LMFDB - Embedded newform 567.2.f.l.379.2

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)

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")

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);

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			379.2
Root			$0.500000 - 2.43956i$ of defining polynomial
Character	$\chi$	$=$	567.379
Dual form			567.2.f.l.190.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.261988 + 0.453777i) q^{2} +(0.862724 + 1.49428i) q^{4} +(1.10074 + 1.90653i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.95205 q^{8} -1.15352 q^{10} +(-2.60074 + 4.50461i) q^{11} +(-1.57676 - 2.73103i) q^{13} +(-0.261988 - 0.453777i) q^{14} +(-1.21404 + 2.10277i) q^{16} -3.24943 q^{17} +7.45090 q^{19} +(-1.89926 + 3.28962i) q^{20} +(-1.36272 - 2.36031i) q^{22} +(-2.20147 - 3.81306i) q^{23} +(0.0767598 - 0.132952i) q^{25} +1.65237 q^{26} -1.72545 q^{28} +(0.576760 - 0.998977i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-2.58817 - 4.48285i) q^{32} +(0.851311 - 1.47451i) q^{34} -2.20147 q^{35} +5.00000 q^{37} +(-1.95205 + 3.38104i) q^{38} +(-2.14869 - 3.72164i) q^{40} +(5.72545 + 9.91677i) q^{41} +(-4.64869 + 8.05177i) q^{43} -8.97487 q^{44} +2.30704 q^{46} +(0.523976 - 0.907554i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.0402203 + 0.0696636i) q^{50} +(2.72062 - 4.71225i) q^{52} -0.249425 q^{53} -11.4509 q^{55} +(0.976024 - 1.69052i) q^{56} +(0.302209 + 0.523440i) q^{58} +(4.04795 + 7.01126i) q^{59} +(-4.30221 + 7.45164i) q^{61} +1.04795 q^{62} -2.14386 q^{64} +(3.47119 - 6.01228i) q^{65} +(3.80221 + 6.58562i) q^{67} +(-2.80336 - 4.85556i) q^{68} +(0.576760 - 0.998977i) q^{70} +9.60442 q^{71} +0.846480 q^{73} +(-1.30994 + 2.26888i) q^{74} +(6.42807 + 11.1337i) q^{76} +(-2.60074 - 4.50461i) q^{77} +(3.80221 - 6.58562i) q^{79} -5.34533 q^{80} -6.00000 q^{82} +(-5.72545 + 9.91677i) q^{83} +(-3.57676 - 6.19513i) q^{85} +(-2.43580 - 4.21894i) q^{86} +(5.07676 - 8.79321i) q^{88} +9.24943 q^{89} +3.15352 q^{91} +(3.79853 - 6.57924i) q^{92} +(0.274551 + 0.475537i) q^{94} +(8.20147 + 14.2054i) q^{95} +(1.72545 - 2.98856i) q^{97} +0.523976 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q - 6 q^{4} - 3 q^{5} - 3 q^{7} - 18 q^{8} + 6 q^{10} - 6 q^{11} - 3 q^{13} - 12 q^{16} + 6 q^{17} - 21 q^{20} + 3 q^{22} + 6 q^{23} - 6 q^{25} - 54 q^{26} + 12 q^{28} - 3 q^{29} - 6 q^{31} + 18 q^{32}+ \cdots - 12 q^{97}+O(q^{100})$ 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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$ .

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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

)

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

$2$	−0.261988	+	0.453777i	−0.185254	+	0.320869i	−0.943662	−	0.330911i	$-0.892644\pi$
$2$	−0.261988	+	0.453777i	−0.185254	+	0.320869i	0.758408	+	0.651780i	$0.225977\pi$
$3$		0			0
$3$		0			0
$4$	0.862724	+	1.49428i	0.431362	+	0.747141i
$5$	1.10074	+	1.90653i	0.492264	+	0.852627i	0.999960	−	0.00890964i	$-0.00283606\pi$
$5$	1.10074	+	1.90653i	0.492264	+	0.852627i	−0.507696	+	0.861536i	$0.669503\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.95205			−0.690153
$9$		0			0
$10$	−1.15352			−0.364775
$11$	−2.60074	+	4.50461i	−0.784151	+	1.35819i	0.145353	+	0.989380i	$0.453568\pi$
$11$	−2.60074	+	4.50461i	−0.784151	+	1.35819i	−0.929505	+	0.368810i	$0.879765\pi$
$12$		0			0
$13$	−1.57676	−	2.73103i	−0.437314	−	0.757451i	0.560167	−	0.828380i	$-0.310737\pi$
$13$	−1.57676	−	2.73103i	−0.437314	−	0.757451i	−0.997481	+	0.0709289i	$0.977404\pi$
$14$	−0.261988	−	0.453777i	−0.0700193	−	0.121277i
$15$		0			0
$16$	−1.21404	+	2.10277i	−0.303509	+	0.525693i
$17$	−3.24943			−0.788101			−0.394051	−	0.919089i	$-0.628927\pi$
$17$	−3.24943			−0.788101			−0.394051	+	0.919089i	$0.628927\pi$
$18$		0			0
$19$	7.45090			1.70935			0.854677	−	0.519161i	$-0.173755\pi$
$19$	7.45090			1.70935			0.854677	+	0.519161i	$0.173755\pi$
$20$	−1.89926	+	3.28962i	−0.424688	+	0.735582i
$21$		0			0
$22$	−1.36272	−	2.36031i	−0.290534	−	0.503219i
$23$	−2.20147	−	3.81306i	−0.459039	−	0.795078i	0.539872	−	0.841747i	$-0.318473\pi$
$23$	−2.20147	−	3.81306i	−0.459039	−	0.795078i	−0.998910	+	0.0466689i	$0.985139\pi$
$24$		0			0
$25$	0.0767598	−	0.132952i	0.0153520	−	0.0265904i
$26$	1.65237			0.324056
$27$		0			0
$28$	−1.72545			−0.326079
$29$	0.576760	−	0.998977i	0.107102	−	0.185505i	−0.807493	−	0.589877i	$-0.799176\pi$
$29$	0.576760	−	0.998977i	0.107102	−	0.185505i	0.914595	+	0.404371i	$0.132510\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	−2.58817	−	4.48285i	−0.457529	−	0.792463i
$33$		0			0
$34$	0.851311	−	1.47451i	0.145999	−	0.252877i
$35$	−2.20147			−0.372117
$36$		0			0
$37$	5.00000			0.821995			0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000			0.821995			0.410997	+	0.911636i	$0.365181\pi$
$38$	−1.95205	+	3.38104i	−0.316664	+	0.548478i
$39$		0			0
$40$	−2.14869	−	3.72164i	−0.339738	−	0.588443i
$41$	5.72545	+	9.91677i	0.894165	+	1.54874i	0.834835	+	0.550501i	$0.185563\pi$
$41$	5.72545	+	9.91677i	0.894165	+	1.54874i	0.0593301	+	0.998238i	$0.481104\pi$
$42$		0			0
$43$	−4.64869	+	8.05177i	−0.708918	+	1.22788i	0.256340	+	0.966587i	$0.417483\pi$
$43$	−4.64869	+	8.05177i	−0.708918	+	1.22788i	−0.965259	+	0.261296i	$0.915850\pi$
$44$	−8.97487			−1.35301
$45$		0			0
$46$	2.30704			0.340154
$47$	0.523976	−	0.907554i	0.0764298	−	0.132380i	−0.825277	−	0.564728i	$-0.808981\pi$
$47$	0.523976	−	0.907554i	0.0764298	−	0.132380i	0.901707	+	0.432347i	$0.142315\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.0402203	+	0.0696636i	0.00568801	+	0.00985192i
$51$		0			0
$52$	2.72062	−	4.71225i	0.377282	−	0.653471i
$53$	−0.249425			−0.0342612			−0.0171306	−	0.999853i	$-0.505453\pi$
$53$	−0.249425			−0.0342612			−0.0171306	+	0.999853i	$0.505453\pi$
$54$		0			0
$55$	−11.4509			−1.54404
$56$	0.976024	−	1.69052i	0.130427	−	0.225906i
$57$		0			0
$58$	0.302209	+	0.523440i	0.0396819	+	0.0687311i
$59$	4.04795	+	7.01126i	0.526999	+	0.912788i	0.999505	+	0.0314611i	$0.0100160\pi$
$59$	4.04795	+	7.01126i	0.526999	+	0.912788i	−0.472506	+	0.881327i	$0.656651\pi$
$60$		0			0
$61$	−4.30221	+	7.45164i	−0.550841	+	0.954085i	0.447373	+	0.894348i	$0.352360\pi$
$61$	−4.30221	+	7.45164i	−0.550841	+	0.954085i	−0.998214	+	0.0597376i	$0.980974\pi$
$62$	1.04795			0.133090
$63$		0			0
$64$	−2.14386			−0.267982
$65$	3.47119	−	6.01228i	0.430549	−	0.745732i
$66$		0			0
$67$	3.80221	+	6.58562i	0.464514	+	0.804561i	0.999179	−	0.0405023i	$-0.0128958\pi$
$67$	3.80221	+	6.58562i	0.464514	+	0.804561i	−0.534666	+	0.845064i	$0.679562\pi$
$68$	−2.80336	−	4.85556i	−0.339957	−	0.588823i
$69$		0			0
$70$	0.576760	−	0.998977i	0.0689360	−	0.119401i
$71$	9.60442			1.13983			0.569917	−	0.821702i	$-0.306975\pi$
$71$	9.60442			1.13983			0.569917	+	0.821702i	$0.306975\pi$
$72$		0			0
$73$	0.846480			0.0990730			0.0495365	−	0.998772i	$-0.484226\pi$
$73$	0.846480			0.0990730			0.0495365	+	0.998772i	$0.484226\pi$
$74$	−1.30994	+	2.26888i	−0.152278	+	0.263752i
$75$		0			0
$76$	6.42807	+	11.1337i	0.737350	+	1.27713i
$77$	−2.60074	−	4.50461i	−0.296381	−	0.513348i
$78$		0			0
$79$	3.80221	−	6.58562i	0.427782	−	0.740940i	−0.568894	−	0.822411i	$-0.692628\pi$
$79$	3.80221	−	6.58562i	0.427782	−	0.740940i	0.996676	+	0.0814710i	$0.0259618\pi$
$80$	−5.34533			−0.597626
$81$		0			0
$82$	−6.00000			−0.662589
$83$	−5.72545	+	9.91677i	−0.628450	+	1.08851i	0.359413	+	0.933178i	$0.382977\pi$
$83$	−5.72545	+	9.91677i	−0.628450	+	1.08851i	−0.987863	+	0.155328i	$0.950356\pi$
$84$		0			0
$85$	−3.57676	−	6.19513i	−0.387954	−	0.671956i
$86$	−2.43580	−	4.21894i	−0.262659	−	0.454939i
$87$		0			0
$88$	5.07676	−	8.79321i	0.541184	−	0.937359i
$89$	9.24943			0.980437			0.490219	−	0.871600i	$-0.336917\pi$
$89$	9.24943			0.980437			0.490219	+	0.871600i	$0.336917\pi$
$90$		0			0
$91$	3.15352			0.330579
$92$	3.79853	−	6.57924i	0.396024	−	0.685933i
$93$		0			0
$94$	0.274551	+	0.475537i	0.0283178	+	0.0490479i
$95$	8.20147	+	14.2054i	0.841453	+	1.45744i
$96$		0			0
$97$	1.72545	−	2.98856i	0.175193	−	0.303443i	−0.765035	−	0.643988i	$-0.777278\pi$
$97$	1.72545	−	2.98856i	0.175193	−	0.303443i	0.940228	+	0.340546i	$0.110612\pi$
$98$	0.523976			0.0529296
$99$		0			0
$100$	0.264890			0.0264890
$101$	8.20147	−	14.2054i	0.816077	−	1.41349i	−0.0924750	−	0.995715i	$-0.529478\pi$
$101$	8.20147	−	14.2054i	0.816077	−	1.41349i	0.908552	−	0.417772i	$-0.137189\pi$
$102$		0			0
$103$	0.571929	+	0.990610i	0.0563539	+	0.0976077i	0.892826	−	0.450402i	$-0.148719\pi$
$103$	0.571929	+	0.990610i	0.0563539	+	0.0976077i	−0.836472	+	0.548009i	$0.815386\pi$
$104$	3.07791	+	5.33110i	0.301814	+	0.522757i
$105$		0			0
$106$	0.0653464	−	0.113183i	0.00634701	−	0.0109933i
$107$	9.10557			0.880268			0.440134	−	0.897932i	$-0.354931\pi$
$107$	9.10557			0.880268			0.440134	+	0.897932i	$0.354931\pi$
$108$		0			0
$109$	−13.7483			−1.31685			−0.658423	−	0.752648i	$-0.728776\pi$
$109$	−13.7483			−1.31685			−0.658423	+	0.752648i	$0.728776\pi$
$110$	3.00000	−	5.19615i	0.286039	−	0.495434i
$111$		0			0
$112$	−1.21404	−	2.10277i	−0.114716	−	0.198693i
$113$	−9.95090	−	17.2355i	−0.936102	−	1.62138i	−0.772658	−	0.634823i	$-0.781073\pi$
$113$	−9.95090	−	17.2355i	−0.936102	−	1.62138i	−0.163444	−	0.986553i	$-0.552260\pi$
$114$		0			0
$115$	4.84648	−	8.39435i	0.451937	−	0.782777i
$116$	1.99034			0.184798
$117$		0			0
$118$	−4.24206			−0.390514
$119$	1.62471	−	2.81408i	0.148937	−	0.257967i
$120$		0			0
$121$	−8.02766	−	13.9043i	−0.729787	−	1.26403i
$122$	−2.25426	−	3.90449i	−0.204091	−	0.353496i
$123$		0			0
$124$	1.72545	−	2.98856i	0.154950	−	0.268381i
$125$	11.3453			1.01476
$126$		0			0
$127$	9.29738			0.825009			0.412504	−	0.910956i	$-0.364654\pi$
$127$	9.29738			0.825009			0.412504	+	0.910956i	$0.364654\pi$
$128$	5.73801	−	9.93853i	0.507173	−	0.878450i
$129$		0			0
$130$	1.81882	+	3.15029i	0.159521	+	0.276299i
$131$	−3.77340	−	6.53572i	−0.329684	−	0.571029i	0.652765	−	0.757560i	$-0.273609\pi$
$131$	−3.77340	−	6.53572i	−0.329684	−	0.571029i	−0.982449	+	0.186531i	$0.940275\pi$
$132$		0			0
$133$	−3.72545	+	6.45267i	−0.323037	+	0.559517i
$134$	−3.98454			−0.344211
$135$		0			0
$136$	6.34303			0.543910
$137$	0.701472	−	1.21499i	0.0599308	−	0.103803i	−0.834503	−	0.551003i	$-0.814245\pi$
$137$	0.701472	−	1.21499i	0.0599308	−	0.103803i	0.894434	+	0.447200i	$0.147579\pi$
$138$		0			0
$139$	7.72545	+	13.3809i	0.655264	+	1.13495i	0.981828	+	0.189775i	$0.0607760\pi$
$139$	7.72545	+	13.3809i	0.655264	+	1.13495i	−0.326564	+	0.945175i	$0.605891\pi$
$140$	−1.89926	−	3.28962i	−0.160517	−	0.278024i
$141$		0			0
$142$	−2.51624	+	4.35826i	−0.211158	+	0.365737i
$143$	16.4029			1.37168
$144$		0			0
$145$	2.53944			0.210889
$146$	−0.221768	+	0.384113i	−0.0183536	+	0.0317894i
$147$		0			0
$148$	4.31362	+	7.47141i	0.354578	+	0.614146i
$149$	−6.70147	−	11.6073i	−0.549006	−	0.950906i	−0.998343	−	0.0575439i	$-0.981673\pi$
$149$	−6.70147	−	11.6073i	−0.549006	−	0.950906i	0.449337	−	0.893362i	$-0.351660\pi$
$150$		0			0
$151$	−5.80221	+	10.0497i	−0.472177	+	0.817835i	−0.999493	−	0.0318346i	$-0.989865\pi$
$151$	−5.80221	+	10.0497i	−0.472177	+	0.817835i	0.527316	+	0.849669i	$0.323198\pi$
$152$	−14.5445			−1.17972
$153$		0			0
$154$	2.72545			0.219623
$155$	2.20147	−	3.81306i	0.176827	−	0.306273i
$156$		0			0
$157$	12.1812	+	21.0984i	0.972164	+	1.68384i	0.688994	+	0.724767i	$0.258053\pi$
$157$	12.1812	+	21.0984i	0.972164	+	1.68384i	0.283170	+	0.959070i	$0.408614\pi$
$158$	1.99227	+	3.45071i	0.158496	+	0.274524i
$159$		0			0
$160$	5.69779	−	9.86886i	0.450450	−	0.780202i
$161$	4.40294			0.347001
$162$		0			0
$163$	5.60442			0.438972			0.219486	−	0.975616i	$-0.429562\pi$
$163$	5.60442			0.438972			0.219486	+	0.975616i	$0.429562\pi$
$164$	−9.87897	+	17.1109i	−0.771418	+	1.33613i
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	11.7254	+	20.3091i	0.907342	+	1.57156i	0.817742	+	0.575585i	$0.195226\pi$
$167$	11.7254	+	20.3091i	0.907342	+	1.57156i	0.0896009	+	0.995978i	$0.471441\pi$
$168$		0			0
$169$	1.52766	−	2.64598i	0.117512	−	0.203537i
$170$	3.74828			0.287480
$171$		0			0
$172$	−16.0421			−1.22320
$173$	11.2543	−	19.4929i	0.855645	−	1.48202i	−0.0203999	−	0.999792i	$-0.506494\pi$
$173$	11.2543	−	19.4929i	0.855645	−	1.48202i	0.876045	−	0.482229i	$-0.160173\pi$
$174$		0			0
$175$	0.0767598	+	0.132952i	0.00580249	+	0.0100502i
$176$	−6.31477	−	10.9375i	−0.475994	−	0.824445i
$177$		0			0
$178$	−2.42324	+	4.19718i	−0.181630	+	0.314592i
$179$	6.49885			0.485747			0.242873	−	0.970058i	$-0.421910\pi$
$179$	6.49885			0.485747			0.242873	+	0.970058i	$0.421910\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−0.826185	+	1.43099i	−0.0612409	+	0.106072i
$183$		0			0
$184$	4.29738	+	7.44328i	0.316807	+	0.548726i
$185$	5.50368	+	9.53265i	0.404639	+	0.700855i
$186$		0			0
$187$	8.45090	−	14.6374i	0.617991	−	1.07039i
$188$	1.80819			0.131876
$189$		0			0
$190$	−8.59476			−0.623529
$191$	6.75426	−	11.6987i	0.488721	−	0.846489i	−0.511195	−	0.859465i	$-0.670797\pi$
$191$	6.75426	−	11.6987i	0.488721	−	0.846489i	0.999916	+	0.0129755i	$0.00413035\pi$
$192$		0			0
$193$	−8.87414	−	15.3705i	−0.638774	−	1.10639i	−0.985702	−	0.168498i	$-0.946108\pi$
$193$	−8.87414	−	15.3705i	−0.638774	−	1.10639i	0.346928	−	0.937892i	$-0.387225\pi$
$194$	0.904094	+	1.56594i	0.0649102	+	0.112428i
$195$		0			0
$196$	0.862724	−	1.49428i	0.0616232	−	0.106734i
$197$	−16.2088			−1.15483			−0.577416	−	0.816450i	$-0.695939\pi$
$197$	−16.2088			−1.15483			−0.577416	+	0.816450i	$0.695939\pi$
$198$		0			0
$199$	−7.14386			−0.506415			−0.253207	−	0.967412i	$-0.581485\pi$
$199$	−7.14386			−0.506415			−0.253207	+	0.967412i	$0.581485\pi$
$200$	−0.149839	+	0.259528i	−0.0105952	+	0.0183514i
$201$		0			0
$202$	4.29738	+	7.44328i	0.302362	+	0.523707i
$203$	0.576760	+	0.998977i	0.0404806	+	0.0701145i
$204$		0			0
$205$	−12.6044	+	21.8315i	−0.880331	+	1.52478i
$206$	−0.599355			−0.0417590
$207$		0			0
$208$	7.65697			0.530915
$209$	−19.3778	+	33.5634i	−1.34039	+	2.32163i
$210$		0			0
$211$	−1.64869	−	2.85561i	−0.113500	−	0.196589i	0.803679	−	0.595063i	$-0.202873\pi$
$211$	−1.64869	−	2.85561i	−0.113500	−	0.196589i	−0.917179	+	0.398475i	$0.869540\pi$
$212$	−0.215185	−	0.372712i	−0.0147790	−	0.0255979i
$213$		0			0
$214$	−2.38555	+	4.13190i	−0.163073	+	0.282451i
$215$	−20.4679			−1.39590
$216$		0			0
$217$	2.00000			0.135769
$218$	3.60189	−	6.23865i	0.243950	−	0.422535i
$219$		0			0
$220$	−9.87897	−	17.1109i	−0.666040	−	1.15361i
$221$	5.12356	+	8.87427i	0.344648	+	0.596948i
$222$		0			0
$223$	11.6044	−	20.0994i	0.777089	−	1.34596i	−0.156523	−	0.987674i	$-0.550029\pi$
$223$	11.6044	−	20.0994i	0.777089	−	1.34596i	0.933613	−	0.358284i	$-0.116638\pi$
$224$	5.17635			0.345859
$225$		0			0
$226$	10.4281			0.693665
$227$	−5.83102	+	10.0996i	−0.387018	+	0.670335i	−0.992047	−	0.125869i	$-0.959828\pi$
$227$	−5.83102	+	10.0996i	−0.387018	+	0.670335i	0.605029	+	0.796204i	$0.293162\pi$
$228$		0			0
$229$	−0.697791	−	1.20861i	−0.0461114	−	0.0798672i	0.842049	−	0.539402i	$-0.181350\pi$
$229$	−0.697791	−	1.20861i	−0.0461114	−	0.0798672i	−0.888160	+	0.459535i	$0.848016\pi$
$230$	2.53944	+	4.39844i	0.167446	+	0.290025i
$231$		0			0
$232$	−1.12586	+	1.95005i	−0.0739165	+	0.128027i
$233$	−8.75057			−0.573269			−0.286635	−	0.958040i	$-0.592537\pi$
$233$	−8.75057			−0.573269			−0.286635	+	0.958040i	$0.592537\pi$
$234$		0			0
$235$	2.30704			0.150495
$236$	−6.98454	+	12.0976i	−0.454655	+	0.787485i
$237$		0			0
$238$	0.851311	+	1.47451i	0.0551823	+	0.0955785i
$239$	2.35131	+	4.07259i	0.152094	+	0.263434i	0.931997	−	0.362466i	$-0.118065\pi$
$239$	2.35131	+	4.07259i	0.152094	+	0.263434i	−0.779903	+	0.625900i	$0.784732\pi$
$240$		0			0
$241$	2.30221	−	3.98754i	0.148298	−	0.256860i	−0.782300	−	0.622901i	$-0.785954\pi$
$241$	2.30221	−	3.98754i	0.148298	−	0.256860i	0.930599	+	0.366041i	$0.119287\pi$
$242$	8.41261			0.540783
$243$		0			0
$244$	−14.8465			−0.950449
$245$	1.10074	−	1.90653i	0.0703235	−	0.121804i
$246$		0			0
$247$	−11.7483	−	20.3486i	−0.747525	−	1.29475i
$248$	1.95205	+	3.38104i	0.123955	+	0.214697i
$249$		0			0
$250$	−2.97234	+	5.14825i	−0.187987	+	0.325604i
$251$	−3.14386			−0.198439			−0.0992193	−	0.995066i	$-0.531635\pi$
$251$	−3.14386			−0.198439			−0.0992193	+	0.995066i	$0.531635\pi$
$252$		0			0
$253$	22.9018			1.43982
$254$	−2.43580	+	4.21894i	−0.152836	+	0.264720i
$255$		0			0
$256$	0.862724	+	1.49428i	0.0539203	+	0.0933927i
$257$	−10.0756	−	17.4515i	−0.628499	−	1.08859i	−0.987853	−	0.155391i	$-0.950336\pi$
$257$	−10.0756	−	17.4515i	−0.628499	−	1.08859i	0.359354	−	0.933201i	$-0.382997\pi$
$258$		0			0
$259$	−2.50000	+	4.33013i	−0.155342	+	0.269061i
$260$	11.9787			0.742889
$261$		0			0
$262$	3.95435			0.244300
$263$	−8.60074	+	14.8969i	−0.530344	+	0.918583i	0.469029	+	0.883183i	$0.344604\pi$
$263$	−8.60074	+	14.8969i	−0.530344	+	0.918583i	−0.999373	+	0.0354002i	$0.988729\pi$
$264$		0			0
$265$	−0.274551	−	0.475537i	−0.0168656	−	0.0292120i
$266$	−1.95205	−	3.38104i	−0.119688	−	0.207305i
$267$		0			0
$268$	−6.56052	+	11.3631i	−0.400747	+	0.694115i
$269$	2.75057			0.167706			0.0838528	−	0.996478i	$-0.473277\pi$
$269$	2.75057			0.167706			0.0838528	+	0.996478i	$0.473277\pi$
$270$		0			0
$271$	−12.8561			−0.780955			−0.390477	−	0.920612i	$-0.627690\pi$
$271$	−12.8561			−0.780955			−0.390477	+	0.920612i	$0.627690\pi$
$272$	3.94492	−	6.83280i	0.239196	−	0.414299i
$273$		0			0
$274$	0.367555	+	0.636624i	0.0222048	+	0.0384599i
$275$	0.399264	+	0.691545i	0.0240765	+	0.0417017i
$276$		0			0
$277$	8.37414	−	14.5044i	0.503153	−	0.871487i	−0.496840	−	0.867842i	$-0.665506\pi$
$277$	8.37414	−	14.5044i	0.503153	−	0.871487i	0.999993	−	0.00364480i	$-0.00116018\pi$
$278$	−8.09591			−0.485560
$279$		0			0
$280$	4.29738			0.256817
$281$	−2.65352	+	4.59603i	−0.158296	+	0.274176i	−0.934254	−	0.356608i	$-0.883933\pi$
$281$	−2.65352	+	4.59603i	−0.158296	+	0.274176i	0.775958	+	0.630784i	$0.217267\pi$
$282$		0			0
$283$	−6.17635	−	10.6977i	−0.367146	−	0.635915i	0.621972	−	0.783039i	$-0.286332\pi$
$283$	−6.17635	−	10.6977i	−0.367146	−	0.635915i	−0.989118	+	0.147124i	$0.952998\pi$
$284$	8.28596	+	14.3517i	0.491682	+	0.851617i
$285$		0			0
$286$	−4.29738	+	7.44328i	−0.254109	+	0.440130i
$287$	−11.4509			−0.675925
$288$		0			0
$289$	−6.44124			−0.378896
$290$	−0.665304	+	1.15234i	−0.0390680	+	0.0676677i
$291$		0			0
$292$	0.730279	+	1.26488i	0.0427364	+	0.0740216i
$293$	−5.14869	−	8.91779i	−0.300790	−	0.520983i	0.675525	−	0.737337i	$-0.263917\pi$
$293$	−5.14869	−	8.91779i	−0.300790	−	0.520983i	−0.976315	+	0.216354i	$0.930584\pi$
$294$		0			0
$295$	−8.91146	+	15.4351i	−0.518845	+	0.898666i
$296$	−9.76024			−0.567302
$297$		0			0
$298$	7.02283			0.406821
$299$	−6.94239	+	12.0246i	−0.401489	+	0.695399i
$300$		0			0
$301$	−4.64869	−	8.05177i	−0.267946	−	0.464096i
$302$	−3.04022	−	5.26582i	−0.174945	−	0.303014i
$303$		0			0
$304$	−9.04565	+	15.6675i	−0.518804	+	0.898595i
$305$	−18.9424			−1.08464
$306$		0			0
$307$	−0.307039			−0.0175236			−0.00876182	−	0.999962i	$-0.502789\pi$
$307$	−0.307039			−0.0175236			−0.00876182	+	0.999962i	$0.502789\pi$
$308$	4.48744	−	7.77247i	0.255695	−	0.442878i
$309$		0			0
$310$	1.15352	+	1.99795i	0.0655155	+	0.113476i
$311$	−0.523976	−	0.907554i	−0.0297120	−	0.0514627i	0.850787	−	0.525511i	$-0.176126\pi$
$311$	−0.523976	−	0.907554i	−0.0297120	−	0.0514627i	−0.880499	+	0.474048i	$0.842792\pi$
$312$		0			0
$313$	−16.0277	+	27.7607i	−0.905937	+	1.56913i	−0.0862819	+	0.996271i	$0.527499\pi$
$313$	−16.0277	+	27.7607i	−0.905937	+	1.56913i	−0.819655	+	0.572858i	$0.805835\pi$
$314$	−12.7653			−0.720387
$315$		0			0
$316$	13.1210			0.738116
$317$	3.22177	−	5.58027i	0.180953	−	0.313419i	−0.761253	−	0.648455i	$-0.775415\pi$
$317$	3.22177	−	5.58027i	0.180953	−	0.313419i	0.942205	+	0.335036i	$0.108749\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$	−2.35982	−	4.08733i	−0.131918	−	0.228489i
$321$		0			0
$322$	−1.15352	+	1.99795i	−0.0642831	+	0.111342i
$323$	−24.2111			−1.34714
$324$		0			0
$325$	−0.484127			−0.0268545
$326$	−1.46829	+	2.54315i	−0.0813211	+	0.140852i
$327$		0			0
$328$	−11.1763	−	19.3580i	−0.617110	−	1.06887i
$329$	0.523976	+	0.907554i	0.0288878	+	0.0500351i
$330$		0			0
$331$	10.3070	−	17.8523i	0.566526	−	0.981252i	−0.430380	−	0.902648i	$-0.641620\pi$
$331$	10.3070	−	17.8523i	0.566526	−	0.981252i	0.996906	−	0.0786041i	$-0.0250463\pi$
$332$	−19.7579			−1.08436
$333$		0			0
$334$	−12.2877			−0.672354
$335$	−8.37046	+	14.4981i	−0.457327	+	0.792113i
$336$		0			0
$337$	−13.2303	−	22.9155i	−0.720699	−	1.24829i	−0.960720	−	0.277520i	$-0.910488\pi$
$337$	−13.2303	−	22.9155i	−0.720699	−	1.24829i	0.240021	−	0.970768i	$-0.422846\pi$
$338$	0.800456	+	1.38643i	0.0435391	+	0.0754119i
$339$		0			0
$340$	6.17152	−	10.6894i	0.334697	−	0.579713i
$341$	10.4029			0.563351
$342$		0			0
$343$	1.00000			0.0539949
$344$	9.07446	−	15.7174i	0.489262	−	0.847427i
$345$		0			0
$346$	5.89696	+	10.2138i	0.317023	+	0.549100i
$347$	2.24574	+	3.88974i	0.120558	+	0.208812i	0.919988	−	0.391947i	$-0.128198\pi$
$347$	2.24574	+	3.88974i	0.120558	+	0.208812i	−0.799430	+	0.600759i	$0.794865\pi$
$348$		0			0
$349$	−1.87897	+	3.25447i	−0.100579	+	0.174208i	−0.911923	−	0.410361i	$-0.865403\pi$
$349$	−1.87897	+	3.25447i	−0.100579	+	0.174208i	0.811344	+	0.584568i	$0.198736\pi$
$350$	−0.0804406			−0.00429973
$351$		0			0
$352$	26.9246			1.43509
$353$	9.62954	−	16.6789i	0.512529	−	0.887726i	−0.487366	−	0.873198i	$-0.662042\pi$
$353$	9.62954	−	16.6789i	0.512529	−	0.887726i	0.999894	−	0.0145280i	$-0.00462458\pi$
$354$		0			0
$355$	10.5719	+	18.3111i	0.561100	+	0.971853i
$356$	7.97970	+	13.8213i	0.422923	+	0.732525i
$357$		0			0
$358$	−1.70262	+	2.94903i	−0.0899864	+	0.155861i
$359$	9.10557			0.480573			0.240287	−	0.970702i	$-0.422759\pi$
$359$	9.10557			0.480573			0.240287	+	0.970702i	$0.422759\pi$
$360$		0			0
$361$	36.5159			1.92189
$362$	−0.523976	+	0.907554i	−0.0275396	+	0.0477000i
$363$		0			0
$364$	2.72062	+	4.71225i	0.142599	+	0.246989i
$365$	0.931752	+	1.61384i	0.0487701	+	0.0844723i
$366$		0			0
$367$	−2.29738	+	3.97918i	−0.119922	+	0.207711i	−0.919737	−	0.392536i	$-0.871598\pi$
$367$	−2.29738	+	3.97918i	−0.119922	+	0.207711i	0.799814	+	0.600247i	$0.204931\pi$
$368$	10.6907			0.557289
$369$		0			0
$370$	−5.76760			−0.299843
$371$	0.124713	−	0.216009i	0.00647475	−	0.0112146i
$372$		0			0
$373$	10.6812	+	18.5003i	0.553050	+	0.957911i	0.998052	+	0.0623818i	$0.0198696\pi$
$373$	10.6812	+	18.5003i	0.553050	+	0.957911i	−0.445002	+	0.895530i	$0.646797\pi$
$374$	4.42807	+	7.66964i	0.228970	+	0.396588i
$375$		0			0
$376$	−1.02283	+	1.77159i	−0.0527483	+	0.0913627i
$377$	−3.63765			−0.187348
$378$		0			0
$379$	−35.1203			−1.80401			−0.902004	−	0.431728i	$-0.857904\pi$
$379$	−35.1203			−1.80401			−0.902004	+	0.431728i	$0.857904\pi$
$380$	−14.1512	+	24.5106i	−0.725942	+	1.25737i
$381$		0			0
$382$	3.53907	+	6.12985i	0.181075	+	0.313630i
$383$	−1.59706	−	2.76618i	−0.0816057	−	0.141345i	0.822334	−	0.569005i	$-0.192671\pi$
$383$	−1.59706	−	2.76618i	−0.0816057	−	0.141345i	−0.903940	+	0.427660i	$0.859338\pi$
$384$		0			0
$385$	5.72545	−	9.91677i	0.291796	−	0.505405i
$386$	9.29968			0.473341
$387$		0			0
$388$	5.95435			0.302286
$389$	−7.40294	+	12.8223i	−0.375344	+	0.650115i	−0.990378	−	0.138385i	$-0.955809\pi$
$389$	−7.40294	+	12.8223i	−0.375344	+	0.650115i	0.615034	+	0.788500i	$0.289142\pi$
$390$		0			0
$391$	7.15352	+	12.3903i	0.361769	+	0.626602i
$392$	0.976024	+	1.69052i	0.0492966	+	0.0853843i
$393$		0			0
$394$	4.24652	−	7.35519i	0.213937	−	0.370549i
$395$	16.7409			0.842327
$396$		0			0
$397$	26.8921			1.34968			0.674839	−	0.737965i	$-0.264213\pi$
$397$	26.8921			1.34968			0.674839	+	0.737965i	$0.264213\pi$
$398$	1.87161	−	3.24172i	0.0938152	−	0.162493i
$399$		0			0
$400$	0.186378	+	0.322816i	0.00931891	+	0.0161408i
$401$	−9.70147	−	16.8034i	−0.484468	−	0.839124i	0.515372	−	0.856966i	$-0.327654\pi$
$401$	−9.70147	−	16.8034i	−0.484468	−	0.839124i	−0.999841	+	0.0178424i	$0.994320\pi$
$402$		0			0
$403$	−3.15352	+	5.46206i	−0.157088	+	0.272084i
$404$	28.3024			1.40810
$405$		0			0
$406$	−0.604417			−0.0299967
$407$	−13.0037	+	22.5230i	−0.644569	+	1.11643i
$408$		0			0
$409$	4.69779	+	8.13681i	0.232291	+	0.402340i	0.958482	−	0.285153i	$-0.0920446\pi$
$409$	4.69779	+	8.13681i	0.232291	+	0.402340i	−0.726191	+	0.687493i	$0.758711\pi$
$410$	−6.60442	−	11.4392i	−0.326169	−	0.564941i
$411$		0			0
$412$	−0.986834	+	1.70925i	−0.0486178	+	0.0842086i
$413$	−8.09591			−0.398373
$414$		0			0
$415$	−25.2088			−1.23745
$416$	−8.16185	+	14.1367i	−0.400168	+	0.693111i
$417$		0			0
$418$	−10.1535	−	17.5864i	−0.496625	−	0.860180i
$419$	12.3299	+	21.3560i	0.602353	+	1.04331i	0.992464	+	0.122539i	$0.0391035\pi$
$419$	12.3299	+	21.3560i	0.602353	+	1.04331i	−0.390110	+	0.920768i	$0.627563\pi$
$420$		0			0
$421$	7.10442	−	12.3052i	0.346248	−	0.599719i	−0.639332	−	0.768931i	$-0.720789\pi$
$421$	7.10442	−	12.3052i	0.346248	−	0.599719i	0.985580	+	0.169212i	$0.0541222\pi$
$422$	1.72775			0.0841055
$423$		0			0
$424$	0.486890			0.0236455
$425$	−0.249425	+	0.432017i	−0.0120989	+	0.0209559i
$426$		0			0
$427$	−4.30221	−	7.45164i	−0.208198	−	0.360610i
$428$	7.85559	+	13.6063i	0.379714	+	0.657685i
$429$		0			0
$430$	5.36235	−	9.28787i	0.258596	−	0.447901i
$431$	−12.9977			−0.626077			−0.313039	−	0.949740i	$-0.601347\pi$
$431$	−12.9977			−0.626077			−0.313039	+	0.949740i	$0.601347\pi$
$432$		0			0
$433$	−0.911456			−0.0438018			−0.0219009	−	0.999760i	$-0.506972\pi$
$433$	−0.911456			−0.0438018			−0.0219009	+	0.999760i	$0.506972\pi$
$434$	−0.523976	+	0.907554i	−0.0251517	+	0.0435640i
$435$		0			0
$436$	−11.8610	−	20.5438i	−0.568038	−	0.983870i
$437$	−16.4029	−	28.4107i	−0.784659	−	1.35907i
$438$		0			0
$439$	5.27455	−	9.13579i	0.251741	−	0.436028i	−0.712265	−	0.701911i	$-0.752330\pi$
$439$	5.27455	−	9.13579i	0.251741	−	0.436028i	0.964005	+	0.265884i	$0.0856637\pi$
$440$	22.3527			1.06562
$441$		0			0
$442$	−5.36925			−0.255389
$443$	8.70032	−	15.0694i	0.413365	−	0.715969i	−0.581890	−	0.813267i	$-0.697687\pi$
$443$	8.70032	−	15.0694i	0.413365	−	0.715969i	0.995255	+	0.0972983i	$0.0310201\pi$
$444$		0			0
$445$	10.1812	+	17.6343i	0.482634	+	0.835947i
$446$	6.08044	+	10.5316i	0.287917	+	0.498687i
$447$		0			0
$448$	1.07193	−	1.85664i	0.0506439	−	0.0877178i
$449$	0.748275			0.0353133			0.0176566	−	0.999844i	$-0.494379\pi$
$449$	0.748275			0.0353133			0.0176566	+	0.999844i	$0.494379\pi$
$450$		0			0
$451$	−59.5615			−2.80464
$452$	17.1698	−	29.7389i	0.807598	−	1.39880i
$453$		0			0
$454$	−3.05531	−	5.29196i	−0.143393	−	0.248364i
$455$	3.47119	+	6.01228i	0.162732	+	0.281860i
$456$		0			0
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	−0.854094	−	0.520119i	$-0.825888\pi$
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	0.877483	+	0.479608i	$0.159221\pi$
$458$	0.731253			0.0341692
$459$		0			0
$460$	16.7247			0.779793
$461$	19.0228	−	32.9485i	0.885981	−	1.53456i	0.0413967	−	0.999143i	$-0.486819\pi$
$461$	19.0228	−	32.9485i	0.885981	−	1.53456i	0.844585	−	0.535422i	$-0.179847\pi$
$462$		0			0
$463$	12.9461	+	22.4232i	0.601655	+	1.04210i	0.992571	+	0.121670i	$0.0388250\pi$
$463$	12.9461	+	22.4232i	0.601655	+	1.04210i	−0.390916	+	0.920426i	$0.627842\pi$
$464$	1.40041	+	2.42559i	0.0650126	+	0.112605i
$465$		0			0
$466$	2.29255	−	3.97081i	0.106200	−	0.183944i
$467$	17.0627			0.789566			0.394783	−	0.918774i	$-0.370820\pi$
$467$	17.0627			0.789566			0.394783	+	0.918774i	$0.370820\pi$
$468$		0			0
$469$	−7.60442			−0.351139
$470$	−0.604417	+	1.04688i	−0.0278797	+	0.0482890i
$471$		0			0
$472$	−7.90179	−	13.6863i	−0.363710	−	0.629963i
$473$	−24.1800	−	41.8810i	−1.11180	−	1.92569i
$474$		0			0
$475$	0.571929	−	0.990610i	0.0262419	−	0.0454523i
$476$	5.60672			0.256983
$477$		0			0
$478$	−2.46406			−0.112704
$479$	−1.40294	+	2.42997i	−0.0641022	+	0.111028i	−0.896295	−	0.443458i	$-0.853752\pi$
$479$	−1.40294	+	2.42997i	−0.0641022	+	0.111028i	0.832193	+	0.554486i	$0.187085\pi$
$480$		0			0
$481$	−7.88380	−	13.6551i	−0.359470	−	0.622621i
$482$	1.20630	+	2.08938i	0.0549456	+	0.0951686i
$483$		0			0
$484$	13.8513	−	23.9912i	0.629605	−	1.09051i
$485$	7.59706			0.344965
$486$		0			0
$487$	−6.50621			−0.294825			−0.147412	−	0.989075i	$-0.547094\pi$
$487$	−6.50621			−0.294825			−0.147412	+	0.989075i	$0.547094\pi$
$488$	8.39811	−	14.5460i	0.380165	−	0.658465i
$489$		0			0
$490$	0.576760	+	0.998977i	0.0260554	+	0.0451292i
$491$	−2.30704	−	3.99591i	−0.104115	−	0.180333i	0.809261	−	0.587449i	$-0.199868\pi$
$491$	−2.30704	−	3.99591i	−0.104115	−	0.180333i	−0.913376	+	0.407116i	$0.866534\pi$
$492$		0			0
$493$	−1.87414	+	3.24610i	−0.0844069	+	0.146197i
$494$	12.3116			0.553927
$495$		0			0
$496$	4.85614			0.218047
$497$	−4.80221	+	8.31767i	−0.215408	+	0.373098i
$498$		0			0
$499$	17.7483	+	30.7409i	0.794522	+	1.37615i	0.923142	+	0.384458i	$0.125612\pi$
$499$	17.7483	+	30.7409i	0.794522	+	1.37615i	−0.128620	+	0.991694i	$0.541055\pi$
$500$	9.78789	+	16.9531i	0.437728	+	0.758167i
$501$		0			0
$502$	0.823654	−	1.42661i	0.0367615	−	0.0636727i
$503$	−18.9211			−0.843651			−0.421825	−	0.906677i	$-0.638611\pi$
$503$	−18.9211			−0.843651			−0.421825	+	0.906677i	$0.638611\pi$
$504$		0			0
$505$	36.1106			1.60690
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$		0			0
$508$	8.02107	+	13.8929i	0.355878	+	0.616398i
$509$	7.40294	+	12.8223i	0.328130	+	0.568337i	0.982141	−	0.188148i	$-0.0602483\pi$
$509$	7.40294	+	12.8223i	0.328130	+	0.568337i	−0.654011	+	0.756485i	$0.726915\pi$
$510$		0			0
$511$	−0.423240	+	0.733074i	−0.0187230	+	0.0324293i
$512$	22.0480			0.974391
$513$		0			0
$514$	10.5588			0.465727
$515$	−1.25909	+	2.18080i	−0.0554820	+	0.0960976i
$516$		0			0
$517$	2.72545	+	4.72062i	0.119865	+	0.207612i
$518$	−1.30994	−	2.26888i	−0.0575555	−	0.0996891i
$519$		0			0
$520$	−6.77593	+	11.7363i	−0.297144	+	0.514669i
$521$	−12.7100			−0.556834			−0.278417	−	0.960460i	$-0.589810\pi$
$521$	−12.7100			−0.556834			−0.278417	+	0.960460i	$0.589810\pi$
$522$		0			0
$523$	0.352692			0.0154222			0.00771108	−	0.999970i	$-0.497545\pi$
$523$	0.352692			0.0154222			0.00771108	+	0.999970i	$0.497545\pi$
$524$	6.51081	−	11.2771i	0.284426	−	0.492640i
$525$		0			0
$526$	−4.50658	−	7.80563i	−0.196496	−	0.340342i
$527$	3.24943	+	5.62817i	0.141547	+	0.245167i
$528$		0			0
$529$	1.80704	−	3.12988i	0.0785669	−	0.136082i
$530$	0.287717			0.0124976
$531$		0			0
$532$	−12.8561			−0.557384
$533$	18.0553	−	31.2727i	0.782062	−	1.35457i
$534$		0			0
$535$	10.0228	+	17.3600i	0.433325	+	0.750540i
$536$	−7.42209	−	12.8554i	−0.320585	−	0.555270i
$537$		0			0
$538$	−0.720618	+	1.24815i	−0.0310681	+	0.0538114i
$539$	5.20147			0.224043
$540$		0			0
$541$	−22.6930			−0.975647			−0.487823	−	0.872942i	$-0.662209\pi$
$541$	−22.6930			−0.975647			−0.487823	+	0.872942i	$0.662209\pi$
$542$	3.36816	−	5.83382i	0.144675	−	0.250584i
$543$		0			0
$544$	8.41007	+	14.5667i	0.360579	+	0.624541i
$545$	−15.1332	−	26.2115i	−0.648236	−	1.12278i
$546$		0			0
$547$	0.746894	−	1.29366i	0.0319349	−	0.0553128i	−0.849616	−	0.527401i	$-0.823166\pi$
$547$	0.746894	−	1.29366i	0.0319349	−	0.0553128i	0.881551	+	0.472089i	$0.156500\pi$
$548$	2.42071			0.103408
$549$		0			0
$550$	−0.418410			−0.0178410
$551$	4.29738	−	7.44328i	0.183074	−	0.317094i
$552$		0			0
$553$	3.80221	+	6.58562i	0.161686	+	0.280049i
$554$	4.38785	+	7.59998i	0.186422	+	0.322892i
$555$		0			0
$556$	−13.3299	+	23.0880i	−0.565312	+	0.979150i
$557$	−8.50115			−0.360205			−0.180103	−	0.983648i	$-0.557643\pi$
$557$	−8.50115			−0.360205			−0.180103	+	0.983648i	$0.557643\pi$
$558$		0			0
$559$	29.3195			1.24008
$560$	2.67267	−	4.62919i	0.112941	−	0.195619i
$561$		0			0
$562$	−1.39038	−	2.40821i	−0.0586497	−	0.101584i
$563$	−11.7003	−	20.2656i	−0.493110	−	0.854091i	0.506859	−	0.862029i	$-0.330807\pi$
$563$	−11.7003	−	20.2656i	−0.493110	−	0.854091i	−0.999968	+	0.00793792i	$0.997473\pi$
$564$		0			0
$565$	21.9066	−	37.9434i	0.921619	−	1.59629i
$566$	6.47252			0.272060
$567$		0			0
$568$	−18.7483			−0.786660
$569$	4.05646	−	7.02600i	0.170056	−	0.294545i	−0.768383	−	0.639990i	$-0.778939\pi$
$569$	4.05646	−	7.02600i	0.170056	−	0.294545i	0.938439	+	0.345445i	$0.112272\pi$
$570$		0			0
$571$	−8.29738	−	14.3715i	−0.347234	−	0.601428i	0.638523	−	0.769603i	$-0.279546\pi$
$571$	−8.29738	−	14.3715i	−0.347234	−	0.601428i	−0.985757	+	0.168175i	$0.946213\pi$
$572$	14.1512	+	24.5106i	0.591692	+	1.02484i
$573$		0			0
$574$	3.00000	−	5.19615i	0.125218	−	0.216883i
$575$	−0.675938			−0.0281886
$576$		0			0
$577$	−10.8921			−0.453445			−0.226723	−	0.973959i	$-0.572801\pi$
$577$	−10.8921			−0.453445			−0.226723	+	0.973959i	$0.572801\pi$
$578$	1.68753	−	2.92288i	0.0701919	−	0.121576i
$579$		0			0
$580$	2.19084	+	3.79464i	0.0909696	+	0.157564i
$581$	−5.72545	−	9.91677i	−0.237532	−	0.411417i
$582$		0			0
$583$	0.648689	−	1.12356i	0.0268660	−	0.0465332i
$584$	−1.65237			−0.0683755
$585$		0			0
$586$	5.39558			0.222889
$587$	21.6597	−	37.5158i	0.893993	−	1.54844i	0.0589466	−	0.998261i	$-0.481226\pi$
$587$	21.6597	−	37.5158i	0.893993	−	1.54844i	0.835046	−	0.550180i	$-0.185441\pi$
$588$		0			0
$589$	−7.45090	−	12.9053i	−0.307009	−	0.531755i
$590$	−4.66939	−	8.08763i	−0.192236	−	0.332962i
$591$		0			0
$592$	−6.07018	+	10.5139i	−0.249483	+	0.432117i
$593$	28.4583			1.16864			0.584320	−	0.811523i	$-0.301361\pi$
$593$	28.4583			1.16864			0.584320	+	0.811523i	$0.301361\pi$
$594$		0			0
$595$	7.15352			0.293266
$596$	11.5630	−	20.0278i	0.473641	−	0.820370i
$597$		0			0
$598$	−3.63765	−	6.30059i	−0.148754	−	0.257650i
$599$	14.8502	+	25.7212i	0.606761	+	1.05094i	0.991770	+	0.128028i	$0.0408649\pi$
$599$	14.8502	+	25.7212i	0.606761	+	1.05094i	−0.385009	+	0.922913i	$0.625802\pi$
$600$		0			0
$601$	−18.7531	+	32.4813i	−0.764955	+	1.32494i	0.175315	+	0.984512i	$0.443906\pi$
$601$	−18.7531	+	32.4813i	−0.764955	+	1.32494i	−0.940270	+	0.340429i	$0.889428\pi$
$602$	4.87161			0.198552
$603$		0			0
$604$	−20.0228			−0.814717
$605$	17.6727	−	30.6100i	0.718496	−	1.24447i
$606$		0			0
$607$	−1.32987	−	2.30340i	−0.0539776	−	0.0934919i	0.837774	−	0.546017i	$-0.183857\pi$
$607$	−1.32987	−	2.30340i	−0.0539776	−	0.0934919i	−0.891752	+	0.452525i	$0.850523\pi$
$608$	−19.2842	−	33.4012i	−0.782078	−	1.35460i
$609$		0			0
$610$	4.96268	−	8.59562i	0.200933	−	0.348026i
$611$	−3.30474			−0.133695
$612$		0			0
$613$	−41.6694			−1.68301			−0.841505	−	0.540249i	$-0.818330\pi$
$613$	−41.6694			−1.68301			−0.841505	+	0.540249i	$0.818330\pi$
$614$	0.0804406	−	0.139327i	0.00324632	−	0.00562279i
$615$		0			0
$616$	5.07676	+	8.79321i	0.204548	+	0.354288i
$617$	21.7759	+	37.7170i	0.876666	+	1.51843i	0.854977	+	0.518665i	$0.173571\pi$
$617$	21.7759	+	37.7170i	0.876666	+	1.51843i	0.0216887	+	0.999765i	$0.493096\pi$
$618$		0			0
$619$	7.03249	−	12.1806i	0.282660	−	0.489581i	−0.689379	−	0.724401i	$-0.742117\pi$
$619$	7.03249	−	12.1806i	0.282660	−	0.489581i	0.972039	+	0.234820i	$0.0754500\pi$
$620$	7.59706			0.305105
$621$		0			0
$622$	0.549103			0.0220170
$623$	−4.62471	+	8.01024i	−0.185285	+	0.320923i
$624$		0			0
$625$	12.1044	+	20.9655i	0.484177	+	0.838619i
$626$	−8.39811	−	14.5460i	−0.335656	−	0.581373i
$627$		0			0
$628$	−21.0180	+	36.4042i	−0.838709	+	1.45269i
$629$	−16.2471			−0.647815
$630$		0			0
$631$	−0.594756			−0.0236769			−0.0118384	−	0.999930i	$-0.503768\pi$
$631$	−0.594756			−0.0236769			−0.0118384	+	0.999930i	$0.503768\pi$
$632$	−7.42209	+	12.8554i	−0.295235	+	0.511362i
$633$		0			0
$634$	1.68813	+	2.92393i	0.0670442	+	0.116124i
$635$	10.2340	+	17.7257i	0.406122	+	0.703424i
$636$		0			0
$637$	−1.57676	+	2.73103i	−0.0624735	+	0.108207i
$638$	−3.14386			−0.124467
$639$		0			0
$640$	25.2641			0.998653
$641$	3.84533	−	6.66031i	0.151881	−	0.263066i	−0.780038	−	0.625733i	$-0.784800\pi$
$641$	3.84533	−	6.66031i	0.151881	−	0.263066i	0.931919	+	0.362666i	$0.118133\pi$
$642$		0			0
$643$	−24.9115	−	43.1479i	−0.982412	−	1.70159i	−0.652916	−	0.757430i	$-0.726455\pi$
$643$	−24.9115	−	43.1479i	−0.982412	−	1.70159i	−0.329496	−	0.944157i	$-0.606879\pi$
$644$	3.79853	+	6.57924i	0.149683	+	0.259258i
$645$		0			0
$646$	6.34303	−	10.9865i	0.249563	−	0.432256i
$647$	28.2761			1.11165			0.555824	−	0.831300i	$-0.312403\pi$
$647$	28.2761			1.11165			0.555824	+	0.831300i	$0.312403\pi$
$648$		0			0
$649$	−42.1106			−1.65299
$650$	0.126836	−	0.219686i	0.00497490	−	0.00861678i
$651$		0			0
$652$	4.83507	+	8.37458i	0.189356	+	0.327974i
$653$	4.77708	+	8.27415i	0.186942	+	0.323792i	0.944229	−	0.329289i	$-0.106809\pi$
$653$	4.77708	+	8.27415i	0.186942	+	0.323792i	−0.757287	+	0.653082i	$0.773476\pi$
$654$		0			0
$655$	8.30704	−	14.3882i	0.324583	−	0.562194i
$656$	−27.8036			−1.08555
$657$		0			0
$658$	−0.549103			−0.0214062
$659$	−24.0996	+	41.7417i	−0.938787	+	1.62603i	−0.171048	+	0.985263i	$0.554715\pi$
$659$	−24.0996	+	41.7417i	−0.938787	+	1.62603i	−0.767738	+	0.640763i	$0.778618\pi$
$660$		0			0
$661$	−1.02766	−	1.77995i	−0.0399712	−	0.0692322i	0.845348	−	0.534217i	$-0.179393\pi$
$661$	−1.02766	−	1.77995i	−0.0399712	−	0.0692322i	−0.885319	+	0.464984i	$0.846060\pi$
$662$	5.40065	+	9.35419i	0.209902	+	0.363561i
$663$		0			0
$664$	11.1763	−	19.3580i	0.433726	−	0.751236i
$665$	−16.4029			−0.636079
$666$		0			0
$667$	−5.07888			−0.196655
$668$	−20.2317	+	35.0423i	−0.782786	+	1.35583i
$669$		0			0
$670$	−4.38592	−	7.59664i	−0.169443	−	0.293484i
$671$	−22.3778	−	38.7595i	−0.863886	−	1.49629i
$672$		0			0
$673$	−1.89558	+	3.28325i	−0.0730694	+	0.126560i	−0.900245	−	0.435384i	$-0.856613\pi$
$673$	−1.89558	+	3.28325i	−0.0730694	+	0.126560i	0.827176	+	0.561943i	$0.189946\pi$
$674$	13.8647			0.534049
$675$		0			0
$676$	5.27179			0.202761
$677$	−11.2568	+	19.4973i	−0.432633	+	0.749343i	−0.997099	−	0.0761134i	$-0.975749\pi$
$677$	−11.2568	+	19.4973i	−0.432633	+	0.749343i	0.564466	+	0.825457i	$0.309082\pi$
$678$		0			0
$679$	1.72545	+	2.98856i	0.0662166	+	0.114691i
$680$	6.98200	+	12.0932i	0.267748	+	0.463752i
$681$		0			0
$682$	−2.72545	+	4.72062i	−0.104363	+	0.180762i
$683$	−15.3933			−0.589008			−0.294504	−	0.955650i	$-0.595154\pi$
$683$	−15.3933			−0.589008			−0.294504	+	0.955650i	$0.595154\pi$
$684$		0			0
$685$	3.08854			0.118007
$686$	−0.261988	+	0.453777i	−0.0100028	+	0.0173253i
$687$		0			0
$688$	−11.2873	−	19.5503i	−0.430326	−	0.745347i
$689$	0.393284	+	0.681187i	0.0149829	+	0.0259512i
$690$		0			0
$691$	11.6044	−	20.0994i	0.441453	−	0.764619i	−0.556345	−	0.830952i	$-0.687797\pi$
$691$	11.6044	−	20.0994i	0.441453	−	0.764619i	0.997798	+	0.0663329i	$0.0211299\pi$
$692$	38.8373			1.47637
$693$		0			0
$694$	−2.35343			−0.0893351
$695$	−17.0074	+	29.4576i	−0.645126	+	1.11739i
$696$		0			0
$697$	−18.6044	−	32.2238i	−0.704693	−	1.22056i
$698$	−0.984535	−	1.70526i	−0.0372652	−	0.0645452i
$699$		0			0
$700$	−0.132445	+	0.229402i	−0.00500595	+	0.00867056i
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	37.2545			1.40508
$704$	5.57561	−	9.65724i	0.210139	−	0.363971i
$705$		0			0
$706$	5.04565	+	8.73933i	0.189896	+	0.328909i
$707$	8.20147	+	14.2054i	0.308448	+	0.534248i
$708$		0			0
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	0.995228	−	0.0975728i	$-0.0311079\pi$
$710$	−11.0789			−0.415783
$711$		0			0
$712$	−18.0553			−0.676652
$713$	−4.40294	+	7.62612i	−0.164892	+	0.285601i
$714$		0			0
$715$	18.0553	+	31.2727i	0.675230	+	1.16953i
$716$	5.60672	+	9.71112i	0.209533	+	0.362922i
$717$		0			0
$718$	−2.38555	+	4.13190i	−0.0890280	+	0.154201i
$719$	−18.2111			−0.679161			−0.339580	−	0.940577i	$-0.610285\pi$
$719$	−18.2111			−0.679161			−0.339580	+	0.940577i	$0.610285\pi$
$720$		0			0
$721$	−1.14386			−0.0425995
$722$	−9.56673	+	16.5701i	−0.356037	+	0.616674i
$723$		0			0
$724$	1.72545	+	2.98856i	0.0641258	+	0.111069i
$725$	−0.0885439	−	0.153363i	−0.00328844	−	0.00569574i
$726$		0			0
$727$	−4.41841	+	7.65291i	−0.163870	+	0.283831i	−0.936253	−	0.351326i	$-0.885731\pi$
$727$	−4.41841	+	7.65291i	−0.163870	+	0.283831i	0.772384	+	0.635156i	$0.219064\pi$
$728$	−6.15582			−0.228150
$729$		0			0
$730$	−0.976432			−0.0361394
$731$	15.1056	−	26.1636i	0.558700	−	0.967696i
$732$		0			0
$733$	22.3202	+	38.6597i	0.824416	+	1.42793i	0.902365	+	0.430972i	$0.141829\pi$
$733$	22.3202	+	38.6597i	0.824416	+	1.42793i	−0.0779496	+	0.996957i	$0.524837\pi$
$734$	−1.20377	−	2.08499i	−0.0444320	−	0.0769585i
$735$		0			0
$736$	−11.3956	+	19.7377i	−0.420047	+	0.727542i
$737$	−39.5542			−1.45700
$738$		0			0
$739$	11.6044			0.426875			0.213438	−	0.976957i	$-0.431534\pi$
$739$	11.6044			0.426875			0.213438	+	0.976957i	$0.431534\pi$
$740$	−9.49632	+	16.4481i	−0.349092	+	0.604644i
$741$		0			0
$742$	0.0653464	+	0.113183i	0.00239894	+	0.00415509i
$743$	−13.3970	−	23.2042i	−0.491487	−	0.851280i	0.508465	−	0.861083i	$-0.330213\pi$
$743$	−13.3970	−	23.2042i	−0.491487	−	0.851280i	−0.999952	+	0.00980228i	$0.996880\pi$
$744$		0			0
$745$	14.7531	−	25.5531i	0.540512	−	0.936194i
$746$	−11.1934			−0.409818
$747$		0			0
$748$	29.1632			1.06631
$749$	−4.55278	+	7.88565i	−0.166355	+	0.288135i
$750$		0			0
$751$	9.10925	+	15.7777i	0.332401	+	0.575736i	0.982982	−	0.183701i	$-0.0588079\pi$
$751$	9.10925	+	15.7777i	0.332401	+	0.575736i	−0.650581	+	0.759437i	$0.725475\pi$
$752$	1.27225	+	2.20360i	0.0463942	+	0.0803572i
$753$		0			0
$754$	0.953020	−	1.65068i	0.0347070	−	0.0601142i
$755$	−25.5468			−0.929743
$756$		0			0
$757$	12.9018			0.468924			0.234462	−	0.972125i	$-0.424667\pi$
$757$	12.9018			0.468924			0.234462	+	0.972125i	$0.424667\pi$
$758$	9.20110	−	15.9368i	0.334199	−	0.578850i
$759$		0			0
$760$	−16.0097	−	27.7295i	−0.580731	−	1.00586i
$761$	−9.10810	−	15.7757i	−0.330168	−	0.571868i	0.652376	−	0.757895i	$-0.273772\pi$
$761$	−9.10810	−	15.7757i	−0.330168	−	0.571868i	−0.982545	+	0.186027i	$0.940439\pi$
$762$		0			0
$763$	6.87414	−	11.9064i	0.248860	−	0.431039i
$764$	23.3082			0.843263
$765$		0			0
$766$	1.67364			0.0604710
$767$	12.7653	−	22.1101i	0.460928	−	0.798351i
$768$		0			0
$769$	−19.3022	−	33.4324i	−0.696055	−	1.20560i	−0.969824	−	0.243808i	$-0.921603\pi$
$769$	−19.3022	−	33.4324i	−0.696055	−	1.20560i	0.273768	−	0.961796i	$-0.411730\pi$
$770$	3.00000	+	5.19615i	0.108112	+	0.187256i
$771$		0			0
$772$	15.3119	−	26.5209i	0.551086	−	0.954509i
$773$	33.9594			1.22144			0.610718	−	0.791849i	$-0.290881\pi$
$773$	33.9594			1.22144			0.610718	+	0.791849i	$0.290881\pi$
$774$		0			0
$775$	−0.307039			−0.0110292
$776$	−3.36816	+	5.83382i	−0.120910	+	0.209422i
$777$		0			0
$778$	−3.87897	−	6.71857i	−0.139068	−	0.240872i
$779$	42.6597	+	73.8888i	1.52844	+	2.64734i
$780$		0			0
$781$	−24.9786	+	43.2641i	−0.893803	+	1.54811i
$782$	−7.49655			−0.268076
$783$		0			0
$784$	2.42807			0.0867168
$785$	−26.8165	+	46.4476i	−0.957123	+	1.65779i
$786$		0			0
$787$	3.42807	+	5.93759i	0.122198	+	0.211652i	0.920634	−	0.390427i	$-0.127673\pi$
$787$	3.42807	+	5.93759i	0.122198	+	0.211652i	−0.798436	+	0.602079i	$0.794339\pi$
$788$	−13.9838	−	24.2206i	−0.498151	−	0.862822i
$789$		0			0
$790$	−4.38592	+	7.59664i	−0.156044	+	0.270276i
$791$	19.9018			0.707626
$792$		0			0
$793$	27.1342			0.963564
$794$	−7.04542	+	12.2030i	−0.250033	+	0.433069i
$795$		0			0
$796$	−6.16318	−	10.6749i	−0.218448	−	0.378363i
$797$	−13.3250	−	23.0796i	−0.471997	−	0.817523i	0.527490	−	0.849561i	$-0.323133\pi$
$797$	−13.3250	−	23.0796i	−0.471997	−	0.817523i	−0.999487	+	0.0320387i	$0.989800\pi$
$798$		0			0
$799$	−1.70262	+	2.94903i	−0.0602344	+	0.104329i
$800$	−0.794670			−0.0280958
$801$		0			0
$802$	10.1667			0.358998
$803$	−2.20147	+	3.81306i	−0.0776883	+	0.134560i
$804$		0			0
$805$	4.84648	+	8.39435i	0.170816	+	0.295862i
$806$	−1.65237	−	2.86199i	−0.0582022	−	0.100809i
$807$		0			0
$808$	−16.0097	+	27.7295i	−0.563218	+	0.975522i
$809$	−45.7100			−1.60708			−0.803539	−	0.595252i	$-0.797052\pi$
$809$	−45.7100			−1.60708			−0.803539	+	0.595252i	$0.797052\pi$
$810$		0			0
$811$	33.2088			1.16612			0.583060	−	0.812429i	$-0.301855\pi$
$811$	33.2088			1.16612			0.583060	+	0.812429i	$0.301855\pi$
$812$	−0.995169	+	1.72368i	−0.0349236	+	0.0604894i
$813$		0			0
$814$	−6.81362	−	11.8015i	−0.238817	−	0.413644i
$815$	6.16898	+	10.6850i	0.216090	+	0.374279i
$816$		0			0
$817$	−34.6369	+	59.9929i	−1.21179	+	2.09889i
$818$	−4.92306			−0.172131
$819$		0			0
$820$	−43.4966			−1.51897
$821$	−0.152370	+	0.263912i	−0.00531774	+	0.00921060i	−0.868672	−	0.495388i	$-0.835026\pi$
$821$	−0.152370	+	0.263912i	−0.00531774	+	0.00921060i	0.863354	+	0.504598i	$0.168359\pi$
$822$		0			0
$823$	−23.2088	−	40.1989i	−0.809009	−	1.40124i	−0.913551	−	0.406724i	$-0.866671\pi$
$823$	−23.2088	−	40.1989i	−0.809009	−	1.40124i	0.104542	−	0.994520i	$-0.466662\pi$
$824$	−1.11643	−	1.93372i	−0.0388928	−	0.0673643i
$825$		0			0
$826$	2.12103	−	3.67373i	0.0738001	−	0.127826i
$827$	−40.8133			−1.41922			−0.709608	−	0.704597i	$-0.751128\pi$
$827$	−40.8133			−1.41922			−0.709608	+	0.704597i	$0.751128\pi$
$828$		0			0
$829$	−7.40524			−0.257195			−0.128597	−	0.991697i	$-0.541047\pi$
$829$	−7.40524			−0.257195			−0.128597	+	0.991697i	$0.541047\pi$
$830$	6.60442	−	11.4392i	0.229243	−	0.397060i
$831$		0			0
$832$	3.38035	+	5.85494i	0.117193	+	0.202983i
$833$	1.62471	+	2.81408i	0.0562930	+	0.0975023i
$834$		0			0
$835$	−25.8133	+	44.7099i	−0.893304	+	1.54725i
$836$	−66.8709			−2.31278
$837$		0			0
$838$	−12.9211			−0.446353
$839$	−9.18601	+	15.9106i	−0.317136	+	0.549296i	−0.979889	−	0.199542i	$-0.936055\pi$
$839$	−9.18601	+	15.9106i	−0.317136	+	0.549296i	0.662753	+	0.748838i	$0.269388\pi$
$840$		0			0
$841$	13.8347	+	23.9624i	0.477058	+	0.826290i
$842$	3.72255	+	6.44764i	0.128287	+	0.222200i
$843$		0			0
$844$	2.84473	−	4.92721i	0.0979196	−	0.169602i
$845$	6.72619			0.231388
$846$		0			0
$847$	16.0553			0.551667
$848$	0.302811	−	0.524484i	0.0103986	−	0.0180109i
$849$		0			0
$850$	−0.130693	−	0.226367i	−0.00448273	−	0.00776431i
$851$	−11.0074	−	19.0653i	−0.377327	−	0.653550i
$852$		0			0
$853$	−18.7808	+	32.5292i	−0.643041	+	1.11378i	0.341709	+	0.939806i	$0.388994\pi$
$853$	−18.7808	+	32.5292i	−0.643041	+	1.11378i	−0.984750	+	0.173974i	$0.944339\pi$
$854$	4.50851			0.154278
$855$		0			0
$856$	−17.7745			−0.607520
$857$	1.07561	−	1.86301i	0.0367421	−	0.0636393i	−0.847070	−	0.531482i	$-0.821635\pi$
$857$	1.07561	−	1.86301i	0.0367421	−	0.0636393i	0.883812	+	0.467843i	$0.154969\pi$
$858$		0			0
$859$	−7.14386	−	12.3735i	−0.243745	−	0.422179i	0.718033	−	0.696009i	$-0.245043\pi$
$859$	−7.14386	−	12.3735i	−0.243745	−	0.422179i	−0.961778	+	0.273830i	$0.911709\pi$
$860$	−17.6582	−	30.5849i	−0.602139	−	1.04293i
$861$		0			0
$862$	3.40524	−	5.89806i	0.115983	−	0.200889i
$863$	27.6810			0.942272			0.471136	−	0.882061i	$-0.343844\pi$
$863$	27.6810			0.942272			0.471136	+	0.882061i	$0.343844\pi$
$864$		0			0
$865$	49.5519			1.68481
$866$	0.238791	−	0.413598i	0.00811444	−	0.0140546i
$867$		0			0
$868$	1.72545	+	2.98856i	0.0585655	+	0.101439i
$869$	19.7771	+	34.2549i	0.670892	+	1.16202i
$870$		0			0
$871$	11.9903	−	20.7679i	0.406277	−	0.703693i
$872$	26.8373			0.908825
$873$		0			0
$874$	17.1895			0.581444
$875$	−5.67267	+	9.82534i	−0.191771	+	0.332157i
$876$		0			0
$877$	9.50000	+	16.4545i	0.320792	+	0.555628i	0.980652	−	0.195761i	$-0.0627176\pi$
$877$	9.50000	+	16.4545i	0.320792	+	0.555628i	−0.659860	+	0.751389i	$0.729384\pi$
$878$	2.76374	+	4.78694i	0.0932717	+	0.161551i
$879$		0			0
$880$	13.9018	−	24.0786i	0.468629	−	0.811690i
$881$	−4.06498			−0.136953			−0.0684763	−	0.997653i	$-0.521814\pi$
$881$	−4.06498			−0.136953			−0.0684763	+	0.997653i	$0.521814\pi$
$882$		0			0
$883$	−20.5255			−0.690739			−0.345370	−	0.938467i	$-0.612246\pi$
$883$	−20.5255			−0.690739			−0.345370	+	0.938467i	$0.612246\pi$
$884$	−8.84045	+	15.3121i	−0.297336	+	0.515002i
$885$		0			0
$886$	4.55876	+	7.89601i	0.153155	+	0.265272i
$887$	−5.05761	−	8.76004i	−0.169818	−	0.294134i	0.768538	−	0.639804i	$-0.220985\pi$
$887$	−5.05761	−	8.76004i	−0.169818	−	0.294134i	−0.938356	+	0.345671i	$0.887651\pi$
$888$		0			0
$889$	−4.64869	+	8.05177i	−0.155912	+	0.270048i
$890$	−10.6694			−0.357639
$891$		0			0
$892$	40.0457			1.34083
$893$	3.90409	−	6.76209i	0.130646	−	0.226285i
$894$		0			0
$895$	7.15352	+	12.3903i	0.239116	+	0.414161i
$896$	5.73801	+	9.93853i	0.191694	+	0.332023i
$897$		0			0
$898$	−0.196039	+	0.339550i	−0.00654192	+	0.0113309i
$899$	−2.30704			−0.0769441
$900$		0			0
$901$	0.810488			0.0270013
$902$	15.6044	−	27.0276i	0.519570	−	0.899922i
$903$		0			0
$904$	19.4246	+	33.6444i	0.646053	+	1.11900i
$905$	2.20147	+	3.81306i	0.0731794	+	0.126750i
$906$		0			0
$907$	−11.1978	+	19.3951i	−0.371817	+	0.644005i	−0.989845	−	0.142151i	$-0.954598\pi$
$907$	−11.1978	+	19.3951i	−0.371817	+	0.644005i	0.618028	+	0.786156i	$0.287932\pi$
$908$	−20.1222			−0.667780
$909$		0			0
$910$	−3.63765			−0.120587
$911$	−16.9018	+	29.2748i	−0.559981	+	0.969916i	0.437516	+	0.899211i	$0.355858\pi$
$911$	−16.9018	+	29.2748i	−0.559981	+	0.969916i	−0.997497	+	0.0707056i	$0.977475\pi$
$912$		0			0
$913$	−29.7808	−	51.5818i	−0.985599	−	1.70711i
$914$	0.261988	+	0.453777i	0.00866580	+	0.0150096i
$915$		0			0
$916$	1.20400	−	2.08540i	0.0397814	−	0.0689034i
$917$	7.54680			0.249217
$918$		0			0
$919$	35.6044			1.17448			0.587241	−	0.809412i	$-0.300214\pi$
$919$	35.6044			1.17448			0.587241	+	0.809412i	$0.300214\pi$
$920$	−9.46056	+	16.3862i	−0.311905	+	0.540236i
$921$		0			0
$922$	9.96751	+	17.2642i	0.328263	+	0.568567i
$923$	−15.1439	−	26.2299i	−0.498466	−	0.863369i
$924$		0			0
$925$	0.383799	−	0.664759i	0.0126192	−	0.0218571i
$926$	−13.5669			−0.445835
$927$		0			0
$928$	−5.97102			−0.196008
$929$	−16.2063	+	28.0701i	−0.531712	+	0.920951i	0.467603	+	0.883938i	$0.345118\pi$
$929$	−16.2063	+	28.0701i	−0.531712	+	0.920951i	−0.999315	+	0.0370130i	$0.988216\pi$
$930$		0			0
$931$	−3.72545	−	6.45267i	−0.122097	−	0.211478i
$932$	−7.54933	−	13.0758i	−0.247287	−	0.428313i
$933$		0			0
$934$	−4.47022	+	7.74265i	−0.146270	+	0.253347i
$935$	37.2088			1.21686
$936$		0			0
$937$	−4.34303			−0.141881			−0.0709403	−	0.997481i	$-0.522600\pi$
$937$	−4.34303			−0.141881			−0.0709403	+	0.997481i	$0.522600\pi$
$938$	1.99227	−	3.45071i	0.0650498	−	0.112670i
$939$		0			0
$940$	1.99034	+	3.44737i	0.0649177	+	0.112441i
$941$	−15.9700	−	27.6609i	−0.520609	−	0.901720i	−0.999713	−	0.0239625i	$-0.992372\pi$
$941$	−15.9700	−	27.6609i	−0.520609	−	0.901720i	0.479104	−	0.877758i	$-0.340962\pi$
$942$		0			0
$943$	25.2088	−	43.6630i	0.820913	−	1.42186i
$944$	−19.6574			−0.639795
$945$		0			0
$946$	25.3395			0.823859
$947$	−20.2568	+	35.0858i	−0.658257	+	1.14013i	0.322809	+	0.946464i	$0.395373\pi$
$947$	−20.2568	+	35.0858i	−0.658257	+	1.14013i	−0.981067	+	0.193671i	$0.937961\pi$
$948$		0			0
$949$	−1.33470	−	2.31176i	−0.0433261	−	0.0750430i
$950$	0.299677	+	0.519056i	0.00972282	+	0.0168404i
$951$		0			0
$952$	−3.17152	+	5.49323i	−0.102789	+	0.178036i
$953$	−9.74828			−0.315778			−0.157889	−	0.987457i	$-0.550469\pi$
$953$	−9.74828			−0.315778			−0.157889	+	0.987457i	$0.550469\pi$
$954$		0			0
$955$	29.7386			0.962319
$956$	−4.05707	+	7.02705i	−0.131215	+	0.227271i
$957$		0			0
$958$	−0.735110	−	1.27325i	−0.0237503	−	0.0411368i
$959$	0.701472	+	1.21499i	0.0226517	+	0.0392339i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	8.26185			0.266373
$963$		0			0
$964$	7.94469			0.255881
$965$	19.5362	−	33.8376i	0.628892	−	1.08927i
$966$		0			0
$967$	−14.8465	−	25.7149i	−0.477431	−	0.826934i	0.522235	−	0.852802i	$-0.325098\pi$
$967$	−14.8465	−	25.7149i	−0.477431	−	0.826934i	−0.999665	+	0.0258677i	$0.991765\pi$
$968$	15.6704	+	27.1419i	0.503665	+	0.872373i
$969$		0			0
$970$	−1.99034	+	3.44737i	−0.0639059	+	0.110688i
$971$	−31.9954			−1.02678			−0.513391	−	0.858155i	$-0.671611\pi$
$971$	−31.9954			−1.02678			−0.513391	+	0.858155i	$0.671611\pi$
$972$		0			0
$973$	−15.4509			−0.495333
$974$	1.70455	−	2.95237i	0.0546173	−	0.0946000i
$975$		0			0
$976$	−10.4461	−	18.0931i	−0.334370	−	0.579147i
$977$	0.904094	+	1.56594i	0.0289245	+	0.0500988i	0.880125	−	0.474741i	$-0.157458\pi$
$977$	0.904094	+	1.56594i	0.0289245	+	0.0500988i	−0.851201	+	0.524840i	$0.824125\pi$
$978$		0			0
$979$	−24.0553	+	41.6650i	−0.768811	+	1.33162i
$980$	3.79853			0.121340
$981$		0			0
$982$	2.41767			0.0771509
$983$	21.7734	−	37.7126i	0.694464	−	1.20285i	−0.275898	−	0.961187i	$-0.588975\pi$
$983$	21.7734	−	37.7126i	0.694464	−	1.20285i	0.970361	−	0.241659i	$-0.0776916\pi$
$984$		0			0
$985$	−17.8416	−	30.9026i	−0.568482	−	0.984640i
$986$	−0.982004	−	1.70088i	−0.0312734	−	0.0541671i
$987$		0			0
$988$	20.2710	−	35.1105i	0.644908	−	1.11701i
$989$	40.9358			1.30168
$990$		0			0
$991$	−33.1010			−1.05149			−0.525743	−	0.850643i	$-0.676213\pi$
$991$	−33.1010			−1.05149			−0.525743	+	0.850643i	$0.676213\pi$
$992$	−5.17635	+	8.96569i	−0.164349	+	0.284661i
$993$		0			0
$994$	−2.51624	−	4.35826i	−0.0798104	−	0.138236i
$995$	−7.86350	−	13.6200i	−0.249290	−	0.431783i
$996$		0			0
$997$	0.269721	−	0.467170i	0.00854214	−	0.0147954i	−0.861723	−	0.507379i	$-0.830614\pi$
$997$	0.269721	−	0.467170i	0.00854214	−	0.0147954i	0.870265	+	0.492584i	$0.163948\pi$
$998$	−18.5994			−0.588752
$999$		0			0

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

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a_p

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.l.379.2		6
3.2	odd	2		567.2.f.m.379.2		6
9.2	odd	6		567.2.a.e.1.2	✓	3
9.4	even	3	inner	567.2.f.l.190.2		6
9.5	odd	6		567.2.f.m.190.2		6
9.7	even	3		567.2.a.f.1.2	yes	3
36.7	odd	6		9072.2.a.cb.1.1		3
36.11	even	6		9072.2.a.bu.1.3		3
63.20	even	6		3969.2.a.o.1.2		3
63.34	odd	6		3969.2.a.n.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.a.e.1.2	✓	3	9.2	odd	6
567.2.a.f.1.2	yes	3	9.7	even	3
567.2.f.l.190.2		6	9.4	even	3	inner
567.2.f.l.379.2		6	1.1	even	1	trivial
567.2.f.m.190.2		6	9.5	odd	6
567.2.f.m.379.2		6	3.2	odd	2
3969.2.a.n.1.2		3	63.34	odd	6
3969.2.a.o.1.2		3	63.20	even	6
9072.2.a.bu.1.3		3	36.11	even	6
9072.2.a.cb.1.1		3	36.7	odd	6

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	567.2.f.l.379.2

Level	$567$
Weight	$2$
Character	567.379
Analytic conductor	$4.528$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$