LMFDB - Embedded newform 567.2.f.m.190.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(190,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.190"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-6,3,0,-3,18,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			190.3
Root			$0.500000 - 0.0585812i$ of defining polynomial
Character	$\chi$	$=$	567.190
Dual form			567.2.f.m.379.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07255 + 1.85771i) q^{2} +(-1.30073 + 2.25294i) q^{4} +(1.87328 - 3.24462i) q^{5} +(-0.500000 - 0.866025i) q^{7} -1.29021 q^{8} +8.03677 q^{10} +(-0.373284 - 0.646547i) q^{11} +(3.01839 - 5.22800i) q^{13} +(1.07255 - 1.85771i) q^{14} +(1.21765 + 2.10904i) q^{16} +0.543637 q^{17} -1.20293 q^{19} +(4.87328 + 8.44078i) q^{20} +(0.800733 - 1.38691i) q^{22} +(-3.74657 + 6.48925i) q^{23} +(-4.51839 - 7.82608i) q^{25} +12.9495 q^{26} +2.60147 q^{28} +(4.01839 + 6.96005i) q^{29} +(-1.00000 + 1.73205i) q^{31} +(-3.90220 + 6.75881i) q^{32} +(0.583079 + 1.00992i) q^{34} -3.74657 q^{35} +5.00000 q^{37} +(-1.29021 - 2.23470i) q^{38} +(-2.41692 + 4.18623i) q^{40} +(-1.39853 + 2.42233i) q^{41} +(-4.91692 - 8.51636i) q^{43} +1.94217 q^{44} -16.0735 q^{46} +(-2.14510 - 3.71543i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(9.69240 - 16.7877i) q^{50} +(7.85223 + 13.6005i) q^{52} -2.45636 q^{53} -2.79707 q^{55} +(0.645103 + 1.11735i) q^{56} +(-8.61985 + 14.9300i) q^{58} +(-7.29021 + 12.6270i) q^{59} +(4.61985 + 8.00182i) q^{61} -4.29021 q^{62} -11.8706 q^{64} +(-11.3086 - 19.5871i) q^{65} +(-5.11985 + 8.86784i) q^{67} +(-0.707127 + 1.22478i) q^{68} +(-4.01839 - 6.96005i) q^{70} +8.23970 q^{71} +10.0368 q^{73} +(5.36276 + 9.28857i) q^{74} +(1.56469 - 2.71013i) q^{76} +(-0.373284 + 0.646547i) q^{77} +(-5.11985 - 8.86784i) q^{79} +9.12405 q^{80} -6.00000 q^{82} +(1.39853 + 2.42233i) q^{83} +(1.01839 - 1.76390i) q^{85} +(10.5473 - 18.2685i) q^{86} +(0.481613 + 0.834179i) q^{88} -6.54364 q^{89} -6.03677 q^{91} +(-9.74657 - 16.8816i) q^{92} +(4.60147 - 7.96997i) q^{94} +(-2.25343 + 3.90306i) q^{95} +(-2.60147 - 4.50587i) q^{97} -2.14510 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 3 q^{5} - 3 q^{7} + 18 q^{8} + 6 q^{10} + 6 q^{11} - 3 q^{13} - 12 q^{16} - 6 q^{17} + 21 q^{20} + 3 q^{22} - 6 q^{23} - 6 q^{25} + 54 q^{26} + 12 q^{28} + 3 q^{29} - 6 q^{31} - 18 q^{32}+ \cdots - 12 q^{97}+O(q^{100}) $ 6 * q - 6 * q^4 + 3 * q^5 - 3 * q^7 + 18 * q^8 + 6 * q^10 + 6 * q^11 - 3 * q^13 - 12 * q^16 - 6 * q^17 + 21 * q^20 + 3 * q^22 - 6 * q^23 - 6 * q^25 + 54 * q^26 + 12 * q^28 + 3 * q^29 - 6 * q^31 - 18 * q^32 + 21 * q^34 - 6 * q^35 + 30 * q^37 + 18 * q^38 + 3 * q^40 - 12 * q^41 - 12 * q^43 + 6 * q^44 - 12 * q^46 - 3 * q^49 + 27 * q^50 - 9 * q^52 - 24 * q^53 - 24 * q^55 - 9 * q^56 - 27 * q^58 - 18 * q^59 + 3 * q^61 + 6 * q^64 - 21 * q^65 - 6 * q^67 + 39 * q^68 - 3 * q^70 + 18 * q^73 + 48 * q^76 + 6 * q^77 - 6 * q^79 - 6 * q^80 - 36 * q^82 + 12 * q^83 - 15 * q^85 + 45 * q^86 + 24 * q^88 - 30 * q^89 + 6 * q^91 - 42 * q^92 + 24 * q^94 - 30 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.07255	+	1.85771i	0.758408	+	1.31360i	0.943662	+	0.330911i	$0.107356\pi$
$2$	1.07255	+	1.85771i	0.758408	+	1.31360i	−0.185254	+	0.982691i	$0.559311\pi$
$3$		0			0
$3$		0			0
$4$	−1.30073	+	2.25294i	−0.650366	+	1.12647i
$5$	1.87328	−	3.24462i	0.837758	−	1.45104i	−0.0540067	−	0.998541i	$-0.517199\pi$
$5$	1.87328	−	3.24462i	0.837758	−	1.45104i	0.891765	−	0.452499i	$-0.149467\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−1.29021			−0.456156
$9$		0			0
$10$	8.03677			2.54145
$11$	−0.373284	−	0.646547i	−0.112549	−	0.194941i	0.804248	−	0.594294i	$-0.202568\pi$
$11$	−0.373284	−	0.646547i	−0.112549	−	0.194941i	−0.916797	+	0.399352i	$0.869235\pi$
$12$		0			0
$13$	3.01839	−	5.22800i	0.837150	−	1.44999i	−0.0551181	−	0.998480i	$-0.517554\pi$
$13$	3.01839	−	5.22800i	0.837150	−	1.44999i	0.892268	−	0.451506i	$-0.149113\pi$
$14$	1.07255	−	1.85771i	0.286651	−	0.496495i
$15$		0			0
$16$	1.21765	+	2.10904i	0.304414	+	0.527260i
$17$	0.543637			0.131851			0.0659257	−	0.997825i	$-0.479000\pi$
$17$	0.543637			0.131851			0.0659257	+	0.997825i	$0.479000\pi$
$18$		0			0
$19$	−1.20293			−0.275971			−0.137986	−	0.990434i	$-0.544063\pi$
$19$	−1.20293			−0.275971			−0.137986	+	0.990434i	$0.544063\pi$
$20$	4.87328	+	8.44078i	1.08970	+	1.88741i
$21$		0			0
$22$	0.800733	−	1.38691i	0.170717	−	0.295690i
$23$	−3.74657	+	6.48925i	−0.781213	+	1.35310i	0.150022	+	0.988683i	$0.452066\pi$
$23$	−3.74657	+	6.48925i	−0.781213	+	1.35310i	−0.931235	+	0.364419i	$0.881268\pi$
$24$		0			0
$25$	−4.51839	−	7.82608i	−0.903677	−	1.56522i
$26$	12.9495			2.53961
$27$		0			0
$28$	2.60147			0.491631
$29$	4.01839	+	6.96005i	0.746196	+	1.29245i	0.949634	+	0.313361i	$0.101455\pi$
$29$	4.01839	+	6.96005i	0.746196	+	1.29245i	−0.203438	+	0.979088i	$0.565212\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	−3.90220	+	6.75881i	−0.689818	+	1.19480i
$33$		0			0
$34$	0.583079	+	1.00992i	0.0999972	+	0.173200i
$35$	−3.74657			−0.633286
$36$		0			0
$37$	5.00000			0.821995			0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000			0.821995			0.410997	+	0.911636i	$0.365181\pi$
$38$	−1.29021	−	2.23470i	−0.209299	−	0.362516i
$39$		0			0
$40$	−2.41692	+	4.18623i	−0.382149	+	0.661901i
$41$	−1.39853	+	2.42233i	−0.218414	+	0.378305i	−0.954323	−	0.298776i	$-0.903422\pi$
$41$	−1.39853	+	2.42233i	−0.218414	+	0.378305i	0.735909	+	0.677080i	$0.236755\pi$
$42$		0			0
$43$	−4.91692	−	8.51636i	−0.749823	−	1.29873i	−0.947907	−	0.318547i	$-0.896805\pi$
$43$	−4.91692	−	8.51636i	−0.749823	−	1.29873i	0.198084	−	0.980185i	$-0.436528\pi$
$44$	1.94217			0.292793
$45$		0			0
$46$	−16.0735			−2.36992
$47$	−2.14510	−	3.71543i	−0.312895	−	0.541951i	0.666092	−	0.745869i	$-0.267966\pi$
$47$	−2.14510	−	3.71543i	−0.312895	−	0.541951i	−0.978988	+	0.203918i	$0.934632\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	9.69240	−	16.7877i	1.37071	−	2.37414i
$51$		0			0
$52$	7.85223	+	13.6005i	1.08891	+	1.88604i
$53$	−2.45636			−0.337407			−0.168704	−	0.985667i	$-0.553958\pi$
$53$	−2.45636			−0.337407			−0.168704	+	0.985667i	$0.553958\pi$
$54$		0			0
$55$	−2.79707			−0.377157
$56$	0.645103	+	1.11735i	0.0862055	+	0.149312i
$57$		0			0
$58$	−8.61985	+	14.9300i	−1.13184	+	1.96041i
$59$	−7.29021	+	12.6270i	−0.949104	+	1.64390i	−0.201786	+	0.979430i	$0.564675\pi$
$59$	−7.29021	+	12.6270i	−0.949104	+	1.64390i	−0.747318	+	0.664467i	$0.768659\pi$
$60$		0			0
$61$	4.61985	+	8.00182i	0.591511	+	1.02453i	0.994029	+	0.109116i	$0.0348019\pi$
$61$	4.61985	+	8.00182i	0.591511	+	1.02453i	−0.402518	+	0.915412i	$0.631865\pi$
$62$	−4.29021			−0.544857
$63$		0			0
$64$	−11.8706			−1.48383
$65$	−11.3086	−	19.5871i	−1.40266	−	2.42948i
$66$		0			0
$67$	−5.11985	+	8.86784i	−0.625490	+	1.08338i	0.362956	+	0.931806i	$0.381767\pi$
$67$	−5.11985	+	8.86784i	−0.625490	+	1.08338i	−0.988446	+	0.151574i	$0.951566\pi$
$68$	−0.707127	+	1.22478i	−0.0857517	+	0.148526i
$69$		0			0
$70$	−4.01839	−	6.96005i	−0.480289	−	0.831885i
$71$	8.23970			0.977873			0.488937	−	0.872319i	$-0.337385\pi$
$71$	8.23970			0.977873			0.488937	+	0.872319i	$0.337385\pi$
$72$		0			0
$73$	10.0368			1.17472			0.587358	−	0.809327i	$-0.300168\pi$
$73$	10.0368			1.17472			0.587358	+	0.809327i	$0.300168\pi$
$74$	5.36276	+	9.28857i	0.623408	+	1.07977i
$75$		0			0
$76$	1.56469	−	2.71013i	0.179482	−	0.310873i
$77$	−0.373284	+	0.646547i	−0.0425397	+	0.0736809i
$78$		0			0
$79$	−5.11985	−	8.86784i	−0.576028	−	0.997710i	−0.995929	−	0.0901404i	$-0.971268\pi$
$79$	−5.11985	−	8.86784i	−0.576028	−	0.997710i	0.419901	−	0.907570i	$-0.362065\pi$
$80$	9.12405			1.02010
$81$		0			0
$82$	−6.00000			−0.662589
$83$	1.39853	+	2.42233i	0.153509	+	0.265886i	0.932515	−	0.361131i	$-0.117609\pi$
$83$	1.39853	+	2.42233i	0.153509	+	0.265886i	−0.779006	+	0.627016i	$0.784276\pi$
$84$		0			0
$85$	1.01839	−	1.76390i	0.110460	−	0.191322i
$86$	10.5473	−	18.2685i	1.13734	−	1.96994i
$87$		0			0
$88$	0.481613	+	0.834179i	0.0513401	+	0.0889237i
$89$	−6.54364			−0.693624			−0.346812	−	0.937935i	$-0.612736\pi$
$89$	−6.54364			−0.693624			−0.346812	+	0.937935i	$0.612736\pi$
$90$		0			0
$91$	−6.03677			−0.632826
$92$	−9.74657	−	16.8816i	−1.01615	−	1.76002i
$93$		0			0
$94$	4.60147	−	7.96997i	0.474605	−	0.822040i
$95$	−2.25343	+	3.90306i	−0.231197	+	0.400445i
$96$		0			0
$97$	−2.60147	−	4.50587i	−0.264139	−	0.457502i	0.703199	−	0.710993i	$-0.251754\pi$
$97$	−2.60147	−	4.50587i	−0.264139	−	0.457502i	−0.967338	+	0.253491i	$0.918421\pi$
$98$	−2.14510			−0.216688
$99$		0			0
$100$	23.5089			2.35089
$101$	−2.25343	−	3.90306i	−0.224225	−	0.388369i	0.731862	−	0.681453i	$-0.238652\pi$
$101$	−2.25343	−	3.90306i	−0.224225	−	0.388369i	−0.956087	+	0.293084i	$0.905318\pi$
$102$		0			0
$103$	5.43531	−	9.41423i	0.535557	−	0.927612i	−0.463579	−	0.886055i	$-0.653435\pi$
$103$	5.43531	−	9.41423i	0.535557	−	0.927612i	0.999136	−	0.0415562i	$-0.0132316\pi$
$104$	−3.89434	+	6.74519i	−0.381871	+	0.661421i
$105$		0			0
$106$	−2.63458	−	4.56322i	−0.255893	−	0.443219i
$107$	3.32698			0.321631			0.160816	−	0.986984i	$-0.448588\pi$
$107$	3.32698			0.321631			0.160816	+	0.986984i	$0.448588\pi$
$108$		0			0
$109$	−5.63091			−0.539343			−0.269672	−	0.962952i	$-0.586915\pi$
$109$	−5.63091			−0.539343			−0.269672	+	0.962952i	$0.586915\pi$
$110$	−3.00000	−	5.19615i	−0.286039	−	0.495434i
$111$		0			0
$112$	1.21765	−	2.10904i	0.115057	−	0.199285i
$113$	1.29707	−	2.24659i	0.122018	−	0.211341i	−0.798545	−	0.601935i	$-0.794397\pi$
$113$	1.29707	−	2.24659i	0.122018	−	0.211341i	0.920563	+	0.390593i	$0.127730\pi$
$114$		0			0
$115$	14.0368	+	24.3124i	1.30894	+	2.26714i
$116$	−20.9074			−1.94120
$117$		0			0
$118$	−31.2765			−2.87923
$119$	−0.271819	−	0.470804i	−0.0249176	−	0.0431585i
$120$		0			0
$121$	5.22132	−	9.04359i	0.474665	−	0.822144i
$122$	−9.91006	+	17.1647i	−0.897214	+	1.55402i
$123$		0			0
$124$	−2.60147	−	4.50587i	−0.233619	−	0.404639i
$125$	−15.1240			−1.35274
$126$		0			0
$127$	9.83384			0.872612			0.436306	−	0.899798i	$-0.356286\pi$
$127$	9.83384			0.872612			0.436306	+	0.899798i	$0.356286\pi$
$128$	−4.92745	−	8.53459i	−0.435529	−	0.754358i
$129$		0			0
$130$	24.2581	−	42.0162i	2.12758	−	3.68507i
$131$	2.68874	−	4.65703i	0.234916	−	0.406887i	−0.724332	−	0.689451i	$-0.757852\pi$
$131$	2.68874	−	4.65703i	0.234916	−	0.406887i	0.959248	+	0.282564i	$0.0911851\pi$
$132$		0			0
$133$	0.601466	+	1.04177i	0.0521537	+	0.0903328i
$134$	−21.9652			−1.89751
$135$		0			0
$136$	−0.701404			−0.0601449
$137$	5.24657	+	9.08732i	0.448245	+	0.776382i	0.998272	−	0.0587643i	$-0.0187160\pi$
$137$	5.24657	+	9.08732i	0.448245	+	0.776382i	−0.550027	+	0.835147i	$0.685383\pi$
$138$		0			0
$139$	3.39853	−	5.88643i	0.288260	−	0.499281i	−0.685135	−	0.728417i	$-0.740257\pi$
$139$	3.39853	−	5.88643i	0.288260	−	0.499281i	0.973394	+	0.229136i	$0.0735899\pi$
$140$	4.87328	−	8.44078i	0.411868	−	0.713376i
$141$		0			0
$142$	8.83751	+	15.3070i	0.741627	+	1.28454i
$143$	−4.50686			−0.376883
$144$		0			0
$145$	30.1103			2.50053
$146$	10.7650	+	18.6454i	0.890914	+	1.54311i
$147$		0			0
$148$	−6.50366	+	11.2647i	−0.534598	+	0.925951i
$149$	0.753432	−	1.30498i	0.0617235	−	0.106908i	−0.833512	−	0.552501i	$-0.813674\pi$
$149$	0.753432	−	1.30498i	0.0617235	−	0.106908i	0.895236	+	0.445592i	$0.147007\pi$
$150$		0			0
$151$	3.11985	+	5.40374i	0.253890	+	0.439750i	0.964593	−	0.263741i	$-0.0849565\pi$
$151$	3.11985	+	5.40374i	0.253890	+	0.439750i	−0.710703	+	0.703492i	$0.751623\pi$
$152$	1.55203			0.125886
$153$		0			0
$154$	−1.60147			−0.129050
$155$	3.74657	+	6.48925i	0.300932	+	0.521229i
$156$		0			0
$157$	−10.2581	+	17.7675i	−0.818685	+	1.41800i	0.0879667	+	0.996123i	$0.471963\pi$
$157$	−10.2581	+	17.7675i	−0.818685	+	1.41800i	−0.906652	+	0.421880i	$0.861370\pi$
$158$	10.9826	−	19.0224i	0.873729	−	1.51334i
$159$		0			0
$160$	14.6199	+	25.3223i	1.15580	+	2.00191i
$161$	7.49314			0.590542
$162$		0			0
$163$	−12.2397			−0.958688			−0.479344	−	0.877627i	$-0.659125\pi$
$163$	−12.2397			−0.958688			−0.479344	+	0.877627i	$0.659125\pi$
$164$	−3.63824	−	6.30162i	−0.284099	−	0.492073i
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−7.39853	+	12.8146i	−0.572516	+	0.991626i	0.423791	+	0.905760i	$0.360699\pi$
$167$	−7.39853	+	12.8146i	−0.572516	+	0.991626i	−0.996307	+	0.0858664i	$0.972634\pi$
$168$		0			0
$169$	−11.7213	−	20.3019i	−0.901640	−	1.56169i
$170$	4.36909			0.335094
$171$		0			0
$172$	25.5824			1.95064
$173$	0.910058	+	1.57627i	0.0691904	+	0.119841i	0.898545	−	0.438881i	$-0.144625\pi$
$173$	0.910058	+	1.57627i	0.0691904	+	0.119841i	−0.829355	+	0.558722i	$0.811292\pi$
$174$		0			0
$175$	−4.51839	+	7.82608i	−0.341558	+	0.591596i
$176$	0.909062	−	1.57454i	0.0685231	−	0.118686i
$177$		0			0
$178$	−7.01839	−	12.1562i	−0.526050	−	0.911146i
$179$	−1.08727			−0.0812667			−0.0406333	−	0.999174i	$-0.512938\pi$
$179$	−1.08727			−0.0812667			−0.0406333	+	0.999174i	$0.512938\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−6.47475	−	11.2146i	−0.479940	−	0.831281i
$183$		0			0
$184$	4.83384	−	8.37246i	0.356356	−	0.617226i
$185$	9.36642	−	16.2231i	0.688633	−	1.19275i
$186$		0			0
$187$	−0.202931	−	0.351487i	−0.0148398	−	0.0257033i
$188$	11.1608			0.813987
$189$		0			0
$190$	−9.66769			−0.701368
$191$	5.41006	+	9.37049i	0.391458	+	0.678025i	0.992642	−	0.121085i	$-0.0386375\pi$
$191$	5.41006	+	9.37049i	0.391458	+	0.678025i	−0.601184	+	0.799111i	$0.705304\pi$
$192$		0			0
$193$	−4.81546	+	8.34061i	−0.346624	+	0.600371i	−0.985647	−	0.168817i	$-0.946005\pi$
$193$	−4.81546	+	8.34061i	−0.346624	+	0.600371i	0.639023	+	0.769187i	$0.279339\pi$
$194$	5.58041	−	9.66555i	0.400650	−	0.693946i
$195$		0			0
$196$	−1.30073	−	2.25294i	−0.0929095	−	0.160924i
$197$	−19.4794			−1.38785			−0.693925	−	0.720047i	$-0.744120\pi$
$197$	−19.4794			−1.38785			−0.693925	+	0.720047i	$0.744120\pi$
$198$		0			0
$199$	−16.8706			−1.19593			−0.597963	−	0.801524i	$-0.704023\pi$
$199$	−16.8706			−1.19593			−0.597963	+	0.801524i	$0.704023\pi$
$200$	5.82965	+	10.0972i	0.412218	+	0.713983i
$201$		0			0
$202$	4.83384	−	8.37246i	0.340108	−	0.589084i
$203$	4.01839	−	6.96005i	0.282035	−	0.488500i
$204$		0			0
$205$	5.23970	+	9.07543i	0.365957	+	0.633856i
$206$	23.3186			1.62468
$207$		0			0
$208$	14.7014			1.01936
$209$	0.449035	+	0.777752i	0.0310604	+	0.0537982i
$210$		0			0
$211$	−1.91692	+	3.32021i	−0.131966	+	0.228572i	−0.924434	−	0.381341i	$-0.875462\pi$
$211$	−1.91692	+	3.32021i	−0.131966	+	0.228572i	0.792468	+	0.609913i	$0.208796\pi$
$212$	3.19507	−	5.53403i	0.219438	−	0.380079i
$213$		0			0
$214$	3.56836	+	6.18057i	0.243928	+	0.422495i
$215$	−36.8432			−2.51268
$216$		0			0
$217$	2.00000			0.135769
$218$	−6.03944	−	10.4606i	−0.409043	−	0.708483i
$219$		0			0
$220$	3.63824	−	6.30162i	0.245290	−	0.424855i
$221$	1.64091	−	2.84213i	0.110379	−	0.191183i
$222$		0			0
$223$	−6.23970	−	10.8075i	−0.417842	−	0.723723i	0.577881	−	0.816121i	$-0.303880\pi$
$223$	−6.23970	−	10.8075i	−0.417842	−	0.723723i	−0.995722	+	0.0923986i	$0.970547\pi$
$224$	7.80440			0.521453
$225$		0			0
$226$	5.56469			0.370158
$227$	−10.9284	−	18.9286i	−0.725346	−	1.25634i	−0.958831	−	0.283976i	$-0.908346\pi$
$227$	−10.9284	−	18.9286i	−0.725346	−	1.25634i	0.233485	−	0.972360i	$-0.424987\pi$
$228$		0			0
$229$	−9.61985	+	16.6621i	−0.635698	+	1.10106i	0.350669	+	0.936499i	$0.385954\pi$
$229$	−9.61985	+	16.6621i	−0.635698	+	1.10106i	−0.986367	+	0.164561i	$0.947379\pi$
$230$	−30.1103	+	52.1526i	−1.98542	+	3.43884i
$231$		0			0
$232$	−5.18454	−	8.97989i	−0.340382	−	0.589559i
$233$	11.4564			0.750531			0.375266	−	0.926917i	$-0.377551\pi$
$233$	11.4564			0.750531			0.375266	+	0.926917i	$0.377551\pi$
$234$		0			0
$235$	−16.0735			−1.04852
$236$	−18.9652	−	32.8487i	−1.23453	−	2.13827i
$237$		0			0
$238$	0.583079	−	1.00992i	0.0377954	−	0.0654635i
$239$	−2.08308	+	3.60800i	−0.134743	+	0.233382i	−0.925499	−	0.378749i	$-0.876354\pi$
$239$	−2.08308	+	3.60800i	−0.134743	+	0.233382i	0.790756	+	0.612131i	$0.209688\pi$
$240$		0			0
$241$	−6.61985	−	11.4659i	−0.426422	−	0.738585i	0.570130	−	0.821555i	$-0.306893\pi$
$241$	−6.61985	−	11.4659i	−0.426422	−	0.738585i	−0.996552	+	0.0829697i	$0.973560\pi$
$242$	22.4005			1.43996
$243$		0			0
$244$	−24.0368			−1.53880
$245$	1.87328	+	3.24462i	0.119680	+	0.207291i
$246$		0			0
$247$	−3.63091	+	6.28892i	−0.231029	+	0.400155i
$248$	1.29021	−	2.23470i	0.0819281	−	0.141904i
$249$		0			0
$250$	−16.2213	−	28.0961i	−1.02593	−	1.77696i
$251$	12.8706			0.812386			0.406193	−	0.913787i	$-0.366856\pi$
$251$	12.8706			0.812386			0.406193	+	0.913787i	$0.366856\pi$
$252$		0			0
$253$	5.59414			0.351700
$254$	10.5473	+	18.2685i	0.661797	+	1.14627i
$255$		0			0
$256$	−1.30073	+	2.25294i	−0.0812958	+	0.140808i
$257$	0.0688875	−	0.119317i	0.00429708	−	0.00744276i	−0.863869	−	0.503717i	$-0.831966\pi$
$257$	0.0688875	−	0.119317i	0.00429708	−	0.00744276i	0.868166	+	0.496274i	$0.165299\pi$
$258$		0			0
$259$	−2.50000	−	4.33013i	−0.155342	−	0.269061i
$260$	58.8378			3.64897
$261$		0			0
$262$	11.5352			0.712650
$263$	5.62672	+	9.74576i	0.346958	+	0.600949i	0.985708	−	0.168466i	$-0.0538812\pi$
$263$	5.62672	+	9.74576i	0.346958	+	0.600949i	−0.638749	+	0.769415i	$0.720548\pi$
$264$		0			0
$265$	−4.60147	+	7.96997i	−0.282666	+	0.489591i
$266$	−1.29021	+	2.23470i	−0.0791076	+	0.137018i
$267$		0			0
$268$	−13.3191	−	23.0694i	−0.813595	−	1.40919i
$269$	−5.45636			−0.332680			−0.166340	−	0.986068i	$-0.553195\pi$
$269$	−5.45636			−0.332680			−0.166340	+	0.986068i	$0.553195\pi$
$270$		0			0
$271$	−3.12938			−0.190097			−0.0950483	−	0.995473i	$-0.530301\pi$
$271$	−3.12938			−0.190097			−0.0950483	+	0.995473i	$0.530301\pi$
$272$	0.661962	+	1.14655i	0.0401373	+	0.0695199i
$273$		0			0
$274$	−11.2544	+	19.4932i	−0.679905	+	1.17763i
$275$	−3.37328	+	5.84270i	−0.203417	+	0.352328i
$276$		0			0
$277$	4.31546	+	7.47459i	0.259291	+	0.449104i	0.966052	−	0.258347i	$-0.0831779\pi$
$277$	4.31546	+	7.47459i	0.259291	+	0.449104i	−0.706761	+	0.707452i	$0.749845\pi$
$278$	14.5804			0.874475
$279$		0			0
$280$	4.83384			0.288877
$281$	−6.53677	−	11.3220i	−0.389951	−	0.675415i	0.602491	−	0.798125i	$-0.294175\pi$
$281$	−6.53677	−	11.3220i	−0.389951	−	0.675415i	−0.992443	+	0.122710i	$0.960841\pi$
$282$		0			0
$283$	6.80440	−	11.7856i	0.404479	−	0.700579i	−0.589781	−	0.807563i	$-0.700786\pi$
$283$	6.80440	−	11.7856i	0.404479	−	0.700579i	0.994261	+	0.106984i	$0.0341194\pi$
$284$	−10.7177	+	18.5635i	−0.635976	+	1.10154i
$285$		0			0
$286$	−4.83384	−	8.37246i	−0.285831	−	0.495074i
$287$	2.79707			0.165106
$288$		0			0
$289$	−16.7045			−0.982615
$290$	32.2949	+	55.9363i	1.89642	+	3.28470i
$291$		0			0
$292$	−13.0552	+	22.6122i	−0.763995	+	1.32328i
$293$	5.41692	−	9.38238i	0.316460	−	0.548125i	−0.663287	−	0.748365i	$-0.730839\pi$
$293$	5.41692	−	9.38238i	0.316460	−	0.548125i	0.979747	+	0.200241i	$0.0641724\pi$
$294$		0			0
$295$	27.3133	+	47.3079i	1.59024	+	2.75437i
$296$	−6.45103			−0.374958
$297$		0			0
$298$	3.23238			0.187247
$299$	22.6172	+	39.1741i	1.30799	+	2.26550i
$300$		0			0
$301$	−4.91692	+	8.51636i	−0.283407	+	0.490875i
$302$	−6.69240	+	11.5916i	−0.385105	+	0.667021i
$303$		0			0
$304$	−1.46475	−	2.53703i	−0.0840094	−	0.145509i
$305$	34.6172			1.98217
$306$		0			0
$307$	18.0735			1.03151			0.515756	−	0.856736i	$-0.327511\pi$
$307$	18.0735			1.03151			0.515756	+	0.856736i	$0.327511\pi$
$308$	−0.971086	−	1.68197i	−0.0553327	−	0.0958391i
$309$		0			0
$310$	−8.03677	+	13.9201i	−0.456458	+	0.790609i
$311$	2.14510	−	3.71543i	0.121638	−	0.210683i	−0.798776	−	0.601629i	$-0.794519\pi$
$311$	2.14510	−	3.71543i	0.121638	−	0.210683i	0.920414	+	0.390946i	$0.127852\pi$
$312$		0			0
$313$	−2.77868	−	4.81282i	−0.157060	−	0.272037i	0.776747	−	0.629813i	$-0.216868\pi$
$313$	−2.77868	−	4.81282i	−0.157060	−	0.272037i	−0.933807	+	0.357776i	$0.883535\pi$
$314$	−44.0093			−2.48359
$315$		0			0
$316$	26.6382			1.49852
$317$	−13.7650	−	23.8416i	−0.773117	−	1.33908i	−0.935847	−	0.352407i	$-0.885363\pi$
$317$	−13.7650	−	23.8416i	−0.773117	−	1.33908i	0.162730	−	0.986671i	$-0.447970\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$	−22.2370	+	38.5157i	−1.24309	+	2.15309i
$321$		0			0
$322$	8.03677	+	13.9201i	0.447872	+	0.775737i
$323$	−0.653958			−0.0363872
$324$		0			0
$325$	−54.5530			−3.02605
$326$	−13.1277	−	22.7379i	−0.727077	−	1.25933i
$327$		0			0
$328$	1.80440	−	3.12531i	0.0996311	−	0.172566i
$329$	−2.14510	+	3.71543i	−0.118263	+	0.204838i
$330$		0			0
$331$	−8.07355	−	13.9838i	−0.443762	−	0.768619i	0.554203	−	0.832382i	$-0.313023\pi$
$331$	−8.07355	−	13.9838i	−0.443762	−	0.768619i	−0.997965	+	0.0637629i	$0.979690\pi$
$332$	−7.27648			−0.399349
$333$		0			0
$334$	−31.7412			−1.73680
$335$	19.1819	+	33.2240i	1.04802	+	1.81522i
$336$		0			0
$337$	0.555160	−	0.961566i	0.0302415	−	0.0523798i	−0.850509	−	0.525961i	$-0.823706\pi$
$337$	0.555160	−	0.961566i	0.0302415	−	0.0523798i	0.880750	+	0.473581i	$0.157039\pi$
$338$	25.1434	−	43.5497i	1.36762	−	2.36879i
$339$		0			0
$340$	2.64930	+	4.58872i	0.143678	+	0.248858i
$341$	1.49314			0.0808579
$342$		0			0
$343$	1.00000			0.0539949
$344$	6.34384	+	10.9879i	0.342037	+	0.592425i
$345$		0			0
$346$	−1.95217	+	3.38125i	−0.104949	+	0.181777i
$347$	−14.4101	+	24.9590i	−0.773572	+	1.33987i	0.162021	+	0.986787i	$0.448199\pi$
$347$	−14.4101	+	24.9590i	−0.773572	+	1.33987i	−0.935593	+	0.353079i	$0.885135\pi$
$348$		0			0
$349$	11.6382	+	20.1580i	0.622981	+	1.07903i	0.988928	+	0.148398i	$0.0474118\pi$
$349$	11.6382	+	20.1580i	0.622981	+	1.07903i	−0.365947	+	0.930636i	$0.619255\pi$
$350$	−19.3848			−1.03616
$351$		0			0
$352$	5.82651			0.310554
$353$	1.18188	+	2.04707i	0.0629049	+	0.108955i	0.895763	−	0.444532i	$-0.146630\pi$
$353$	1.18188	+	2.04707i	0.0629049	+	0.108955i	−0.832858	+	0.553487i	$0.813297\pi$
$354$		0			0
$355$	15.4353	−	26.7347i	0.819221	−	1.41893i
$356$	8.51152	−	14.7424i	0.451110	−	0.781345i
$357$		0			0
$358$	−1.16616	−	2.01984i	−0.0616333	−	0.106752i
$359$	3.32698			0.175591			0.0877956	−	0.996139i	$-0.472018\pi$
$359$	3.32698			0.175591			0.0877956	+	0.996139i	$0.472018\pi$
$360$		0			0
$361$	−17.5530			−0.923840
$362$	2.14510	+	3.71543i	0.112744	+	0.195278i
$363$		0			0
$364$	7.85223	−	13.6005i	0.411569	−	0.712858i
$365$	18.8017	−	32.5655i	0.984127	−	1.70456i
$366$		0			0
$367$	−2.83384	−	4.90836i	−0.147925	−	0.256214i	0.782535	−	0.622606i	$-0.213926\pi$
$367$	−2.83384	−	4.90836i	−0.147925	−	0.256214i	−0.930461	+	0.366392i	$0.880593\pi$
$368$	−18.2481			−0.951248
$369$		0			0
$370$	40.1839			2.08906
$371$	1.22818	+	2.12727i	0.0637640	+	0.110442i
$372$		0			0
$373$	−11.7581	+	20.3656i	−0.608811	+	1.05449i	0.382626	+	0.923903i	$0.375020\pi$
$373$	−11.7581	+	20.3656i	−0.608811	+	1.05449i	−0.991437	+	0.130588i	$0.958313\pi$
$374$	0.435308	−	0.753976i	0.0225092	−	0.0389872i
$375$		0			0
$376$	2.76762	+	4.79366i	0.142729	+	0.247214i
$377$	48.5162			2.49871
$378$		0			0
$379$	36.7927			1.88991			0.944956	−	0.327197i	$-0.106104\pi$
$379$	36.7927			1.88991			0.944956	+	0.327197i	$0.106104\pi$
$380$	−5.86223	−	10.1537i	−0.300726	−	0.520872i
$381$		0			0
$382$	−11.6051	+	20.1007i	−0.593770	+	1.02844i
$383$	13.4931	−	23.3708i	0.689467	−	1.19419i	−0.282543	−	0.959255i	$-0.591178\pi$
$383$	13.4931	−	23.3708i	0.689467	−	1.19419i	0.972010	−	0.234937i	$-0.0754885\pi$
$384$		0			0
$385$	1.39853	+	2.42233i	0.0712759	+	0.123454i
$386$	−20.6593			−1.05153
$387$		0			0
$388$	13.5352			0.687148
$389$	−4.49314	−	7.78234i	−0.227811	−	0.394580i	0.729348	−	0.684143i	$-0.239824\pi$
$389$	−4.49314	−	7.78234i	−0.227811	−	0.394580i	−0.957159	+	0.289563i	$0.906490\pi$
$390$		0			0
$391$	−2.03677	+	3.52780i	−0.103004	+	0.178408i
$392$	0.645103	−	1.11735i	0.0325826	−	0.0564347i
$393$		0			0
$394$	−20.8927	−	36.1872i	−1.05256	−	1.82308i
$395$	−38.3638			−1.93029
$396$		0			0
$397$	28.5015			1.43045			0.715225	−	0.698894i	$-0.246324\pi$
$397$	28.5015			1.43045			0.715225	+	0.698894i	$0.246324\pi$
$398$	−18.0946	−	31.3408i	−0.907000	−	1.57097i
$399$		0			0
$400$	11.0037	−	19.0589i	0.550183	−	0.952945i
$401$	3.75343	−	6.50113i	0.187437	−	0.324651i	−0.756958	−	0.653464i	$-0.773315\pi$
$401$	3.75343	−	6.50113i	0.187437	−	0.324651i	0.944395	+	0.328813i	$0.106648\pi$
$402$		0			0
$403$	6.03677	+	10.4560i	0.300713	+	0.520850i
$404$	11.7245			0.583313
$405$		0			0
$406$	17.2397			0.855592
$407$	−1.86642	−	3.23274i	−0.0925150	−	0.160241i
$408$		0			0
$409$	13.6199	−	23.5903i	0.673458	−	1.16646i	−0.303459	−	0.952845i	$-0.598141\pi$
$409$	13.6199	−	23.5903i	0.673458	−	1.16646i	0.976917	−	0.213619i	$-0.0685253\pi$
$410$	−11.2397	+	19.4677i	−0.555089	+	0.961443i
$411$		0			0
$412$	14.1398	+	24.4908i	0.696616	+	1.20657i
$413$	14.5804			0.717455
$414$		0			0
$415$	10.4794			0.514414
$416$	23.5567	+	40.8014i	1.15496	+	2.00045i
$417$		0			0
$418$	−0.963226	+	1.66836i	−0.0471129	+	0.0816020i
$419$	9.84117	−	17.0454i	0.480773	−	0.832723i	−0.518984	−	0.854784i	$-0.673690\pi$
$419$	9.84117	−	17.0454i	0.480773	−	0.832723i	0.999757	+	0.0220613i	$0.00702291\pi$
$420$		0			0
$421$	−10.7397	−	18.6017i	−0.523421	−	0.906592i	−0.999628	−	0.0272590i	$-0.991322\pi$
$421$	−10.7397	−	18.6017i	−0.523421	−	0.906592i	0.476207	−	0.879333i	$-0.342011\pi$
$422$	−8.22399			−0.400337
$423$		0			0
$424$	3.16921			0.153911
$425$	−2.45636	−	4.25455i	−0.119151	−	0.206376i
$426$		0			0
$427$	4.61985	−	8.00182i	0.223570	−	0.387235i
$428$	−4.32751	+	7.49547i	−0.209178	+	0.362307i
$429$		0			0
$430$	−39.5162	−	68.4440i	−1.90564	−	3.30066i
$431$	2.17455			0.104744			0.0523722	−	0.998628i	$-0.483322\pi$
$431$	2.17455			0.104744			0.0523722	+	0.998628i	$0.483322\pi$
$432$		0			0
$433$	35.3133			1.69705			0.848523	−	0.529158i	$-0.177492\pi$
$433$	35.3133			1.69705			0.848523	+	0.529158i	$0.177492\pi$
$434$	2.14510	+	3.71543i	0.102968	+	0.178346i
$435$		0			0
$436$	7.32431	−	12.6861i	0.350771	−	0.607553i
$437$	4.50686	−	7.80612i	0.215593	−	0.373417i
$438$		0			0
$439$	9.60147	+	16.6302i	0.458253	+	0.793717i	0.998869	−	0.0475522i	$-0.0151421\pi$
$439$	9.60147	+	16.6302i	0.458253	+	0.793717i	−0.540616	+	0.841270i	$0.681809\pi$
$440$	3.60879			0.172042
$441$		0			0
$442$	7.03983			0.334851
$443$	2.65929	+	4.60603i	0.126347	+	0.218839i	0.922259	−	0.386573i	$-0.126341\pi$
$443$	2.65929	+	4.60603i	0.126347	+	0.218839i	−0.795912	+	0.605413i	$0.793008\pi$
$444$		0			0
$445$	−12.2581	+	21.2316i	−0.581089	+	1.00648i
$446$	13.3848	−	23.1832i	0.633789	−	1.09775i
$447$		0			0
$448$	5.93531	+	10.2803i	0.280417	+	0.485696i
$449$	7.36909			0.347769			0.173884	−	0.984766i	$-0.444368\pi$
$449$	7.36909			0.347769			0.173884	+	0.984766i	$0.444368\pi$
$450$		0			0
$451$	2.08820			0.0983296
$452$	3.37428	+	5.84442i	0.158713	+	0.274899i
$453$		0			0
$454$	23.4426	−	40.6038i	1.10022	−	1.90563i
$455$	−11.3086	+	19.5871i	−0.530155	+	0.918255i
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$	−41.2711			−1.92847
$459$		0			0
$460$	−73.0324			−3.40515
$461$	−15.2324	−	26.3833i	−0.709443	−	1.22879i	−0.965064	−	0.262014i	$-0.915613\pi$
$461$	−15.2324	−	26.3833i	−0.709443	−	1.22879i	0.255622	−	0.966777i	$-0.417720\pi$
$462$		0			0
$463$	13.7508	−	23.8170i	0.639052	−	1.10687i	−0.346589	−	0.938017i	$-0.612660\pi$
$463$	13.7508	−	23.8170i	0.639052	−	1.10687i	0.985641	−	0.168854i	$-0.0540066\pi$
$464$	−9.78601	+	16.9499i	−0.454304	+	0.786878i
$465$		0			0
$466$	12.2875	+	21.2826i	0.569209	+	0.985899i
$467$	39.1755			1.81282			0.906412	−	0.422394i	$-0.138810\pi$
$467$	39.1755			1.81282			0.906412	+	0.422394i	$0.138810\pi$
$468$		0			0
$469$	10.2397			0.472826
$470$	−17.2397	−	29.8600i	−0.795208	−	1.37734i
$471$		0			0
$472$	9.40586	−	16.2914i	0.432940	−	0.749874i
$473$	−3.67082	+	6.35804i	−0.168784	+	0.292343i
$474$		0			0
$475$	5.43531	+	9.41423i	0.249389	+	0.431954i
$476$	1.41425			0.0648222
$477$		0			0
$478$	−8.93684			−0.408761
$479$	−10.4931	−	18.1746i	−0.479444	−	0.830421i	0.520278	−	0.853997i	$-0.325828\pi$
$479$	−10.4931	−	18.1746i	−0.479444	−	0.830421i	−0.999722	+	0.0235760i	$0.992495\pi$
$480$		0			0
$481$	15.0919	−	26.1400i	0.688133	−	1.19188i
$482$	14.2003	−	24.5956i	0.646804	−	1.12030i
$483$		0			0
$484$	13.5831	+	23.5266i	0.617413	+	1.06939i
$485$	−19.4931			−0.885138
$486$		0			0
$487$	28.6456			1.29805			0.649027	−	0.760765i	$-0.275176\pi$
$487$	28.6456			1.29805			0.649027	+	0.760765i	$0.275176\pi$
$488$	−5.96056	−	10.3240i	−0.269822	−	0.467345i
$489$		0			0
$490$	−4.01839	+	6.96005i	−0.181532	+	0.314423i
$491$	−16.0735	+	27.8402i	−0.725389	+	1.25641i	0.233425	+	0.972375i	$0.425007\pi$
$491$	−16.0735	+	27.8402i	−0.725389	+	1.25641i	−0.958814	+	0.284036i	$0.908327\pi$
$492$		0			0
$493$	2.18454	+	3.78374i	0.0983869	+	0.170411i
$494$	−15.5774			−0.700858
$495$		0			0
$496$	−4.87062			−0.218697
$497$	−4.11985	−	7.13579i	−0.184801	−	0.320084i
$498$		0			0
$499$	9.63091	−	16.6812i	0.431139	−	0.746754i	−0.565833	−	0.824520i	$-0.691445\pi$
$499$	9.63091	−	16.6812i	0.431139	−	0.746754i	0.996972	+	0.0777656i	$0.0247786\pi$
$500$	19.6723	−	34.0735i	0.879774	−	1.52381i
$501$		0			0
$502$	13.8044	+	23.9099i	0.616120	+	1.06715i
$503$	−36.2206			−1.61500			−0.807499	−	0.589869i	$-0.799180\pi$
$503$	−36.2206			−1.61500			−0.807499	+	0.589869i	$0.799180\pi$
$504$		0			0
$505$	−16.8853			−0.751385
$506$	6.00000	+	10.3923i	0.266733	+	0.461994i
$507$		0			0
$508$	−12.7912	+	22.1550i	−0.567518	+	0.982970i
$509$	4.49314	−	7.78234i	0.199155	−	0.344946i	−0.749100	−	0.662457i	$-0.769514\pi$
$509$	4.49314	−	7.78234i	0.199155	−	0.344946i	0.948255	+	0.317511i	$0.102847\pi$
$510$		0			0
$511$	−5.01839	−	8.69210i	−0.222000	−	0.384516i
$512$	−25.2902			−1.11768
$513$		0			0
$514$	0.295541			0.0130358
$515$	−20.3638	−	35.2711i	−0.897334	−	1.55423i
$516$		0			0
$517$	−1.60147	+	2.77382i	−0.0704324	+	0.121992i
$518$	5.36276	−	9.28857i	0.235626	−	0.408116i
$519$		0			0
$520$	14.5904	+	25.2713i	0.639832	+	1.10822i
$521$	−17.5667			−0.769610			−0.384805	−	0.922998i	$-0.625731\pi$
$521$	−17.5667			−0.769610			−0.384805	+	0.922998i	$0.625731\pi$
$522$		0			0
$523$	−25.6088			−1.11979			−0.559897	−	0.828562i	$-0.689159\pi$
$523$	−25.6088			−1.11979			−0.559897	+	0.828562i	$0.689159\pi$
$524$	6.99466	+	12.1151i	0.305563	+	0.529251i
$525$		0			0
$526$	−12.0699	+	20.9057i	−0.526272	+	0.911530i
$527$	−0.543637	+	0.941607i	−0.0236812	+	0.0410171i
$528$		0			0
$529$	−16.5735	−	28.7062i	−0.720589	−	1.24810i
$530$	−19.7412			−0.857504
$531$		0			0
$532$	−3.12938			−0.135676
$533$	8.44264	+	14.6231i	0.365691	+	0.633396i
$534$		0			0
$535$	6.23238	−	10.7948i	0.269449	−	0.466700i
$536$	6.60566	−	11.4413i	0.285321	−	0.494191i
$537$		0			0
$538$	−5.85223	−	10.1364i	−0.252308	−	0.437009i
$539$	0.746568			0.0321570
$540$		0			0
$541$	−41.0735			−1.76589			−0.882945	−	0.469477i	$-0.844443\pi$
$541$	−41.0735			−1.76589			−0.882945	+	0.469477i	$0.844443\pi$
$542$	−3.35642	−	5.81350i	−0.144171	−	0.249711i
$543$		0			0
$544$	−2.12138	+	3.67434i	−0.0909534	+	0.157536i
$545$	−10.5483	+	18.2702i	−0.451839	+	0.782609i
$546$		0			0
$547$	18.3228	+	31.7360i	0.783426	+	1.35693i	0.929935	+	0.367724i	$0.119863\pi$
$547$	18.3228	+	31.7360i	0.783426	+	1.35693i	−0.146509	+	0.989209i	$0.546804\pi$
$548$	−27.2975			−1.16609
$549$		0			0
$550$	−14.4721			−0.617092
$551$	−4.83384	−	8.37246i	−0.205929	−	0.356679i
$552$		0			0
$553$	−5.11985	+	8.86784i	−0.217718	+	0.377099i
$554$	−9.25710	+	16.0338i	−0.393296	+	0.681209i
$555$		0			0
$556$	8.84117	+	15.3134i	0.374949	+	0.649431i
$557$	13.9127			0.589501			0.294751	−	0.955574i	$-0.404763\pi$
$557$	13.9127			0.589501			0.294751	+	0.955574i	$0.404763\pi$
$558$		0			0
$559$	−59.3647			−2.51086
$560$	−4.56202	−	7.90166i	−0.192781	−	0.333906i
$561$		0			0
$562$	14.0221	−	24.2869i	0.591485	−	1.02448i
$563$	0.340706	−	0.590120i	0.0143590	−	0.0248706i	−0.858757	−	0.512384i	$-0.828763\pi$
$563$	0.340706	−	0.590120i	0.0143590	−	0.0248706i	0.873116	+	0.487513i	$0.162096\pi$
$564$		0			0
$565$	−4.85956	−	8.41700i	−0.204443	−	0.354106i
$566$	29.1923			1.22704
$567$		0			0
$568$	−10.6309			−0.446063
$569$	17.0299	+	29.4967i	0.713931	+	1.23656i	0.963370	+	0.268174i	$0.0864203\pi$
$569$	17.0299	+	29.4967i	0.713931	+	1.23656i	−0.249439	+	0.968390i	$0.580246\pi$
$570$		0			0
$571$	−8.83384	+	15.3007i	−0.369685	+	0.640313i	−0.989516	−	0.144422i	$-0.953868\pi$
$571$	−8.83384	+	15.3007i	−0.369685	+	0.640313i	0.619831	+	0.784735i	$0.287201\pi$
$572$	5.86223	−	10.1537i	0.245112	−	0.424546i
$573$		0			0
$574$	3.00000	+	5.19615i	0.125218	+	0.216883i
$575$	67.7138			2.82386
$576$		0			0
$577$	−12.5015			−0.520445			−0.260223	−	0.965549i	$-0.583796\pi$
$577$	−12.5015			−0.520445			−0.260223	+	0.965549i	$0.583796\pi$
$578$	−17.9164	−	31.0321i	−0.745224	−	1.29077i
$579$		0			0
$580$	−39.1655	+	67.8366i	−1.62626	+	2.81676i
$581$	1.39853	−	2.42233i	0.0580210	−	0.100495i
$582$		0			0
$583$	0.916921	+	1.58815i	0.0379750	+	0.0657746i
$584$	−12.9495			−0.535854
$585$		0			0
$586$	23.2397			0.960023
$587$	22.6823	+	39.2870i	0.936200	+	1.62155i	0.772479	+	0.635040i	$0.219016\pi$
$587$	22.6823	+	39.2870i	0.936200	+	1.62155i	0.163721	+	0.986507i	$0.447650\pi$
$588$		0			0
$589$	1.20293	−	2.08354i	0.0495659	−	0.0858507i
$590$	−58.5897	+	101.480i	−2.41210	+	4.17788i
$591$		0			0
$592$	6.08827	+	10.5452i	0.250226	+	0.433405i
$593$	9.93577			0.408013			0.204007	−	0.978970i	$-0.434604\pi$
$593$	9.93577			0.408013			0.204007	+	0.978970i	$0.434604\pi$
$594$		0			0
$595$	−2.03677			−0.0834996
$596$	1.96003	+	3.39487i	0.0802858	+	0.139059i
$597$		0			0
$598$	−48.5162	+	84.0325i	−1.98397	+	3.43634i
$599$	−9.17035	+	15.8835i	−0.374690	+	0.648983i	−0.990281	−	0.139084i	$-0.955584\pi$
$599$	−9.17035	+	15.8835i	−0.374690	+	0.648983i	0.615590	+	0.788066i	$0.288918\pi$
$600$		0			0
$601$	−1.17722	−	2.03900i	−0.0480197	−	0.0831725i	0.841017	−	0.541009i	$-0.181958\pi$
$601$	−1.17722	−	2.03900i	−0.0480197	−	0.0831725i	−0.889036	+	0.457837i	$0.848624\pi$
$602$	−21.0946			−0.859752
$603$		0			0
$604$	−16.2324			−0.660486
$605$	−19.5620	−	33.8824i	−0.795309	−	1.37752i
$606$		0			0
$607$	20.8412	−	36.0980i	0.845917	−	1.46517i	−0.0389055	−	0.999243i	$-0.512387\pi$
$607$	20.8412	−	36.0980i	0.845917	−	1.46517i	0.884822	−	0.465928i	$-0.154280\pi$
$608$	4.69408	−	8.13038i	0.190370	−	0.329730i
$609$		0			0
$610$	37.1287	+	64.3088i	1.50330	+	2.60379i
$611$	−25.8990			−1.04776
$612$		0			0
$613$	21.5897			0.872001			0.436000	−	0.899946i	$-0.356395\pi$
$613$	21.5897			0.872001			0.436000	+	0.899946i	$0.356395\pi$
$614$	19.3848	+	33.5755i	0.782307	+	1.35500i
$615$		0			0
$616$	0.481613	−	0.834179i	0.0194047	−	0.0336100i
$617$	−0.409593	+	0.709437i	−0.0164896	+	0.0285608i	−0.874152	−	0.485652i	$-0.838582\pi$
$617$	−0.409593	+	0.709437i	−0.0164896	+	0.0285608i	0.857663	+	0.514212i	$0.171916\pi$
$618$		0			0
$619$	−15.6750	−	27.1499i	−0.630032	−	1.09125i	−0.987545	−	0.157339i	$-0.949708\pi$
$619$	−15.6750	−	27.1499i	−0.630032	−	1.09125i	0.357513	−	0.933908i	$-0.383625\pi$
$620$	−19.4931			−0.782863
$621$		0			0
$622$	9.20293			0.369004
$623$	3.27182	+	5.66696i	0.131083	+	0.227042i
$624$		0			0
$625$	−5.73970	+	9.94146i	−0.229588	+	0.397658i
$626$	5.96056	−	10.3240i	0.238232	−	0.412630i
$627$		0			0
$628$	−26.6861	−	46.2216i	−1.06489	−	1.84444i
$629$	2.71819			0.108381
$630$		0			0
$631$	−1.66769			−0.0663895			−0.0331947	−	0.999449i	$-0.510568\pi$
$631$	−1.66769			−0.0663895			−0.0331947	+	0.999449i	$0.510568\pi$
$632$	6.60566	+	11.4413i	0.262759	+	0.455112i
$633$		0			0
$634$	29.5272	−	51.1427i	1.17268	−	2.03114i
$635$	18.4216	−	31.9071i	0.731038	−	1.26620i
$636$		0			0
$637$	3.01839	+	5.22800i	0.119593	+	0.207141i
$638$	12.8706			0.509553
$639$		0			0
$640$	−36.9220			−1.45947
$641$	−7.62405	−	13.2052i	−0.301132	−	0.521576i	0.675261	−	0.737579i	$-0.264031\pi$
$641$	−7.62405	−	13.2052i	−0.301132	−	0.521576i	−0.976393	+	0.216003i	$0.930698\pi$
$642$		0			0
$643$	11.3133	−	19.5951i	0.446151	−	0.772756i	−0.551981	−	0.833857i	$-0.686128\pi$
$643$	11.3133	−	19.5951i	0.446151	−	0.772756i	0.998132	+	0.0611006i	$0.0194611\pi$
$644$	−9.74657	+	16.8816i	−0.384069	+	0.665226i
$645$		0			0
$646$	−0.701404	−	1.21487i	−0.0275964	−	0.0477983i
$647$	42.0040			1.65135			0.825673	−	0.564148i	$-0.190795\pi$
$647$	42.0040			1.65135			0.825673	+	0.564148i	$0.190795\pi$
$648$		0			0
$649$	10.8853			0.427284
$650$	−58.5108	−	101.344i	−2.29498	−	3.97503i
$651$		0			0
$652$	15.9206	−	27.5753i	0.623498	−	1.07993i
$653$	11.1777	−	19.3603i	0.437416	−	0.757628i	−0.560073	−	0.828443i	$-0.689227\pi$
$653$	11.1777	−	19.3603i	0.437416	−	0.757628i	0.997489	+	0.0708158i	$0.0225602\pi$
$654$		0			0
$655$	−10.0735	−	17.4479i	−0.393606	−	0.681746i
$656$	−6.81172			−0.265953
$657$		0			0
$658$	−9.20293			−0.358768
$659$	15.7140	+	27.2174i	0.612130	+	1.06024i	0.990881	+	0.134742i	$0.0430205\pi$
$659$	15.7140	+	27.2174i	0.612130	+	1.06024i	−0.378751	+	0.925499i	$0.623646\pi$
$660$		0			0
$661$	12.2213	−	21.1679i	0.475354	−	0.823338i	−0.524247	−	0.851566i	$-0.675653\pi$
$661$	12.2213	−	21.1679i	0.475354	−	0.823338i	0.999601	+	0.0282285i	$0.00898660\pi$
$662$	17.3186	−	29.9967i	0.673106	−	1.16585i
$663$		0			0
$664$	−1.80440	−	3.12531i	−0.0700242	−	0.121285i
$665$	4.50686			0.174769
$666$		0			0
$667$	−60.2206			−2.33175
$668$	−19.2470	−	33.3368i	−0.744690	−	1.28984i
$669$		0			0
$670$	−41.1471	+	71.2689i	−1.58965	+	2.75336i
$671$	3.44904	−	5.97390i	0.133149	−	0.230620i
$672$		0			0
$673$	−19.7397	−	34.1902i	−0.760910	−	1.31793i	−0.942382	−	0.334538i	$-0.891420\pi$
$673$	−19.7397	−	34.1902i	−0.760910	−	1.31793i	0.181472	−	0.983396i	$-0.441914\pi$
$674$	2.38175			0.0917417
$675$		0			0
$676$	60.9852			2.34558
$677$	−21.1892	−	36.7008i	−0.814367	−	1.41053i	−0.909781	−	0.415088i	$-0.863751\pi$
$677$	−21.1892	−	36.7008i	−0.814367	−	1.41053i	0.0954141	−	0.995438i	$-0.469582\pi$
$678$		0			0
$679$	−2.60147	+	4.50587i	−0.0998351	+	0.172919i
$680$	−1.31393	+	2.27579i	−0.0503868	+	0.0872726i
$681$		0			0
$682$	1.60147	+	2.77382i	0.0613233	+	0.106215i
$683$	22.4143			0.857658			0.428829	−	0.903386i	$-0.358926\pi$
$683$	22.4143			0.857658			0.428829	+	0.903386i	$0.358926\pi$
$684$		0			0
$685$	39.3133			1.50208
$686$	1.07255	+	1.85771i	0.0409502	+	0.0709278i
$687$		0			0
$688$	11.9742	−	20.7400i	0.456513	−	0.790703i
$689$	−7.41425	+	12.8419i	−0.282461	+	0.489236i
$690$		0			0
$691$	−6.23970	−	10.8075i	−0.237370	−	0.411136i	0.722589	−	0.691278i	$-0.242952\pi$
$691$	−6.23970	−	10.8075i	−0.237370	−	0.411136i	−0.959959	+	0.280142i	$0.909619\pi$
$692$	−4.73497			−0.179996
$693$		0			0
$694$	−61.8221			−2.34674
$695$	−12.7328	−	22.0539i	−0.482984	−	0.836553i
$696$		0			0
$697$	−0.760295	+	1.31687i	−0.0287982	+	0.0498800i
$698$	−24.9652	+	43.2410i	−0.944947	+	1.63670i
$699$		0			0
$700$	−11.7544	−	20.3593i	−0.444276	−	0.769508i
$701$	−15.0000			−0.566542			−0.283271	−	0.959040i	$-0.591420\pi$
$701$	−15.0000			−0.566542			−0.283271	+	0.959040i	$0.591420\pi$
$702$		0			0
$703$	−6.01466			−0.226847
$704$	4.43111	+	7.67491i	0.167004	+	0.289259i
$705$		0			0
$706$	−2.53525	+	4.39118i	−0.0954152	+	0.165264i
$707$	−2.25343	+	3.90306i	−0.0847490	+	0.146790i
$708$		0			0
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	0.995228	+	0.0975728i	$0.0311079\pi$
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	−0.413114	+	0.910679i	$0.635559\pi$
$710$	66.2206			2.48522
$711$		0			0
$712$	8.44264			0.316401
$713$	−7.49314	−	12.9785i	−0.280620	−	0.486048i
$714$		0			0
$715$	−8.44264	+	14.6231i	−0.315737	+	0.546872i
$716$	1.41425	−	2.44956i	0.0528531	−	0.0915443i
$717$		0			0
$718$	3.56836	+	6.18057i	0.133170	+	0.230657i
$719$	−6.65396			−0.248151			−0.124075	−	0.992273i	$-0.539596\pi$
$719$	−6.65396			−0.248151			−0.124075	+	0.992273i	$0.539596\pi$
$720$		0			0
$721$	−10.8706			−0.404843
$722$	−18.8264	−	32.6084i	−0.700648	−	1.21356i
$723$		0			0
$724$	−2.60147	+	4.50587i	−0.0966827	+	0.167459i
$725$	36.3133	−	62.8964i	1.34864	−	2.33591i
$726$		0			0
$727$	−18.4721	−	31.9946i	−0.685092	−	1.18661i	−0.973408	−	0.229078i	$-0.926429\pi$
$727$	−18.4721	−	31.9946i	−0.685092	−	1.18661i	0.288316	−	0.957535i	$-0.406905\pi$
$728$	7.78868			0.288668
$729$		0			0
$730$	80.6633			2.98548
$731$	−2.67302	−	4.62981i	−0.0988653	−	0.171240i
$732$		0			0
$733$	19.0662	−	33.0237i	0.704227	−	1.21976i	−0.262743	−	0.964866i	$-0.584627\pi$
$733$	19.0662	−	33.0237i	0.704227	−	1.21976i	0.966970	−	0.254891i	$-0.0820396\pi$
$734$	6.07888	−	10.5289i	0.224376	−	0.388630i
$735$		0			0
$736$	−29.2397	−	50.6447i	−1.07779	−	1.86679i
$737$	7.64464			0.281594
$738$		0			0
$739$	−6.23970			−0.229531			−0.114766	−	0.993393i	$-0.536612\pi$
$739$	−6.23970			−0.229531			−0.114766	+	0.993393i	$0.536612\pi$
$740$	24.3664	+	42.2039i	0.895727	+	1.55145i
$741$		0			0
$742$	−2.63458	+	4.56322i	−0.0967183	+	0.167521i
$743$	5.54783	−	9.60913i	0.203530	−	0.352525i	−0.746133	−	0.665797i	$-0.768092\pi$
$743$	5.54783	−	9.60913i	0.203530	−	0.352525i	0.949663	+	0.313272i	$0.101425\pi$
$744$		0			0
$745$	−2.82278	−	4.88920i	−0.103419	−	0.179127i
$746$	−50.4446			−1.84691
$747$		0			0
$748$	1.05584			0.0386052
$749$	−1.66349	−	2.88125i	−0.0607826	−	0.105279i
$750$		0			0
$751$	−18.1934	+	31.5119i	−0.663887	+	1.14989i	0.315699	+	0.948859i	$0.397761\pi$
$751$	−18.1934	+	31.5119i	−0.663887	+	1.14989i	−0.979586	+	0.201026i	$0.935572\pi$
$752$	5.22399	−	9.04821i	0.190499	−	0.329954i
$753$		0			0
$754$	52.0361	+	90.1292i	1.89504	+	3.28231i
$755$	23.3775			0.850794
$756$		0			0
$757$	−4.40586			−0.160134			−0.0800669	−	0.996789i	$-0.525513\pi$
$757$	−4.40586			−0.160134			−0.0800669	+	0.996789i	$0.525513\pi$
$758$	39.4620	+	68.3502i	1.43333	+	2.48259i
$759$		0			0
$760$	2.90739	−	5.03575i	0.105462	−	0.182666i
$761$	−23.6061	+	40.8870i	−0.855721	+	1.48215i	0.0202528	+	0.999795i	$0.493553\pi$
$761$	−23.6061	+	40.8870i	−0.855721	+	1.48215i	−0.875974	+	0.482358i	$0.839780\pi$
$762$		0			0
$763$	2.81546	+	4.87651i	0.101926	+	0.176542i
$764$	−28.1482			−1.01836
$765$		0			0
$766$	57.8883			2.09159
$767$	44.0093	+	76.2264i	1.58908	+	2.75237i
$768$		0			0
$769$	−10.3801	+	17.9789i	−0.374318	+	0.648337i	−0.990225	−	0.139482i	$-0.955456\pi$
$769$	−10.3801	+	17.9789i	−0.374318	+	0.648337i	0.615907	+	0.787819i	$0.288790\pi$
$770$	−3.00000	+	5.19615i	−0.108112	+	0.187256i
$771$		0			0
$772$	−12.5272	−	21.6978i	−0.450865	−	0.780922i
$773$	−0.976953			−0.0351386			−0.0175693	−	0.999846i	$-0.505593\pi$
$773$	−0.976953			−0.0351386			−0.0175693	+	0.999846i	$0.505593\pi$
$774$		0			0
$775$	18.0735			0.649221
$776$	3.35642	+	5.81350i	0.120489	+	0.208692i
$777$		0			0
$778$	9.63824	−	16.6939i	0.345548	−	0.598506i
$779$	1.68234	−	2.91390i	0.0602761	−	0.104401i
$780$		0			0
$781$	−3.07575	−	5.32736i	−0.110059	−	0.190628i
$782$	−8.73818			−0.312477
$783$		0			0
$784$	−2.43531			−0.0869753
$785$	38.4326	+	66.5673i	1.37172	+	2.37589i
$786$		0			0
$787$	−1.43531	+	2.48603i	−0.0511632	+	0.0886173i	−0.890473	−	0.455037i	$-0.849626\pi$
$787$	−1.43531	+	2.48603i	−0.0511632	+	0.0886173i	0.839310	+	0.543654i	$0.182960\pi$
$788$	25.3375	−	43.8858i	0.902611	−	1.56337i
$789$		0			0
$790$	−41.1471	−	71.2689i	−1.46395	−	2.53563i
$791$	−2.59414			−0.0922369
$792$		0			0
$793$	55.7780			1.98074
$794$	30.5694	+	52.9477i	1.08487	+	1.87904i
$795$		0			0
$796$	21.9442	−	38.0084i	0.777790	−	1.34717i
$797$	0.612525	−	1.06092i	0.0216967	−	0.0375798i	−0.854973	−	0.518672i	$-0.826427\pi$
$797$	0.612525	−	1.06092i	0.0216967	−	0.0375798i	0.876670	+	0.481092i	$0.159760\pi$
$798$		0			0
$799$	−1.16616	−	2.01984i	−0.0412557	−	0.0714569i
$800$	70.5266			2.49349
$801$		0			0
$802$	16.1030			0.568616
$803$	−3.74657	−	6.48925i	−0.132214	−	0.229001i
$804$		0			0
$805$	14.0368	−	24.3124i	0.494731	−	0.856900i
$806$	−12.9495	+	22.4292i	−0.456127	+	0.790035i
$807$		0			0
$808$	2.90739	+	5.03575i	0.102282	+	0.177157i
$809$	15.4333			0.542607			0.271303	−	0.962494i	$-0.412545\pi$
$809$	15.4333			0.542607			0.271303	+	0.962494i	$0.412545\pi$
$810$		0			0
$811$	−2.47941			−0.0870638			−0.0435319	−	0.999052i	$-0.513861\pi$
$811$	−2.47941			−0.0870638			−0.0435319	+	0.999052i	$0.513861\pi$
$812$	10.4537	+	18.1063i	0.366853	+	0.635408i
$813$		0			0
$814$	4.00366	−	6.93455i	0.140328	−	0.243056i
$815$	−22.9284	+	39.7132i	−0.803148	+	1.39109i
$816$		0			0
$817$	5.91472	+	10.2446i	0.206930	+	0.358413i
$818$	58.4320			2.04303
$819$		0			0
$820$	−27.2618			−0.952024
$821$	−14.4495	−	25.0273i	−0.504291	−	0.873458i	−0.999988	−	0.00496193i	$-0.998421\pi$
$821$	−14.4495	−	25.0273i	−0.504291	−	0.873458i	0.495697	−	0.868496i	$-0.334913\pi$
$822$		0			0
$823$	12.4794	−	21.6150i	0.435005	−	0.753451i	−0.562291	−	0.826939i	$-0.690080\pi$
$823$	12.4794	−	21.6150i	0.435005	−	0.753451i	0.997296	+	0.0734888i	$0.0234133\pi$
$824$	−7.01266	+	12.1463i	−0.244298	+	0.423136i
$825$		0			0
$826$	15.6382	+	27.0862i	0.544124	+	0.942450i
$827$	−12.7191			−0.442287			−0.221143	−	0.975241i	$-0.570979\pi$
$827$	−12.7191			−0.442287			−0.221143	+	0.975241i	$0.570979\pi$
$828$		0			0
$829$	−6.33231			−0.219930			−0.109965	−	0.993935i	$-0.535074\pi$
$829$	−6.33231			−0.219930			−0.109965	+	0.993935i	$0.535074\pi$
$830$	11.2397	+	19.4677i	0.390136	+	0.675735i
$831$		0			0
$832$	−35.8301	+	62.0596i	−1.24219	+	2.15153i
$833$	−0.271819	+	0.470804i	−0.00941796	+	0.0163124i
$834$		0			0
$835$	27.7191	+	48.0109i	0.959260	+	1.66149i
$836$	−2.33630			−0.0808026
$837$		0			0
$838$	42.2206			1.45849
$839$	−22.7118	−	39.3380i	−0.784098	−	1.35810i	−0.929536	−	0.368730i	$-0.879793\pi$
$839$	−22.7118	−	39.3380i	−0.784098	−	1.35810i	0.145439	−	0.989367i	$-0.453541\pi$
$840$		0			0
$841$	−17.7949	+	30.8216i	−0.613616	+	1.06281i
$842$	23.0378	−	39.9026i	0.793934	−	1.37513i
$843$		0			0
$844$	−4.98680	−	8.63740i	−0.171653	−	0.297312i
$845$	−87.8294			−3.02142
$846$		0			0
$847$	−10.4426			−0.358813
$848$	−2.99100	−	5.18056i	−0.102711	−	0.177901i
$849$		0			0
$850$	5.26915	−	9.12644i	0.180730	−	0.313034i
$851$	−18.7328	+	32.4462i	−0.642154	+	1.11224i
$852$		0			0
$853$	12.0441	+	20.8610i	0.412382	+	0.714267i	0.995150	−	0.0983720i	$-0.0313635\pi$
$853$	12.0441	+	20.8610i	0.412382	+	0.714267i	−0.582768	+	0.812639i	$0.698030\pi$
$854$	19.8201			0.678230
$855$		0			0
$856$	−4.29249			−0.146714
$857$	8.93111	+	15.4691i	0.305081	+	0.528416i	0.977279	−	0.211955i	$-0.0679831\pi$
$857$	8.93111	+	15.4691i	0.305081	+	0.528416i	−0.672198	+	0.740371i	$0.734650\pi$
$858$		0			0
$859$	−16.8706	+	29.2208i	−0.575618	+	0.997000i	0.420356	+	0.907359i	$0.361905\pi$
$859$	−16.8706	+	29.2208i	−0.575618	+	0.997000i	−0.995974	+	0.0896404i	$0.971428\pi$
$860$	47.9231	−	83.0053i	1.63416	−	2.83046i
$861$		0			0
$862$	2.33231	+	4.03969i	0.0794390	+	0.137592i
$863$	−54.1555			−1.84347			−0.921737	−	0.387815i	$-0.873230\pi$
$863$	−54.1555			−1.84347			−0.921737	+	0.387815i	$0.873230\pi$
$864$		0			0
$865$	6.81919			0.231859
$866$	37.8753	+	65.6019i	1.28705	+	2.22924i
$867$		0			0
$868$	−2.60147	+	4.50587i	−0.0882995	+	0.152939i
$869$	−3.82232	+	6.62045i	−0.129663	+	0.224583i
$870$		0			0
$871$	30.9074	+	53.5332i	1.04726	+	1.81390i
$872$	7.26503			0.246025
$873$		0			0
$874$	19.3354			0.654029
$875$	7.56202	+	13.0978i	0.255643	+	0.442787i
$876$		0			0
$877$	9.50000	−	16.4545i	0.320792	−	0.555628i	−0.659860	−	0.751389i	$-0.729384\pi$
$877$	9.50000	−	16.4545i	0.320792	−	0.555628i	0.980652	+	0.195761i	$0.0627176\pi$
$878$	−20.5961	+	35.6735i	−0.695086	+	1.20392i
$879$		0			0
$880$	−3.40586	−	5.89913i	−0.114812	−	0.198860i
$881$	−41.3500			−1.39312			−0.696559	−	0.717500i	$-0.745287\pi$
$881$	−41.3500			−1.39312			−0.696559	+	0.717500i	$0.745287\pi$
$882$		0			0
$883$	52.4603			1.76543			0.882716	−	0.469908i	$-0.155713\pi$
$883$	52.4603			1.76543			0.882716	+	0.469908i	$0.155713\pi$
$884$	4.26876	+	7.39372i	0.143574	+	0.248678i
$885$		0			0
$886$	−5.70446	+	9.88041i	−0.191645	+	0.331939i
$887$	−10.6172	+	18.3895i	−0.356490	+	0.617459i	−0.987372	−	0.158420i	$-0.949360\pi$
$887$	−10.6172	+	18.3895i	−0.356490	+	0.617459i	0.630882	+	0.775879i	$0.282693\pi$
$888$		0			0
$889$	−4.91692	−	8.51636i	−0.164908	−	0.285629i
$890$	−52.5897			−1.76281
$891$		0			0
$892$	32.4648			1.08700
$893$	2.58041	+	4.46940i	0.0863502	+	0.149563i
$894$		0			0
$895$	−2.03677	+	3.52780i	−0.0680818	+	0.117921i
$896$	−4.92745	+	8.53459i	−0.164615	+	0.285121i
$897$		0			0
$898$	7.90373	+	13.6897i	0.263751	+	0.456830i
$899$	−16.0735			−0.536083
$900$		0			0
$901$	−1.33537			−0.0444876
$902$	2.23970	+	3.87928i	0.0745740	+	0.129166i
$903$		0			0
$904$	−1.67349	+	2.89856i	−0.0556593	+	0.0964047i
$905$	3.74657	−	6.48925i	0.124540	−	0.215710i
$906$		0			0
$907$	−20.1199	−	34.8486i	−0.668069	−	1.15713i	−0.978443	−	0.206515i	$-0.933788\pi$
$907$	−20.1199	−	34.8486i	−0.668069	−	1.15713i	0.310375	−	0.950614i	$-0.399545\pi$
$908$	56.8599			1.88696
$909$		0			0
$910$	−48.5162			−1.60830
$911$	−0.405862	−	0.702974i	−0.0134468	−	0.0232906i	0.859224	−	0.511600i	$-0.170947\pi$
$911$	−0.405862	−	0.702974i	−0.0134468	−	0.0232906i	−0.872671	+	0.488310i	$0.837614\pi$
$912$		0			0
$913$	1.04410	−	1.80844i	0.0345547	−	0.0598505i
$914$	−1.07255	+	1.85771i	−0.0354768	+	0.0614477i
$915$		0			0
$916$	−25.0257	−	43.3458i	−0.826873	−	1.43219i
$917$	−5.37748			−0.177580
$918$		0			0
$919$	17.7603			0.585858			0.292929	−	0.956134i	$-0.405370\pi$
$919$	17.7603			0.585858			0.292929	+	0.956134i	$0.405370\pi$
$920$	−18.1103	−	31.3680i	−0.597080	−	1.03417i
$921$		0			0
$922$	32.6750	−	56.5948i	1.07609	−	1.86385i
$923$	24.8706	−	43.0772i	0.818626	−	1.41790i
$924$		0			0
$925$	−22.5919	−	39.1304i	−0.742818	−	1.28660i
$926$	58.9936			1.93865
$927$		0			0
$928$	−62.7222			−2.05896
$929$	0.799737	+	1.38518i	0.0262385	+	0.0454464i	0.878846	−	0.477105i	$-0.158314\pi$
$929$	0.799737	+	1.38518i	0.0262385	+	0.0454464i	−0.852608	+	0.522551i	$0.824980\pi$
$930$		0			0
$931$	0.601466	−	1.04177i	0.0197122	−	0.0341426i
$932$	−14.9017	+	25.8104i	−0.488120	+	0.845449i
$933$		0			0
$934$	42.0177	+	72.7768i	1.37486	+	2.38133i
$935$	−1.52059			−0.0497286
$936$		0			0
$937$	2.70140			0.0882510			0.0441255	−	0.999026i	$-0.485950\pi$
$937$	2.70140			0.0882510			0.0441255	+	0.999026i	$0.485950\pi$
$938$	10.9826	+	19.0224i	0.358595	+	0.621105i
$939$		0			0
$940$	20.9074	−	36.2127i	0.681924	−	1.18113i
$941$	18.3959	−	31.8626i	0.599688	−	1.03869i	−0.393179	−	0.919462i	$-0.628625\pi$
$941$	18.3959	−	31.8626i	0.599688	−	1.03869i	0.992867	−	0.119228i	$-0.0380420\pi$
$942$		0			0
$943$	−10.4794	−	18.1509i	−0.341257	−	0.591074i
$944$	−35.5078			−1.15568
$945$		0			0
$946$	−15.7486			−0.512030
$947$	−12.1892	−	21.1123i	−0.396096	−	0.686058i	0.597144	−	0.802134i	$-0.296302\pi$
$947$	−12.1892	−	21.1123i	−0.396096	−	0.686058i	−0.993240	+	0.116075i	$0.962969\pi$
$948$		0			0
$949$	30.2949	−	52.4722i	0.983413	−	1.70332i
$950$	−11.6593	+	20.1945i	−0.378277	+	0.655196i
$951$		0			0
$952$	0.350702	+	0.607433i	0.0113663	+	0.0196870i
$953$	1.63091			0.0528304			0.0264152	−	0.999651i	$-0.491591\pi$
$953$	1.63091			0.0528304			0.0264152	+	0.999651i	$0.491591\pi$
$954$		0			0
$955$	40.5383			1.31179
$956$	−5.41906	−	9.38608i	−0.175265	−	0.303568i
$957$		0			0
$958$	22.5089	−	38.9865i	0.727228	−	1.25960i
$959$	5.24657	−	9.08732i	0.169421	−	0.293445i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	64.7475			2.08754
$963$		0			0
$964$	34.4426			1.10932
$965$	18.0414	+	31.2487i	0.580774	+	1.00593i
$966$		0			0
$967$	−24.0368	+	41.6329i	−0.772971	+	1.33882i	0.162958	+	0.986633i	$0.447897\pi$
$967$	−24.0368	+	41.6329i	−0.772971	+	1.33882i	−0.935928	+	0.352191i	$0.885437\pi$
$968$	−6.73657	+	11.6681i	−0.216522	+	0.375026i
$969$		0			0
$970$	−20.9074	−	36.2127i	−0.671296	−	1.16272i
$971$	10.3491			0.332118			0.166059	−	0.986116i	$-0.446896\pi$
$971$	10.3491			0.332118			0.166059	+	0.986116i	$0.446896\pi$
$972$		0			0
$973$	−6.79707			−0.217904
$974$	30.7238	+	53.2153i	0.984455	+	1.70513i
$975$		0			0
$976$	−11.2508	+	19.4869i	−0.360128	+	0.623760i
$977$	5.58041	−	9.66555i	0.178533	−	0.309228i	−0.762845	−	0.646581i	$-0.776198\pi$
$977$	5.58041	−	9.66555i	0.178533	−	0.309228i	0.941378	+	0.337353i	$0.109531\pi$
$978$		0			0
$979$	2.44264	+	4.23077i	0.0780670	+	0.135216i
$980$	−9.74657			−0.311343
$981$		0			0
$982$	−68.9588			−2.20056
$983$	−20.6887	−	35.8339i	−0.659868	−	1.14293i	−0.980649	−	0.195772i	$-0.937279\pi$
$983$	−20.6887	−	35.8339i	−0.659868	−	1.14293i	0.320781	−	0.947153i	$-0.396055\pi$
$984$		0			0
$985$	−36.4905	+	63.2033i	−1.16268	+	2.01383i
$986$	−4.68607	+	8.11651i	−0.149235	+	0.258482i
$987$		0			0
$988$	−9.44569	−	16.3604i	−0.300507	−	0.520494i
$989$	73.6863			2.34309
$990$		0			0
$991$	0.977882			0.0310634			0.0155317	−	0.999879i	$-0.495056\pi$
$991$	0.977882			0.0310634			0.0155317	+	0.999879i	$0.495056\pi$
$992$	−7.80440	−	13.5176i	−0.247790	−	0.429185i
$993$		0			0
$994$	8.83751	−	15.3070i	0.280309	−	0.485509i
$995$	−31.6035	+	54.7388i	−1.00190	+	1.73534i
$996$		0			0
$997$	14.0552	+	24.3443i	0.445131	+	0.770990i	0.998061	−	0.0622375i	$-0.0198236\pi$
$997$	14.0552	+	24.3443i	0.445131	+	0.770990i	−0.552930	+	0.833228i	$0.686490\pi$
$998$	41.3186			1.30792
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.m.190.3		6
3.2	odd	2		567.2.f.l.190.1		6
9.2	odd	6		567.2.f.l.379.1		6
9.4	even	3		567.2.a.e.1.1	✓	3
9.5	odd	6		567.2.a.f.1.3	yes	3
9.7	even	3	inner	567.2.f.m.379.3		6
36.23	even	6		9072.2.a.cb.1.3		3
36.31	odd	6		9072.2.a.bu.1.1		3
63.13	odd	6		3969.2.a.o.1.1		3
63.41	even	6		3969.2.a.n.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.a.e.1.1	✓	3	9.4	even	3
567.2.a.f.1.3	yes	3	9.5	odd	6
567.2.f.l.190.1		6	3.2	odd	2
567.2.f.l.379.1		6	9.2	odd	6
567.2.f.m.190.3		6	1.1	even	1	trivial
567.2.f.m.379.3		6	9.7	even	3	inner
3969.2.a.n.1.3		3	63.41	even	6
3969.2.a.o.1.1		3	63.13	odd	6
9072.2.a.bu.1.1		3	36.31	odd	6
9072.2.a.cb.1.3		3	36.23	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.07255 + 1.85771i) q^{2} +(-1.30073 + 2.25294i) q^{4} +(1.87328 - 3.24462i) q^{5} +(-0.500000 - 0.866025i) q^{7} -1.29021 q^{8} +8.03677 q^{10} +(-0.373284 - 0.646547i) q^{11} +(3.01839 - 5.22800i) q^{13} +(1.07255 - 1.85771i) q^{14} +(1.21765 + 2.10904i) q^{16} +0.543637 q^{17} -1.20293 q^{19} +(4.87328 + 8.44078i) q^{20} +(0.800733 - 1.38691i) q^{22} +(-3.74657 + 6.48925i) q^{23} +(-4.51839 - 7.82608i) q^{25} +12.9495 q^{26} +2.60147 q^{28} +(4.01839 + 6.96005i) q^{29} +(-1.00000 + 1.73205i) q^{31} +(-3.90220 + 6.75881i) q^{32} +(0.583079 + 1.00992i) q^{34} -3.74657 q^{35} +5.00000 q^{37} +(-1.29021 - 2.23470i) q^{38} +(-2.41692 + 4.18623i) q^{40} +(-1.39853 + 2.42233i) q^{41} +(-4.91692 - 8.51636i) q^{43} +1.94217 q^{44} -16.0735 q^{46} +(-2.14510 - 3.71543i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(9.69240 - 16.7877i) q^{50} +(7.85223 + 13.6005i) q^{52} -2.45636 q^{53} -2.79707 q^{55} +(0.645103 + 1.11735i) q^{56} +(-8.61985 + 14.9300i) q^{58} +(-7.29021 + 12.6270i) q^{59} +(4.61985 + 8.00182i) q^{61} -4.29021 q^{62} -11.8706 q^{64} +(-11.3086 - 19.5871i) q^{65} +(-5.11985 + 8.86784i) q^{67} +(-0.707127 + 1.22478i) q^{68} +(-4.01839 - 6.96005i) q^{70} +8.23970 q^{71} +10.0368 q^{73} +(5.36276 + 9.28857i) q^{74} +(1.56469 - 2.71013i) q^{76} +(-0.373284 + 0.646547i) q^{77} +(-5.11985 - 8.86784i) q^{79} +9.12405 q^{80} -6.00000 q^{82} +(1.39853 + 2.42233i) q^{83} +(1.01839 - 1.76390i) q^{85} +(10.5473 - 18.2685i) q^{86} +(0.481613 + 0.834179i) q^{88} -6.54364 q^{89} -6.03677 q^{91} +(-9.74657 - 16.8816i) q^{92} +(4.60147 - 7.96997i) q^{94} +(-2.25343 + 3.90306i) q^{95} +(-2.60147 - 4.50587i) q^{97} -2.14510 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 3 q^{5} - 3 q^{7} + 18 q^{8} + 6 q^{10} + 6 q^{11} - 3 q^{13} - 12 q^{16} - 6 q^{17} + 21 q^{20} + 3 q^{22} - 6 q^{23} - 6 q^{25} + 54 q^{26} + 12 q^{28} + 3 q^{29} - 6 q^{31} - 18 q^{32}+ \cdots - 12 q^{97}+O(q^{100}) \) 6 * q - 6 * q^4 + 3 * q^5 - 3 * q^7 + 18 * q^8 + 6 * q^10 + 6 * q^11 - 3 * q^13 - 12 * q^16 - 6 * q^17 + 21 * q^20 + 3 * q^22 - 6 * q^23 - 6 * q^25 + 54 * q^26 + 12 * q^28 + 3 * q^29 - 6 * q^31 - 18 * q^32 + 21 * q^34 - 6 * q^35 + 30 * q^37 + 18 * q^38 + 3 * q^40 - 12 * q^41 - 12 * q^43 + 6 * q^44 - 12 * q^46 - 3 * q^49 + 27 * q^50 - 9 * q^52 - 24 * q^53 - 24 * q^55 - 9 * q^56 - 27 * q^58 - 18 * q^59 + 3 * q^61 + 6 * q^64 - 21 * q^65 - 6 * q^67 + 39 * q^68 - 3 * q^70 + 18 * q^73 + 48 * q^76 + 6 * q^77 - 6 * q^79 - 6 * q^80 - 36 * q^82 + 12 * q^83 - 15 * q^85 + 45 * q^86 + 24 * q^88 - 30 * q^89 + 6 * q^91 - 42 * q^92 + 24 * q^94 - 30 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more