LMFDB - Embedded newform 637.2.e.i.508.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.1
Root			$1.17146 + 2.02903i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.i.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17146 - 2.02903i) q^{2} +(-0.573183 + 0.992782i) q^{3} +(-1.74464 + 3.02181i) q^{4} +(-0.671462 - 1.16301i) q^{5} +2.68585 q^{6} +3.48929 q^{8} +(0.842923 + 1.45999i) q^{9} +O(q^{10})$	\(q+(-1.17146 - 2.02903i) q^{2} +(-0.573183 + 0.992782i) q^{3} +(-1.74464 + 3.02181i) q^{4} +(-0.671462 - 1.16301i) q^{5} +2.68585 q^{6} +3.48929 q^{8} +(0.842923 + 1.45999i) q^{9} +(-1.57318 + 2.72483i) q^{10} +(-0.573183 + 0.992782i) q^{11} +(-2.00000 - 3.46410i) q^{12} -1.00000 q^{13} +1.53948 q^{15} +(-0.598279 - 1.03625i) q^{16} +(2.91611 - 5.05084i) q^{17} +(1.97490 - 3.42063i) q^{18} +(-1.67146 - 2.89506i) q^{19} +4.68585 q^{20} +2.68585 q^{22} +(1.58757 + 2.74975i) q^{23} +(-2.00000 + 3.46410i) q^{24} +(1.59828 - 2.76830i) q^{25} +(1.17146 + 2.02903i) q^{26} -5.37169 q^{27} +10.4893 q^{29} +(-1.80344 - 3.12365i) q^{30} +(0.817827 - 1.41652i) q^{31} +(2.08757 - 3.61577i) q^{32} +(-0.657077 - 1.13809i) q^{33} -13.6644 q^{34} -5.88240 q^{36} +(-4.25903 - 7.37685i) q^{37} +(-3.91611 + 6.78289i) q^{38} +(0.573183 - 0.992782i) q^{39} +(-2.34292 - 4.05806i) q^{40} +0.292731 q^{41} -8.15371 q^{43} +(-2.00000 - 3.46410i) q^{44} +(1.13198 - 1.96065i) q^{45} +(3.71955 - 6.44245i) q^{46} +(-5.30712 - 9.19219i) q^{47} +1.37169 q^{48} -7.48929 q^{50} +(3.34292 + 5.79011i) q^{51} +(1.74464 - 3.02181i) q^{52} +(0.391010 - 0.677249i) q^{53} +(6.29273 + 10.8993i) q^{54} +1.53948 q^{55} +3.83221 q^{57} +(-12.2878 - 21.2831i) q^{58} +(6.32150 - 10.9492i) q^{59} +(-2.68585 + 4.65202i) q^{60} +(-1.00000 - 1.73205i) q^{61} -3.83221 q^{62} -12.1751 q^{64} +(0.671462 + 1.16301i) q^{65} +(-1.53948 + 2.66646i) q^{66} +(3.05019 - 5.28309i) q^{67} +(10.1751 + 17.6239i) q^{68} -3.63986 q^{69} +1.53948 q^{71} +(2.94120 + 5.09431i) q^{72} +(-7.65004 + 13.2503i) q^{73} +(-9.97858 + 17.2834i) q^{74} +(1.83221 + 3.17348i) q^{75} +11.6644 q^{76} -2.68585 q^{78} +(-0.441202 - 0.764184i) q^{79} +(-0.803442 + 1.39160i) q^{80} +(0.550192 - 0.952961i) q^{81} +(-0.342923 - 0.593960i) q^{82} +12.1292 q^{83} -7.83221 q^{85} +(9.55176 + 16.5441i) q^{86} +(-6.01228 + 10.4136i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(2.86802 + 4.96755i) q^{89} -5.30429 q^{90} -11.0790 q^{92} +(0.937529 + 1.62385i) q^{93} +(-12.4342 + 21.5366i) q^{94} +(-2.24464 + 3.88784i) q^{95} +(2.39312 + 4.14500i) q^{96} +5.34292 q^{97} -1.93260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9	$ 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9} - 8 q^{10} - 2 q^{11} - 12 q^{12} - 6 q^{13} - 12 q^{15} + q^{16} + 4 q^{17} + 15 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} + 5 q^{25} + q^{26} + 16 q^{27} + 48 q^{29} - 20 q^{30} - 4 q^{31} - 7 q^{32} - 16 q^{33} - 28 q^{34} - 2 q^{36} - 10 q^{38} + 2 q^{39} - 2 q^{40} - 4 q^{41} + 20 q^{43} - 12 q^{44} + 22 q^{45} + 18 q^{46} - 8 q^{47} - 40 q^{48} - 30 q^{50} + 8 q^{51} + 3 q^{52} - 8 q^{53} + 32 q^{54} - 12 q^{55} - 4 q^{57} - 12 q^{58} - 4 q^{59} + 8 q^{60} - 6 q^{61} + 4 q^{62} - 34 q^{64} - 2 q^{65} + 12 q^{66} + 12 q^{67} + 22 q^{68} + 12 q^{69} - 12 q^{71} + q^{72} - 10 q^{73} - 30 q^{74} - 16 q^{75} + 16 q^{76} + 8 q^{78} + 14 q^{79} - 14 q^{80} - 3 q^{81} + 10 q^{82} + 24 q^{83} - 20 q^{85} + 26 q^{86} - 26 q^{87} - 12 q^{88} + 2 q^{89} + 56 q^{90} - 24 q^{92} + 22 q^{93} - 10 q^{94} - 6 q^{95} - 4 q^{96} + 20 q^{97} + 28 q^{99}+O(q^{100}) $ 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9 - 8 * q^10 - 2 * q^11 - 12 * q^12 - 6 * q^13 - 12 * q^15 + q^16 + 4 * q^17 + 15 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 + 5 * q^25 + q^26 + 16 * q^27 + 48 * q^29 - 20 * q^30 - 4 * q^31 - 7 * q^32 - 16 * q^33 - 28 * q^34 - 2 * q^36 - 10 * q^38 + 2 * q^39 - 2 * q^40 - 4 * q^41 + 20 * q^43 - 12 * q^44 + 22 * q^45 + 18 * q^46 - 8 * q^47 - 40 * q^48 - 30 * q^50 + 8 * q^51 + 3 * q^52 - 8 * q^53 + 32 * q^54 - 12 * q^55 - 4 * q^57 - 12 * q^58 - 4 * q^59 + 8 * q^60 - 6 * q^61 + 4 * q^62 - 34 * q^64 - 2 * q^65 + 12 * q^66 + 12 * q^67 + 22 * q^68 + 12 * q^69 - 12 * q^71 + q^72 - 10 * q^73 - 30 * q^74 - 16 * q^75 + 16 * q^76 + 8 * q^78 + 14 * q^79 - 14 * q^80 - 3 * q^81 + 10 * q^82 + 24 * q^83 - 20 * q^85 + 26 * q^86 - 26 * q^87 - 12 * q^88 + 2 * q^89 + 56 * q^90 - 24 * q^92 + 22 * q^93 - 10 * q^94 - 6 * q^95 - 4 * q^96 + 20 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.17146	−	2.02903i	−0.828348	−	1.43474i	−0.899333	−	0.437264i	$-0.855947\pi$
$2$	−1.17146	−	2.02903i	−0.828348	−	1.43474i	0.0709847	−	0.997477i	$-0.477386\pi$
$3$	−0.573183	+	0.992782i	−0.330927	+	0.573183i	−0.982694	−	0.185237i	$-0.940695\pi$
$3$	−0.573183	+	0.992782i	−0.330927	+	0.573183i	0.651767	+	0.758420i	$0.274028\pi$
$4$	−1.74464	+	3.02181i	−0.872322	+	1.51091i
$5$	−0.671462	−	1.16301i	−0.300287	−	0.520112i	0.675914	−	0.736980i	$-0.263749\pi$
$5$	−0.671462	−	1.16301i	−0.300287	−	0.520112i	−0.976201	+	0.216869i	$0.930416\pi$
$6$	2.68585			1.09649
$7$		0			0
$7$		0			0
$8$	3.48929			1.23365
$9$	0.842923	+	1.45999i	0.280974	+	0.486662i
$10$	−1.57318	+	2.72483i	−0.497484	+	0.861668i
$11$	−0.573183	+	0.992782i	−0.172821	+	0.299335i	−0.939405	−	0.342809i	$-0.888622\pi$
$11$	−0.573183	+	0.992782i	−0.172821	+	0.299335i	0.766584	+	0.642144i	$0.221955\pi$
$12$	−2.00000	−	3.46410i	−0.577350	−	1.00000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	1.53948			0.397492
$16$	−0.598279	−	1.03625i	−0.149570	−	0.259062i
$17$	2.91611	−	5.05084i	0.707260	−	1.22501i	−0.258610	−	0.965982i	$-0.583265\pi$
$17$	2.91611	−	5.05084i	0.707260	−	1.22501i	0.965870	−	0.259028i	$-0.0834021\pi$
$18$	1.97490	−	3.42063i	0.465489	−	0.806251i
$19$	−1.67146	−	2.89506i	−0.383460	−	0.664171i	0.608095	−	0.793865i	$-0.291934\pi$
$19$	−1.67146	−	2.89506i	−0.383460	−	0.664171i	−0.991554	+	0.129693i	$0.958601\pi$
$20$	4.68585			1.04779
$21$		0			0
$22$	2.68585			0.572624
$23$	1.58757	+	2.74975i	0.331031	+	0.573362i	0.982714	−	0.185129i	$-0.0592703\pi$
$23$	1.58757	+	2.74975i	0.331031	+	0.573362i	−0.651684	+	0.758491i	$0.725937\pi$
$24$	−2.00000	+	3.46410i	−0.408248	+	0.707107i
$25$	1.59828	−	2.76830i	0.319656	−	0.553660i
$26$	1.17146	+	2.02903i	0.229743	+	0.397926i
$27$	−5.37169			−1.03378
$28$		0			0
$29$	10.4893			1.94781			0.973906	−	0.226952i	$-0.0728760\pi$
$29$	10.4893			1.94781			0.973906	+	0.226952i	$0.0728760\pi$
$30$	−1.80344	−	3.12365i	−0.329262	−	0.570299i
$31$	0.817827	−	1.41652i	0.146886	−	0.254414i	−0.783189	−	0.621784i	$-0.786408\pi$
$31$	0.817827	−	1.41652i	0.146886	−	0.254414i	0.930075	+	0.367370i	$0.119742\pi$
$32$	2.08757	−	3.61577i	0.369033	−	0.639184i
$33$	−0.657077	−	1.13809i	−0.114382	−	0.198116i
$34$	−13.6644			−2.34343
$35$		0			0
$36$	−5.88240			−0.980401
$37$	−4.25903	−	7.37685i	−0.700180	−	1.21275i	−0.968403	−	0.249391i	$-0.919770\pi$
$37$	−4.25903	−	7.37685i	−0.700180	−	1.21275i	0.268223	−	0.963357i	$-0.413564\pi$
$38$	−3.91611	+	6.78289i	−0.635276	+	1.10033i
$39$	0.573183	−	0.992782i	0.0917827	−	0.158972i
$40$	−2.34292	−	4.05806i	−0.370449	−	0.641636i
$41$	0.292731			0.0457169			0.0228584	−	0.999739i	$-0.492723\pi$
$41$	0.292731			0.0457169			0.0228584	+	0.999739i	$0.492723\pi$
$42$		0			0
$43$	−8.15371			−1.24343			−0.621715	−	0.783244i	$-0.713564\pi$
$43$	−8.15371			−1.24343			−0.621715	+	0.783244i	$0.713564\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$	1.13198	−	1.96065i	0.168746	−	0.292276i
$46$	3.71955	−	6.44245i	0.548417	−	0.949887i
$47$	−5.30712	−	9.19219i	−0.774122	−	1.34082i	−0.935286	−	0.353892i	$-0.884858\pi$
$47$	−5.30712	−	9.19219i	−0.774122	−	1.34082i	0.161164	−	0.986928i	$-0.448475\pi$
$48$	1.37169			0.197987
$49$		0			0
$50$	−7.48929			−1.05915
$51$	3.34292	+	5.79011i	0.468103	+	0.810778i
$52$	1.74464	−	3.02181i	0.241939	−	0.419050i
$53$	0.391010	−	0.677249i	0.0537093	−	0.0930273i	−0.837921	−	0.545792i	$-0.816229\pi$
$53$	0.391010	−	0.677249i	0.0537093	−	0.0930273i	0.891630	+	0.452765i	$0.149562\pi$
$54$	6.29273	+	10.8993i	0.856332	+	1.48321i
$55$	1.53948			0.207584
$56$		0			0
$57$	3.83221			0.507589
$58$	−12.2878	−	21.2831i	−1.61347	−	2.79461i
$59$	6.32150	−	10.9492i	0.822989	−	1.42546i	−0.0804572	−	0.996758i	$-0.525638\pi$
$59$	6.32150	−	10.9492i	0.822989	−	1.42546i	0.903446	−	0.428701i	$-0.141029\pi$
$60$	−2.68585	+	4.65202i	−0.346741	+	0.600573i
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	−3.83221			−0.486691
$63$		0			0
$64$	−12.1751			−1.52189
$65$	0.671462	+	1.16301i	0.0832846	+	0.144253i
$66$	−1.53948	+	2.66646i	−0.189497	+	0.328218i
$67$	3.05019	−	5.28309i	0.372640	−	0.645432i	−0.617331	−	0.786704i	$-0.711786\pi$
$67$	3.05019	−	5.28309i	0.372640	−	0.645432i	0.989971	+	0.141272i	$0.0451192\pi$
$68$	10.1751	+	17.6239i	1.23392	+	2.13721i
$69$	−3.63986			−0.438188
$70$		0			0
$71$	1.53948			0.182703			0.0913514	−	0.995819i	$-0.470881\pi$
$71$	1.53948			0.182703			0.0913514	+	0.995819i	$0.470881\pi$
$72$	2.94120	+	5.09431i	0.346624	+	0.600370i
$73$	−7.65004	+	13.2503i	−0.895369	+	1.55083i	−0.0620224	+	0.998075i	$0.519755\pi$
$73$	−7.65004	+	13.2503i	−0.895369	+	1.55083i	−0.833347	+	0.552750i	$0.813578\pi$
$74$	−9.97858	+	17.2834i	−1.15999	+	2.00915i
$75$	1.83221	+	3.17348i	0.211566	+	0.366442i
$76$	11.6644			1.33800
$77$		0			0
$78$	−2.68585			−0.304112
$79$	−0.441202	−	0.764184i	−0.0496391	−	0.0859774i	0.840138	−	0.542372i	$-0.182474\pi$
$79$	−0.441202	−	0.764184i	−0.0496391	−	0.0859774i	−0.889777	+	0.456395i	$0.849140\pi$
$80$	−0.803442	+	1.39160i	−0.0898276	+	0.155586i
$81$	0.550192	−	0.952961i	0.0611325	−	0.105885i
$82$	−0.342923	−	0.593960i	−0.0378695	−	0.0655919i
$83$	12.1292			1.33135			0.665674	−	0.746243i	$-0.268144\pi$
$83$	12.1292			1.33135			0.665674	+	0.746243i	$0.268144\pi$
$84$		0			0
$85$	−7.83221			−0.849523
$86$	9.55176	+	16.5441i	1.02999	+	1.78400i
$87$	−6.01228	+	10.4136i	−0.644584	+	1.11645i
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	2.86802	+	4.96755i	0.304009	+	0.526560i	0.977040	−	0.213055i	$-0.0683412\pi$
$89$	2.86802	+	4.96755i	0.304009	+	0.526560i	−0.673031	+	0.739614i	$0.735008\pi$
$90$	−5.30429			−0.559121
$91$		0			0
$92$	−11.0790			−1.15506
$93$	0.937529	+	1.62385i	0.0972172	+	0.168385i
$94$	−12.4342	+	21.5366i	−1.28249	+	2.22133i
$95$	−2.24464	+	3.88784i	−0.230296	+	0.398884i
$96$	2.39312	+	4.14500i	0.244246	+	0.423047i
$97$	5.34292			0.542492			0.271246	−	0.962510i	$-0.412564\pi$
$97$	5.34292			0.542492			0.271246	+	0.962510i	$0.412564\pi$
$98$		0			0
$99$	−1.93260			−0.194233
$100$	5.57686	+	9.65940i	0.557686	+	0.965940i
$101$	5.57318	−	9.65304i	0.554552	−	0.960513i	−0.443386	−	0.896331i	$-0.646223\pi$
$101$	5.57318	−	9.65304i	0.554552	−	0.960513i	0.997938	−	0.0641821i	$-0.0204438\pi$
$102$	7.83221	−	13.5658i	0.775505	−	1.34321i
$103$	−1.70727	−	2.95708i	−0.168222	−	0.291369i	0.769573	−	0.638559i	$-0.220469\pi$
$103$	−1.70727	−	2.95708i	−0.168222	−	0.291369i	−0.937795	+	0.347190i	$0.887136\pi$
$104$	−3.48929			−0.342153
$105$		0			0
$106$	−1.83221			−0.177960
$107$	−2.48929	−	4.31157i	−0.240649	−	0.416816i	0.720251	−	0.693714i	$-0.244027\pi$
$107$	−2.48929	−	4.31157i	−0.240649	−	0.416816i	−0.960899	+	0.276898i	$0.910693\pi$
$108$	9.37169	−	16.2322i	0.901792	−	1.56195i
$109$	6.74832	−	11.6884i	0.646372	−	1.11955i	−0.337611	−	0.941286i	$-0.609619\pi$
$109$	6.74832	−	11.6884i	0.646372	−	1.11955i	0.983983	−	0.178263i	$-0.0570477\pi$
$110$	−1.80344	−	3.12365i	−0.171951	−	0.297829i
$111$	9.76481			0.926835
$112$		0			0
$113$	16.4464			1.54715			0.773576	−	0.633704i	$-0.218466\pi$
$113$	16.4464			1.54715			0.773576	+	0.633704i	$0.218466\pi$
$114$	−4.48929	−	7.77568i	−0.420460	−	0.728259i
$115$	2.13198	−	3.69270i	0.198808	−	0.344346i
$116$	−18.3001	+	31.6967i	−1.69912	+	2.94296i
$117$	−0.842923	−	1.45999i	−0.0779283	−	0.134976i
$118$	−29.6216			−2.72689
$119$		0			0
$120$	5.37169			0.490366
$121$	4.84292	+	8.38819i	0.440266	+	0.762563i
$122$	−2.34292	+	4.05806i	−0.212118	+	0.367400i
$123$	−0.167788	+	0.290618i	−0.0151290	+	0.0262041i
$124$	2.85363	+	4.94264i	0.256264	+	0.443862i
$125$	−11.0073			−0.984527
$126$		0			0
$127$	12.0575			1.06993			0.534967	−	0.844873i	$-0.320324\pi$
$127$	12.0575			1.06993			0.534967	+	0.844873i	$0.320324\pi$
$128$	10.0876	+	17.4722i	0.891623	+	1.54434i
$129$	4.67357	−	8.09486i	0.411485	−	0.712712i
$130$	1.57318	−	2.72483i	0.137977	−	0.238984i
$131$	−1.83221	−	3.17348i	−0.160081	−	0.277269i	0.774816	−	0.632186i	$-0.217842\pi$
$131$	−1.83221	−	3.17348i	−0.160081	−	0.277269i	−0.934898	+	0.354918i	$0.884509\pi$
$132$	4.58546			0.399113
$133$		0			0
$134$	−14.2927			−1.23470
$135$	3.60688	+	6.24731i	0.310431	+	0.537683i
$136$	10.1751	−	17.6239i	0.872511	−	1.51123i
$137$	6.55176	−	11.3480i	0.559755	−	0.969523i	−0.437762	−	0.899091i	$-0.644229\pi$
$137$	6.55176	−	11.3480i	0.559755	−	0.969523i	0.997517	−	0.0704325i	$-0.0224379\pi$
$138$	4.26396	+	7.38540i	0.362973	+	0.628687i
$139$	−7.49663			−0.635856			−0.317928	−	0.948115i	$-0.602987\pi$
$139$	−7.49663			−0.635856			−0.317928	+	0.948115i	$0.602987\pi$
$140$		0			0
$141$	12.1678			1.02471
$142$	−1.80344	−	3.12365i	−0.151342	−	0.262131i
$143$	0.573183	−	0.992782i	0.0479319	−	0.0830206i
$144$	1.00861	−	1.74696i	0.0840505	−	0.145580i
$145$	−7.04315	−	12.1991i	−0.584902	−	1.01308i
$146$	35.8469			2.96671
$147$		0			0
$148$	29.7220			2.44313
$149$	−1.08389	−	1.87736i	−0.0887961	−	0.153799i	0.818206	−	0.574925i	$-0.194969\pi$
$149$	−1.08389	−	1.87736i	−0.0887961	−	0.153799i	−0.907002	+	0.421125i	$0.861635\pi$
$150$	4.29273	−	7.43523i	0.350500	−	0.607084i
$151$	−7.45559	+	12.9135i	−0.606727	+	1.05088i	0.385049	+	0.922896i	$0.374185\pi$
$151$	−7.45559	+	12.9135i	−0.606727	+	1.05088i	−0.991776	+	0.127986i	$0.959149\pi$
$152$	−5.83221	−	10.1017i	−0.473055	−	0.819355i
$153$	9.83221			0.794887
$154$		0			0
$155$	−2.19656			−0.176432
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	11.4342	−	19.8046i	0.912546	−	1.58058i	0.102090	−	0.994775i	$-0.467447\pi$
$157$	11.4342	−	19.8046i	0.912546	−	1.58058i	0.810456	−	0.585800i	$-0.199220\pi$
$158$	−1.03370	+	1.79042i	−0.0822369	+	0.142439i
$159$	0.448240	+	0.776375i	0.0355478	+	0.0615705i
$160$	−5.60688			−0.443263
$161$		0			0
$162$	−2.57812			−0.202556
$163$	−3.53948	−	6.13056i	−0.277234	−	0.480183i	0.693463	−	0.720493i	$-0.256084\pi$
$163$	−3.53948	−	6.13056i	−0.277234	−	0.480183i	−0.970696	+	0.240310i	$0.922751\pi$
$164$	−0.510711	+	0.884578i	−0.0398799	+	0.0690739i
$165$	−0.882404	+	1.52837i	−0.0686950	+	0.118983i
$166$	−14.2088	−	24.6104i	−1.10282	−	1.91014i
$167$	−2.61423			−0.202295			−0.101148	−	0.994871i	$-0.532251\pi$
$167$	−2.61423			−0.202295			−0.101148	+	0.994871i	$0.532251\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	9.17513	+	15.8918i	0.703701	+	1.21885i
$171$	2.81783	−	4.88062i	0.215485	−	0.373230i
$172$	14.2253	−	24.6390i	1.08467	−	1.87871i
$173$	5.50157	+	9.52899i	0.418276	+	0.724476i	0.995766	−	0.0919219i	$-0.0293010\pi$
$173$	5.50157	+	9.52899i	0.418276	+	0.724476i	−0.577490	+	0.816398i	$0.695968\pi$
$174$	28.1726			2.13576
$175$		0			0
$176$	1.37169			0.103395
$177$	7.24675	+	12.5517i	0.544699	+	0.943446i
$178$	6.71955	−	11.6386i	0.503651	−	0.872350i
$179$	−11.9807	+	20.7512i	−0.895478	+	1.55101i	−0.0622667	+	0.998060i	$0.519833\pi$
$179$	−11.9807	+	20.7512i	−0.895478	+	1.55101i	−0.833212	+	0.552954i	$0.813500\pi$
$180$	3.94981	+	6.84127i	0.294401	+	0.509918i
$181$	−6.56090			−0.487668			−0.243834	−	0.969817i	$-0.578405\pi$
$181$	−6.56090			−0.487668			−0.243834	+	0.969817i	$0.578405\pi$
$182$		0			0
$183$	2.29273			0.169484
$184$	5.53948	+	9.59466i	0.408376	+	0.707328i
$185$	−5.71955	+	9.90655i	−0.420510	+	0.728344i
$186$	2.19656	−	3.80455i	0.161059	−	0.278963i
$187$	3.34292	+	5.79011i	0.244459	+	0.423415i
$188$	37.0361			2.70114
$189$		0			0
$190$	10.5181			0.763060
$191$	2.19656	+	3.80455i	0.158937	+	0.275288i	0.934486	−	0.356001i	$-0.115860\pi$
$191$	2.19656	+	3.80455i	0.158937	+	0.275288i	−0.775548	+	0.631288i	$0.782527\pi$
$192$	6.97858	−	12.0873i	0.503635	−	0.872322i
$193$	4.14637	−	7.18172i	0.298462	−	0.516951i	−0.677322	−	0.735686i	$-0.736860\pi$
$193$	4.14637	−	7.18172i	0.298462	−	0.516951i	0.975784	+	0.218735i	$0.0701931\pi$
$194$	−6.25903	−	10.8410i	−0.449372	−	0.778335i
$195$	−1.53948			−0.110245
$196$		0			0
$197$	−3.17092			−0.225919			−0.112959	−	0.993600i	$-0.536033\pi$
$197$	−3.17092			−0.225919			−0.112959	+	0.993600i	$0.536033\pi$
$198$	2.26396	+	3.92130i	0.160893	+	0.278674i
$199$	−6.79851	+	11.7754i	−0.481934	+	0.834733i	−0.999785	−	0.0207372i	$-0.993399\pi$
$199$	−6.79851	+	11.7754i	−0.481934	+	0.834733i	0.517851	+	0.855471i	$0.326732\pi$
$200$	5.57686	−	9.65940i	0.394343	−	0.683023i
$201$	3.49663	+	6.05635i	0.246634	+	0.427182i
$202$	−26.1151			−1.83745
$203$		0			0
$204$	−23.3288			−1.63335
$205$	−0.196558	−	0.340448i	−0.0137282	−	0.0237779i
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$	−2.67639	+	4.63565i	−0.186022	+	0.322200i
$208$	0.598279	+	1.03625i	0.0414832	+	0.0718510i
$209$	3.83221			0.265080
$210$		0			0
$211$	9.27552			0.638553			0.319277	−	0.947662i	$-0.396560\pi$
$211$	9.27552			0.638553			0.319277	+	0.947662i	$0.396560\pi$
$212$	1.36435	+	2.36312i	0.0937037	+	0.162300i
$213$	−0.882404	+	1.52837i	−0.0604613	+	0.104722i
$214$	−5.83221	+	10.1017i	−0.398682	+	0.690537i
$215$	5.47490	+	9.48281i	0.373385	+	0.646722i
$216$	−18.7434			−1.27533
$217$		0			0
$218$	−31.6216			−2.14168
$219$	−8.76974	−	15.1896i	−0.592604	−	1.02642i
$220$	−2.68585	+	4.65202i	−0.181080	+	0.313639i
$221$	−2.91611	+	5.05084i	−0.196159	+	0.339756i
$222$	−11.4391	−	19.8131i	−0.767742	−	1.32977i
$223$	19.5928			1.31203			0.656016	−	0.754747i	$-0.272240\pi$
$223$	19.5928			1.31203			0.656016	+	0.754747i	$0.272240\pi$
$224$		0			0
$225$	5.38890			0.359260
$226$	−19.2664	−	33.3703i	−1.28158	−	2.21976i
$227$	−9.83221	+	17.0299i	−0.652587	+	1.13031i	0.329906	+	0.944014i	$0.392983\pi$
$227$	−9.83221	+	17.0299i	−0.652587	+	1.13031i	−0.982493	+	0.186300i	$0.940350\pi$
$228$	−6.68585	+	11.5802i	−0.442781	+	0.766919i
$229$	3.88240	+	6.72452i	0.256556	+	0.444369i	0.965317	−	0.261080i	$-0.0840787\pi$
$229$	3.88240	+	6.72452i	0.256556	+	0.444369i	−0.708761	+	0.705449i	$0.750745\pi$
$230$	−9.99013			−0.658730
$231$		0			0
$232$	36.6002			2.40292
$233$	−6.09828	−	10.5625i	−0.399512	−	0.691974i	0.594154	−	0.804351i	$-0.297487\pi$
$233$	−6.09828	−	10.5625i	−0.399512	−	0.691974i	−0.993666	+	0.112377i	$0.964154\pi$
$234$	−1.97490	+	3.42063i	−0.129104	+	0.223614i
$235$	−7.12705	+	12.3444i	−0.464917	+	0.805260i
$236$	22.0575	+	38.2048i	1.43582	+	2.48692i
$237$	1.01156			0.0657077
$238$		0			0
$239$	−10.2927			−0.665781			−0.332891	−	0.942965i	$-0.608024\pi$
$239$	−10.2927			−0.665781			−0.332891	+	0.942965i	$0.608024\pi$
$240$	−0.921039	−	1.59529i	−0.0594528	−	0.102975i
$241$	−2.01438	+	3.48902i	−0.129758	+	0.224747i	−0.923583	−	0.383399i	$-0.874753\pi$
$241$	−2.01438	+	3.48902i	−0.129758	+	0.224747i	0.793825	+	0.608147i	$0.208087\pi$
$242$	11.3466	−	19.6529i	0.729387	−	1.26334i
$243$	−7.42682	−	12.8636i	−0.476431	−	0.825202i
$244$	6.97858			0.446758
$245$		0			0
$246$	0.786230			0.0501282
$247$	1.67146	+	2.89506i	0.106353	+	0.184208i
$248$	2.85363	−	4.94264i	0.181206	−	0.313858i
$249$	−6.95222	+	12.0416i	−0.440579	+	0.763105i
$250$	12.8947	+	22.3342i	0.815531	+	1.41254i
$251$	−2.91117			−0.183752			−0.0918758	−	0.995770i	$-0.529286\pi$
$251$	−2.91117			−0.183752			−0.0918758	+	0.995770i	$0.529286\pi$
$252$		0			0
$253$	−3.63986			−0.228836
$254$	−14.1249	−	24.4651i	−0.886278	−	1.53508i
$255$	4.48929	−	7.77568i	0.281130	−	0.486932i
$256$	11.4593	−	19.8480i	0.716204	−	1.24050i
$257$	−9.79851	−	16.9715i	−0.611214	−	1.05865i	−0.991036	−	0.133594i	$-0.957348\pi$
$257$	−9.79851	−	16.9715i	−0.611214	−	1.05865i	0.379822	−	0.925060i	$-0.375985\pi$
$258$	−21.8996			−1.36341
$259$		0			0
$260$	−4.68585			−0.290604
$261$	8.84166	+	15.3142i	0.547285	+	0.947926i
$262$	−4.29273	+	7.43523i	−0.265206	+	0.459350i
$263$	−3.78412	+	6.55430i	−0.233339	+	0.404155i	−0.958789	−	0.284120i	$-0.908299\pi$
$263$	−3.78412	+	6.55430i	−0.233339	+	0.404155i	0.725450	+	0.688275i	$0.241632\pi$
$264$	−2.29273	−	3.97113i	−0.141108	−	0.244406i
$265$	−1.05019			−0.0645128
$266$		0			0
$267$	−6.57560			−0.402420
$268$	10.6430	+	18.4342i	0.650125	+	1.12605i
$269$	−4.73604	+	8.20306i	−0.288761	+	0.500149i	−0.973514	−	0.228626i	$-0.926577\pi$
$269$	−4.73604	+	8.20306i	−0.288761	+	0.500149i	0.684753	+	0.728775i	$0.259910\pi$
$270$	8.45065	−	14.6370i	0.514290	−	0.890777i
$271$	14.6858	+	25.4366i	0.892102	+	1.54517i	0.837351	+	0.546665i	$0.184103\pi$
$271$	14.6858	+	25.4366i	0.892102	+	1.54517i	0.0547504	+	0.998500i	$0.482564\pi$
$272$	−6.97858			−0.423138
$273$		0			0
$274$	−30.7005			−1.85469
$275$	1.83221	+	3.17348i	0.110487	+	0.191368i
$276$	6.35027	−	10.9990i	0.382241	−	0.662061i
$277$	0.951913	−	1.64876i	0.0571949	−	0.0990645i	−0.836010	−	0.548714i	$-0.815118\pi$
$277$	0.951913	−	1.64876i	0.0571949	−	0.0990645i	0.893205	+	0.449649i	$0.148451\pi$
$278$	8.78202	+	15.2109i	0.526711	+	0.912289i
$279$	2.75746			0.165085
$280$		0			0
$281$	−20.5756			−1.22744			−0.613719	−	0.789525i	$-0.710327\pi$
$281$	−20.5756			−1.22744			−0.613719	+	0.789525i	$0.710327\pi$
$282$	−14.2541	−	24.6888i	−0.848819	−	1.47020i
$283$	−13.4966	+	23.3769i	−0.802292	+	1.38961i	0.115813	+	0.993271i	$0.463053\pi$
$283$	−13.4966	+	23.3769i	−0.802292	+	1.38961i	−0.918104	+	0.396339i	$0.870281\pi$
$284$	−2.68585	+	4.65202i	−0.159376	+	0.276047i
$285$	−2.57318	−	4.45688i	−0.152422	−	0.264003i
$286$	−2.68585			−0.158817
$287$		0			0
$288$	7.03863			0.414756
$289$	−8.50735	−	14.7352i	−0.500432	−	0.866774i
$290$	−16.5016	+	28.5816i	−0.969005	+	1.67837i
$291$	−3.06247	+	5.30436i	−0.179525	+	0.310947i
$292$	−26.6932	−	46.2340i	−1.56210	−	2.70564i
$293$	14.9070			0.870874			0.435437	−	0.900219i	$-0.356594\pi$
$293$	14.9070			0.870874			0.435437	+	0.900219i	$0.356594\pi$
$294$		0			0
$295$	−16.9786			−0.988531
$296$	−14.8610	−	25.7400i	−0.863777	−	1.49611i
$297$	3.07896	−	5.33292i	0.178659	−	0.309447i
$298$	−2.53948	+	4.39851i	−0.147108	+	0.254799i
$299$	−1.58757	−	2.74975i	−0.0918114	−	0.159022i
$300$	−12.7862			−0.738213
$301$		0			0
$302$	34.9357			2.01033
$303$	6.38890	+	11.0659i	0.367033	+	0.635720i
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	−1.34292	+	2.32601i	−0.0768956	+	0.133187i
$306$	−11.5181	−	19.9499i	−0.658444	−	1.14046i
$307$	−26.0288			−1.48554			−0.742770	−	0.669546i	$-0.766488\pi$
$307$	−26.0288			−1.48554			−0.742770	+	0.669546i	$0.766488\pi$
$308$		0			0
$309$	3.91431			0.222677
$310$	2.57318	+	4.45688i	0.146147	+	0.253134i
$311$	9.74832	−	16.8846i	0.552776	−	0.957437i	−0.445296	−	0.895383i	$-0.646902\pi$
$311$	9.74832	−	16.8846i	0.552776	−	0.957437i	0.998073	−	0.0620536i	$-0.0197650\pi$
$312$	2.00000	−	3.46410i	0.113228	−	0.196116i
$313$	−1.74097	−	3.01545i	−0.0984055	−	0.170443i	0.812619	−	0.582795i	$-0.198041\pi$
$313$	−1.74097	−	3.01545i	−0.0984055	−	0.170443i	−0.911025	+	0.412352i	$0.864708\pi$
$314$	−53.5787			−3.02362
$315$		0			0
$316$	3.07896			0.173205
$317$	−2.51071	−	4.34868i	−0.141016	−	0.244246i	0.786864	−	0.617127i	$-0.211703\pi$
$317$	−2.51071	−	4.34868i	−0.141016	−	0.244246i	−0.927879	+	0.372881i	$0.878370\pi$
$318$	1.05019	−	1.81899i	0.0588918	−	0.102004i
$319$	−6.01228	+	10.4136i	−0.336623	+	0.583048i
$320$	8.17513	+	14.1597i	0.457004	+	0.791554i
$321$	5.70727			0.318549
$322$		0			0
$323$	−19.4966			−1.08482
$324$	1.91978	+	3.32515i	0.106654	+	0.184731i
$325$	−1.59828	+	2.76830i	−0.0886566	+	0.153558i
$326$	−8.29273	+	14.3634i	−0.459292	+	0.795517i
$327$	7.73604	+	13.3992i	0.427804	+	0.740978i
$328$	1.02142			0.0563986
$329$		0			0
$330$	4.13481			0.227614
$331$	3.07475	+	5.32562i	0.169004	+	0.292723i	0.938070	−	0.346446i	$-0.112612\pi$
$331$	3.07475	+	5.32562i	0.169004	+	0.292723i	−0.769066	+	0.639169i	$0.779278\pi$
$332$	−21.1611	+	36.6520i	−1.16136	+	2.01154i
$333$	7.18007	−	12.4362i	0.393465	−	0.681502i
$334$	3.06247	+	5.30436i	0.167571	+	0.290241i
$335$	−8.19235			−0.447596
$336$		0			0
$337$	−25.6258			−1.39593			−0.697963	−	0.716134i	$-0.745910\pi$
$337$	−25.6258			−1.39593			−0.697963	+	0.716134i	$0.745910\pi$
$338$	−1.17146	−	2.02903i	−0.0637191	−	0.110365i
$339$	−9.42682	+	16.3277i	−0.511994	+	0.886800i
$340$	13.6644	−	23.6675i	0.741057	−	1.28355i
$341$	0.937529	+	1.62385i	0.0507700	+	0.0879363i
$342$	−13.2039			−0.713985
$343$		0			0
$344$	−28.4507			−1.53396
$345$	2.44403	+	4.23318i	0.131582	+	0.227907i
$346$	12.8898	−	22.3257i	0.692957	−	1.20024i
$347$	8.35027	−	14.4631i	0.448266	−	0.776419i	−0.550007	−	0.835160i	$-0.685375\pi$
$347$	8.35027	−	14.4631i	0.448266	−	0.776419i	0.998273	+	0.0587404i	$0.0187084\pi$
$348$	−20.9786	−	36.3360i	−1.12457	−	1.94781i
$349$	23.5500			1.26060			0.630300	−	0.776351i	$-0.282932\pi$
$349$	23.5500			1.26060			0.630300	+	0.776351i	$0.282932\pi$
$350$		0			0
$351$	5.37169			0.286720
$352$	2.39312	+	4.14500i	0.127553	+	0.220929i
$353$	−3.82487	+	6.62486i	−0.203577	+	0.352606i	−0.949678	−	0.313227i	$-0.898590\pi$
$353$	−3.82487	+	6.62486i	−0.203577	+	0.352606i	0.746101	+	0.665832i	$0.231923\pi$
$354$	16.9786	−	29.4078i	0.902401	−	1.56300i
$355$	−1.03370	−	1.79042i	−0.0548632	−	0.0950259i
$356$	−20.0147			−1.06078
$357$		0			0
$358$	56.1396			2.96707
$359$	−9.18741	−	15.9131i	−0.484893	−	0.839860i	0.514956	−	0.857216i	$-0.327808\pi$
$359$	−9.18741	−	15.9131i	−0.484893	−	0.839860i	−0.999849	+	0.0173569i	$0.994475\pi$
$360$	3.94981	−	6.84127i	0.208173	−	0.360566i
$361$	3.91243	−	6.77653i	0.205918	−	0.356660i
$362$	7.68585	+	13.3123i	0.403959	+	0.699678i
$363$	−11.1035			−0.582784
$364$		0			0
$365$	20.5468			1.07547
$366$	−2.68585	−	4.65202i	−0.140391	−	0.243165i
$367$	2.66936	−	4.62346i	0.139339	−	0.241343i	−0.787907	−	0.615794i	$-0.788835\pi$
$367$	2.66936	−	4.62346i	0.139339	−	0.241343i	0.927247	+	0.374451i	$0.122169\pi$
$368$	1.89962	−	3.29023i	0.0990243	−	0.171515i
$369$	0.246750	+	0.427383i	0.0128453	+	0.0222487i
$370$	26.8009			1.39331
$371$		0			0
$372$	−6.54262			−0.339219
$373$	−10.7606	−	18.6379i	−0.557163	−	0.965034i	−0.997732	−	0.0673152i	$-0.978557\pi$
$373$	−10.7606	−	18.6379i	−0.557163	−	0.965034i	0.440569	−	0.897719i	$-0.354777\pi$
$374$	7.83221	−	13.5658i	0.404994	−	0.701470i
$375$	6.30922	−	10.9279i	0.325807	−	0.564314i
$376$	−18.5181	−	32.0742i	−0.954996	−	1.65410i
$377$	−10.4893			−0.540226
$378$		0			0
$379$	4.61002			0.236801			0.118400	−	0.992966i	$-0.462223\pi$
$379$	4.61002			0.236801			0.118400	+	0.992966i	$0.462223\pi$
$380$	−7.83221	−	13.5658i	−0.401784	−	0.695910i
$381$	−6.91117	+	11.9705i	−0.354070	+	0.613267i
$382$	5.14637	−	8.91377i	0.263311	−	0.456068i
$383$	−4.16779	−	7.21882i	−0.212964	−	0.368865i	0.739677	−	0.672962i	$-0.234978\pi$
$383$	−4.16779	−	7.21882i	−0.212964	−	0.368865i	−0.952641	+	0.304098i	$0.901645\pi$
$384$	−23.1281			−1.18025
$385$		0			0
$386$	−19.4292			−0.988922
$387$	−6.87295	−	11.9043i	−0.349372	−	0.605130i
$388$	−9.32150	+	16.1453i	−0.473227	+	0.819654i
$389$	3.22112	−	5.57914i	0.163317	−	0.282873i	−0.772739	−	0.634724i	$-0.781114\pi$
$389$	3.22112	−	5.57914i	0.163317	−	0.282873i	0.936056	+	0.351850i	$0.114447\pi$
$390$	1.80344	+	3.12365i	0.0913209	+	0.158172i
$391$	18.5181			0.936498
$392$		0			0
$393$	4.20077			0.211901
$394$	3.71462	+	6.43390i	0.187140	+	0.324135i
$395$	−0.592500	+	1.02624i	−0.0298119	+	0.0516358i
$396$	3.37169	−	5.83994i	0.169434	−	0.293468i
$397$	0.700231	+	1.21284i	0.0351436	+	0.0608705i	0.883062	−	0.469256i	$-0.155478\pi$
$397$	0.700231	+	1.21284i	0.0351436	+	0.0608705i	−0.847919	+	0.530126i	$0.822144\pi$
$398$	31.8568			1.59684
$399$		0			0
$400$	−3.82487			−0.191243
$401$	3.48929	+	6.04363i	0.174247	+	0.301804i	0.939900	−	0.341449i	$-0.110918\pi$
$401$	3.48929	+	6.04363i	0.174247	+	0.301804i	−0.765654	+	0.643253i	$0.777584\pi$
$402$	8.19235	−	14.1896i	0.408597	−	0.707711i
$403$	−0.817827	+	1.41652i	−0.0407389	+	0.0705618i
$404$	19.4464	+	33.6822i	0.967497	+	1.67575i
$405$	−1.47773			−0.0734291
$406$		0			0
$407$	9.76481			0.484024
$408$	11.6644	+	20.2034i	0.577475	+	1.00022i
$409$	−9.18952	+	15.9167i	−0.454392	+	0.787031i	−0.998653	−	0.0518854i	$-0.983477\pi$
$409$	−9.18952	+	15.9167i	−0.454392	+	0.787031i	0.544261	+	0.838916i	$0.316810\pi$
$410$	−0.460519	+	0.797643i	−0.0227434	+	0.0393928i
$411$	7.51071	+	13.0089i	0.370476	+	0.641683i
$412$	11.9143			0.586976
$413$		0			0
$414$	12.5412			0.616365
$415$	−8.14426	−	14.1063i	−0.399786	−	0.692450i
$416$	−2.08757	+	3.61577i	−0.102351	+	0.177278i
$417$	4.29694	−	7.44252i	0.210422	−	0.364462i
$418$	−4.48929	−	7.77568i	−0.219578	−	0.380321i
$419$	30.0393			1.46751			0.733757	−	0.679412i	$-0.237765\pi$
$419$	30.0393			1.46751			0.733757	+	0.679412i	$0.237765\pi$
$420$		0			0
$421$	−8.31729			−0.405360			−0.202680	−	0.979245i	$-0.564965\pi$
$421$	−8.31729			−0.405360			−0.202680	+	0.979245i	$0.564965\pi$
$422$	−10.8659	−	18.8203i	−0.528944	−	0.916159i
$423$	8.94698	−	15.4966i	0.435017	−	0.753472i
$424$	1.36435	−	2.36312i	0.0662585	−	0.114763i
$425$	−9.32150	−	16.1453i	−0.452159	−	0.783163i
$426$	4.13481			0.200332
$427$		0			0
$428$	17.3717			0.839692
$429$	0.657077	+	1.13809i	0.0317240	+	0.0549475i
$430$	12.8273	−	22.2175i	0.618586	−	1.07142i
$431$	−4.82487	+	8.35691i	−0.232406	+	0.402538i	−0.958516	−	0.285040i	$-0.907993\pi$
$431$	−4.82487	+	8.35691i	−0.232406	+	0.402538i	0.726110	+	0.687579i	$0.241326\pi$
$432$	3.21377	+	5.56641i	0.154623	+	0.267814i
$433$	−26.3074			−1.26425			−0.632127	−	0.774865i	$-0.717818\pi$
$433$	−26.3074			−1.26425			−0.632127	+	0.774865i	$0.717818\pi$
$434$		0			0
$435$	16.1481			0.774240
$436$	23.5468	+	40.7843i	1.12769	+	1.95321i
$437$	5.30712	−	9.19219i	0.253874	−	0.439722i
$438$	−20.5468	+	35.5881i	−0.981765	+	1.70047i
$439$	16.9070	+	29.2837i	0.806925	+	1.39764i	0.914984	+	0.403491i	$0.132203\pi$
$439$	16.9070	+	29.2837i	0.806925	+	1.39764i	−0.108058	+	0.994145i	$0.534463\pi$
$440$	5.37169			0.256085
$441$		0			0
$442$	13.6644			0.649950
$443$	−13.2232	−	22.9033i	−0.628254	−	1.08817i	−0.987902	−	0.155080i	$-0.950436\pi$
$443$	−13.2232	−	22.9033i	−0.628254	−	1.08817i	0.359648	−	0.933088i	$-0.382897\pi$
$444$	−17.0361	+	29.5074i	−0.808498	+	1.40036i
$445$	3.85153	−	6.67104i	0.182580	−	0.316238i
$446$	−22.9522	−	39.7544i	−1.08682	−	1.88243i
$447$	2.48508			0.117540
$448$		0			0
$449$	2.64300			0.124731			0.0623655	−	0.998053i	$-0.480136\pi$
$449$	2.64300			0.124731			0.0623655	+	0.998053i	$0.480136\pi$
$450$	−6.31289	−	10.9343i	−0.297593	−	0.515446i
$451$	−0.167788	+	0.290618i	−0.00790084	+	0.0136847i
$452$	−28.6932	+	49.6981i	−1.34961	+	2.33760i
$453$	−8.54683	−	14.8035i	−0.401565	−	0.695531i
$454$	46.0722			2.16228
$455$		0			0
$456$	13.3717			0.626187
$457$	16.8445	+	29.1755i	0.787952	+	1.36477i	0.927220	+	0.374518i	$0.122192\pi$
$457$	16.8445	+	29.1755i	0.787952	+	1.36477i	−0.139268	+	0.990255i	$0.544475\pi$
$458$	9.09617	−	15.7550i	0.425036	−	0.736184i
$459$	−15.6644	+	27.1316i	−0.731153	+	1.26639i
$460$	7.43910	+	12.8849i	0.346850	+	0.600761i
$461$	−33.0790			−1.54064			−0.770320	−	0.637657i	$-0.779904\pi$
$461$	−33.0790			−1.54064			−0.770320	+	0.637657i	$0.779904\pi$
$462$		0			0
$463$	−2.51806			−0.117024			−0.0585120	−	0.998287i	$-0.518636\pi$
$463$	−2.51806			−0.117024			−0.0585120	+	0.998287i	$0.518636\pi$
$464$	−6.27552	−	10.8695i	−0.291334	−	0.504605i
$465$	1.25903	−	2.18070i	0.0583861	−	0.101128i
$466$	−14.2878	+	24.7472i	−0.661869	+	1.14639i
$467$	1.28780	+	2.23053i	0.0595922	+	0.103217i	0.894282	−	0.447503i	$-0.147687\pi$
$467$	1.28780	+	2.23053i	0.0595922	+	0.103217i	−0.834690	+	0.550720i	$0.814353\pi$
$468$	5.88240			0.271914
$469$		0			0
$470$	33.3963			1.54045
$471$	13.1077	+	22.7033i	0.603972	+	1.04611i
$472$	22.0575	−	38.2048i	1.01528	−	1.75852i
$473$	4.67357	−	8.09486i	0.214891	−	0.372202i
$474$	−1.18500	−	2.05248i	−0.0544289	−	0.0942736i
$475$	−10.6858			−0.490300
$476$		0			0
$477$	1.31836			0.0603638
$478$	12.0575	+	20.8843i	0.551499	+	0.955224i
$479$	0.256923	−	0.445005i	0.0117391	−	0.0203328i	−0.860096	−	0.510132i	$-0.829597\pi$
$479$	0.256923	−	0.445005i	0.0117391	−	0.0203328i	0.871835	+	0.489799i	$0.162930\pi$
$480$	3.21377	−	5.56641i	0.146688	−	0.254071i
$481$	4.25903	+	7.37685i	0.194195	+	0.336356i
$482$	9.43910			0.429939
$483$		0			0
$484$	−33.7967			−1.53621
$485$	−3.58757	−	6.21385i	−0.162903	−	0.282156i
$486$	−17.4005	+	30.1385i	−0.789301	+	1.36711i
$487$	−18.0288	+	31.2267i	−0.816962	+	1.41502i	0.0909493	+	0.995856i	$0.471010\pi$
$487$	−18.0288	+	31.2267i	−0.816962	+	1.41502i	−0.907911	+	0.419163i	$0.862323\pi$
$488$	−3.48929	−	6.04363i	−0.157953	−	0.273582i
$489$	8.11508			0.366976
$490$		0			0
$491$	−9.22846			−0.416475			−0.208237	−	0.978078i	$-0.566773\pi$
$491$	−9.22846			−0.416475			−0.208237	+	0.978078i	$0.566773\pi$
$492$	−0.585462	−	1.01405i	−0.0263947	−	0.0457169i
$493$	30.5879	−	52.9798i	1.37761	−	2.38609i
$494$	3.91611	−	6.78289i	0.176194	−	0.305177i
$495$	1.29766	+	2.24762i	0.0583257	+	0.101023i
$496$	−1.95715			−0.0878788
$497$		0			0
$498$	32.5770			1.45981
$499$	−0.501568	−	0.868741i	−0.0224533	−	0.0388902i	0.854580	−	0.519319i	$-0.173814\pi$
$499$	−0.501568	−	0.868741i	−0.0224533	−	0.0388902i	−0.877034	+	0.480429i	$0.840481\pi$
$500$	19.2039	−	33.2621i	0.858825	−	1.48753i
$501$	1.49843	−	2.59536i	0.0669450	−	0.115952i
$502$	3.41033	+	5.90686i	0.152210	+	0.263636i
$503$	30.3503			1.35325			0.676626	−	0.736327i	$-0.263441\pi$
$503$	30.3503			1.35325			0.676626	+	0.736327i	$0.263441\pi$
$504$		0			0
$505$	−14.9687			−0.666099
$506$	4.26396	+	7.38540i	0.189556	+	0.328321i
$507$	−0.573183	+	0.992782i	−0.0254559	+	0.0440910i
$508$	−21.0361	+	36.4356i	−0.933327	+	1.61657i
$509$	5.29977	+	9.17947i	0.234908	+	0.406873i	0.959246	−	0.282572i	$-0.0911877\pi$
$509$	5.29977	+	9.17947i	0.234908	+	0.406873i	−0.724338	+	0.689445i	$0.757854\pi$
$510$	−21.0361			−0.931495
$511$		0			0
$512$	−13.3461			−0.589818
$513$	8.97858	+	15.5514i	0.396414	+	0.686609i
$514$	−22.9572	+	39.7630i	−1.01260	+	1.75387i
$515$	−2.29273	+	3.97113i	−0.101030	+	0.174989i
$516$	16.3074	+	28.2453i	0.717894	+	1.24343i
$517$	12.1678			0.535139
$518$		0			0
$519$	−12.6136			−0.553676
$520$	2.34292	+	4.05806i	0.102744	+	0.177958i
$521$	−8.13229	+	14.0855i	−0.356282	+	0.617099i	−0.987337	−	0.158640i	$-0.949289\pi$
$521$	−8.13229	+	14.0855i	−0.356282	+	0.617099i	0.631054	+	0.775739i	$0.282622\pi$
$522$	20.7153	−	35.8800i	0.906686	−	1.57043i
$523$	3.61110	+	6.25460i	0.157902	+	0.273495i	0.934112	−	0.356980i	$-0.116194\pi$
$523$	3.61110	+	6.25460i	0.157902	+	0.273495i	−0.776210	+	0.630475i	$0.782860\pi$
$524$	12.7862			0.558569
$525$		0			0
$526$	17.7318			0.773144
$527$	−4.76974	−	8.26143i	−0.207773	−	0.359874i
$528$	−0.786230	+	1.36179i	−0.0342163	+	0.0592643i
$529$	6.45926	−	11.1878i	0.280837	−	0.486425i
$530$	1.23026	+	2.13087i	0.0534391	+	0.0925592i
$531$	21.3142			0.924955
$532$		0			0
$533$	−0.292731			−0.0126796
$534$	7.70306	+	13.3421i	0.333344	+	0.577369i
$535$	−3.34292	+	5.79011i	−0.144527	+	0.250328i
$536$	10.6430	−	18.4342i	0.459708	−	0.796237i
$537$	−13.7342	−	23.7884i	−0.592676	−	1.02655i
$538$	22.1923			0.956780
$539$		0			0
$540$	−25.1709			−1.08318
$541$	−8.67670	−	15.0285i	−0.373041	−	0.646125i	0.616991	−	0.786970i	$-0.288351\pi$
$541$	−8.67670	−	15.0285i	−0.373041	−	0.646125i	−0.990032	+	0.140845i	$0.955018\pi$
$542$	34.4078	−	59.5961i	1.47794	−	2.55987i
$543$	3.76060	−	6.51354i	0.161383	−	0.279523i
$544$	−12.1751	−	21.0880i	−0.522005	−	0.904138i
$545$	−18.1249			−0.776387
$546$		0			0
$547$	−34.1109			−1.45848			−0.729238	−	0.684261i	$-0.760125\pi$
$547$	−34.1109			−1.45848			−0.729238	+	0.684261i	$0.760125\pi$
$548$	22.8610	+	39.5964i	0.976573	+	1.69147i
$549$	1.68585	−	2.91997i	0.0719502	−	0.124621i
$550$	4.29273	−	7.43523i	0.183043	−	0.317039i
$551$	−17.5324	−	30.3671i	−0.746907	−	1.29368i
$552$	−12.7005			−0.540571
$553$		0			0
$554$	−4.46052			−0.189509
$555$	−6.55669	−	11.3565i	−0.278316	−	0.482058i
$556$	13.0790	−	22.6534i	0.554672	−	0.960719i
$557$	6.61110	−	11.4508i	0.280121	−	0.485184i	−0.691293	−	0.722574i	$-0.742959\pi$
$557$	6.61110	−	11.4508i	0.280121	−	0.485184i	0.971414	+	0.237390i	$0.0762920\pi$
$558$	−3.23026	−	5.59497i	−0.136748	−	0.236854i
$559$	8.15371			0.344865
$560$		0			0
$561$	−7.66442			−0.323592
$562$	24.1035	+	41.7485i	1.01675	+	1.76106i
$563$	−20.6858	+	35.8289i	−0.871804	+	1.51001i	−0.0116762	+	0.999932i	$0.503717\pi$
$563$	−20.6858	+	35.8289i	−0.871804	+	1.51001i	−0.860128	+	0.510078i	$0.829617\pi$
$564$	−21.2285	+	36.7688i	−0.893880	+	1.54824i
$565$	−11.0432	−	19.1273i	−0.464589	−	0.804692i
$566$	63.2432			2.65831
$567$		0			0
$568$	5.37169			0.225391
$569$	1.34082	+	2.32236i	0.0562100	+	0.0973586i	0.892761	−	0.450530i	$-0.148765\pi$
$569$	1.34082	+	2.32236i	0.0562100	+	0.0973586i	−0.836551	+	0.547889i	$0.815432\pi$
$570$	−6.02877	+	10.4421i	−0.252517	+	0.437373i
$571$	14.4658	−	25.0554i	0.605373	−	1.04854i	−0.386619	−	0.922239i	$-0.626357\pi$
$571$	14.4658	−	25.0554i	0.605373	−	1.04854i	0.991992	−	0.126298i	$-0.0403095\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$	−5.03612			−0.210387
$574$		0			0
$575$	10.1495			0.423263
$576$	−10.2627	−	17.7755i	−0.427613	−	0.740647i
$577$	18.7648	−	32.5016i	0.781189	−	1.35306i	−0.150060	−	0.988677i	$-0.547947\pi$
$577$	18.7648	−	32.5016i	0.781189	−	1.35306i	0.931249	−	0.364382i	$-0.118720\pi$
$578$	−19.9321	+	34.5233i	−0.829064	+	1.43598i
$579$	4.75325	+	8.23287i	0.197538	+	0.342146i
$580$	49.1512			2.04089
$581$		0			0
$582$	14.3503			0.594838
$583$	0.448240	+	0.776375i	0.0185642	+	0.0321542i
$584$	−26.6932	+	46.2340i	−1.10457	+	1.91318i
$585$	−1.13198	+	1.96065i	−0.0468016	+	0.0810628i
$586$	−17.4629	−	30.2467i	−0.721387	−	1.24948i
$587$	−23.0649			−0.951990			−0.475995	−	0.879448i	$-0.657912\pi$
$587$	−23.0649			−0.951990			−0.475995	+	0.879448i	$0.657912\pi$
$588$		0			0
$589$	−5.46787			−0.225299
$590$	19.8898	+	34.4501i	0.818848	+	1.41829i
$591$	1.81752	−	3.14804i	0.0747627	−	0.129493i
$592$	−5.09617	+	8.82683i	−0.209451	+	0.362781i
$593$	−5.52510	−	9.56975i	−0.226889	−	0.392982i	0.729996	−	0.683452i	$-0.239522\pi$
$593$	−5.52510	−	9.56975i	−0.226889	−	0.392982i	−0.956884	+	0.290469i	$0.906189\pi$
$594$	−14.4275			−0.591969
$595$		0			0
$596$	7.56404			0.309835
$597$	−7.79358	−	13.4989i	−0.318970	−	0.552472i
$598$	−3.71955	+	6.44245i	−0.152104	+	0.263451i
$599$	22.3022	−	38.6285i	0.911242	−	1.57832i	0.0989311	−	0.995094i	$-0.468458\pi$
$599$	22.3022	−	38.6285i	0.911242	−	1.57832i	0.812311	−	0.583224i	$-0.198209\pi$
$600$	6.39312	+	11.0732i	0.260998	+	0.452062i
$601$	−47.8715			−1.95272			−0.976359	−	0.216156i	$-0.930648\pi$
$601$	−47.8715			−1.95272			−0.976359	+	0.216156i	$0.930648\pi$
$602$		0			0
$603$	10.2843			0.418809
$604$	−26.0147	−	45.0588i	−1.05852	−	1.83342i
$605$	6.50367	−	11.2647i	0.264412	−	0.457975i
$606$	14.9687	−	25.9266i	0.608062	−	1.05319i
$607$	22.5345	+	39.0310i	0.914649	+	1.58422i	0.807414	+	0.589985i	$0.200866\pi$
$607$	22.5345	+	39.0310i	0.914649	+	1.58422i	0.107235	+	0.994234i	$0.465800\pi$
$608$	−13.9572			−0.566037
$609$		0			0
$610$	6.29273			0.254785
$611$	5.30712	+	9.19219i	0.214703	+	0.371876i
$612$	−17.1537	+	29.7111i	−0.693398	+	1.20100i
$613$	12.7606	−	22.1020i	0.515396	−	0.892691i	−0.484445	−	0.874822i	$-0.660978\pi$
$613$	12.7606	−	22.1020i	0.515396	−	0.892691i	0.999840	−	0.0178695i	$-0.00568836\pi$
$614$	30.4917	+	52.8132i	1.23054	+	2.13137i
$615$	0.450654			0.0181721
$616$		0			0
$617$	29.2432			1.17729			0.588643	−	0.808393i	$-0.299663\pi$
$617$	29.2432			1.17729			0.588643	+	0.808393i	$0.299663\pi$
$618$	−4.58546	−	7.94225i	−0.184454	−	0.319484i
$619$	2.39312	−	4.14500i	0.0961874	−	0.166601i	−0.813916	−	0.580982i	$-0.802669\pi$
$619$	2.39312	−	4.14500i	0.0961874	−	0.166601i	0.910104	+	0.414381i	$0.136002\pi$
$620$	3.83221	−	6.63759i	0.153905	−	0.266572i
$621$	−8.52792	−	14.7708i	−0.342214	−	0.592732i
$622$	−45.6791			−1.83157
$623$		0			0
$624$	−1.37169			−0.0549116
$625$	−0.600384	−	1.03990i	−0.0240154	−	0.0415958i
$626$	−4.07896	+	7.06497i	−0.163028	+	0.282373i
$627$	−2.19656	+	3.80455i	−0.0877221	+	0.151939i
$628$	39.8971	+	69.1038i	1.59207	+	2.75754i
$629$	−49.6791			−1.98084
$630$		0			0
$631$	−28.3931			−1.13031			−0.565156	−	0.824984i	$-0.691184\pi$
$631$	−28.3931			−1.13031			−0.565156	+	0.824984i	$0.691184\pi$
$632$	−1.53948	−	2.66646i	−0.0612373	−	0.106066i
$633$	−5.31657	+	9.20856i	−0.211315	+	0.366008i
$634$	−5.88240	+	10.1886i	−0.233620	+	0.404642i
$635$	−8.09617	−	14.0230i	−0.321287	−	0.556485i
$636$	−3.12808			−0.124036
$637$		0			0
$638$	28.1726			1.11536
$639$	1.29766	+	2.24762i	0.0513348	+	0.0889145i
$640$	13.5468	−	23.4638i	0.535485	−	0.927488i
$641$	−2.98068	+	5.16269i	−0.117730	+	0.203914i	−0.918868	−	0.394566i	$-0.870895\pi$
$641$	−2.98068	+	5.16269i	−0.117730	+	0.203914i	0.801138	+	0.598480i	$0.204228\pi$
$642$	−6.68585	−	11.5802i	−0.263869	−	0.457035i
$643$	−31.1940			−1.23017			−0.615086	−	0.788460i	$-0.710879\pi$
$643$	−31.1940			−1.23017			−0.615086	+	0.788460i	$0.710879\pi$
$644$		0			0
$645$	−12.5525			−0.494253
$646$	22.8396	+	39.5593i	0.898610	+	1.55644i
$647$	7.45559	−	12.9135i	0.293109	−	0.507680i	−0.681434	−	0.731880i	$-0.738643\pi$
$647$	7.45559	−	12.9135i	0.293109	−	0.507680i	0.974543	+	0.224199i	$0.0719767\pi$
$648$	1.91978	−	3.32515i	0.0754160	−	0.130624i
$649$	7.24675	+	12.5517i	0.284460	+	0.492699i
$650$	7.48929			0.293754
$651$		0			0
$652$	24.7005			0.967348
$653$	1.78623	+	3.09384i	0.0699006	+	0.121071i	0.898857	−	0.438241i	$-0.144398\pi$
$653$	1.78623	+	3.09384i	0.0699006	+	0.121071i	−0.828957	+	0.559313i	$0.811065\pi$
$654$	18.1249	−	31.3933i	0.708741	−	1.22758i
$655$	−2.46052	+	4.26174i	−0.0961404	+	0.166520i
$656$	−0.175135	−	0.303342i	−0.00683786	−	0.0118435i
$657$	−25.7936			−1.00630
$658$		0			0
$659$	−3.90383			−0.152071			−0.0760357	−	0.997105i	$-0.524226\pi$
$659$	−3.90383			−0.152071			−0.0760357	+	0.997105i	$0.524226\pi$
$660$	−3.07896	−	5.33292i	−0.119848	−	0.207584i
$661$	6.89679	−	11.9456i	0.268254	−	0.464630i	−0.700157	−	0.713989i	$-0.746887\pi$
$661$	6.89679	−	11.9456i	0.268254	−	0.464630i	0.968411	+	0.249359i	$0.0802200\pi$
$662$	7.20390	−	12.4775i	0.279988	−	0.484953i
$663$	−3.34292	−	5.79011i	−0.129828	−	0.224869i
$664$	42.3221			1.64242
$665$		0			0
$666$	−33.6447			−1.30371
$667$	16.6525	+	28.8429i	0.644786	+	1.11680i
$668$	4.56090	−	7.89972i	0.176467	−	0.305649i
$669$	−11.2303	+	19.4514i	−0.434187	+	0.752034i
$670$	9.59702	+	16.6225i	0.370765	+	0.642184i
$671$	2.29273			0.0885099
$672$		0			0
$673$	5.70306			0.219837			0.109918	−	0.993941i	$-0.464941\pi$
$673$	5.70306			0.219837			0.109918	+	0.993941i	$0.464941\pi$
$674$	30.0196	+	51.9955i	1.15631	+	2.00279i
$675$	−8.58546	+	14.8705i	−0.330455	+	0.572364i
$676$	−1.74464	+	3.02181i	−0.0671017	+	0.116224i
$677$	17.6307	+	30.5373i	0.677604	+	1.17364i	0.975701	+	0.219108i	$0.0703148\pi$
$677$	17.6307	+	30.5373i	0.677604	+	1.17364i	−0.298097	+	0.954536i	$0.596352\pi$
$678$	44.1726			1.69644
$679$		0			0
$680$	−27.3288			−1.04801
$681$	−11.2713	−	19.5225i	−0.431917	−	0.748103i
$682$	2.19656	−	3.80455i	0.0841105	−	0.145684i
$683$	−0.518058	+	0.897302i	−0.0198229	+	0.0343343i	−0.875767	−	0.482735i	$-0.839644\pi$
$683$	−0.518058	+	0.897302i	−0.0198229	+	0.0343343i	0.855944	+	0.517069i	$0.172977\pi$
$684$	9.83221	+	17.0299i	0.375944	+	0.651154i
$685$	−17.5970			−0.672348
$686$		0			0
$687$	−8.90131			−0.339606
$688$	4.87819	+	8.44928i	0.185979	+	0.322126i
$689$	−0.391010	+	0.677249i	−0.0148963	+	0.0258011i
$690$	5.72617	−	9.91802i	0.217992	−	0.377573i
$691$	1.83925	+	3.18567i	0.0699684	+	0.121189i	0.898887	−	0.438180i	$-0.144377\pi$
$691$	1.83925	+	3.18567i	0.0699684	+	0.121189i	−0.828919	+	0.559369i	$0.811043\pi$
$692$	−38.3931			−1.45949
$693$		0			0
$694$	−39.1281			−1.48528
$695$	5.03370	+	8.71863i	0.190939	+	0.330716i
$696$	−20.9786	+	36.3360i	−0.795191	+	1.37731i
$697$	0.853635	−	1.47854i	0.0323337	−	0.0560036i
$698$	−27.5879	−	47.7836i	−1.04422	−	1.80864i
$699$	13.9817			0.528837
$700$		0			0
$701$	−0.0617493			−0.00233224			−0.00116612	−	0.999999i	$-0.500371\pi$
$701$	−0.0617493			−0.00233224			−0.00116612	+	0.999999i	$0.500371\pi$
$702$	−6.29273	−	10.8993i	−0.237504	−	0.411369i
$703$	−14.2376	+	24.6603i	−0.536981	+	0.930079i
$704$	6.97858	−	12.0873i	0.263015	−	0.455555i
$705$	−8.17020	−	14.1512i	−0.307708	−	0.532965i
$706$	17.9227			0.674531
$707$		0			0
$708$	−50.5720			−1.90061
$709$	21.4917	+	37.2247i	0.807138	+	1.39800i	0.914838	+	0.403820i	$0.132318\pi$
$709$	21.4917	+	37.2247i	0.807138	+	1.39800i	−0.107701	+	0.994183i	$0.534349\pi$
$710$	−2.42188	+	4.19483i	−0.0908917	+	0.157429i
$711$	0.743798	−	1.28830i	0.0278946	−	0.0483149i
$712$	10.0073	+	17.3332i	0.375041	+	0.649590i
$713$	5.19342			0.194495
$714$		0			0
$715$	−1.53948			−0.0575733
$716$	−41.8041	−	72.4068i	−1.56229	−	2.70597i
$717$	5.89962	−	10.2184i	0.220325	−	0.381614i
$718$	−21.5254	+	37.2831i	−0.803321	+	1.39139i
$719$	8.82728	+	15.2893i	0.329202	+	0.570195i	0.982354	−	0.187033i	$-0.0598870\pi$
$719$	8.82728	+	15.2893i	0.329202	+	0.570195i	−0.653152	+	0.757227i	$0.726554\pi$
$720$	−2.70896			−0.100957
$721$		0			0
$722$	−18.3331			−0.682286
$723$	−2.30922	−	3.99969i	−0.0858809	−	0.148750i
$724$	11.4464	−	19.8258i	0.425404	−	0.736821i
$725$	16.7648	−	29.0375i	0.622629	−	1.07843i
$726$	13.0073	+	22.5294i	0.482748	+	0.836144i
$727$	23.8077			0.882977			0.441488	−	0.897267i	$-0.354451\pi$
$727$	23.8077			0.882977			0.441488	+	0.897267i	$0.354451\pi$
$728$		0			0
$729$	20.3288			0.752920
$730$	−24.0698	−	41.6901i	−0.890864	−	1.54302i
$731$	−23.7771	+	41.1831i	−0.879427	+	1.52321i
$732$	−4.00000	+	6.92820i	−0.147844	+	0.256074i
$733$	15.6746	+	27.1492i	0.578954	+	1.00278i	0.995600	+	0.0937093i	$0.0298724\pi$
$733$	15.6746	+	27.1492i	0.578954	+	1.00278i	−0.416645	+	0.909069i	$0.636794\pi$
$734$	−12.5082			−0.461686
$735$		0			0
$736$	13.2566			0.488645
$737$	3.49663	+	6.05635i	0.128800	+	0.223088i
$738$	0.578116	−	1.00133i	0.0212807	−	0.0368593i
$739$	12.4054	−	21.4868i	0.456340	−	0.790404i	−0.542424	−	0.840105i	$-0.682493\pi$
$739$	12.4054	−	21.4868i	0.456340	−	0.790404i	0.998764	+	0.0497009i	$0.0158268\pi$
$740$	−19.9572	−	34.5668i	−0.733640	−	1.27070i
$741$	−3.83221			−0.140780
$742$		0			0
$743$	21.3717			0.784051			0.392026	−	0.919954i	$-0.371774\pi$
$743$	21.3717			0.784051			0.392026	+	0.919954i	$0.371774\pi$
$744$	3.27131	+	5.66607i	0.119932	+	0.207728i
$745$	−1.45559	+	2.52115i	−0.0533286	+	0.0923678i
$746$	−25.2113	+	43.6672i	−0.923049	+	1.59877i
$747$	10.2239	+	17.7084i	0.374075	+	0.647916i
$748$	−23.3288			−0.852987
$749$		0			0
$750$	−29.5640			−1.07953
$751$	−9.61213	−	16.6487i	−0.350751	−	0.607519i	0.635630	−	0.771994i	$-0.280740\pi$
$751$	−9.61213	−	16.6487i	−0.350751	−	0.607519i	−0.986381	+	0.164475i	$0.947407\pi$
$752$	−6.35027	+	10.9990i	−0.231571	+	0.401092i
$753$	1.66863	−	2.89016i	0.0608084	−	0.105323i
$754$	12.2878	+	21.2831i	0.447495	+	0.775084i
$755$	20.0246			0.728768
$756$		0			0
$757$	−19.8610			−0.721860			−0.360930	−	0.932593i	$-0.617541\pi$
$757$	−19.8610			−0.721860			−0.360930	+	0.932593i	$0.617541\pi$
$758$	−5.40046	−	9.35387i	−0.196154	−	0.339748i
$759$	2.08631	−	3.61359i	0.0757282	−	0.131165i
$760$	−7.83221	+	13.5658i	−0.284104	+	0.492083i
$761$	3.06037	+	5.30071i	0.110938	+	0.192151i	0.916149	−	0.400838i	$-0.131281\pi$
$761$	3.06037	+	5.30071i	0.110938	+	0.192151i	−0.805211	+	0.592989i	$0.797948\pi$
$762$	32.3847			1.17317
$763$		0			0
$764$	−15.3288			−0.554578
$765$	−6.60195	−	11.4349i	−0.238694	−	0.413430i
$766$	−9.76481	+	16.9131i	−0.352817	+	0.611097i
$767$	−6.32150	+	10.9492i	−0.228256	+	0.395351i
$768$	13.1365	+	22.7531i	0.474023	+	0.821031i
$769$	−3.82800			−0.138041			−0.0690206	−	0.997615i	$-0.521987\pi$
$769$	−3.82800			−0.138041			−0.0690206	+	0.997615i	$0.521987\pi$
$770$		0			0
$771$	22.4653			0.809070
$772$	14.4679	+	25.0591i	0.520710	+	0.901896i
$773$	−3.26817	+	5.66064i	−0.117548	+	0.203599i	−0.918795	−	0.394734i	$-0.870837\pi$
$773$	−3.26817	+	5.66064i	−0.117548	+	0.203599i	0.801247	+	0.598333i	$0.204170\pi$
$774$	−16.1028	+	27.8909i	−0.578803	+	1.00252i
$775$	−2.61423	−	4.52798i	−0.0939060	−	0.162650i
$776$	18.6430			0.669245
$777$		0			0
$778$	−15.0937			−0.541134
$779$	−0.489289	−	0.847473i	−0.0175306	−	0.0303639i
$780$	2.68585	−	4.65202i	0.0961687	−	0.166569i
$781$	−0.882404	+	1.52837i	−0.0315749	+	0.0546893i
$782$	−21.6932	−	37.5737i	−0.775747	−	1.34363i
$783$	−56.3452			−2.01361
$784$		0			0
$785$	−30.7104			−1.09610
$786$	−4.92104	−	8.52349i	−0.175528	−	0.304023i
$787$	15.4033	−	26.6793i	0.549068	−	0.951014i	−0.449271	−	0.893396i	$-0.648316\pi$
$787$	15.4033	−	26.6793i	0.549068	−	0.951014i	0.998339	−	0.0576179i	$-0.0183505\pi$
$788$	5.53213	−	9.58194i	0.197074	−	0.341342i
$789$	−4.33799	−	7.51362i	−0.154437	−	0.267492i
$790$	2.77636			0.0987786
$791$		0			0
$792$	−6.74338			−0.239616
$793$	1.00000	+	1.73205i	0.0355110	+	0.0615069i
$794$	1.64059	−	2.84158i	0.0582222	−	0.100844i
$795$	0.601952	−	1.04261i	0.0213490	−	0.0369776i
$796$	−23.7220	−	41.0876i	−0.840803	−	1.45631i
$797$	38.8156			1.37492			0.687460	−	0.726222i	$-0.258726\pi$
$797$	38.8156			1.37492			0.687460	+	0.726222i	$0.258726\pi$
$798$		0			0
$799$	−61.9044			−2.19002
$800$	−6.67303	−	11.5580i	−0.235927	−	0.408638i
$801$	−4.83504	+	8.37453i	−0.170838	+	0.295900i
$802$	8.17513	−	14.1597i	0.288674	−	0.499998i
$803$	−8.76974	−	15.1896i	−0.309477	−	0.536031i
$804$	−24.4015			−0.860576
$805$		0			0
$806$	3.83221			0.134984
$807$	−5.42923	−	9.40370i	−0.191118	−	0.331026i
$808$	19.4464	−	33.6822i	0.684123	−	1.18494i
$809$	−0.520163	+	0.900949i	−0.0182880	+	0.0316757i	−0.875025	−	0.484079i	$-0.839155\pi$
$809$	−0.520163	+	0.900949i	−0.0182880	+	0.0316757i	0.856737	+	0.515754i	$0.172488\pi$
$810$	1.73111	+	2.99836i	0.0608248	+	0.105352i
$811$	−12.6712			−0.444944			−0.222472	−	0.974939i	$-0.571413\pi$
$811$	−12.6712			−0.444944			−0.222472	+	0.974939i	$0.571413\pi$
$812$		0			0
$813$	−33.6707			−1.18088
$814$	−11.4391	−	19.8131i	−0.400940	−	0.694449i
$815$	−4.75325	+	8.23287i	−0.166499	+	0.288385i
$816$	4.00000	−	6.92820i	0.140028	−	0.242536i
$817$	13.6286	+	23.6055i	0.476805	+	0.825850i
$818$	43.0607			1.50558
$819$		0			0
$820$	1.37169			0.0479016
$821$	−13.5181	−	23.4140i	−0.471783	−	0.817153i	0.527695	−	0.849434i	$-0.323056\pi$
$821$	−13.5181	−	23.4140i	−0.471783	−	0.817153i	−0.999479	+	0.0322807i	$0.989723\pi$
$822$	17.5970	−	30.4789i	0.613767	−	1.06307i
$823$	15.8181	−	27.3978i	0.551386	−	0.955028i	−0.446789	−	0.894639i	$-0.647433\pi$
$823$	15.8181	−	27.3978i	0.551386	−	0.955028i	0.998175	−	0.0603886i	$-0.0192340\pi$
$824$	−5.95715	−	10.3181i	−0.207527	−	0.359448i
$825$	−4.20077			−0.146252
$826$		0			0
$827$	56.4800			1.96400			0.982002	−	0.188872i	$-0.0604832\pi$
$827$	56.4800			1.96400			0.982002	+	0.188872i	$0.0604832\pi$
$828$	−9.33871	−	16.1751i	−0.324543	−	0.562124i
$829$	−21.3380	+	36.9585i	−0.741099	+	1.28362i	0.210896	+	0.977508i	$0.432362\pi$
$829$	−21.3380	+	36.9585i	−0.741099	+	1.28362i	−0.951995	+	0.306113i	$0.900972\pi$
$830$	−19.0814	+	33.0499i	−0.662324	+	1.14718i
$831$	1.09124	+	1.89008i	0.0378547	+	0.0655663i
$832$	12.1751			0.422097
$833$		0			0
$834$	−20.1348			−0.697211
$835$	1.75536	+	3.04037i	0.0607466	+	0.105216i
$836$	−6.68585	+	11.5802i	−0.231235	+	0.400510i
$837$	−4.39312	+	7.60910i	−0.151848	+	0.263009i
$838$	−35.1898	−	60.9506i	−1.21561	−	2.10550i
$839$	40.1642			1.38662			0.693311	−	0.720639i	$-0.256151\pi$
$839$	40.1642			1.38662			0.693311	+	0.720639i	$0.256151\pi$
$840$		0			0
$841$	81.0252			2.79397
$842$	9.74338	+	16.8760i	0.335779	+	0.581587i
$843$	11.7936	−	20.4271i	0.406192	−	0.703546i
$844$	−16.1825	+	28.0289i	−0.557024	+	0.964794i
$845$	−0.671462	−	1.16301i	−0.0230990	−	0.0400086i
$846$	−41.9242			−1.44138
$847$		0			0
$848$	−0.935731			−0.0321331
$849$	−15.4721	−	26.7984i	−0.531000	−	0.919719i
$850$	−21.8396	+	37.8272i	−0.749091	+	1.29746i
$851$	13.5230	−	23.4225i	0.463562	−	0.802913i
$852$	−3.07896	−	5.33292i	−0.105483	−	0.182703i
$853$	−19.6932			−0.674282			−0.337141	−	0.941454i	$-0.609460\pi$
$853$	−19.6932			−0.674282			−0.337141	+	0.941454i	$0.609460\pi$
$854$		0			0
$855$	−7.56825			−0.258829
$856$	−8.68585	−	15.0443i	−0.296876	−	0.514205i
$857$	0.832212	−	1.44143i	0.0284278	−	0.0492384i	−0.851461	−	0.524417i	$-0.824283\pi$
$857$	0.832212	−	1.44143i	0.0284278	−	0.0492384i	0.879889	+	0.475179i	$0.157617\pi$
$858$	1.53948	−	2.66646i	0.0525570	−	0.0910314i
$859$	−20.6472	−	35.7620i	−0.704474	−	1.22018i	−0.966881	−	0.255227i	$-0.917850\pi$
$859$	−20.6472	−	35.7620i	−0.704474	−	1.22018i	0.262407	−	0.964957i	$-0.415484\pi$
$860$	−38.2070			−1.30285
$861$		0			0
$862$	22.6086			0.770051
$863$	15.6644	+	27.1316i	0.533223	+	0.923570i	0.999247	+	0.0387975i	$0.0123527\pi$
$863$	15.6644	+	27.1316i	0.533223	+	0.923570i	−0.466024	+	0.884772i	$0.654314\pi$
$864$	−11.2138	+	19.4228i	−0.381500	+	0.660778i
$865$	7.38818	−	12.7967i	0.251206	−	0.435101i
$866$	30.8181	+	53.3786i	1.04724	+	1.81388i
$867$	19.5051			0.662426
$868$		0			0
$869$	1.01156			0.0343147
$870$	−18.9168	−	32.7649i	−0.641341	−	1.11083i
$871$	−3.05019	+	5.28309i	−0.103352	+	0.179011i
$872$	23.5468	−	40.7843i	0.797396	−	1.38113i
$873$	4.50367	+	7.80059i	0.152426	+	0.264010i
$874$	−24.8683			−0.841184
$875$		0			0
$876$	61.2003			2.06777
$877$	26.9020	+	46.5957i	0.908417	+	1.57342i	0.816264	+	0.577680i	$0.196042\pi$
$877$	26.9020	+	46.5957i	0.908417	+	1.57342i	0.0921533	+	0.995745i	$0.470625\pi$
$878$	39.6117	−	68.6095i	1.33683	−	2.31546i
$879$	−8.54441	+	14.7994i	−0.288196	+	0.499170i
$880$	−0.921039	−	1.59529i	−0.0310482	−	0.0537771i
$881$	−8.09196			−0.272625			−0.136313	−	0.990666i	$-0.543525\pi$
$881$	−8.09196			−0.272625			−0.136313	+	0.990666i	$0.543525\pi$
$882$		0			0
$883$	−27.0705			−0.910996			−0.455498	−	0.890237i	$-0.650539\pi$
$883$	−27.0705			−0.910996			−0.455498	+	0.890237i	$0.650539\pi$
$884$	−10.1751	−	17.6239i	−0.342227	−	0.592754i
$885$	9.73183	−	16.8560i	0.327132	−	0.566609i
$886$	−30.9810	+	53.6606i	−1.04083	+	1.80276i
$887$	−19.2467	−	33.3363i	−0.646243	−	1.11933i	−0.984013	−	0.178097i	$-0.943006\pi$
$887$	−19.2467	−	33.3363i	−0.646243	−	1.11933i	0.337770	−	0.941229i	$-0.390327\pi$
$888$	34.0722			1.14339
$889$		0			0
$890$	−18.0477			−0.604959
$891$	0.630721	+	1.09244i	0.0211300	+	0.0365982i
$892$	−34.1825	+	59.2058i	−1.14451	+	1.98236i
$893$	−17.7413	+	30.7288i	−0.593689	+	1.02830i
$894$	−2.91117	−	5.04230i	−0.0973642	−	0.168640i
$895$	32.1783			1.07560
$896$		0			0
$897$	3.63986			0.121532
$898$	−3.09617	−	5.36273i	−0.103321	−	0.178957i
$899$	8.57842	−	14.8583i	0.286106	−	0.495551i
$900$	−9.40172	+	16.2843i	−0.313391	+	0.542809i
$901$	−2.28045	−	3.94986i	−0.0759729	−	0.131589i
$902$	0.786230			0.0261786
$903$		0			0
$904$	57.3864			1.90864
$905$	4.40539	+	7.63037i	0.146440	+	0.253642i
$906$	−20.0246	+	34.6836i	−0.665271	+	1.15228i
$907$	−7.85153	+	13.5992i	−0.260706	+	0.451556i	−0.966430	−	0.256931i	$-0.917289\pi$
$907$	−7.85153	+	13.5992i	−0.260706	+	0.451556i	0.705724	+	0.708487i	$0.250622\pi$
$908$	−34.3074	−	59.4222i	−1.13853	−	1.97200i
$909$	18.7911			0.623260
$910$		0			0
$911$	44.9399			1.48893			0.744463	−	0.667663i	$-0.232705\pi$
$911$	44.9399			1.48893			0.744463	+	0.667663i	$0.232705\pi$
$912$	−2.29273	−	3.97113i	−0.0759199	−	0.131497i
$913$	−6.95222	+	12.0416i	−0.230085	+	0.398519i
$914$	39.4653	−	68.3560i	1.30540	−	2.26102i
$915$	−1.53948	−	2.66646i	−0.0508937	−	0.0881504i
$916$	−27.0937			−0.895200
$917$		0			0
$918$	73.4011			2.42260
$919$	13.6216	+	23.5933i	0.449334	+	0.778270i	0.998343	−	0.0575468i	$-0.0183279\pi$
$919$	13.6216	+	23.5933i	0.449334	+	0.778270i	−0.549008	+	0.835817i	$0.684995\pi$
$920$	7.43910	−	12.8849i	0.245260	−	0.424802i
$921$	14.9192	−	25.8409i	0.491606	−	0.851486i
$922$	38.7507	+	67.1182i	1.27619	+	2.21042i
$923$	−1.53948			−0.0506726
$924$		0			0
$925$	−27.2285			−0.895266
$926$	2.94981	+	5.10922i	0.0969367	+	0.167899i
$927$	2.87819	−	4.98518i	0.0945323	−	0.163735i
$928$	21.8971	−	37.9269i	0.718807	−	1.24501i
$929$	−8.57108	−	14.8455i	−0.281208	−	0.487066i	0.690475	−	0.723357i	$-0.257402\pi$
$929$	−8.57108	−	14.8455i	−0.281208	−	0.487066i	−0.971683	+	0.236290i	$0.924068\pi$
$930$	−5.89962			−0.193456
$931$		0			0
$932$	42.5573			1.39401
$933$	11.1751	+	19.3559i	0.365857	+	0.633684i
$934$	3.01721	−	5.22596i	0.0987262	−	0.170999i
$935$	4.48929	−	7.77568i	0.146815	−	0.254292i
$936$	−2.94120	−	5.09431i	−0.0961362	−	0.166513i
$937$	51.5197			1.68308			0.841538	−	0.540197i	$-0.181650\pi$
$937$	51.5197			1.68308			0.841538	+	0.540197i	$0.181650\pi$
$938$		0			0
$939$	3.99158			0.130260
$940$	−24.8683	−	43.0732i	−0.811115	−	1.40489i
$941$	16.3787	−	28.3688i	0.533931	−	0.924796i	−0.465283	−	0.885162i	$-0.654047\pi$
$941$	16.3787	−	28.3688i	0.533931	−	0.924796i	0.999214	−	0.0396342i	$-0.0126193\pi$
$942$	30.7104	−	53.1920i	1.00060	−	1.73309i
$943$	0.464730	+	0.804936i	0.0151337	+	0.0262123i
$944$	−15.1281			−0.492377
$945$		0			0
$946$	−21.8996			−0.712018
$947$	−10.4647	−	18.1254i	−0.340058	−	0.588998i	0.644385	−	0.764701i	$-0.277113\pi$
$947$	−10.4647	−	18.1254i	−0.340058	−	0.588998i	−0.984443	+	0.175703i	$0.943780\pi$
$948$	−1.76481	+	3.05674i	−0.0573183	+	0.0992782i
$949$	7.65004	−	13.2503i	0.248331	−	0.430122i
$950$	12.5181	+	21.6819i	0.406139	+	0.703454i
$951$	5.75639			0.186664
$952$		0			0
$953$	46.4120			1.50343			0.751716	−	0.659487i	$-0.229226\pi$
$953$	46.4120			1.50343			0.751716	+	0.659487i	$0.229226\pi$
$954$	−1.54441	−	2.67500i	−0.0500022	−	0.0866064i
$955$	2.94981	−	5.10922i	0.0954535	−	0.165330i
$956$	17.9572	−	31.1027i	0.580776	−	1.00593i
$957$	−6.89227	−	11.9378i	−0.222795	−	0.385893i
$958$	−1.20390			−0.0388964
$959$		0			0
$960$	−18.7434			−0.604940
$961$	14.1623	+	24.5299i	0.456849	+	0.791286i
$962$	9.97858	−	17.2834i	0.321722	−	0.557239i
$963$	4.19656	−	7.26865i	0.135232	−	0.234229i
$964$	−7.02877	−	12.1742i	−0.226381	−	0.392104i
$965$	−11.1365			−0.358497
$966$		0			0
$967$	−23.2186			−0.746660			−0.373330	−	0.927699i	$-0.621784\pi$
$967$	−23.2186			−0.746660			−0.373330	+	0.927699i	$0.621784\pi$
$968$	16.8984	+	29.2688i	0.543134	+	0.940735i
$969$	11.1751	−	19.3559i	0.358997	−	0.621801i
$970$	−8.40539	+	14.5586i	−0.269881	+	0.467448i
$971$	−7.05019	−	12.2113i	−0.226251	−	0.391879i	0.730443	−	0.682974i	$-0.239314\pi$
$971$	−7.05019	−	12.2113i	−0.226251	−	0.391879i	−0.956694	+	0.291095i	$0.905980\pi$
$972$	51.8286			1.66240
$973$		0			0
$974$	84.4800			2.70692
$975$	−1.83221	−	3.17348i	−0.0586777	−	0.101633i
$976$	−1.19656	+	2.07250i	−0.0383009	+	0.0663391i
$977$	1.47701	−	2.55826i	0.0472537	−	0.0818458i	−0.841431	−	0.540364i	$-0.818286\pi$
$977$	1.47701	−	2.55826i	0.0472537	−	0.0818458i	0.888685	+	0.458519i	$0.151620\pi$
$978$	−9.50650	−	16.4657i	−0.303984	−	0.526516i
$979$	−6.57560			−0.210157
$980$		0			0
$981$	22.7533			0.726455
$982$	10.8108	+	18.7248i	0.344986	+	0.597534i
$983$	−17.5184	+	30.3427i	−0.558749	+	0.967782i	0.438852	+	0.898559i	$0.355385\pi$
$983$	−17.5184	+	30.3427i	−0.558749	+	0.967782i	−0.997601	+	0.0692225i	$0.977948\pi$
$984$	−0.585462	+	1.01405i	−0.0186638	+	0.0323267i
$985$	2.12915	+	3.68780i	0.0678405	+	0.117503i
$986$	−143.330			−4.56456
$987$		0			0
$988$	−11.6644			−0.371095
$989$	−12.9446	−	22.4206i	−0.411613	−	0.712935i
$990$	3.04033	−	5.26600i	0.0966279	−	0.167364i
$991$	−23.9859	+	41.5448i	−0.761938	+	1.31972i	0.179912	+	0.983683i	$0.442419\pi$
$991$	−23.9859	+	41.5448i	−0.761938	+	1.31972i	−0.941850	+	0.336033i	$0.890915\pi$
$992$	−3.41454	−	5.91415i	−0.108412	−	0.187775i
$993$	−7.04958			−0.223712
$994$		0			0
$995$	18.2598			0.578873
$996$	−24.2583	−	42.0166i	−0.768654	−	1.33135i
$997$	−19.2211	+	33.2919i	−0.608739	+	1.05437i	0.382710	+	0.923869i	$0.374991\pi$
$997$	−19.2211	+	33.2919i	−0.608739	+	1.05437i	−0.991449	+	0.130498i	$0.958342\pi$
$998$	−1.17513	+	2.03539i	−0.0371982	+	0.0644292i
$999$	22.8782	+	39.6262i	0.723834	+	1.25372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.i.508.1		6
7.2	even	3	inner	637.2.e.i.79.1		6
7.3	odd	6		91.2.a.d.1.3	✓	3
7.4	even	3		637.2.a.j.1.3		3
7.5	odd	6		637.2.e.j.79.1		6
7.6	odd	2		637.2.e.j.508.1		6
21.11	odd	6		5733.2.a.x.1.1		3
21.17	even	6		819.2.a.i.1.1		3
28.3	even	6		1456.2.a.t.1.2		3
35.24	odd	6		2275.2.a.m.1.1		3
56.3	even	6		5824.2.a.bs.1.2		3
56.45	odd	6		5824.2.a.by.1.2		3
91.25	even	6		8281.2.a.bg.1.1		3
91.31	even	12		1183.2.c.f.337.1		6
91.38	odd	6		1183.2.a.i.1.1		3
91.73	even	12		1183.2.c.f.337.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.d.1.3	✓	3	7.3	odd	6
637.2.a.j.1.3		3	7.4	even	3
637.2.e.i.79.1		6	7.2	even	3	inner
637.2.e.i.508.1		6	1.1	even	1	trivial
637.2.e.j.79.1		6	7.5	odd	6
637.2.e.j.508.1		6	7.6	odd	2
819.2.a.i.1.1		3	21.17	even	6
1183.2.a.i.1.1		3	91.38	odd	6
1183.2.c.f.337.1		6	91.31	even	12
1183.2.c.f.337.6		6	91.73	even	12
1456.2.a.t.1.2		3	28.3	even	6
2275.2.a.m.1.1		3	35.24	odd	6
5733.2.a.x.1.1		3	21.11	odd	6
5824.2.a.bs.1.2		3	56.3	even	6
5824.2.a.by.1.2		3	56.45	odd	6
8281.2.a.bg.1.1		3	91.25	even	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.17146 - 2.02903i) q^{2} +(-0.573183 + 0.992782i) q^{3} +(-1.74464 + 3.02181i) q^{4} +(-0.671462 - 1.16301i) q^{5} +2.68585 q^{6} +3.48929 q^{8} +(0.842923 + 1.45999i) q^{9} +O(q^{10})\)	\(q+(-1.17146 - 2.02903i) q^{2} +(-0.573183 + 0.992782i) q^{3} +(-1.74464 + 3.02181i) q^{4} +(-0.671462 - 1.16301i) q^{5} +2.68585 q^{6} +3.48929 q^{8} +(0.842923 + 1.45999i) q^{9} +(-1.57318 + 2.72483i) q^{10} +(-0.573183 + 0.992782i) q^{11} +(-2.00000 - 3.46410i) q^{12} -1.00000 q^{13} +1.53948 q^{15} +(-0.598279 - 1.03625i) q^{16} +(2.91611 - 5.05084i) q^{17} +(1.97490 - 3.42063i) q^{18} +(-1.67146 - 2.89506i) q^{19} +4.68585 q^{20} +2.68585 q^{22} +(1.58757 + 2.74975i) q^{23} +(-2.00000 + 3.46410i) q^{24} +(1.59828 - 2.76830i) q^{25} +(1.17146 + 2.02903i) q^{26} -5.37169 q^{27} +10.4893 q^{29} +(-1.80344 - 3.12365i) q^{30} +(0.817827 - 1.41652i) q^{31} +(2.08757 - 3.61577i) q^{32} +(-0.657077 - 1.13809i) q^{33} -13.6644 q^{34} -5.88240 q^{36} +(-4.25903 - 7.37685i) q^{37} +(-3.91611 + 6.78289i) q^{38} +(0.573183 - 0.992782i) q^{39} +(-2.34292 - 4.05806i) q^{40} +0.292731 q^{41} -8.15371 q^{43} +(-2.00000 - 3.46410i) q^{44} +(1.13198 - 1.96065i) q^{45} +(3.71955 - 6.44245i) q^{46} +(-5.30712 - 9.19219i) q^{47} +1.37169 q^{48} -7.48929 q^{50} +(3.34292 + 5.79011i) q^{51} +(1.74464 - 3.02181i) q^{52} +(0.391010 - 0.677249i) q^{53} +(6.29273 + 10.8993i) q^{54} +1.53948 q^{55} +3.83221 q^{57} +(-12.2878 - 21.2831i) q^{58} +(6.32150 - 10.9492i) q^{59} +(-2.68585 + 4.65202i) q^{60} +(-1.00000 - 1.73205i) q^{61} -3.83221 q^{62} -12.1751 q^{64} +(0.671462 + 1.16301i) q^{65} +(-1.53948 + 2.66646i) q^{66} +(3.05019 - 5.28309i) q^{67} +(10.1751 + 17.6239i) q^{68} -3.63986 q^{69} +1.53948 q^{71} +(2.94120 + 5.09431i) q^{72} +(-7.65004 + 13.2503i) q^{73} +(-9.97858 + 17.2834i) q^{74} +(1.83221 + 3.17348i) q^{75} +11.6644 q^{76} -2.68585 q^{78} +(-0.441202 - 0.764184i) q^{79} +(-0.803442 + 1.39160i) q^{80} +(0.550192 - 0.952961i) q^{81} +(-0.342923 - 0.593960i) q^{82} +12.1292 q^{83} -7.83221 q^{85} +(9.55176 + 16.5441i) q^{86} +(-6.01228 + 10.4136i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(2.86802 + 4.96755i) q^{89} -5.30429 q^{90} -11.0790 q^{92} +(0.937529 + 1.62385i) q^{93} +(-12.4342 + 21.5366i) q^{94} +(-2.24464 + 3.88784i) q^{95} +(2.39312 + 4.14500i) q^{96} +5.34292 q^{97} -1.93260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9	\( 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9} - 8 q^{10} - 2 q^{11} - 12 q^{12} - 6 q^{13} - 12 q^{15} + q^{16} + 4 q^{17} + 15 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} + 5 q^{25} + q^{26} + 16 q^{27} + 48 q^{29} - 20 q^{30} - 4 q^{31} - 7 q^{32} - 16 q^{33} - 28 q^{34} - 2 q^{36} - 10 q^{38} + 2 q^{39} - 2 q^{40} - 4 q^{41} + 20 q^{43} - 12 q^{44} + 22 q^{45} + 18 q^{46} - 8 q^{47} - 40 q^{48} - 30 q^{50} + 8 q^{51} + 3 q^{52} - 8 q^{53} + 32 q^{54} - 12 q^{55} - 4 q^{57} - 12 q^{58} - 4 q^{59} + 8 q^{60} - 6 q^{61} + 4 q^{62} - 34 q^{64} - 2 q^{65} + 12 q^{66} + 12 q^{67} + 22 q^{68} + 12 q^{69} - 12 q^{71} + q^{72} - 10 q^{73} - 30 q^{74} - 16 q^{75} + 16 q^{76} + 8 q^{78} + 14 q^{79} - 14 q^{80} - 3 q^{81} + 10 q^{82} + 24 q^{83} - 20 q^{85} + 26 q^{86} - 26 q^{87} - 12 q^{88} + 2 q^{89} + 56 q^{90} - 24 q^{92} + 22 q^{93} - 10 q^{94} - 6 q^{95} - 4 q^{96} + 20 q^{97} + 28 q^{99}+O(q^{100}) \) 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9 - 8 * q^10 - 2 * q^11 - 12 * q^12 - 6 * q^13 - 12 * q^15 + q^16 + 4 * q^17 + 15 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 + 5 * q^25 + q^26 + 16 * q^27 + 48 * q^29 - 20 * q^30 - 4 * q^31 - 7 * q^32 - 16 * q^33 - 28 * q^34 - 2 * q^36 - 10 * q^38 + 2 * q^39 - 2 * q^40 - 4 * q^41 + 20 * q^43 - 12 * q^44 + 22 * q^45 + 18 * q^46 - 8 * q^47 - 40 * q^48 - 30 * q^50 + 8 * q^51 + 3 * q^52 - 8 * q^53 + 32 * q^54 - 12 * q^55 - 4 * q^57 - 12 * q^58 - 4 * q^59 + 8 * q^60 - 6 * q^61 + 4 * q^62 - 34 * q^64 - 2 * q^65 + 12 * q^66 + 12 * q^67 + 22 * q^68 + 12 * q^69 - 12 * q^71 + q^72 - 10 * q^73 - 30 * q^74 - 16 * q^75 + 16 * q^76 + 8 * q^78 + 14 * q^79 - 14 * q^80 - 3 * q^81 + 10 * q^82 + 24 * q^83 - 20 * q^85 + 26 * q^86 - 26 * q^87 - 12 * q^88 + 2 * q^89 + 56 * q^90 - 24 * q^92 + 22 * q^93 - 10 * q^94 - 6 * q^95 - 4 * q^96 + 20 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more