1.13888	+	1.97260i	−0.0466896	+	0.0808687i
$596$	−7.83719			−0.321024
$597$		0			0
$598$	−1.02503	+	0.482625i	−0.0419165	+	0.0197360i
$599$	−6.44845	+	11.1690i	−0.263477	+	0.456355i	−0.967163	−	0.254155i	$-0.918202\pi$
$599$	−6.44845	+	11.1690i	−0.263477	+	0.456355i	0.703687	+	0.710510i	$0.251536\pi$
$600$		0			0
$601$	−23.8355			−0.972269			−0.486135	−	0.873884i	$-0.661593\pi$
$601$	−23.8355			−0.972269			−0.486135	+	0.873884i	$0.661593\pi$
$602$	0.118617	+	0.205451i	0.00483447	+	0.00837355i
$603$		0			0
$604$	−8.65388	−	14.9890i	−0.352121	−	0.609892i
$605$	10.0545	−	17.4149i	0.408773	−	0.708016i
$606$		0			0
$607$	−34.7796			−1.41166			−0.705831	−	0.708380i	$-0.749426\pi$
$607$	−34.7796			−1.41166			−0.705831	+	0.708380i	$0.749426\pi$
$608$	−0.297986	−	0.516127i	−0.0120849	−	0.0209317i
$609$		0			0
$610$	−1.84102	−	3.18873i	−0.0745405	−	0.129108i
$611$	4.32832	−	2.03795i	0.175105	−	0.0824468i
$612$		0			0
$613$	−20.8146	+	36.0519i	−0.840694	+	1.45612i	0.0486150	+	0.998818i	$0.484519\pi$
$613$	−20.8146	+	36.0519i	−0.840694	+	1.45612i	−0.889309	+	0.457307i	$0.848814\pi$
$614$	1.78230			0.0719277
$615$		0			0
$616$	0.184980	−	0.320396i	0.00745307	−	0.0129091i
$617$	39.2398			1.57974			0.789868	−	0.613277i	$-0.210149\pi$
$617$	39.2398			1.57974			0.789868	+	0.613277i	$0.210149\pi$
$618$		0			0
$619$	15.9718	+	27.6639i	0.641959	+	1.11191i	0.984995	+	0.172584i	$0.0552116\pi$
$619$	15.9718	+	27.6639i	0.641959	+	1.11191i	−0.343035	+	0.939322i	$0.611455\pi$
$620$	14.0464	+	24.3291i	0.564119	+	0.977082i
$621$		0			0
$622$	0.0238331	−	0.0412802i	0.000955621	−	0.00165518i
$623$	0.842306	+	1.45892i	0.0337463	+	0.0584503i
$624$		0			0
$625$	13.1826	−	22.8330i	0.527305	−	0.913319i
$626$	0.674112	+	1.16760i	0.0269429	+	0.0466665i
$627$		0			0
$628$	−12.4270	+	21.5242i	−0.495892	+	0.858911i
$629$	−48.1029			−1.91799
$630$		0			0
$631$	15.2846	+	26.4736i	0.608469	+	1.05390i	0.991493	+	0.130160i	$0.0415493\pi$
$631$	15.2846	+	26.4736i	0.608469	+	1.05390i	−0.383024	+	0.923738i	$0.625117\pi$
$632$	0.921578	+	1.59622i	0.0366584	+	0.0634942i
$633$		0			0
$634$	1.15806	+	2.00583i	0.0459926	+	0.0796615i
$635$	−2.08616	−	3.61334i	−0.0827869	−	0.143391i
$636$		0			0
$637$	22.7736	−	10.7228i	0.902325	−	0.424852i
$638$	−1.88279			−0.0745403
$639$		0			0
$640$	−7.87547	+	13.6407i	−0.311305	+	0.539197i
$641$	18.0877	−	31.3288i	0.714421	−	1.23741i	−0.248761	−	0.968565i	$-0.580023\pi$
$641$	18.0877	−	31.3288i	0.714421	−	1.23741i	0.963182	−	0.268849i	$-0.0866433\pi$
$642$		0			0
$643$	−8.27644			−0.326391			−0.163195	−	0.986594i	$-0.552180\pi$
$643$	−8.27644			−0.326391			−0.163195	+	0.986594i	$0.552180\pi$
$644$	0.517830			0.0204053
$645$		0			0
$646$	−0.135449	+	0.234604i	−0.00532915	+	0.00923036i
$647$	−6.67339	+	11.5586i	−0.262358	+	0.454417i	−0.966868	−	0.255277i	$-0.917833\pi$
$647$	−6.67339	+	11.5586i	−0.262358	+	0.454417i	0.704510	+	0.709694i	$0.251167\pi$
$648$		0			0
$649$	−20.0923			−0.788691
$650$	−2.51006	+	1.18184i	−0.0984527	+	0.0463556i
$651$		0			0
$652$	−2.08902	−	3.61829i	−0.0818123	−	0.141703i
$653$	4.85882	+	8.41572i	0.190140	+	0.329333i	0.945297	−	0.326212i	$-0.105772\pi$
$653$	4.85882	+	8.41572i	0.190140	+	0.329333i	−0.755156	+	0.655545i	$0.772439\pi$
$654$		0			0
$655$	−20.5518	−	35.5968i	−0.803026	−	1.39088i
$656$	13.7062	+	23.7398i	0.535136	+	0.926883i
$657$		0			0
$658$	0.0295729			0.00115287
$659$	−11.8520	+	20.5283i	−0.461689	+	0.799669i	−0.999045	−	0.0436865i	$-0.986090\pi$
$659$	−11.8520	+	20.5283i	−0.461689	+	0.799669i	0.537356	+	0.843355i	$0.319423\pi$
$660$		0			0
$661$	9.86814	+	17.0921i	0.383826	+	0.664807i	0.991606	−	0.129299i	$-0.0412728\pi$
$661$	9.86814	+	17.0921i	0.383826	+	0.664807i	−0.607779	+	0.794106i	$0.707939\pi$
$662$	−0.940137	+	1.62837i	−0.0365395	+	0.0632882i
$663$		0			0
$664$	−3.36888	−	5.83507i	−0.130738	−	0.226445i
$665$	−0.0657876	+	0.113948i	−0.00255114	+	0.00441870i
$666$		0			0
$667$	−2.65314	−	4.59537i	−0.102730	−	0.177933i
$668$	9.20117	+	15.9369i	0.356004	+	0.616617i
$669$		0			0
$670$	6.65213			0.256994
$671$	−15.1086	+	26.1688i	−0.583260	+	1.01024i
$672$		0			0
$673$	7.08528			0.273117			0.136559	−	0.990632i	$-0.456396\pi$
$673$	7.08528			0.273117			0.136559	+	0.990632i	$0.456396\pi$
$674$	−1.09797	+	1.90174i	−0.0422923	+	0.0732525i
$675$		0			0
$676$	25.2957	+	4.26665i	0.972913	+	0.164102i
$677$	16.5344	+	28.6383i	0.635467	+	1.10066i	0.986416	+	0.164266i	$0.0525256\pi$
$677$	16.5344	+	28.6383i	0.635467	+	1.10066i	−0.350949	+	0.936394i	$0.614141\pi$
$678$		0			0
$679$	−1.09928	−	1.90401i	−0.0421866	−	0.0730693i
$680$	10.8371			0.415585
$681$		0			0
$682$	−1.55903	+	2.70032i	−0.0596984	+	0.103401i
$683$	−6.21557	−	10.7657i	−0.237832	−	0.411937i	0.722260	−	0.691622i	$-0.243104\pi$
$683$	−6.21557	−	10.7657i	−0.237832	−	0.411937i	−0.960092	+	0.279684i	$0.909770\pi$
$684$		0			0
$685$	12.9144	+	22.3683i	0.493433	+	0.854651i
$686$	0.311613			0.0118974
$687$		0			0
$688$	−20.4399	+	35.4030i	−0.779264	+	1.34973i
$689$	−2.13894	+	25.5415i	−0.0814873	+	0.973053i
$690$		0			0
$691$	−31.8087			−1.21006			−0.605030	−	0.796203i	$-0.706839\pi$
$691$	−31.8087			−1.21006			−0.605030	+	0.796203i	$0.706839\pi$
$692$	8.43399	−	14.6081i	0.320612	−	0.555317i
$693$		0			0
$694$	1.39095			0.0527998
$695$	−9.59447	+	16.6181i	−0.363939	+	0.630361i
$696$		0			0
$697$	19.1209	−	33.1184i	0.724256	−	1.25445i
$698$	−1.73063			−0.0655053
$699$		0			0
$700$	1.26805			0.0479277
$701$	21.3043			0.804652			0.402326	−	0.915496i	$-0.368202\pi$
$701$	21.3043			0.804652			0.402326	+	0.915496i	$0.368202\pi$
$702$		0			0
$703$	−2.77867			−0.104800
$704$	30.7754			1.15989
$705$		0			0
$706$	0.276177			0.0103941
$707$	1.19026	−	2.06159i	0.0447643	−	0.0775340i
$708$		0			0
$709$	−3.70329	+	6.41429i	−0.139080	+	0.240894i	−0.927149	−	0.374694i	$-0.877748\pi$
$709$	−3.70329	+	6.41429i	−0.139080	+	0.240894i	0.788069	+	0.615587i	$0.211081\pi$
$710$	−2.28862			−0.0858904
$711$		0			0
$712$	4.00752	−	6.94123i	0.150188	−	0.260134i
$713$	−8.78765			−0.329100
$714$		0			0
$715$	38.5490	+	26.7793i	1.44165	+	1.00149i
$716$	3.14817	−	5.45279i	0.117653	−	0.203780i
$717$		0			0
$718$	5.22121			0.194854
$719$	−19.8553	−	34.3905i	−0.740479	−	1.28255i	−0.952277	−	0.305234i	$-0.901265\pi$
$719$	−19.8553	−	34.3905i	−0.740479	−	1.28255i	0.211798	−	0.977313i	$-0.432068\pi$
$720$		0			0
$721$	−0.993900	−	1.72149i	−0.0370148	−	0.0641115i
$722$	1.54414	−	2.67454i	0.0574671	−	0.0995359i
$723$		0			0
$724$	2.96771			0.110294
$725$	−6.49694	−	11.2530i	−0.241290	−	0.417927i
$726$		0			0
$727$	−7.16724	−	12.4140i	−0.265818	−	0.460411i	0.701959	−	0.712217i	$-0.252309\pi$
$727$	−7.16724	−	12.4140i	−0.265818	−	0.460411i	−0.967778	+	0.251806i	$0.918975\pi$
$728$	0.262229	+	0.182165i	0.00971884	+	0.00675150i
$729$		0			0
$730$	0.301564	−	0.522325i	0.0111614	−	0.0193321i
$731$	57.0297			2.10932
$732$		0			0
$733$	−3.57055	+	6.18437i	−0.131881	+	0.228425i	−0.924402	−	0.381420i	$-0.875435\pi$
$733$	−3.57055	+	6.18437i	−0.131881	+	0.228425i	0.792521	+	0.609845i	$0.208768\pi$
$734$	3.07475			0.113491
$735$		0			0
$736$	−1.85193	−	3.20764i	−0.0682632	−	0.118235i
$737$	−27.2959	−	47.2778i	−1.00546	−	1.74150i
$738$		0			0
$739$	−0.0763939	+	0.132318i	−0.00281019	+	0.00486740i	−0.867427	−	0.497564i	$-0.834228\pi$
$739$	−0.0763939	+	0.132318i	−0.00281019	+	0.00486740i	0.864617	+	0.502432i	$0.167561\pi$
$740$	27.6033	+	47.8102i	1.01472	+	1.75754i
$741$		0			0
$742$	−0.0792186	+	0.137211i	−0.00290821	+	0.00503716i
$743$	12.0334	+	20.8424i	0.441462	+	0.764634i	0.997798	−	0.0663228i	$-0.0211267\pi$
$743$	12.0334	+	20.8424i	0.441462	+	0.764634i	−0.556336	+	0.830957i	$0.687793\pi$
$744$		0			0
$745$	6.18796	−	10.7179i	0.226709	−	0.392672i
$746$	2.38422			0.0872925
$747$		0			0
$748$	−22.0848	−	38.2520i	−0.807500	−	1.39863i
$749$	−0.370585	−	0.641871i	−0.0135409	−	0.0234535i
$750$		0			0
$751$	0.999421	+	1.73105i	0.0364694	+	0.0631669i	0.883684	−	0.468084i	$-0.155056\pi$
$751$	0.999421	+	1.73105i	0.0364694	+	0.0631669i	−0.847215	+	0.531251i	$0.821722\pi$
$752$	2.54798	+	4.41323i	0.0929153	+	0.160934i
$753$		0			0
$754$	0.135604	−	1.61926i	0.00493839	−	0.0589701i
$755$	27.3312			0.994683
$756$		0			0
$757$	3.61667	−	6.26425i	0.131450	−	0.227678i	−0.792786	−	0.609500i	$-0.791370\pi$
$757$	3.61667	−	6.26425i	0.131450	−	0.227678i	0.924236	+	0.381822i	$0.124703\pi$
$758$	−1.58677	+	2.74837i	−0.0576341	+	0.0998252i
$759$		0			0
$760$	0.626009			0.0227077
$761$	−18.4602			−0.669181			−0.334591	−	0.942364i	$-0.608598\pi$
$761$	−18.4602			−0.669181			−0.334591	+	0.942364i	$0.608598\pi$
$762$		0			0
$763$	−0.212088	+	0.367347i	−0.00767811	+	0.0132989i
$764$	−19.8435	+	34.3699i	−0.717912	+	1.24346i
$765$		0			0
$766$	1.34932			0.0487531
$767$	1.44710	−	17.2801i	0.0522518	−	0.623947i
$768$		0			0
$769$	−14.4442	−	25.0181i	−0.520872	−	0.902177i	−0.999705	−	0.0242713i	$-0.992273\pi$
$769$	−14.4442	−	25.0181i	−0.520872	−	0.902177i	0.478833	−	0.877906i	$-0.341060\pi$
$770$	0.145073	+	0.251273i	0.00522806	+	0.00905527i
$771$		0			0
$772$	7.79171	+	13.4956i	0.280430	+	0.485718i
$773$	10.7888	+	18.6867i	0.388045	+	0.672113i	0.992186	−	0.124764i	$-0.0398172\pi$
$773$	10.7888	+	18.6867i	0.388045	+	0.672113i	−0.604142	+	0.796877i	$0.706484\pi$
$774$		0			0
$775$	−21.5190			−0.772985
$776$	−5.23016	+	9.05891i	−0.187752	+	0.325196i
$777$		0			0
$778$	−0.595452	−	1.03135i	−0.0213480	−	0.0369758i
$779$	1.10452	−	1.91309i	0.0395736	−	0.0685435i
$780$		0			0
$781$	9.39095	+	16.2656i	0.336035	+	0.582029i
$782$	−0.841791	+	1.45802i	−0.0301024	+	0.0521388i
$783$		0			0
$784$	13.4063	+	23.2204i	0.478796	+	0.829300i
$785$	−19.6239	−	33.9895i	−0.700405	−	1.21314i
$786$		0			0
$787$	27.8276			0.991946			0.495973	−	0.868338i	$-0.334811\pi$
$787$	27.8276			0.991946			0.495973	+	0.868338i	$0.334811\pi$
$788$	−22.9546	+	39.7586i	−0.817725	+	1.41634i
$789$		0			0
$790$	−1.44551			−0.0514291
$791$	−0.479454	+	0.830439i	−0.0170474	+	0.0295270i
$792$		0			0
$793$	−21.4179	−	14.8786i	−0.760573	−	0.528356i
$794$	−0.659941	−	1.14305i	−0.0234204	−	0.0405654i
$795$		0			0
$796$	9.06387	+	15.6991i	0.321260	+	0.556439i
$797$	38.9009			1.37794			0.688970	−	0.724790i	$-0.258063\pi$
$797$	38.9009			1.37794			0.688970	+	0.724790i	$0.258063\pi$
$798$		0			0
$799$	3.55458	−	6.15671i	0.125752	−	0.217809i
$800$	−4.53497	−	7.85480i	−0.160335	−	0.277709i
$801$		0			0
$802$	−0.00921727	−	0.0159648i	−0.000325473	−	0.000563736i
$803$	−4.94966			−0.174670
$804$		0			0
$805$	−0.408859	+	0.708165i	−0.0144104	+	0.0249595i
$806$	−2.21009	−	1.53531i	−0.0778470	−	0.0540789i
$807$		0			0
$808$	−11.3260			−0.398448
$809$	−11.2678	+	19.5163i	−0.396153	+	0.686157i	−0.993248	−	0.116013i	$-0.962988\pi$
$809$	−11.2678	+	19.5163i	−0.396153	+	0.686157i	0.597094	+	0.802171i	$0.296322\pi$
$810$		0			0
$811$	−26.2480			−0.921692			−0.460846	−	0.887480i	$-0.652454\pi$
$811$	−26.2480			−0.921692			−0.460846	+	0.887480i	$0.652454\pi$
$812$	−0.371344	+	0.643186i	−0.0130316	+	0.0225714i
$813$		0			0
$814$	−3.06372	+	5.30652i	−0.107383	+	0.185993i
$815$	6.59765			0.231106
$816$		0			0
$817$	3.29433			0.115254
$818$	4.16926			0.145775
$819$		0			0
$820$	−43.8892			−1.53268
$821$	3.38370			0.118092			0.0590460	−	0.998255i	$-0.481194\pi$
$821$	3.38370			0.118092			0.0590460	+	0.998255i	$0.481194\pi$
$822$		0			0
$823$	38.6239			1.34634			0.673172	−	0.739486i	$-0.264931\pi$
$823$	38.6239			1.34634			0.673172	+	0.739486i	$0.264931\pi$
$824$	−4.72878	+	8.19048i	−0.164735	+	0.285329i
$825$		0			0
$826$	0.0535953	−	0.0928297i	0.00186482	−	0.00322996i
$827$	11.8393			0.411694			0.205847	−	0.978584i	$-0.434005\pi$
$827$	11.8393			0.411694			0.205847	+	0.978584i	$0.434005\pi$
$828$		0			0
$829$	−7.44930	+	12.9026i	−0.258725	+	0.448125i	−0.965901	−	0.258913i	$-0.916636\pi$
$829$	−7.44930	+	12.9026i	−0.258725	+	0.448125i	0.707176	+	0.707038i	$0.249969\pi$
$830$	5.28416			0.183416
$831$		0			0
$832$	−2.21653	+	26.4680i	−0.0768444	+	0.917611i
$833$	18.7026	−	32.3938i	0.648006	−	1.12238i
$834$		0			0
$835$	−29.0596			−1.00565
$836$	−1.27573	−	2.20963i	−0.0441221	−	0.0764217i
$837$		0			0
$838$	1.27464	+	2.20774i	0.0440316	+	0.0762650i
$839$	26.4068	−	45.7380i	0.911665	−	1.57905i	0.0999523	−	0.994992i	$-0.468131\pi$
$839$	26.4068	−	45.7380i	0.911665	−	1.57905i	0.811712	−	0.584057i	$-0.198536\pi$
$840$		0			0
$841$	−21.3896			−0.737572
$842$	−0.678892	−	1.17588i	−0.0233962	−	0.0405233i
$843$		0			0
$844$	12.3166	+	21.3329i	0.423954	+	0.734309i
$845$	−25.8075	+	31.2248i	−0.887806	+	1.07416i
$846$		0			0
$847$	0.440203	−	0.762455i	0.0151256	−	0.0261982i
$848$	−27.3017			−0.937543
$849$		0			0
$850$	−2.06136	+	3.57037i	−0.0707039	+	0.122463i
$851$	−17.2690			−0.591973
$852$		0			0
$853$	11.5316	+	19.9733i	0.394834	+	0.683873i	0.993080	−	0.117440i	$-0.0374686\pi$
$853$	11.5316	+	19.9733i	0.394834	+	0.683873i	−0.598246	+	0.801313i	$0.704135\pi$
$854$	−0.0806029	−	0.139608i	−0.00275817	−	0.00477730i
$855$		0			0
$856$	−1.76317	+	3.05389i	−0.0602638	+	0.104380i
$857$	13.4357	+	23.2713i	0.458955	+	0.794933i	0.998906	−	0.0467630i	$-0.0148906\pi$
$857$	13.4357	+	23.2713i	0.458955	+	0.794933i	−0.539951	+	0.841696i	$0.681557\pi$
$858$		0			0
$859$	−15.1421	+	26.2269i	−0.516642	+	0.894850i	0.483172	+	0.875526i	$0.339485\pi$
$859$	−15.1421	+	26.2269i	−0.516642	+	0.894850i	−0.999813	+	0.0193240i	$0.993849\pi$
$860$	−32.7258	−	56.6828i	−1.11594	−	1.93287i
$861$		0			0
$862$	−1.54118	+	2.66940i	−0.0524927	+	0.0909201i
$863$	4.43659			0.151023			0.0755116	−	0.997145i	$-0.475941\pi$
$863$	4.43659			0.151023			0.0755116	+	0.997145i	$0.475941\pi$
$864$		0			0
$865$	13.3183	+	23.0681i	0.452837	+	0.784337i
$866$	−0.889348	−	1.54040i	−0.0302213	−	0.0523448i
$867$		0			0
$868$	0.614978	+	1.06517i	0.0208737	+	0.0361543i
$869$	5.93141	+	10.2735i	0.201209	+	0.348505i
$870$		0			0
$871$	42.6265	−	20.0703i	1.44434	−	0.680057i
$872$	2.01814			0.0683430
$873$		0			0
$874$	−0.0486262	+	0.0842230i	−0.00164480	+	0.00284889i
$875$	0.0616127	−	0.106716i	0.00208289	−	0.00360767i
$876$		0			0
$877$	8.62930			0.291391			0.145695	−	0.989329i	$-0.453458\pi$
$877$	8.62930			0.291391			0.145695	+	0.989329i	$0.453458\pi$
$878$	−5.77293			−0.194827
$879$		0			0
$880$	−24.9987	+	43.2991i	−0.842707	+	1.45961i
$881$	−16.9018	+	29.2748i	−0.569436	+	0.986292i	0.427186	+	0.904164i	$0.359505\pi$
$881$	−16.9018	+	29.2748i	−0.569436	+	0.986292i	−0.996622	+	0.0821281i	$0.973828\pi$
$882$		0			0
$883$	17.4612			0.587615			0.293807	−	0.955865i	$-0.405078\pi$
$883$	17.4612			0.587615			0.293807	+	0.955865i	$0.405078\pi$
$884$	34.4887	−	16.2387i	1.15998	−	0.546166i
$885$		0			0
$886$	−0.769497	−	1.33281i	−0.0258518	−	0.0447766i
$887$	−17.0959	−	29.6110i	−0.574024	−	0.994238i	−0.996147	−	0.0876999i	$-0.972048\pi$
$887$	−17.0959	−	29.6110i	−0.574024	−	0.994238i	0.422123	−	0.906539i	$-0.361285\pi$
$888$		0			0
$889$	−0.0913359	−	0.158198i	−0.00306331	−	0.00530580i
$890$	3.14294	+	5.44373i	0.105352	+	0.182474i
$891$		0			0
$892$	19.5121			0.653312
$893$	0.205331	−	0.355644i	0.00687114	−	0.0119012i
$894$		0			0
$895$	4.97136	+	8.61064i	0.166174	+	0.287822i
$896$	−0.344802	+	0.597214i	−0.0115190	+	0.0199515i
$897$		0			0
$898$	1.76634	+	3.05938i	0.0589434	+	0.102093i
$899$	6.30176	−	10.9150i	0.210176	−	0.364035i
$900$		0			0
$901$	19.0437	+	32.9847i	0.634438	+	1.09888i
$902$	−2.43566	−	4.21868i	−0.0810985	−	0.140467i
$903$		0			0
$904$	4.56229			0.151740
$905$	−2.34319	+	4.05853i	−0.0778904	+	0.134910i
$906$		0			0
$907$	−15.3735			−0.510467			−0.255234	−	0.966879i	$-0.582152\pi$
$907$	−15.3735			−0.510467			−0.255234	+	0.966879i	$0.582152\pi$
$908$	−9.90390	+	17.1541i	−0.328672	+	0.569277i
$909$		0			0
$910$	−0.226553	+	0.106670i	−0.00751014	+	0.00353609i
$911$	−24.6800	−	42.7470i	−0.817685	−	1.41627i	−0.907384	−	0.420302i	$-0.861924\pi$
$911$	−24.6800	−	42.7470i	−0.817685	−	1.41627i	0.0896996	−	0.995969i	$-0.471409\pi$
$912$		0			0
$913$	−21.6826	−	37.5554i	−0.717590	−	1.24290i
$914$	3.58009			0.118419
$915$		0			0
$916$	5.63835	−	9.76591i	0.186296	−	0.322675i
$917$	−0.899795	−	1.55849i	−0.0297138	−	0.0514659i
$918$		0			0
$919$	−7.37698	−	12.7773i	−0.243344	−	0.421485i	0.718321	−	0.695712i	$-0.244911\pi$
$919$	−7.37698	−	12.7773i	−0.243344	−	0.421485i	−0.961665	+	0.274228i	$0.911578\pi$
$920$	3.89054			0.128267
$921$		0			0
$922$	−2.65589	+	4.60013i	−0.0874670	+	0.151497i
$923$	−14.6653	+	6.90505i	−0.482716	+	0.227283i
$924$		0			0
$925$	−42.2879			−1.39042
$926$	0.907632	−	1.57206i	0.0298266	−	0.0516612i
$927$		0			0
$928$	5.31220			0.174382
$929$	−24.1792	+	41.8796i	−0.793294	+	1.37403i	0.130622	+	0.991432i	$0.458302\pi$
$929$	−24.1792	+	41.8796i	−0.793294	+	1.37403i	−0.923917	+	0.382594i	$0.875031\pi$
$930$		0			0
$931$	1.08036	−	1.87123i	0.0354073	−	0.0613272i
$932$	40.4503			1.32500
$933$		0			0
$934$	3.63323			0.118883
$935$	69.7494			2.28105
$936$		0			0
$937$	26.8065			0.875730			0.437865	−	0.899041i	$-0.355735\pi$
$937$	26.8065			0.875730			0.437865	+	0.899041i	$0.355735\pi$
$938$	0.291242			0.00950939
$939$		0			0
$940$	−8.15901			−0.266117
$941$	−13.4825	+	23.3523i	−0.439516	+	0.761264i	−0.997652	−	0.0684856i	$-0.978183\pi$
$941$	−13.4825	+	23.3523i	−0.439516	+	0.761264i	0.558136	+	0.829749i	$0.311517\pi$
$942$		0			0
$943$	6.86442	−	11.8895i	0.223536	−	0.387176i
$944$	18.4709			0.601177
$945$		0			0
$946$	3.63228	−	6.29129i	0.118096	−	0.204547i
$947$	14.0675			0.457131			0.228566	−	0.973529i	$-0.426596\pi$
$947$	14.0675			0.457131			0.228566	+	0.973529i	$0.426596\pi$
$948$		0			0
$949$	0.356488	−	4.25688i	0.0115721	−	0.138184i
$950$	−0.119075	+	0.206243i	−0.00386329	+	0.00669141i
$951$		0			0
$952$	0.474469			0.0153776
$953$	20.9114	+	36.2196i	0.677386	+	1.17327i	0.975765	+	0.218819i	$0.0702206\pi$
$953$	20.9114	+	36.2196i	0.677386	+	1.17327i	−0.298380	+	0.954447i	$0.596446\pi$
$954$		0			0
$955$	−31.3354	−	54.2745i	−1.01399	−	1.75628i
$956$	29.5674	−	51.2123i	0.956279	−	1.65632i
$957$		0			0
$958$	−3.27442			−0.105792
$959$	0.565414	+	0.979325i	0.0182582	+	0.0316241i
$960$		0			0
$961$	5.06373	+	8.77063i	0.163346	+	0.282924i
$962$	−4.34313	−	3.01710i	−0.140028	−	0.0972751i
$963$		0			0
$964$	15.1249	−	26.1970i	0.487139	−	0.843750i
$965$	−24.6082			−0.792166
$966$		0			0
$967$	−10.2769	+	17.8001i	−0.330483	+	0.572413i	−0.982607	−	0.185699i	$-0.940545\pi$
$967$	−10.2769	+	17.8001i	−0.330483	+	0.572413i	0.652124	+	0.758113i	$0.273878\pi$
$968$	−4.18880			−0.134633
$969$		0			0
$970$	−4.10181	−	7.10454i	−0.131701	−	0.228113i
$971$	−2.68759	−	4.65505i	−0.0862489	−	0.149388i	0.819674	−	0.572831i	$-0.194155\pi$
$971$	−2.68759	−	4.65505i	−0.0862489	−	0.149388i	−0.905923	+	0.423443i	$0.860821\pi$
$972$		0			0
$973$	−0.420062	+	0.727569i	−0.0134666	+	0.0233248i
$974$	−0.0582299	−	0.100857i	−0.00186581	−	0.00323167i
$975$		0			0
$976$	13.8894	−	24.0571i	0.444588	−	0.770049i
$977$	5.14437	+	8.91031i	0.164583	+	0.285066i	0.936507	−	0.350649i	$-0.114039\pi$
$977$	5.14437	+	8.91031i	0.164583	+	0.285066i	−0.771924	+	0.635715i	$0.780706\pi$
$978$		0			0
$979$	25.7930	−	44.6748i	0.824348	−	1.42781i
$980$	−42.9290			−1.37132
$981$		0			0
$982$	−0.832158	−	1.44134i	−0.0265552	−	0.0459950i
$983$	−21.7938	−	37.7480i	−0.695115	−	1.20397i	−0.970142	−	0.242538i	$-0.922020\pi$
$983$	−21.7938	−	37.7480i	−0.695115	−	1.20397i	0.275027	−	0.961437i	$-0.411313\pi$
$984$		0			0
$985$	−36.2483	−	62.7839i	−1.15497	−	2.00046i
$986$	−1.20732	−	2.09114i	−0.0384490	−	0.0665956i
$987$		0			0
$988$	1.99224	−	0.938030i	0.0633817	−	0.0298427i
$989$	20.4737			0.651027
$990$		0			0
$991$	1.44149	−	2.49674i	0.0457905	−	0.0793115i	−0.842222	−	0.539131i	$-0.818753\pi$
$991$	1.44149	−	2.49674i	0.0457905	−	0.0793115i	0.888012	+	0.459820i	$0.152086\pi$
$992$	4.39874	−	7.61883i	0.139660	−	0.241898i
$993$		0			0
$994$	−0.100200			−0.00317814
$995$	−28.6260			−0.907506
$996$		0			0
$997$	2.64813	−	4.58669i	0.0838671	−	0.145262i	−0.821041	−	0.570870i	$-0.806606\pi$
$997$	2.64813	−	4.58669i	0.0838671	−	0.145262i	0.904908	+	0.425607i	$0.139940\pi$
$998$	3.26128	−	5.64870i	0.103234	−	0.178807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.h.a.334.7		24
3.2	odd	2		117.2.h.a.22.6	yes	24
9.2	odd	6		117.2.f.a.61.7	✓	24
9.7	even	3		351.2.f.a.100.6		24
13.3	even	3		351.2.f.a.172.6		24
39.29	odd	6		117.2.f.a.94.7	yes	24
117.16	even	3	inner	351.2.h.a.289.7		24
117.29	odd	6		117.2.h.a.16.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.7	✓	24	9.2	odd	6
117.2.f.a.94.7	yes	24	39.29	odd	6
117.2.h.a.16.6	yes	24	117.29	odd	6
117.2.h.a.22.6	yes	24	3.2	odd	2
351.2.f.a.100.6		24	9.7	even	3
351.2.f.a.172.6		24	13.3	even	3
351.2.h.a.289.7		24	117.16	even	3	inner
351.2.h.a.334.7		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+0.163365 q^{2} -1.97331 q^{4} +(1.55806 - 2.69863i) q^{5} +(0.0682144 - 0.118151i) q^{7} -0.649100 q^{8} +(0.254532 - 0.440862i) q^{10} -4.17771 q^{11} +(0.300890 - 3.59297i) q^{13} +(0.0111438 - 0.0193017i) q^{14} +3.84058 q^{16} +(-2.67892 - 4.64002i) q^{17} +(-0.154748 - 0.268032i) q^{19} +(-3.07453 + 5.32524i) q^{20} -0.682491 q^{22} +(-0.961735 - 1.66577i) q^{23} +(-2.35507 - 4.07910i) q^{25} +(0.0491549 - 0.586967i) q^{26} +(-0.134608 + 0.233148i) q^{28} +2.75870 q^{29} +(2.28432 - 3.95657i) q^{31} +1.92562 q^{32} +(-0.437642 - 0.758018i) q^{34} +(-0.212564 - 0.368171i) q^{35} +(4.48902 - 7.77522i) q^{37} +(-0.0252804 - 0.0437870i) q^{38} +(-1.01133 + 1.75168i) q^{40} +(3.56877 + 6.18129i) q^{41} +(-5.32209 + 9.21812i) q^{43} +8.24392 q^{44} +(-0.157114 - 0.272129i) q^{46} +(0.663436 + 1.14910i) q^{47} +(3.49069 + 6.04606i) q^{49} +(-0.384737 - 0.666383i) q^{50} +(-0.593749 + 7.09006i) q^{52} -7.10873 q^{53} +(-6.50910 + 11.2741i) q^{55} +(-0.0442780 + 0.0766917i) q^{56} +0.450675 q^{58} +4.80940 q^{59} +(3.61647 - 6.26392i) q^{61} +(0.373179 - 0.646365i) q^{62} -7.36659 q^{64} +(-9.22731 - 6.41004i) q^{65} +(6.53369 + 11.3167i) q^{67} +(5.28634 + 9.15621i) q^{68} +(-0.0347255 - 0.0601463i) q^{70} +(-2.24787 - 3.89343i) q^{71} +1.18478 q^{73} +(0.733350 - 1.27020i) q^{74} +(0.305366 + 0.528910i) q^{76} +(-0.284980 + 0.493599i) q^{77} +(-1.41978 - 2.45913i) q^{79} +(5.98384 - 10.3643i) q^{80} +(0.583013 + 1.00981i) q^{82} +(5.19008 + 8.98948i) q^{83} -16.6956 q^{85} +(-0.869443 + 1.50592i) q^{86} +2.71175 q^{88} +(-6.17396 + 10.6936i) q^{89} +(-0.403988 - 0.280643i) q^{91} +(1.89780 + 3.28709i) q^{92} +(0.108382 + 0.187723i) q^{94} -0.964425 q^{95} +(8.05756 - 13.9561i) q^{97} +(0.570257 + 0.987715i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 18 q^{4} + 2 q^{5} + 3 q^{7} + 18 q^{8} - 6 q^{11} - 2 q^{14} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 11 q^{20} - 18 q^{22} - 17 q^{23} - 6 q^{25} + 12 q^{26} + 24 q^{29} - 6 q^{31} + 38 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 18 * q^4 + 2 * q^5 + 3 * q^7 + 18 * q^8 - 6 * q^11 - 2 * q^14 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 11 * q^20 - 18 * q^22 - 17 * q^23 - 6 * q^25 + 12 * q^26 + 24 * q^29 - 6 * q^31 + 38 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 - 5 * q^41 - 3 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 + 3 * q^49 + 20 * q^50 - 24 * q^52 + 20 * q^53 + 3 * q^55 - 40 * q^56 + 18 * q^58 - 38 * q^59 - 6 * q^61 - 19 * q^62 - 42 * q^64 + 2 * q^65 - 6 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 - 29 * q^74 - 15 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 - 78 * q^88 + q^89 - 6 * q^91 + 10 * q^92 - 9 * q^94 + 100 * q^95 + 24 * q^97 + 61 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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