LMFDB - Embedded newform 147.2.e.e.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.2.e.e.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 + 2.09077i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.292893 + 0.507306i) q^{5} +2.41421 q^{6} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.20711 + 2.09077i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.292893 + 0.507306i) q^{5} +2.41421 q^{6} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(1.00000 - 1.73205i) q^{11} +(1.91421 + 3.31552i) q^{12} -5.41421 q^{13} +0.585786 q^{15} +(-1.50000 - 2.59808i) q^{16} +(3.12132 - 5.40629i) q^{17} +(1.20711 - 2.09077i) q^{18} +(1.41421 + 2.44949i) q^{19} -2.24264 q^{20} +4.82843 q^{22} +(-1.82843 - 3.16693i) q^{23} +(-2.20711 + 3.82282i) q^{24} +(2.32843 - 4.03295i) q^{25} +(-6.53553 - 11.3199i) q^{26} -1.00000 q^{27} -1.17157 q^{29} +(0.707107 + 1.22474i) q^{30} +(-3.41421 + 5.91359i) q^{31} +(-0.792893 + 1.37333i) q^{32} +(-1.00000 - 1.73205i) q^{33} +15.0711 q^{34} +3.82843 q^{36} +(2.00000 + 3.46410i) q^{37} +(-3.41421 + 5.91359i) q^{38} +(-2.70711 + 4.68885i) q^{39} +(-1.29289 - 2.23936i) q^{40} +2.24264 q^{41} -5.65685 q^{43} +(3.82843 + 6.63103i) q^{44} +(0.292893 - 0.507306i) q^{45} +(4.41421 - 7.64564i) q^{46} +(1.41421 + 2.44949i) q^{47} -3.00000 q^{48} +11.2426 q^{50} +(-3.12132 - 5.40629i) q^{51} +(10.3640 - 17.9509i) q^{52} +(1.00000 - 1.73205i) q^{53} +(-1.20711 - 2.09077i) q^{54} +1.17157 q^{55} +2.82843 q^{57} +(-1.41421 - 2.44949i) q^{58} +(-3.41421 + 5.91359i) q^{59} +(-1.12132 + 1.94218i) q^{60} +(1.87868 + 3.25397i) q^{61} -16.4853 q^{62} -9.82843 q^{64} +(-1.58579 - 2.74666i) q^{65} +(2.41421 - 4.18154i) q^{66} +(-2.82843 + 4.89898i) q^{67} +(11.9497 + 20.6976i) q^{68} -3.65685 q^{69} -13.3137 q^{71} +(2.20711 + 3.82282i) q^{72} +(-2.94975 + 5.10911i) q^{73} +(-4.82843 + 8.36308i) q^{74} +(-2.32843 - 4.03295i) q^{75} -10.8284 q^{76} -13.0711 q^{78} +(-1.17157 - 2.02922i) q^{79} +(0.878680 - 1.52192i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.70711 + 4.68885i) q^{82} +15.3137 q^{83} +3.65685 q^{85} +(-6.82843 - 11.8272i) q^{86} +(-0.585786 + 1.01461i) q^{87} +(-4.41421 + 7.64564i) q^{88} +(-2.87868 - 4.98602i) q^{89} +1.41421 q^{90} +14.0000 q^{92} +(3.41421 + 5.91359i) q^{93} +(-3.41421 + 5.91359i) q^{94} +(-0.828427 + 1.43488i) q^{95} +(0.792893 + 1.37333i) q^{96} -5.41421 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} - 2 q^{9} + 4 q^{11} + 2 q^{12} - 16 q^{13} + 8 q^{15} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{20} + 8 q^{22} + 4 q^{23} - 6 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 16 q^{29} - 8 q^{31} - 6 q^{32} - 4 q^{33} + 32 q^{34} + 4 q^{36} + 8 q^{37} - 8 q^{38} - 8 q^{39} - 8 q^{40} - 8 q^{41} + 4 q^{44} + 4 q^{45} + 12 q^{46} - 12 q^{48} + 28 q^{50} - 4 q^{51} + 16 q^{52} + 4 q^{53} - 2 q^{54} + 16 q^{55} - 8 q^{59} + 4 q^{60} + 16 q^{61} - 32 q^{62} - 28 q^{64} - 12 q^{65} + 4 q^{66} + 28 q^{68} + 8 q^{69} - 8 q^{71} + 6 q^{72} + 8 q^{73} - 8 q^{74} + 2 q^{75} - 32 q^{76} - 24 q^{78} - 16 q^{79} + 12 q^{80} - 2 q^{81} + 8 q^{82} + 16 q^{83} - 8 q^{85} - 16 q^{86} - 8 q^{87} - 12 q^{88} - 20 q^{89} + 56 q^{92} + 8 q^{93} - 8 q^{94} + 8 q^{95} + 6 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 - 2 * q^9 + 4 * q^11 + 2 * q^12 - 16 * q^13 + 8 * q^15 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^20 + 8 * q^22 + 4 * q^23 - 6 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 16 * q^29 - 8 * q^31 - 6 * q^32 - 4 * q^33 + 32 * q^34 + 4 * q^36 + 8 * q^37 - 8 * q^38 - 8 * q^39 - 8 * q^40 - 8 * q^41 + 4 * q^44 + 4 * q^45 + 12 * q^46 - 12 * q^48 + 28 * q^50 - 4 * q^51 + 16 * q^52 + 4 * q^53 - 2 * q^54 + 16 * q^55 - 8 * q^59 + 4 * q^60 + 16 * q^61 - 32 * q^62 - 28 * q^64 - 12 * q^65 + 4 * q^66 + 28 * q^68 + 8 * q^69 - 8 * q^71 + 6 * q^72 + 8 * q^73 - 8 * q^74 + 2 * q^75 - 32 * q^76 - 24 * q^78 - 16 * q^79 + 12 * q^80 - 2 * q^81 + 8 * q^82 + 16 * q^83 - 8 * q^85 - 16 * q^86 - 8 * q^87 - 12 * q^88 - 20 * q^89 + 56 * q^92 + 8 * q^93 - 8 * q^94 + 8 * q^95 + 6 * q^96 - 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.20711	+	2.09077i	0.853553	+	1.47840i	0.877981	+	0.478696i	$0.158890\pi$
$2$	1.20711	+	2.09077i	0.853553	+	1.47840i	−0.0244272	+	0.999702i	$0.507776\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.91421	+	3.31552i	−0.957107	+	1.65776i
$5$	0.292893	+	0.507306i	0.130986	+	0.226874i	0.924057	−	0.382255i	$-0.124852\pi$
$5$	0.292893	+	0.507306i	0.130986	+	0.226874i	−0.793071	+	0.609129i	$0.791519\pi$
$6$	2.41421			0.985599
$7$		0			0
$7$		0			0
$8$	−4.41421			−1.56066
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.707107	+	1.22474i	−0.223607	+	0.387298i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	1.91421	+	3.31552i	0.552586	+	0.957107i
$13$	−5.41421			−1.50163			−0.750816	−	0.660511i	$-0.770340\pi$
$13$	−5.41421			−1.50163			−0.750816	+	0.660511i	$0.770340\pi$
$14$		0			0
$15$	0.585786			0.151249
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	3.12132	−	5.40629i	0.757031	−	1.31122i	−0.187327	−	0.982298i	$-0.559982\pi$
$17$	3.12132	−	5.40629i	0.757031	−	1.31122i	0.944358	−	0.328919i	$-0.106684\pi$
$18$	1.20711	−	2.09077i	0.284518	−	0.492799i
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	0.981399	−	0.191977i	$-0.0614899\pi$
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	−0.656957	+	0.753928i	$0.728157\pi$
$20$	−2.24264			−0.501470
$21$		0			0
$22$	4.82843			1.02942
$23$	−1.82843	−	3.16693i	−0.381253	−	0.660350i	0.609988	−	0.792410i	$-0.291174\pi$
$23$	−1.82843	−	3.16693i	−0.381253	−	0.660350i	−0.991242	+	0.132060i	$0.957841\pi$
$24$	−2.20711	+	3.82282i	−0.450524	+	0.780330i
$25$	2.32843	−	4.03295i	0.465685	−	0.806591i
$26$	−6.53553	−	11.3199i	−1.28172	−	2.22001i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.17157			−0.217556			−0.108778	−	0.994066i	$-0.534694\pi$
$29$	−1.17157			−0.217556			−0.108778	+	0.994066i	$0.534694\pi$
$30$	0.707107	+	1.22474i	0.129099	+	0.223607i
$31$	−3.41421	+	5.91359i	−0.613211	+	1.06211i	0.377485	+	0.926016i	$0.376789\pi$
$31$	−3.41421	+	5.91359i	−0.613211	+	1.06211i	−0.990696	+	0.136097i	$0.956544\pi$
$32$	−0.792893	+	1.37333i	−0.140165	+	0.242773i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	15.0711			2.58467
$35$		0			0
$36$	3.82843			0.638071
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	−3.41421	+	5.91359i	−0.553859	+	0.959311i
$39$	−2.70711	+	4.68885i	−0.433484	+	0.750816i
$40$	−1.29289	−	2.23936i	−0.204424	−	0.354073i
$41$	2.24264			0.350242			0.175121	−	0.984547i	$-0.443968\pi$
$41$	2.24264			0.350242			0.175121	+	0.984547i	$0.443968\pi$
$42$		0			0
$43$	−5.65685			−0.862662			−0.431331	−	0.902194i	$-0.641956\pi$
$43$	−5.65685			−0.862662			−0.431331	+	0.902194i	$0.641956\pi$
$44$	3.82843	+	6.63103i	0.577157	+	0.999665i
$45$	0.292893	−	0.507306i	0.0436619	−	0.0756247i
$46$	4.41421	−	7.64564i	0.650840	−	1.12729i
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	0.950541	−	0.310599i	$-0.100530\pi$
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	−0.744257	+	0.667893i	$0.767196\pi$
$48$	−3.00000			−0.433013
$49$		0			0
$50$	11.2426			1.58995
$51$	−3.12132	−	5.40629i	−0.437072	−	0.757031i
$52$	10.3640	−	17.9509i	1.43722	−	2.48934i
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$	−1.20711	−	2.09077i	−0.164266	−	0.284518i
$55$	1.17157			0.157975
$56$		0			0
$57$	2.82843			0.374634
$58$	−1.41421	−	2.44949i	−0.185695	−	0.321634i
$59$	−3.41421	+	5.91359i	−0.444493	+	0.769884i	−0.998017	−	0.0629492i	$-0.979949\pi$
$59$	−3.41421	+	5.91359i	−0.444493	+	0.769884i	0.553524	+	0.832833i	$0.313283\pi$
$60$	−1.12132	+	1.94218i	−0.144762	+	0.250735i
$61$	1.87868	+	3.25397i	0.240540	+	0.416628i	0.960868	−	0.277006i	$-0.0893421\pi$
$61$	1.87868	+	3.25397i	0.240540	+	0.416628i	−0.720328	+	0.693634i	$0.756009\pi$
$62$	−16.4853			−2.09363
$63$		0			0
$64$	−9.82843			−1.22855
$65$	−1.58579	−	2.74666i	−0.196693	−	0.340682i
$66$	2.41421	−	4.18154i	0.297169	−	0.514712i
$67$	−2.82843	+	4.89898i	−0.345547	+	0.598506i	−0.985453	−	0.169948i	$-0.945640\pi$
$67$	−2.82843	+	4.89898i	−0.345547	+	0.598506i	0.639906	+	0.768453i	$0.278973\pi$
$68$	11.9497	+	20.6976i	1.44912	+	2.50995i
$69$	−3.65685			−0.440234
$70$		0			0
$71$	−13.3137			−1.58005			−0.790023	−	0.613077i	$-0.789932\pi$
$71$	−13.3137			−1.58005			−0.790023	+	0.613077i	$0.789932\pi$
$72$	2.20711	+	3.82282i	0.260110	+	0.450524i
$73$	−2.94975	+	5.10911i	−0.345242	+	0.597976i	−0.985398	−	0.170269i	$-0.945536\pi$
$73$	−2.94975	+	5.10911i	−0.345242	+	0.597976i	0.640156	+	0.768245i	$0.278870\pi$
$74$	−4.82843	+	8.36308i	−0.561293	+	0.972188i
$75$	−2.32843	−	4.03295i	−0.268864	−	0.465685i
$76$	−10.8284			−1.24211
$77$		0			0
$78$	−13.0711			−1.48001
$79$	−1.17157	−	2.02922i	−0.131812	−	0.228306i	0.792563	−	0.609790i	$-0.208746\pi$
$79$	−1.17157	−	2.02922i	−0.131812	−	0.228306i	−0.924375	+	0.381485i	$0.875413\pi$
$80$	0.878680	−	1.52192i	0.0982394	−	0.170156i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.70711	+	4.68885i	0.298950	+	0.517796i
$83$	15.3137			1.68090			0.840449	−	0.541891i	$-0.182291\pi$
$83$	15.3137			1.68090			0.840449	+	0.541891i	$0.182291\pi$
$84$		0			0
$85$	3.65685			0.396642
$86$	−6.82843	−	11.8272i	−0.736328	−	1.27536i
$87$	−0.585786	+	1.01461i	−0.0628029	+	0.108778i
$88$	−4.41421	+	7.64564i	−0.470557	+	0.815028i
$89$	−2.87868	−	4.98602i	−0.305139	−	0.528517i	0.672153	−	0.740412i	$-0.265370\pi$
$89$	−2.87868	−	4.98602i	−0.305139	−	0.528517i	−0.977292	+	0.211895i	$0.932036\pi$
$90$	1.41421			0.149071
$91$		0			0
$92$	14.0000			1.45960
$93$	3.41421	+	5.91359i	0.354037	+	0.613211i
$94$	−3.41421	+	5.91359i	−0.352149	+	0.609940i
$95$	−0.828427	+	1.43488i	−0.0849948	+	0.147215i
$96$	0.792893	+	1.37333i	0.0809243	+	0.140165i
$97$	−5.41421			−0.549730			−0.274865	−	0.961483i	$-0.588633\pi$
$97$	−5.41421			−0.549730			−0.274865	+	0.961483i	$0.588633\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	8.91421	+	15.4399i	0.891421	+	1.54399i
$101$	8.53553	−	14.7840i	0.849317	−	1.47106i	−0.0325010	−	0.999472i	$-0.510347\pi$
$101$	8.53553	−	14.7840i	0.849317	−	1.47106i	0.881818	−	0.471589i	$-0.156319\pi$
$102$	7.53553	−	13.0519i	0.746129	−	1.29233i
$103$	−6.24264	−	10.8126i	−0.615106	−	1.06539i	−0.990366	−	0.138475i	$-0.955780\pi$
$103$	−6.24264	−	10.8126i	−0.615106	−	1.06539i	0.375260	−	0.926919i	$-0.377553\pi$
$104$	23.8995			2.34354
$105$		0			0
$106$	4.82843			0.468978
$107$	5.82843	+	10.0951i	0.563455	+	0.975933i	0.997192	+	0.0748933i	$0.0238616\pi$
$107$	5.82843	+	10.0951i	0.563455	+	0.975933i	−0.433736	+	0.901040i	$0.642805\pi$
$108$	1.91421	−	3.31552i	0.184195	−	0.319036i
$109$	−2.82843	+	4.89898i	−0.270914	+	0.469237i	−0.969096	−	0.246683i	$-0.920659\pi$
$109$	−2.82843	+	4.89898i	−0.270914	+	0.469237i	0.698182	+	0.715920i	$0.253993\pi$
$110$	1.41421	+	2.44949i	0.134840	+	0.233550i
$111$	4.00000			0.379663
$112$		0			0
$113$	17.3137			1.62874			0.814368	−	0.580348i	$-0.197084\pi$
$113$	17.3137			1.62874			0.814368	+	0.580348i	$0.197084\pi$
$114$	3.41421	+	5.91359i	0.319770	+	0.553859i
$115$	1.07107	−	1.85514i	0.0998776	−	0.172993i
$116$	2.24264	−	3.88437i	0.208224	−	0.360654i
$117$	2.70711	+	4.68885i	0.250272	+	0.433484i
$118$	−16.4853			−1.51759
$119$		0			0
$120$	−2.58579			−0.236049
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−4.53553	+	7.85578i	−0.410628	+	0.711228i
$123$	1.12132	−	1.94218i	0.101106	−	0.175121i
$124$	−13.0711	−	22.6398i	−1.17382	−	2.03311i
$125$	5.65685			0.505964
$126$		0			0
$127$	9.65685			0.856907			0.428454	−	0.903564i	$-0.359059\pi$
$127$	9.65685			0.856907			0.428454	+	0.903564i	$0.359059\pi$
$128$	−10.2782	−	17.8023i	−0.908471	−	1.57352i
$129$	−2.82843	+	4.89898i	−0.249029	+	0.431331i
$130$	3.82843	−	6.63103i	0.335775	−	0.581580i
$131$	3.65685	+	6.33386i	0.319501	+	0.553392i	0.980384	−	0.197097i	$-0.0631514\pi$
$131$	3.65685	+	6.33386i	0.319501	+	0.553392i	−0.660883	+	0.750489i	$0.729818\pi$
$132$	7.65685			0.666444
$133$		0			0
$134$	−13.6569			−1.17977
$135$	−0.292893	−	0.507306i	−0.0252082	−	0.0436619i
$136$	−13.7782	+	23.8645i	−1.18147	+	2.04636i
$137$	7.07107	−	12.2474i	0.604122	−	1.04637i	−0.388067	−	0.921631i	$-0.626857\pi$
$137$	7.07107	−	12.2474i	0.604122	−	1.04637i	0.992190	−	0.124739i	$-0.0398094\pi$
$138$	−4.41421	−	7.64564i	−0.375763	−	0.650840i
$139$	6.34315			0.538019			0.269009	−	0.963138i	$-0.413304\pi$
$139$	6.34315			0.538019			0.269009	+	0.963138i	$0.413304\pi$
$140$		0			0
$141$	2.82843			0.238197
$142$	−16.0711	−	27.8359i	−1.34865	−	2.33594i
$143$	−5.41421	+	9.37769i	−0.452759	+	0.784202i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	−0.343146	−	0.594346i	−0.0284967	−	0.0493577i
$146$	−14.2426			−1.17873
$147$		0			0
$148$	−15.3137			−1.25878
$149$	2.65685	+	4.60181i	0.217658	+	0.376995i	0.954092	−	0.299515i	$-0.0968249\pi$
$149$	2.65685	+	4.60181i	0.217658	+	0.376995i	−0.736434	+	0.676510i	$0.763492\pi$
$150$	5.62132	−	9.73641i	0.458979	−	0.794975i
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	−0.999909	−	0.0134886i	$-0.995706\pi$
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	0.511636	+	0.859202i	$0.329040\pi$
$152$	−6.24264	−	10.8126i	−0.506345	−	0.877015i
$153$	−6.24264			−0.504688
$154$		0			0
$155$	−4.00000			−0.321288
$156$	−10.3640	−	17.9509i	−0.829781	−	1.43722i
$157$	10.1213	−	17.5306i	0.807769	−	1.39910i	−0.106636	−	0.994298i	$-0.534008\pi$
$157$	10.1213	−	17.5306i	0.807769	−	1.39910i	0.914406	−	0.404799i	$-0.132659\pi$
$158$	2.82843	−	4.89898i	0.225018	−	0.389742i
$159$	−1.00000	−	1.73205i	−0.0793052	−	0.137361i
$160$	−0.928932			−0.0734385
$161$		0			0
$162$	−2.41421			−0.189679
$163$	−5.65685	−	9.79796i	−0.443079	−	0.767435i	0.554837	−	0.831959i	$-0.312781\pi$
$163$	−5.65685	−	9.79796i	−0.443079	−	0.767435i	−0.997916	+	0.0645236i	$0.979447\pi$
$164$	−4.29289	+	7.43551i	−0.335219	+	0.580616i
$165$	0.585786	−	1.01461i	0.0456034	−	0.0789874i
$166$	18.4853	+	32.0174i	1.43474	+	2.48504i
$167$	−19.7990			−1.53209			−0.766046	−	0.642786i	$-0.777779\pi$
$167$	−19.7990			−1.53209			−0.766046	+	0.642786i	$0.777779\pi$
$168$		0			0
$169$	16.3137			1.25490
$170$	4.41421	+	7.64564i	0.338555	+	0.586394i
$171$	1.41421	−	2.44949i	0.108148	−	0.187317i
$172$	10.8284	−	18.7554i	0.825660	−	1.43008i
$173$	3.46447	+	6.00063i	0.263398	+	0.456220i	0.967143	−	0.254234i	$-0.0818233\pi$
$173$	3.46447	+	6.00063i	0.263398	+	0.456220i	−0.703744	+	0.710453i	$0.748490\pi$
$174$	−2.82843			−0.214423
$175$		0			0
$176$	−6.00000			−0.452267
$177$	3.41421	+	5.91359i	0.256628	+	0.444493i
$178$	6.94975	−	12.0373i	0.520906	−	0.902235i
$179$	4.17157	−	7.22538i	0.311798	−	0.540050i	−0.666954	−	0.745099i	$-0.732402\pi$
$179$	4.17157	−	7.22538i	0.311798	−	0.540050i	0.978752	+	0.205049i	$0.0657354\pi$
$180$	1.12132	+	1.94218i	0.0835783	+	0.144762i
$181$	5.41421			0.402435			0.201218	−	0.979547i	$-0.435510\pi$
$181$	5.41421			0.402435			0.201218	+	0.979547i	$0.435510\pi$
$182$		0			0
$183$	3.75736			0.277752
$184$	8.07107	+	13.9795i	0.595007	+	1.03058i
$185$	−1.17157	+	2.02922i	−0.0861358	+	0.149191i
$186$	−8.24264	+	14.2767i	−0.604380	+	1.04682i
$187$	−6.24264	−	10.8126i	−0.456507	−	0.790693i
$188$	−10.8284			−0.789744
$189$		0			0
$190$	−4.00000			−0.290191
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$	−4.91421	+	8.51167i	−0.354653	+	0.614277i
$193$	8.65685	−	14.9941i	0.623134	−	1.07930i	−0.365765	−	0.930707i	$-0.619192\pi$
$193$	8.65685	−	14.9941i	0.623134	−	1.07930i	0.988899	−	0.148592i	$-0.0474742\pi$
$194$	−6.53553	−	11.3199i	−0.469224	−	0.812720i
$195$	−3.17157			−0.227121
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	−2.41421	−	4.18154i	−0.171571	−	0.297169i
$199$	5.17157	−	8.95743i	0.366603	−	0.634975i	−0.622429	−	0.782676i	$-0.713854\pi$
$199$	5.17157	−	8.95743i	0.366603	−	0.634975i	0.989032	+	0.147701i	$0.0471874\pi$
$200$	−10.2782	+	17.8023i	−0.726777	+	1.25881i
$201$	2.82843	+	4.89898i	0.199502	+	0.345547i
$202$	41.2132			2.89975
$203$		0			0
$204$	23.8995			1.67330
$205$	0.656854	+	1.13770i	0.0458767	+	0.0794608i
$206$	15.0711	−	26.1039i	1.05005	−	1.81874i
$207$	−1.82843	+	3.16693i	−0.127084	+	0.220117i
$208$	8.12132	+	14.0665i	0.563112	+	0.975339i
$209$	5.65685			0.391293
$210$		0			0
$211$	−20.9706			−1.44367			−0.721837	−	0.692064i	$-0.756702\pi$
$211$	−20.9706			−1.44367			−0.721837	+	0.692064i	$0.756702\pi$
$212$	3.82843	+	6.63103i	0.262937	+	0.455421i
$213$	−6.65685	+	11.5300i	−0.456120	+	0.790023i
$214$	−14.0711	+	24.3718i	−0.961878	+	1.66602i
$215$	−1.65685	−	2.86976i	−0.112997	−	0.195716i
$216$	4.41421			0.300349
$217$		0			0
$218$	−13.6569			−0.924959
$219$	2.94975	+	5.10911i	0.199325	+	0.345242i
$220$	−2.24264	+	3.88437i	−0.151199	+	0.261884i
$221$	−16.8995	+	29.2708i	−1.13678	+	1.96897i
$222$	4.82843	+	8.36308i	0.324063	+	0.561293i
$223$	8.97056			0.600713			0.300357	−	0.953827i	$-0.402894\pi$
$223$	8.97056			0.600713			0.300357	+	0.953827i	$0.402894\pi$
$224$		0			0
$225$	−4.65685			−0.310457
$226$	20.8995	+	36.1990i	1.39021	+	2.40792i
$227$	−7.89949	+	13.6823i	−0.524308	+	0.908128i	0.475292	+	0.879828i	$0.342343\pi$
$227$	−7.89949	+	13.6823i	−0.524308	+	0.908128i	−0.999599	+	0.0282996i	$0.990991\pi$
$228$	−5.41421	+	9.37769i	−0.358565	+	0.621053i
$229$	4.12132	+	7.13834i	0.272345	+	0.471715i	0.969462	−	0.245243i	$-0.0788676\pi$
$229$	4.12132	+	7.13834i	0.272345	+	0.471715i	−0.697117	+	0.716957i	$0.745534\pi$
$230$	5.17157			0.341003
$231$		0			0
$232$	5.17157			0.339530
$233$	−11.0711	−	19.1757i	−0.725290	−	1.25624i	−0.958855	−	0.283898i	$-0.908372\pi$
$233$	−11.0711	−	19.1757i	−0.725290	−	1.25624i	0.233565	−	0.972341i	$-0.424961\pi$
$234$	−6.53553	+	11.3199i	−0.427241	+	0.740003i
$235$	−0.828427	+	1.43488i	−0.0540406	+	0.0936011i
$236$	−13.0711	−	22.6398i	−0.850854	−	1.47372i
$237$	−2.34315			−0.152204
$238$		0			0
$239$	−4.34315			−0.280935			−0.140467	−	0.990085i	$-0.544861\pi$
$239$	−4.34315			−0.280935			−0.140467	+	0.990085i	$0.544861\pi$
$240$	−0.878680	−	1.52192i	−0.0567185	−	0.0982394i
$241$	−3.87868	+	6.71807i	−0.249848	+	0.432749i	−0.963483	−	0.267768i	$-0.913714\pi$
$241$	−3.87868	+	6.71807i	−0.249848	+	0.432749i	0.713636	+	0.700517i	$0.247047\pi$
$242$	−8.44975	+	14.6354i	−0.543170	+	0.940799i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−14.3848			−0.920891
$245$		0			0
$246$	5.41421			0.345198
$247$	−7.65685	−	13.2621i	−0.487194	−	0.843845i
$248$	15.0711	−	26.1039i	0.957014	−	1.65760i
$249$	7.65685	−	13.2621i	0.485233	−	0.840449i
$250$	6.82843	+	11.8272i	0.431868	+	0.748017i
$251$	−4.48528			−0.283108			−0.141554	−	0.989931i	$-0.545210\pi$
$251$	−4.48528			−0.283108			−0.141554	+	0.989931i	$0.545210\pi$
$252$		0			0
$253$	−7.31371			−0.459809
$254$	11.6569	+	20.1903i	0.731416	+	1.26685i
$255$	1.82843	−	3.16693i	0.114501	−	0.198321i
$256$	14.9853	−	25.9553i	0.936580	−	1.62220i
$257$	−9.60660	−	16.6391i	−0.599243	−	1.03792i	−0.992933	−	0.118677i	$-0.962135\pi$
$257$	−9.60660	−	16.6391i	−0.599243	−	1.03792i	0.393690	−	0.919243i	$-0.371198\pi$
$258$	−13.6569			−0.850239
$259$		0			0
$260$	12.1421			0.753023
$261$	0.585786	+	1.01461i	0.0362593	+	0.0628029i
$262$	−8.82843	+	15.2913i	−0.545422	+	0.944699i
$263$	8.65685	−	14.9941i	0.533805	−	0.924577i	−0.465416	−	0.885092i	$-0.654095\pi$
$263$	8.65685	−	14.9941i	0.533805	−	0.924577i	0.999220	−	0.0394843i	$-0.0125715\pi$
$264$	4.41421	+	7.64564i	0.271676	+	0.470557i
$265$	1.17157			0.0719691
$266$		0			0
$267$	−5.75736			−0.352345
$268$	−10.8284	−	18.7554i	−0.661451	−	1.14567i
$269$	5.36396	−	9.29065i	0.327046	−	0.566461i	−0.654878	−	0.755735i	$-0.727280\pi$
$269$	5.36396	−	9.29065i	0.327046	−	0.566461i	0.981924	+	0.189274i	$0.0606133\pi$
$270$	0.707107	−	1.22474i	0.0430331	−	0.0745356i
$271$	9.07107	+	15.7116i	0.551028	+	0.954409i	0.998201	+	0.0599610i	$0.0190976\pi$
$271$	9.07107	+	15.7116i	0.551028	+	0.954409i	−0.447173	+	0.894448i	$0.647569\pi$
$272$	−18.7279			−1.13555
$273$		0			0
$274$	34.1421			2.06260
$275$	−4.65685	−	8.06591i	−0.280819	−	0.486393i
$276$	7.00000	−	12.1244i	0.421350	−	0.729800i
$277$	−6.65685	+	11.5300i	−0.399972	+	0.692771i	−0.993722	−	0.111878i	$-0.964313\pi$
$277$	−6.65685	+	11.5300i	−0.399972	+	0.692771i	0.593750	+	0.804649i	$0.297647\pi$
$278$	7.65685	+	13.2621i	0.459228	+	0.795406i
$279$	6.82843			0.408807
$280$		0			0
$281$	−16.4853			−0.983429			−0.491715	−	0.870756i	$-0.663630\pi$
$281$	−16.4853			−0.983429			−0.491715	+	0.870756i	$0.663630\pi$
$282$	3.41421	+	5.91359i	0.203313	+	0.352149i
$283$	4.24264	−	7.34847i	0.252199	−	0.436821i	−0.711932	−	0.702248i	$-0.752180\pi$
$283$	4.24264	−	7.34847i	0.252199	−	0.436821i	0.964131	+	0.265427i	$0.0855130\pi$
$284$	25.4853	−	44.1418i	1.51227	−	2.61933i
$285$	0.828427	+	1.43488i	0.0490718	+	0.0849948i
$286$	−26.1421			−1.54582
$287$		0			0
$288$	1.58579			0.0934434
$289$	−10.9853	−	19.0271i	−0.646193	−	1.11924i
$290$	0.828427	−	1.43488i	0.0486469	−	0.0842589i
$291$	−2.70711	+	4.68885i	−0.158693	+	0.274865i
$292$	−11.2929	−	19.5599i	−0.660867	−	1.14465i
$293$	−19.4142			−1.13419			−0.567095	−	0.823652i	$-0.691933\pi$
$293$	−19.4142			−1.13419			−0.567095	+	0.823652i	$0.691933\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	−8.82843	−	15.2913i	−0.513142	−	0.888788i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	−6.41421	+	11.1097i	−0.371565	+	0.643570i
$299$	9.89949	+	17.1464i	0.572503	+	0.991604i
$300$	17.8284			1.02932
$301$		0			0
$302$	−28.9706			−1.66707
$303$	−8.53553	−	14.7840i	−0.490354	−	0.849317i
$304$	4.24264	−	7.34847i	0.243332	−	0.421464i
$305$	−1.10051	+	1.90613i	−0.0630147	+	0.109145i
$306$	−7.53553	−	13.0519i	−0.430778	−	0.746129i
$307$	−1.85786			−0.106034			−0.0530170	−	0.998594i	$-0.516884\pi$
$307$	−1.85786			−0.106034			−0.0530170	+	0.998594i	$0.516884\pi$
$308$		0			0
$309$	−12.4853			−0.710263
$310$	−4.82843	−	8.36308i	−0.274236	−	0.474991i
$311$	−11.0711	+	19.1757i	−0.627783	+	1.08735i	0.360213	+	0.932870i	$0.382704\pi$
$311$	−11.0711	+	19.1757i	−0.627783	+	1.08735i	−0.987996	+	0.154481i	$0.950629\pi$
$312$	11.9497	−	20.6976i	0.676521	−	1.17177i
$313$	−8.94975	−	15.5014i	−0.505870	−	0.876192i	−0.999977	−	0.00679098i	$-0.997838\pi$
$313$	−8.94975	−	15.5014i	−0.505870	−	0.876192i	0.494107	−	0.869401i	$-0.335495\pi$
$314$	48.8701			2.75790
$315$		0			0
$316$	8.97056			0.504634
$317$	−5.00000	−	8.66025i	−0.280828	−	0.486408i	0.690761	−	0.723083i	$-0.257276\pi$
$317$	−5.00000	−	8.66025i	−0.280828	−	0.486408i	−0.971589	+	0.236675i	$0.923942\pi$
$318$	2.41421	−	4.18154i	0.135382	−	0.234489i
$319$	−1.17157	+	2.02922i	−0.0655955	+	0.113615i
$320$	−2.87868	−	4.98602i	−0.160923	−	0.278727i
$321$	11.6569			0.650622
$322$		0			0
$323$	17.6569			0.982454
$324$	−1.91421	−	3.31552i	−0.106345	−	0.184195i
$325$	−12.6066	+	21.8353i	−0.699288	+	1.21120i
$326$	13.6569	−	23.6544i	0.756383	−	1.31009i
$327$	2.82843	+	4.89898i	0.156412	+	0.270914i
$328$	−9.89949			−0.546608
$329$		0			0
$330$	2.82843			0.155700
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−29.3137	+	50.7728i	−1.60880	+	2.78652i
$333$	2.00000	−	3.46410i	0.109599	−	0.189832i
$334$	−23.8995	−	41.3951i	−1.30772	−	2.26504i
$335$	−3.31371			−0.181047
$336$		0			0
$337$	−18.3431			−0.999215			−0.499607	−	0.866252i	$-0.666522\pi$
$337$	−18.3431			−0.999215			−0.499607	+	0.866252i	$0.666522\pi$
$338$	19.6924	+	34.1082i	1.07112	+	1.85524i
$339$	8.65685	−	14.9941i	0.470176	−	0.814368i
$340$	−7.00000	+	12.1244i	−0.379628	+	0.657536i
$341$	6.82843	+	11.8272i	0.369780	+	0.640478i
$342$	6.82843			0.369239
$343$		0			0
$344$	24.9706			1.34632
$345$	−1.07107	−	1.85514i	−0.0576644	−	0.0998776i
$346$	−8.36396	+	14.4868i	−0.449649	+	0.778815i
$347$	−5.34315	+	9.25460i	−0.286835	+	0.496813i	−0.973053	−	0.230584i	$-0.925937\pi$
$347$	−5.34315	+	9.25460i	−0.286835	+	0.496813i	0.686217	+	0.727396i	$0.259270\pi$
$348$	−2.24264	−	3.88437i	−0.120218	−	0.208224i
$349$	−9.89949			−0.529908			−0.264954	−	0.964261i	$-0.585357\pi$
$349$	−9.89949			−0.529908			−0.264954	+	0.964261i	$0.585357\pi$
$350$		0			0
$351$	5.41421			0.288989
$352$	1.58579	+	2.74666i	0.0845227	+	0.146398i
$353$	5.36396	−	9.29065i	0.285495	−	0.494492i	−0.687234	−	0.726436i	$-0.741175\pi$
$353$	5.36396	−	9.29065i	0.285495	−	0.494492i	0.972729	+	0.231944i	$0.0745087\pi$
$354$	−8.24264	+	14.2767i	−0.438091	+	0.758797i
$355$	−3.89949	−	6.75412i	−0.206964	−	0.358472i
$356$	22.0416			1.16820
$357$		0			0
$358$	20.1421			1.06454
$359$	5.82843	+	10.0951i	0.307613	+	0.532801i	0.977840	−	0.209355i	$-0.0671366\pi$
$359$	5.82843	+	10.0951i	0.307613	+	0.532801i	−0.670227	+	0.742156i	$0.733803\pi$
$360$	−1.29289	+	2.23936i	−0.0681415	+	0.118024i
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$	6.53553	+	11.3199i	0.343500	+	0.594960i
$363$	7.00000			0.367405
$364$		0			0
$365$	−3.45584			−0.180887
$366$	4.53553	+	7.85578i	0.237076	+	0.410628i
$367$	9.65685	−	16.7262i	0.504084	−	0.873099i	−0.495905	−	0.868377i	$-0.665164\pi$
$367$	9.65685	−	16.7262i	0.504084	−	0.873099i	0.999989	−	0.00472187i	$-0.00150302\pi$
$368$	−5.48528	+	9.50079i	−0.285940	+	0.495263i
$369$	−1.12132	−	1.94218i	−0.0583736	−	0.101106i
$370$	−5.65685			−0.294086
$371$		0			0
$372$	−26.1421			−1.35541
$373$	16.6569	+	28.8505i	0.862459	+	1.49382i	0.869548	+	0.493848i	$0.164410\pi$
$373$	16.6569	+	28.8505i	0.862459	+	1.49382i	−0.00708885	+	0.999975i	$0.502256\pi$
$374$	15.0711	−	26.1039i	0.779306	−	1.34980i
$375$	2.82843	−	4.89898i	0.146059	−	0.252982i
$376$	−6.24264	−	10.8126i	−0.321940	−	0.557616i
$377$	6.34315			0.326689
$378$		0			0
$379$	31.3137			1.60848			0.804239	−	0.594307i	$-0.202573\pi$
$379$	31.3137			1.60848			0.804239	+	0.594307i	$0.202573\pi$
$380$	−3.17157	−	5.49333i	−0.162698	−	0.281802i
$381$	4.82843	−	8.36308i	0.247368	−	0.428454i
$382$	−21.7279	+	37.6339i	−1.11170	+	1.92552i
$383$	−14.8284	−	25.6836i	−0.757697	−	1.31237i	−0.944022	−	0.329882i	$-0.892991\pi$
$383$	−14.8284	−	25.6836i	−0.757697	−	1.31237i	0.186325	−	0.982488i	$-0.440342\pi$
$384$	−20.5563			−1.04901
$385$		0			0
$386$	41.7990			2.12751
$387$	2.82843	+	4.89898i	0.143777	+	0.249029i
$388$	10.3640	−	17.9509i	0.526150	−	0.911319i
$389$	−5.07107	+	8.78335i	−0.257113	+	0.445333i	−0.965467	−	0.260524i	$-0.916105\pi$
$389$	−5.07107	+	8.78335i	−0.257113	+	0.445333i	0.708354	+	0.705857i	$0.249438\pi$
$390$	−3.82843	−	6.63103i	−0.193860	−	0.335775i
$391$	−22.8284			−1.15448
$392$		0			0
$393$	7.31371			0.368928
$394$	2.41421	+	4.18154i	0.121626	+	0.210663i
$395$	0.686292	−	1.18869i	0.0345311	−	0.0598096i
$396$	3.82843	−	6.63103i	0.192386	−	0.333222i
$397$	17.1924	+	29.7781i	0.862861	+	1.49452i	0.869155	+	0.494539i	$0.164663\pi$
$397$	17.1924	+	29.7781i	0.862861	+	1.49452i	−0.00629405	+	0.999980i	$0.502003\pi$
$398$	24.9706			1.25166
$399$		0			0
$400$	−13.9706			−0.698528
$401$	−11.0711	−	19.1757i	−0.552863	−	0.957586i	−0.998066	−	0.0621570i	$-0.980202\pi$
$401$	−11.0711	−	19.1757i	−0.552863	−	0.957586i	0.445204	−	0.895429i	$-0.353131\pi$
$402$	−6.82843	+	11.8272i	−0.340571	+	0.589886i
$403$	18.4853	−	32.0174i	0.920817	−	1.59490i
$404$	32.6777	+	56.5994i	1.62577	+	2.81592i
$405$	−0.585786			−0.0291080
$406$		0			0
$407$	8.00000			0.396545
$408$	13.7782	+	23.8645i	0.682121	+	1.18147i
$409$	−9.29289	+	16.0958i	−0.459504	+	0.795884i	−0.998935	−	0.0461457i	$-0.985306\pi$
$409$	−9.29289	+	16.0958i	−0.459504	+	0.795884i	0.539431	+	0.842030i	$0.318639\pi$
$410$	−1.58579	+	2.74666i	−0.0783164	+	0.135648i
$411$	−7.07107	−	12.2474i	−0.348790	−	0.604122i
$412$	47.7990			2.35489
$413$		0			0
$414$	−8.82843			−0.433894
$415$	4.48528	+	7.76874i	0.220174	+	0.381352i
$416$	4.29289	−	7.43551i	0.210476	−	0.364556i
$417$	3.17157	−	5.49333i	0.155313	−	0.269009i
$418$	6.82843	+	11.8272i	0.333989	+	0.578486i
$419$	−38.8284			−1.89689			−0.948446	−	0.316938i	$-0.897345\pi$
$419$	−38.8284			−1.89689			−0.948446	+	0.316938i	$0.897345\pi$
$420$		0			0
$421$	−28.6274			−1.39521			−0.697607	−	0.716480i	$-0.745752\pi$
$421$	−28.6274			−1.39521			−0.697607	+	0.716480i	$0.745752\pi$
$422$	−25.3137	−	43.8446i	−1.23225	−	2.13432i
$423$	1.41421	−	2.44949i	0.0687614	−	0.119098i
$424$	−4.41421	+	7.64564i	−0.214373	+	0.371305i
$425$	−14.5355	−	25.1763i	−0.705077	−	1.22123i
$426$	−32.1421			−1.55729
$427$		0			0
$428$	−44.6274			−2.15715
$429$	5.41421	+	9.37769i	0.261401	+	0.452759i
$430$	4.00000	−	6.92820i	0.192897	−	0.334108i
$431$	−3.48528	+	6.03668i	−0.167880	+	0.290777i	−0.937674	−	0.347515i	$-0.887025\pi$
$431$	−3.48528	+	6.03668i	−0.167880	+	0.290777i	0.769794	+	0.638292i	$0.220359\pi$
$432$	1.50000	+	2.59808i	0.0721688	+	0.125000i
$433$	11.7574			0.565023			0.282511	−	0.959264i	$-0.408833\pi$
$433$	11.7574			0.565023			0.282511	+	0.959264i	$0.408833\pi$
$434$		0			0
$435$	−0.686292			−0.0329052
$436$	−10.8284	−	18.7554i	−0.518588	−	0.898220i
$437$	5.17157	−	8.95743i	0.247390	−	0.428492i
$438$	−7.12132	+	12.3345i	−0.340270	+	0.589365i
$439$	17.6569	+	30.5826i	0.842716	+	1.45963i	0.887590	+	0.460634i	$0.152378\pi$
$439$	17.6569	+	30.5826i	0.842716	+	1.45963i	−0.0448746	+	0.998993i	$0.514289\pi$
$440$	−5.17157			−0.246545
$441$		0			0
$442$	−81.5980			−3.88122
$443$	−0.514719	−	0.891519i	−0.0244550	−	0.0423573i	0.853539	−	0.521029i	$-0.174452\pi$
$443$	−0.514719	−	0.891519i	−0.0244550	−	0.0423573i	−0.877994	+	0.478672i	$0.841118\pi$
$444$	−7.65685	+	13.2621i	−0.363378	+	0.629390i
$445$	1.68629	−	2.92074i	0.0799379	−	0.138456i
$446$	10.8284	+	18.7554i	0.512741	+	0.888093i
$447$	5.31371			0.251330
$448$		0			0
$449$	17.3137			0.817084			0.408542	−	0.912739i	$-0.366037\pi$
$449$	17.3137			0.817084			0.408542	+	0.912739i	$0.366037\pi$
$450$	−5.62132	−	9.73641i	−0.264992	−	0.458979i
$451$	2.24264	−	3.88437i	0.105602	−	0.182908i
$452$	−33.1421	+	57.4039i	−1.55887	+	2.70005i
$453$	6.00000	+	10.3923i	0.281905	+	0.488273i
$454$	−38.1421			−1.79010
$455$		0			0
$456$	−12.4853			−0.584677
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	−9.94975	+	17.2335i	−0.464921	+	0.805267i
$459$	−3.12132	+	5.40629i	−0.145691	+	0.252344i
$460$	4.10051	+	7.10228i	0.191187	+	0.331146i
$461$	19.4142			0.904210			0.452105	−	0.891965i	$-0.350673\pi$
$461$	19.4142			0.904210			0.452105	+	0.891965i	$0.350673\pi$
$462$		0			0
$463$	18.6274			0.865689			0.432845	−	0.901468i	$-0.357510\pi$
$463$	18.6274			0.865689			0.432845	+	0.901468i	$0.357510\pi$
$464$	1.75736	+	3.04384i	0.0815834	+	0.141307i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	26.7279	−	46.2941i	1.23815	−	2.14453i
$467$	19.8995	+	34.4669i	0.920839	+	1.59494i	0.798120	+	0.602498i	$0.205828\pi$
$467$	19.8995	+	34.4669i	0.920839	+	1.59494i	0.122718	+	0.992442i	$0.460839\pi$
$468$	−20.7279			−0.958149
$469$		0			0
$470$	−4.00000			−0.184506
$471$	−10.1213	−	17.5306i	−0.466366	−	0.807769i
$472$	15.0711	−	26.1039i	0.693702	−	1.20153i
$473$	−5.65685	+	9.79796i	−0.260102	+	0.450511i
$474$	−2.82843	−	4.89898i	−0.129914	−	0.225018i
$475$	13.1716			0.604353
$476$		0			0
$477$	−2.00000			−0.0915737
$478$	−5.24264	−	9.08052i	−0.239793	−	0.415333i
$479$	15.0711	−	26.1039i	0.688615	−	1.19272i	−0.283671	−	0.958922i	$-0.591553\pi$
$479$	15.0711	−	26.1039i	0.688615	−	1.19272i	0.972286	−	0.233794i	$-0.0751142\pi$
$480$	−0.464466	+	0.804479i	−0.0211999	+	0.0367193i
$481$	−10.8284	−	18.7554i	−0.493734	−	0.855172i
$482$	−18.7279			−0.853033
$483$		0			0
$484$	−26.7990			−1.21814
$485$	−1.58579	−	2.74666i	−0.0720069	−	0.124720i
$486$	−1.20711	+	2.09077i	−0.0547555	+	0.0948393i
$487$	9.31371	−	16.1318i	0.422044	−	0.731002i	−0.574095	−	0.818789i	$-0.694646\pi$
$487$	9.31371	−	16.1318i	0.422044	−	0.731002i	0.996139	+	0.0877864i	$0.0279793\pi$
$488$	−8.29289	−	14.3637i	−0.375402	−	0.650215i
$489$	−11.3137			−0.511624
$490$		0			0
$491$	38.9706			1.75872			0.879358	−	0.476160i	$-0.157972\pi$
$491$	38.9706			1.75872			0.879358	+	0.476160i	$0.157972\pi$
$492$	4.29289	+	7.43551i	0.193539	+	0.335219i
$493$	−3.65685	+	6.33386i	−0.164696	+	0.285263i
$494$	18.4853	−	32.0174i	0.831692	−	1.44053i
$495$	−0.585786	−	1.01461i	−0.0263291	−	0.0456034i
$496$	20.4853			0.919816
$497$		0			0
$498$	36.9706			1.65669
$499$	9.65685	+	16.7262i	0.432300	+	0.748766i	0.997071	−	0.0764820i	$-0.0243688\pi$
$499$	9.65685	+	16.7262i	0.432300	+	0.748766i	−0.564771	+	0.825248i	$0.691035\pi$
$500$	−10.8284	+	18.7554i	−0.484262	+	0.838766i
$501$	−9.89949	+	17.1464i	−0.442277	+	0.766046i
$502$	−5.41421	−	9.37769i	−0.241648	−	0.418547i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	−8.82843	−	15.2913i	−0.392471	−	0.679781i
$507$	8.15685	−	14.1281i	0.362259	−	0.627450i
$508$	−18.4853	+	32.0174i	−0.820152	+	1.42054i
$509$	−12.7782	−	22.1324i	−0.566383	−	0.981003i	−0.996920	−	0.0784305i	$-0.975009\pi$
$509$	−12.7782	−	22.1324i	−0.566383	−	0.981003i	0.430537	−	0.902573i	$-0.358324\pi$
$510$	8.82843			0.390929
$511$		0			0
$512$	31.2426			1.38074
$513$	−1.41421	−	2.44949i	−0.0624391	−	0.108148i
$514$	23.1924	−	40.1704i	1.02297	−	1.77184i
$515$	3.65685	−	6.33386i	0.161140	−	0.279103i
$516$	−10.8284	−	18.7554i	−0.476695	−	0.825660i
$517$	5.65685			0.248788
$518$		0			0
$519$	6.92893			0.304146
$520$	7.00000	+	12.1244i	0.306970	+	0.531688i
$521$	−16.2929	+	28.2201i	−0.713805	+	1.23635i	0.249614	+	0.968345i	$0.419696\pi$
$521$	−16.2929	+	28.2201i	−0.713805	+	1.23635i	−0.963419	+	0.268000i	$0.913637\pi$
$522$	−1.41421	+	2.44949i	−0.0618984	+	0.107211i
$523$	−7.17157	−	12.4215i	−0.313591	−	0.543156i	0.665546	−	0.746357i	$-0.268199\pi$
$523$	−7.17157	−	12.4215i	−0.313591	−	0.543156i	−0.979137	+	0.203201i	$0.934865\pi$
$524$	−28.0000			−1.22319
$525$		0			0
$526$	41.7990			1.82252
$527$	21.3137	+	36.9164i	0.928440	+	1.60810i
$528$	−3.00000	+	5.19615i	−0.130558	+	0.226134i
$529$	4.81371	−	8.33759i	0.209292	−	0.362504i
$530$	1.41421	+	2.44949i	0.0614295	+	0.106399i
$531$	6.82843			0.296328
$532$		0			0
$533$	−12.1421			−0.525934
$534$	−6.94975	−	12.0373i	−0.300745	−	0.520906i
$535$	−3.41421	+	5.91359i	−0.147609	+	0.255667i
$536$	12.4853	−	21.6251i	0.539282	−	0.934064i
$537$	−4.17157	−	7.22538i	−0.180017	−	0.311798i
$538$	25.8995			1.11661
$539$		0			0
$540$	2.24264			0.0965079
$541$	2.65685	+	4.60181i	0.114227	+	0.197847i	0.917471	−	0.397804i	$-0.130228\pi$
$541$	2.65685	+	4.60181i	0.114227	+	0.197847i	−0.803243	+	0.595651i	$0.796894\pi$
$542$	−21.8995	+	37.9310i	−0.940664	+	1.62928i
$543$	2.70711	−	4.68885i	0.116173	−	0.201218i
$544$	4.94975	+	8.57321i	0.212219	+	0.367574i
$545$	−3.31371			−0.141944
$546$		0			0
$547$	−3.02944			−0.129529			−0.0647647	−	0.997901i	$-0.520630\pi$
$547$	−3.02944			−0.129529			−0.0647647	+	0.997901i	$0.520630\pi$
$548$	27.0711	+	46.8885i	1.15642	+	2.00298i
$549$	1.87868	−	3.25397i	0.0801801	−	0.138876i
$550$	11.2426	−	19.4728i	0.479388	−	0.830324i
$551$	−1.65685	−	2.86976i	−0.0705844	−	0.122256i
$552$	16.1421			0.687055
$553$		0			0
$554$	−32.1421			−1.36559
$555$	1.17157	+	2.02922i	0.0497305	+	0.0861358i
$556$	−12.1421	+	21.0308i	−0.514941	+	0.891904i
$557$	−13.0000	+	22.5167i	−0.550828	+	0.954062i	0.447387	+	0.894340i	$0.352355\pi$
$557$	−13.0000	+	22.5167i	−0.550828	+	0.954062i	−0.998215	+	0.0597213i	$0.980979\pi$
$558$	8.24264	+	14.2767i	0.348939	+	0.604380i
$559$	30.6274			1.29540
$560$		0			0
$561$	−12.4853			−0.527129
$562$	−19.8995	−	34.4669i	−0.839410	−	1.45390i
$563$	−3.41421	+	5.91359i	−0.143892	+	0.249228i	−0.928959	−	0.370183i	$-0.879295\pi$
$563$	−3.41421	+	5.91359i	−0.143892	+	0.249228i	0.785067	+	0.619411i	$0.212628\pi$
$564$	−5.41421	+	9.37769i	−0.227980	+	0.394872i
$565$	5.07107	+	8.78335i	0.213341	+	0.369518i
$566$	20.4853			0.861061
$567$		0			0
$568$	58.7696			2.46592
$569$	−0.242641	−	0.420266i	−0.0101720	−	0.0176185i	0.860895	−	0.508783i	$-0.169905\pi$
$569$	−0.242641	−	0.420266i	−0.0101720	−	0.0176185i	−0.871067	+	0.491165i	$0.836571\pi$
$570$	−2.00000	+	3.46410i	−0.0837708	+	0.145095i
$571$	−16.8284	+	29.1477i	−0.704248	+	1.21979i	0.262715	+	0.964874i	$0.415382\pi$
$571$	−16.8284	+	29.1477i	−0.704248	+	1.21979i	−0.966962	+	0.254919i	$0.917951\pi$
$572$	−20.7279	−	35.9018i	−0.866678	−	1.50113i
$573$	18.0000			0.751961
$574$		0			0
$575$	−17.0294			−0.710177
$576$	4.91421	+	8.51167i	0.204759	+	0.354653i
$577$	−7.05025	+	12.2114i	−0.293506	+	0.508367i	−0.974636	−	0.223795i	$-0.928155\pi$
$577$	−7.05025	+	12.2114i	−0.293506	+	0.508367i	0.681130	+	0.732162i	$0.261489\pi$
$578$	26.5208	−	45.9354i	1.10312	−	1.91066i
$579$	−8.65685	−	14.9941i	−0.359767	−	0.623134i
$580$	2.62742			0.109098
$581$		0			0
$582$	−13.0711			−0.541813
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	13.0208	−	22.5527i	0.538805	−	0.933238i
$585$	−1.58579	+	2.74666i	−0.0655642	+	0.113561i
$586$	−23.4350	−	40.5907i	−0.968092	−	1.67678i
$587$	17.1716			0.708747			0.354373	−	0.935104i	$-0.384694\pi$
$587$	17.1716			0.708747			0.354373	+	0.935104i	$0.384694\pi$
$588$		0			0
$589$	−19.3137			−0.795807
$590$	−4.82843	−	8.36308i	−0.198783	−	0.344303i
$591$	1.00000	−	1.73205i	0.0411345	−	0.0712470i
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	−10.5355	−	18.2481i	−0.432643	−	0.749359i	0.564457	−	0.825462i	$-0.309085\pi$
$593$	−10.5355	−	18.2481i	−0.432643	−	0.749359i	−0.997100	+	0.0761034i	$0.975752\pi$
$594$	−4.82843			−0.198113
$595$		0			0
$596$	−20.3431			−0.833288
$597$	−5.17157	−	8.95743i	−0.211658	−	0.366603i
$598$	−23.8995	+	41.3951i	−0.977323	+	1.69277i
$599$	1.00000	−	1.73205i	0.0408589	−	0.0707697i	−0.844873	−	0.534967i	$-0.820324\pi$
$599$	1.00000	−	1.73205i	0.0408589	−	0.0707697i	0.885732	+	0.464198i	$0.153657\pi$
$600$	10.2782	+	17.8023i	0.419605	+	0.726777i
$601$	0.928932			0.0378919			0.0189460	−	0.999821i	$-0.493969\pi$
$601$	0.928932			0.0378919			0.0189460	+	0.999821i	$0.493969\pi$
$602$		0			0
$603$	5.65685			0.230365
$604$	−22.9706	−	39.7862i	−0.934659	−	1.61888i
$605$	−2.05025	+	3.55114i	−0.0833546	+	0.144374i
$606$	20.6066	−	35.6917i	0.837086	−	1.44988i
$607$	−14.8284	−	25.6836i	−0.601867	−	1.04246i	−0.992538	−	0.121934i	$-0.961090\pi$
$607$	−14.8284	−	25.6836i	−0.601867	−	1.04246i	0.390671	−	0.920530i	$-0.372243\pi$
$608$	−4.48528			−0.181902
$609$		0			0
$610$	−5.31371			−0.215146
$611$	−7.65685	−	13.2621i	−0.309763	−	0.536526i
$612$	11.9497	−	20.6976i	0.483040	−	0.836650i
$613$	−13.6569	+	23.6544i	−0.551595	+	0.955391i	0.446565	+	0.894751i	$0.352647\pi$
$613$	−13.6569	+	23.6544i	−0.551595	+	0.955391i	−0.998160	+	0.0606394i	$0.980686\pi$
$614$	−2.24264	−	3.88437i	−0.0905056	−	0.156760i
$615$	1.31371			0.0529738
$616$		0			0
$617$	−7.51472			−0.302531			−0.151266	−	0.988493i	$-0.548335\pi$
$617$	−7.51472			−0.302531			−0.151266	+	0.988493i	$0.548335\pi$
$618$	−15.0711	−	26.1039i	−0.606247	−	1.05005i
$619$	−2.48528	+	4.30463i	−0.0998919	+	0.173018i	−0.911640	−	0.410990i	$-0.865183\pi$
$619$	−2.48528	+	4.30463i	−0.0998919	+	0.173018i	0.811748	+	0.584008i	$0.198516\pi$
$620$	7.65685	−	13.2621i	0.307507	−	0.532617i
$621$	1.82843	+	3.16693i	0.0733723	+	0.127084i
$622$	−53.4558			−2.14338
$623$		0			0
$624$	16.2426			0.650226
$625$	−9.98528	−	17.2950i	−0.399411	−	0.691801i
$626$	21.6066	−	37.4237i	0.863573	−	1.49575i
$627$	2.82843	−	4.89898i	0.112956	−	0.195646i
$628$	38.7487	+	67.1148i	1.54624	+	2.67817i
$629$	24.9706			0.995642
$630$		0			0
$631$	0.686292			0.0273208			0.0136604	−	0.999907i	$-0.495652\pi$
$631$	0.686292			0.0273208			0.0136604	+	0.999907i	$0.495652\pi$
$632$	5.17157	+	8.95743i	0.205714	+	0.356307i
$633$	−10.4853	+	18.1610i	−0.416753	+	0.721837i
$634$	12.0711	−	20.9077i	0.479403	−	0.830351i
$635$	2.82843	+	4.89898i	0.112243	+	0.194410i
$636$	7.65685			0.303614
$637$		0			0
$638$	−5.65685			−0.223957
$639$	6.65685	+	11.5300i	0.263341	+	0.456120i
$640$	6.02082	−	10.4284i	0.237994	−	0.412217i
$641$	2.58579	−	4.47871i	0.102132	−	0.176899i	−0.810431	−	0.585835i	$-0.800767\pi$
$641$	2.58579	−	4.47871i	0.102132	−	0.176899i	0.912563	+	0.408936i	$0.134100\pi$
$642$	14.0711	+	24.3718i	0.555341	+	0.961878i
$643$	−50.4264			−1.98862			−0.994312	−	0.106510i	$-0.966033\pi$
$643$	−50.4264			−1.98862			−0.994312	+	0.106510i	$0.966033\pi$
$644$		0			0
$645$	−3.31371			−0.130477
$646$	21.3137	+	36.9164i	0.838577	+	1.45246i
$647$	10.5858	−	18.3351i	0.416170	−	0.720828i	−0.579380	−	0.815057i	$-0.696705\pi$
$647$	10.5858	−	18.3351i	0.416170	−	0.720828i	0.995551	+	0.0942294i	$0.0300387\pi$
$648$	2.20711	−	3.82282i	0.0867033	−	0.150175i
$649$	6.82843	+	11.8272i	0.268039	+	0.464258i
$650$	−60.8701			−2.38752
$651$		0			0
$652$	43.3137			1.69630
$653$	−9.75736	−	16.9002i	−0.381835	−	0.661358i	0.609490	−	0.792794i	$-0.291374\pi$
$653$	−9.75736	−	16.9002i	−0.381835	−	0.661358i	−0.991325	+	0.131436i	$0.958041\pi$
$654$	−6.82843	+	11.8272i	−0.267013	+	0.462479i
$655$	−2.14214	+	3.71029i	−0.0837002	+	0.144973i
$656$	−3.36396	−	5.82655i	−0.131341	−	0.227489i
$657$	5.89949			0.230161
$658$		0			0
$659$	−13.3137			−0.518628			−0.259314	−	0.965793i	$-0.583497\pi$
$659$	−13.3137			−0.518628			−0.259314	+	0.965793i	$0.583497\pi$
$660$	2.24264	+	3.88437i	0.0872947	+	0.151199i
$661$	3.77817	−	6.54399i	0.146954	−	0.254532i	−0.783146	−	0.621838i	$-0.786386\pi$
$661$	3.77817	−	6.54399i	0.146954	−	0.254532i	0.930100	+	0.367306i	$0.119720\pi$
$662$	−4.82843	+	8.36308i	−0.187662	+	0.325040i
$663$	16.8995	+	29.2708i	0.656322	+	1.13678i
$664$	−67.5980			−2.62331
$665$		0			0
$666$	9.65685			0.374196
$667$	2.14214	+	3.71029i	0.0829438	+	0.143663i
$668$	37.8995	−	65.6439i	1.46638	−	2.53984i
$669$	4.48528	−	7.76874i	0.173411	−	0.300357i
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	7.51472			0.290102
$672$		0			0
$673$	0.686292			0.0264546			0.0132273	−	0.999913i	$-0.495789\pi$
$673$	0.686292			0.0264546			0.0132273	+	0.999913i	$0.495789\pi$
$674$	−22.1421	−	38.3513i	−0.852883	−	1.47724i
$675$	−2.32843	+	4.03295i	−0.0896212	+	0.155228i
$676$	−31.2279	+	54.0883i	−1.20107	+	2.08032i
$677$	14.2929	+	24.7560i	0.549321	+	0.951451i	0.998321	+	0.0579196i	$0.0184467\pi$
$677$	14.2929	+	24.7560i	0.549321	+	0.951451i	−0.449001	+	0.893531i	$0.648220\pi$
$678$	41.7990			1.60528
$679$		0			0
$680$	−16.1421			−0.619023
$681$	7.89949	+	13.6823i	0.302709	+	0.524308i
$682$	−16.4853	+	28.5533i	−0.631254	+	1.09336i
$683$	4.17157	−	7.22538i	0.159621	−	0.276471i	−0.775111	−	0.631825i	$-0.782306\pi$
$683$	4.17157	−	7.22538i	0.159621	−	0.276471i	0.934732	+	0.355354i	$0.115640\pi$
$684$	5.41421	+	9.37769i	0.207018	+	0.358565i
$685$	8.28427			0.316526
$686$		0			0
$687$	8.24264			0.314476
$688$	8.48528	+	14.6969i	0.323498	+	0.560316i
$689$	−5.41421	+	9.37769i	−0.206265	+	0.357262i
$690$	2.58579	−	4.47871i	0.0984392	−	0.170502i
$691$	−11.6569	−	20.1903i	−0.443448	−	0.768074i	0.554495	−	0.832187i	$-0.312911\pi$
$691$	−11.6569	−	20.1903i	−0.443448	−	0.768074i	−0.997943	+	0.0641132i	$0.979578\pi$
$692$	−26.5269			−1.00840
$693$		0			0
$694$	−25.7990			−0.979316
$695$	1.85786	+	3.21792i	0.0704728	+	0.122062i
$696$	2.58579	−	4.47871i	0.0980140	−	0.169765i
$697$	7.00000	−	12.1244i	0.265144	−	0.459243i
$698$	−11.9497	−	20.6976i	−0.452305	−	0.783415i
$699$	−22.1421			−0.837492
$700$		0			0
$701$	−22.8284			−0.862218			−0.431109	−	0.902300i	$-0.641878\pi$
$701$	−22.8284			−0.862218			−0.431109	+	0.902300i	$0.641878\pi$
$702$	6.53553	+	11.3199i	0.246668	+	0.427241i
$703$	−5.65685	+	9.79796i	−0.213352	+	0.369537i
$704$	−9.82843	+	17.0233i	−0.370423	+	0.641591i
$705$	0.828427	+	1.43488i	0.0312004	+	0.0540406i
$706$	25.8995			0.974740
$707$		0			0
$708$	−26.1421			−0.982482
$709$	−10.1421	−	17.5667i	−0.380896	−	0.659731i	0.610295	−	0.792174i	$-0.291051\pi$
$709$	−10.1421	−	17.5667i	−0.380896	−	0.659731i	−0.991191	+	0.132443i	$0.957718\pi$
$710$	9.41421	−	16.3059i	0.353309	−	0.611949i
$711$	−1.17157	+	2.02922i	−0.0439374	+	0.0761018i
$712$	12.7071	+	22.0094i	0.476219	+	0.824835i
$713$	24.9706			0.935155
$714$		0			0
$715$	−6.34315			−0.237220
$716$	15.9706	+	27.6618i	0.596848	+	1.03377i
$717$	−2.17157	+	3.76127i	−0.0810989	+	0.140467i
$718$	−14.0711	+	24.3718i	−0.525128	+	0.909548i
$719$	−12.9706	−	22.4657i	−0.483720	−	0.837828i	0.516105	−	0.856525i	$-0.327381\pi$
$719$	−12.9706	−	22.4657i	−0.483720	−	0.837828i	−0.999825	+	0.0186972i	$0.994048\pi$
$720$	−1.75736			−0.0654929
$721$		0			0
$722$	26.5563			0.988325
$723$	3.87868	+	6.71807i	0.144250	+	0.249848i
$724$	−10.3640	+	17.9509i	−0.385174	+	0.667140i
$725$	−2.72792	+	4.72490i	−0.101312	+	0.175478i
$726$	8.44975	+	14.6354i	0.313600	+	0.543170i
$727$	4.48528			0.166350			0.0831749	−	0.996535i	$-0.473494\pi$
$727$	4.48528			0.166350			0.0831749	+	0.996535i	$0.473494\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−4.17157	−	7.22538i	−0.154397	−	0.267423i
$731$	−17.6569	+	30.5826i	−0.653062	+	1.13114i
$732$	−7.19239	+	12.4576i	−0.265838	+	0.460445i
$733$	−4.84924	−	8.39913i	−0.179111	−	0.310229i	0.762465	−	0.647029i	$-0.223989\pi$
$733$	−4.84924	−	8.39913i	−0.179111	−	0.310229i	−0.941576	+	0.336800i	$0.890655\pi$
$734$	46.6274			1.72105
$735$		0			0
$736$	5.79899			0.213754
$737$	5.65685	+	9.79796i	0.208373	+	0.360912i
$738$	2.70711	−	4.68885i	0.0996500	−	0.172599i
$739$	−13.6569	+	23.6544i	−0.502376	+	0.870140i	0.497621	+	0.867395i	$0.334207\pi$
$739$	−13.6569	+	23.6544i	−0.502376	+	0.870140i	−0.999996	+	0.00274517i	$0.999126\pi$
$740$	−4.48528	−	7.76874i	−0.164882	−	0.285584i
$741$	−15.3137			−0.562563
$742$		0			0
$743$	−17.0294			−0.624749			−0.312375	−	0.949959i	$-0.601124\pi$
$743$	−17.0294			−0.624749			−0.312375	+	0.949959i	$0.601124\pi$
$744$	−15.0711	−	26.1039i	−0.552532	−	0.957014i
$745$	−1.55635	+	2.69568i	−0.0570202	+	0.0987619i
$746$	−40.2132	+	69.6513i	−1.47231	+	2.55012i
$747$	−7.65685	−	13.2621i	−0.280150	−	0.485233i
$748$	47.7990			1.74770
$749$		0			0
$750$	13.6569			0.498678
$751$	−1.17157	−	2.02922i	−0.0427513	−	0.0740474i	0.843858	−	0.536567i	$-0.180279\pi$
$751$	−1.17157	−	2.02922i	−0.0427513	−	0.0740474i	−0.886609	+	0.462519i	$0.846946\pi$
$752$	4.24264	−	7.34847i	0.154713	−	0.267971i
$753$	−2.24264	+	3.88437i	−0.0817264	+	0.141554i
$754$	7.65685	+	13.2621i	0.278846	+	0.482976i
$755$	−7.02944			−0.255827
$756$		0			0
$757$	37.6569			1.36866			0.684331	−	0.729172i	$-0.260094\pi$
$757$	37.6569			1.36866			0.684331	+	0.729172i	$0.260094\pi$
$758$	37.7990	+	65.4698i	1.37292	+	2.37797i
$759$	−3.65685	+	6.33386i	−0.132735	+	0.229904i
$760$	3.65685	−	6.33386i	0.132648	−	0.229753i
$761$	23.2635	+	40.2935i	0.843300	+	1.46064i	0.887090	+	0.461597i	$0.152723\pi$
$761$	23.2635	+	40.2935i	0.843300	+	1.46064i	−0.0437901	+	0.999041i	$0.513943\pi$
$762$	23.3137			0.844567
$763$		0			0
$764$	−68.9117			−2.49314
$765$	−1.82843	−	3.16693i	−0.0661069	−	0.114501i
$766$	35.7990	−	62.0057i	1.29347	−	2.24036i
$767$	18.4853	−	32.0174i	0.667465	−	1.15608i
$768$	−14.9853	−	25.9553i	−0.540735	−	0.936580i
$769$	29.6985			1.07095			0.535477	−	0.844550i	$-0.320132\pi$
$769$	29.6985			1.07095			0.535477	+	0.844550i	$0.320132\pi$
$770$		0			0
$771$	−19.2132			−0.691947
$772$	33.1421	+	57.4039i	1.19281	+	2.06601i
$773$	10.7782	−	18.6683i	0.387664	−	0.671454i	−0.604471	−	0.796627i	$-0.706615\pi$
$773$	10.7782	−	18.6683i	0.387664	−	0.671454i	0.992135	+	0.125174i	$0.0399488\pi$
$774$	−6.82843	+	11.8272i	−0.245443	+	0.425119i
$775$	15.8995	+	27.5387i	0.571127	+	0.989220i
$776$	23.8995			0.857942

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 + 2.09077i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.292893 + 0.507306i) q^{5} +2.41421 q^{6} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.20711 + 2.09077i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.292893 + 0.507306i) q^{5} +2.41421 q^{6} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(1.00000 - 1.73205i) q^{11} +(1.91421 + 3.31552i) q^{12} -5.41421 q^{13} +0.585786 q^{15} +(-1.50000 - 2.59808i) q^{16} +(3.12132 - 5.40629i) q^{17} +(1.20711 - 2.09077i) q^{18} +(1.41421 + 2.44949i) q^{19} -2.24264 q^{20} +4.82843 q^{22} +(-1.82843 - 3.16693i) q^{23} +(-2.20711 + 3.82282i) q^{24} +(2.32843 - 4.03295i) q^{25} +(-6.53553 - 11.3199i) q^{26} -1.00000 q^{27} -1.17157 q^{29} +(0.707107 + 1.22474i) q^{30} +(-3.41421 + 5.91359i) q^{31} +(-0.792893 + 1.37333i) q^{32} +(-1.00000 - 1.73205i) q^{33} +15.0711 q^{34} +3.82843 q^{36} +(2.00000 + 3.46410i) q^{37} +(-3.41421 + 5.91359i) q^{38} +(-2.70711 + 4.68885i) q^{39} +(-1.29289 - 2.23936i) q^{40} +2.24264 q^{41} -5.65685 q^{43} +(3.82843 + 6.63103i) q^{44} +(0.292893 - 0.507306i) q^{45} +(4.41421 - 7.64564i) q^{46} +(1.41421 + 2.44949i) q^{47} -3.00000 q^{48} +11.2426 q^{50} +(-3.12132 - 5.40629i) q^{51} +(10.3640 - 17.9509i) q^{52} +(1.00000 - 1.73205i) q^{53} +(-1.20711 - 2.09077i) q^{54} +1.17157 q^{55} +2.82843 q^{57} +(-1.41421 - 2.44949i) q^{58} +(-3.41421 + 5.91359i) q^{59} +(-1.12132 + 1.94218i) q^{60} +(1.87868 + 3.25397i) q^{61} -16.4853 q^{62} -9.82843 q^{64} +(-1.58579 - 2.74666i) q^{65} +(2.41421 - 4.18154i) q^{66} +(-2.82843 + 4.89898i) q^{67} +(11.9497 + 20.6976i) q^{68} -3.65685 q^{69} -13.3137 q^{71} +(2.20711 + 3.82282i) q^{72} +(-2.94975 + 5.10911i) q^{73} +(-4.82843 + 8.36308i) q^{74} +(-2.32843 - 4.03295i) q^{75} -10.8284 q^{76} -13.0711 q^{78} +(-1.17157 - 2.02922i) q^{79} +(0.878680 - 1.52192i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.70711 + 4.68885i) q^{82} +15.3137 q^{83} +3.65685 q^{85} +(-6.82843 - 11.8272i) q^{86} +(-0.585786 + 1.01461i) q^{87} +(-4.41421 + 7.64564i) q^{88} +(-2.87868 - 4.98602i) q^{89} +1.41421 q^{90} +14.0000 q^{92} +(3.41421 + 5.91359i) q^{93} +(-3.41421 + 5.91359i) q^{94} +(-0.828427 + 1.43488i) q^{95} +(0.792893 + 1.37333i) q^{96} -5.41421 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} - 2 q^{9} + 4 q^{11} + 2 q^{12} - 16 q^{13} + 8 q^{15} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{20} + 8 q^{22} + 4 q^{23} - 6 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 16 q^{29} - 8 q^{31} - 6 q^{32} - 4 q^{33} + 32 q^{34} + 4 q^{36} + 8 q^{37} - 8 q^{38} - 8 q^{39} - 8 q^{40} - 8 q^{41} + 4 q^{44} + 4 q^{45} + 12 q^{46} - 12 q^{48} + 28 q^{50} - 4 q^{51} + 16 q^{52} + 4 q^{53} - 2 q^{54} + 16 q^{55} - 8 q^{59} + 4 q^{60} + 16 q^{61} - 32 q^{62} - 28 q^{64} - 12 q^{65} + 4 q^{66} + 28 q^{68} + 8 q^{69} - 8 q^{71} + 6 q^{72} + 8 q^{73} - 8 q^{74} + 2 q^{75} - 32 q^{76} - 24 q^{78} - 16 q^{79} + 12 q^{80} - 2 q^{81} + 8 q^{82} + 16 q^{83} - 8 q^{85} - 16 q^{86} - 8 q^{87} - 12 q^{88} - 20 q^{89} + 56 q^{92} + 8 q^{93} - 8 q^{94} + 8 q^{95} + 6 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 - 2 * q^9 + 4 * q^11 + 2 * q^12 - 16 * q^13 + 8 * q^15 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^20 + 8 * q^22 + 4 * q^23 - 6 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 16 * q^29 - 8 * q^31 - 6 * q^32 - 4 * q^33 + 32 * q^34 + 4 * q^36 + 8 * q^37 - 8 * q^38 - 8 * q^39 - 8 * q^40 - 8 * q^41 + 4 * q^44 + 4 * q^45 + 12 * q^46 - 12 * q^48 + 28 * q^50 - 4 * q^51 + 16 * q^52 + 4 * q^53 - 2 * q^54 + 16 * q^55 - 8 * q^59 + 4 * q^60 + 16 * q^61 - 32 * q^62 - 28 * q^64 - 12 * q^65 + 4 * q^66 + 28 * q^68 + 8 * q^69 - 8 * q^71 + 6 * q^72 + 8 * q^73 - 8 * q^74 + 2 * q^75 - 32 * q^76 - 24 * q^78 - 16 * q^79 + 12 * q^80 - 2 * q^81 + 8 * q^82 + 16 * q^83 - 8 * q^85 - 16 * q^86 - 8 * q^87 - 12 * q^88 - 20 * q^89 + 56 * q^92 + 8 * q^93 - 8 * q^94 + 8 * q^95 + 6 * q^96 - 16 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more