LMFDB - Embedded newform 726.2.h.c.161.1

Error: no document with id 214232042 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(161,726)] 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("726.161"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,2,-2,-5,2,5,-2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.185640625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.1
Root			$-0.245684 - 1.71454i$ of defining polynomial
Character	$\chi$	$=$	726.161
Dual form			726.2.h.c.239.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.20654 + 1.24268i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.24568 - 1.71454i) q^{5} +(1.70654 - 0.296161i) q^{6} +(3.26124 - 1.05964i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.0885088 - 2.99869i) q^{9} +2.11929i q^{10} +(-1.55470 - 0.763481i) q^{12} +(-1.10940 + 1.52696i) q^{13} +(-3.26124 - 1.05964i) q^{14} +(3.63359 + 0.520675i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.17274 + 3.03167i) q^{17} +(-1.69098 + 2.47802i) q^{18} +(0.229139 + 0.0744518i) q^{19} +(1.24568 - 1.71454i) q^{20} +(-2.61803 + 5.33119i) q^{21} -4.97072i q^{23} +(0.809017 + 1.53150i) q^{24} +(0.157176 - 0.483737i) q^{25} +(1.79505 - 0.583248i) q^{26} +(3.83321 + 3.50806i) q^{27} +(2.01556 + 2.77418i) q^{28} +(1.28812 + 3.96443i) q^{29} +(-2.63359 - 2.55701i) q^{30} +(-5.30198 - 3.85211i) q^{31} +1.00000 q^{32} +5.15778 q^{34} +(-5.87928 - 4.27155i) q^{35} +(2.82458 - 1.01082i) q^{36} +(-2.72744 - 8.39419i) q^{37} +(-0.141616 - 0.194917i) q^{38} +(-0.558984 - 3.22098i) q^{39} +(-2.01556 + 0.654895i) q^{40} +(2.45223 - 7.54718i) q^{41} +(5.25163 - 2.77418i) q^{42} -6.51583i q^{43} +(-5.03112 + 3.88718i) q^{45} +(-2.92172 + 4.02140i) q^{46} +(-3.20495 - 1.04135i) q^{47} +(0.245684 - 1.71454i) q^{48} +(3.84975 - 2.79701i) q^{49} +(-0.411491 + 0.298966i) q^{50} +(1.26719 - 8.84322i) q^{51} +(-1.79505 - 0.583248i) q^{52} +(3.65283 - 5.02768i) q^{53} +(-1.03914 - 5.09119i) q^{54} -3.42908i q^{56} +(-0.368986 + 0.194917i) q^{57} +(1.28812 - 3.96443i) q^{58} +(2.63628 - 0.856580i) q^{59} +(0.627650 + 3.61665i) q^{60} +(0.951618 + 1.30979i) q^{61} +(2.02518 + 6.23285i) q^{62} +(-3.46619 - 9.68569i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.00000 q^{65} -9.98396 q^{67} +(-4.17274 - 3.03167i) q^{68} +(6.17702 + 5.99739i) q^{69} +(2.24568 + 6.91151i) q^{70} +(-5.85410 - 8.05748i) q^{71} +(-2.87928 - 0.842471i) q^{72} +(2.35838 - 0.766285i) q^{73} +(-2.72744 + 8.39419i) q^{74} +(0.411491 + 0.778968i) q^{75} +0.240931i q^{76} +(-1.44102 + 2.93439i) q^{78} +(6.65877 - 9.16501i) q^{79} +(2.01556 + 0.654895i) q^{80} +(-8.98433 + 0.530822i) q^{81} +(-6.42001 + 4.66441i) q^{82} +(-5.55630 + 4.03689i) q^{83} +(-5.87928 - 0.842471i) q^{84} +(10.3958 + 3.37781i) q^{85} +(-3.82991 + 5.27142i) q^{86} +(-6.48070 - 3.18254i) q^{87} -2.47254i q^{89} +(6.35509 - 0.187575i) q^{90} +(-2.00000 + 6.15537i) q^{91} +(4.72744 - 1.53604i) q^{92} +(11.1840 - 1.94093i) q^{93} +(1.98077 + 2.72629i) q^{94} +(-0.157785 - 0.485611i) q^{95} +(-1.20654 + 1.24268i) q^{96} +(10.6968 + 7.77169i) q^{97} -4.75856 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 5 q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} + 2 q^{9} - 3 q^{12} + 10 q^{13} - 5 q^{14} + 4 q^{15} - 2 q^{16} - 15 q^{17} - 18 q^{18} + 10 q^{19} + 5 q^{20} - 12 q^{21} + 2 q^{24}+ \cdots + 22 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 5 * q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 + 2 * q^9 - 3 * q^12 + 10 * q^13 - 5 * q^14 + 4 * q^15 - 2 * q^16 - 15 * q^17 - 18 * q^18 + 10 * q^19 + 5 * q^20 - 12 * q^21 + 2 * q^24 - q^25 + 20 * q^27 + 22 * q^29 + 4 * q^30 - 2 * q^31 + 8 * q^32 + 10 * q^34 - 17 * q^35 + 2 * q^36 + 6 * q^37 - 15 * q^38 - 8 * q^39 + 3 * q^41 + 8 * q^42 - 8 * q^45 - 10 * q^46 - 40 * q^47 - 3 * q^48 + 7 * q^49 - 6 * q^50 - 40 * q^51 + 30 * q^53 - 15 * q^54 - 5 * q^57 + 22 * q^58 + 35 * q^59 + 9 * q^60 + 20 * q^61 + 13 * q^62 - 21 * q^63 - 2 * q^64 + 32 * q^65 - 2 * q^67 - 15 * q^68 + 44 * q^69 + 13 * q^70 - 20 * q^71 + 7 * q^72 + 5 * q^73 + 6 * q^74 + 6 * q^75 - 8 * q^78 + 25 * q^79 - 26 * q^81 - 2 * q^82 - 9 * q^83 - 17 * q^84 + 40 * q^85 - 10 * q^86 - 42 * q^87 + 27 * q^90 - 16 * q^91 + 10 * q^92 + 42 * q^93 - 10 * q^94 + 30 * q^95 + 2 * q^96 - q^97 + 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−1.20654	+	1.24268i	−0.696598	+	0.717462i
$3$	−1.20654	+	1.24268i	−0.696598	+	0.717462i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.24568	−	1.71454i	−0.557087	−	0.766765i	0.433865	−	0.900978i	$-0.357149\pi$
$5$	−1.24568	−	1.71454i	−0.557087	−	0.766765i	−0.990952	+	0.134213i	$0.957149\pi$
$6$	1.70654	−	0.296161i	0.696693	−	0.120907i
$7$	3.26124	−	1.05964i	1.23263	−	0.400507i	0.380966	−	0.924589i	$-0.375591\pi$
$7$	3.26124	−	1.05964i	1.23263	−	0.400507i	0.851668	+	0.524082i	$0.175591\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.0885088	−	2.99869i	−0.0295029	−	0.999565i
$10$			2.11929i			0.670177i
$11$		0			0
$11$		0			0
$12$	−1.55470	−	0.763481i	−0.448804	−	0.220398i
$13$	−1.10940	+	1.52696i	−0.307693	+	0.423503i	−0.934660	−	0.355543i	$-0.884296\pi$
$13$	−1.10940	+	1.52696i	−0.307693	+	0.423503i	0.626967	+	0.779046i	$0.284296\pi$
$14$	−3.26124	−	1.05964i	−0.871604	−	0.283201i
$15$	3.63359	+	0.520675i	0.938190	+	0.134438i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.17274	+	3.03167i	−1.01204	+	0.735288i	−0.964635	−	0.263588i	$-0.915094\pi$
$17$	−4.17274	+	3.03167i	−1.01204	+	0.735288i	−0.0474016	+	0.998876i	$0.515094\pi$
$18$	−1.69098	+	2.47802i	−0.398569	+	0.584075i
$19$	0.229139	+	0.0744518i	0.0525681	+	0.0170804i	0.335183	−	0.942153i	$-0.391202\pi$
$19$	0.229139	+	0.0744518i	0.0525681	+	0.0170804i	−0.282615	+	0.959233i	$0.591202\pi$
$20$	1.24568	−	1.71454i	0.278544	−	0.383382i
$21$	−2.61803	+	5.33119i	−0.571302	+	1.16336i
$22$		0			0
$23$		−	4.97072i		−	1.03647i	−0.855239	−	0.518234i	$-0.826590\pi$
$23$		−	4.97072i		−	1.03647i	0.855239	−	0.518234i	$-0.173410\pi$
$24$	0.809017	+	1.53150i	0.165140	+	0.312616i
$25$	0.157176	−	0.483737i	0.0314351	−	0.0967474i
$26$	1.79505	−	0.583248i	0.352039	−	0.114384i
$27$	3.83321	+	3.50806i	0.737701	+	0.675127i
$28$	2.01556	+	2.77418i	0.380905	+	0.524271i
$29$	1.28812	+	3.96443i	0.239198	+	0.736177i	0.996537	+	0.0831543i	$0.0264994\pi$
$29$	1.28812	+	3.96443i	0.239198	+	0.736177i	−0.757338	+	0.653023i	$0.773501\pi$
$30$	−2.63359	−	2.55701i	−0.480826	−	0.466844i
$31$	−5.30198	−	3.85211i	−0.952264	−	0.691860i	−0.000922588	−	1.00000i	$-0.500294\pi$
$31$	−5.30198	−	3.85211i	−0.952264	−	0.691860i	−0.951341	+	0.308139i	$0.900294\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	5.15778			0.884553
$35$	−5.87928	−	4.27155i	−0.993779	−	0.722023i
$36$	2.82458	−	1.01082i	0.470763	−	0.168471i
$37$	−2.72744	−	8.39419i	−0.448388	−	1.38000i	−0.878725	−	0.477328i	$-0.841605\pi$
$37$	−2.72744	−	8.39419i	−0.448388	−	1.38000i	0.430337	−	0.902668i	$-0.358395\pi$
$38$	−0.141616	−	0.194917i	−0.0229731	−	0.0316198i
$39$	−0.558984	−	3.22098i	−0.0895090	−	0.515769i
$40$	−2.01556	+	0.654895i	−0.318688	+	0.103548i
$41$	2.45223	−	7.54718i	0.382974	−	1.17867i	−0.554966	−	0.831873i	$-0.687269\pi$
$41$	2.45223	−	7.54718i	0.382974	−	1.17867i	0.937940	−	0.346798i	$-0.112731\pi$
$42$	5.25163	−	2.77418i	0.810344	−	0.428065i
$43$		−	6.51583i		−	0.993655i	−0.867849	−	0.496828i	$-0.834498\pi$
$43$		−	6.51583i		−	0.993655i	0.867849	−	0.496828i	$-0.165502\pi$
$44$		0			0
$45$	−5.03112	+	3.88718i	−0.749995	+	0.579466i
$46$	−2.92172	+	4.02140i	−0.430784	+	0.592923i
$47$	−3.20495	−	1.04135i	−0.467490	−	0.151897i	0.0657937	−	0.997833i	$-0.479042\pi$
$47$	−3.20495	−	1.04135i	−0.467490	−	0.151897i	−0.533283	+	0.845937i	$0.679042\pi$
$48$	0.245684	−	1.71454i	0.0354615	−	0.247472i
$49$	3.84975	−	2.79701i	0.549965	−	0.399573i
$50$	−0.411491	+	0.298966i	−0.0581936	+	0.0422802i
$51$	1.26719	−	8.84322i	0.177442	−	1.23830i
$52$	−1.79505	−	0.583248i	−0.248929	−	0.0808819i
$53$	3.65283	−	5.02768i	0.501754	−	0.690606i	−0.480747	−	0.876859i	$-0.659635\pi$
$53$	3.65283	−	5.02768i	0.501754	−	0.690606i	0.982502	+	0.186254i	$0.0596346\pi$
$54$	−1.03914	−	5.09119i	−0.141409	−	0.692823i
$55$		0			0
$56$		−	3.42908i		−	0.458229i
$57$	−0.368986	+	0.194917i	−0.0488734	+	0.0258174i
$58$	1.28812	−	3.96443i	0.169139	−	0.520556i
$59$	2.63628	−	0.856580i	0.343215	−	0.111517i	−0.132338	−	0.991205i	$-0.542248\pi$
$59$	2.63628	−	0.856580i	0.343215	−	0.111517i	0.475552	+	0.879688i	$0.342248\pi$
$60$	0.627650	+	3.61665i	0.0810293	+	0.466908i
$61$	0.951618	+	1.30979i	0.121842	+	0.167701i	0.865581	−	0.500769i	$-0.166949\pi$
$61$	0.951618	+	1.30979i	0.121842	+	0.167701i	−0.743739	+	0.668470i	$0.766949\pi$
$62$	2.02518	+	6.23285i	0.257198	+	0.791573i
$63$	−3.46619	−	9.68569i	−0.436699	−	1.22028i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.00000			0.496139
$66$		0			0
$67$	−9.98396			−1.21973			−0.609867	−	0.792504i	$-0.708777\pi$
$67$	−9.98396			−1.21973			−0.609867	+	0.792504i	$0.708777\pi$
$68$	−4.17274	−	3.03167i	−0.506019	−	0.367644i
$69$	6.17702	+	5.99739i	0.743626	+	0.722001i
$70$	2.24568	+	6.91151i	0.268411	+	0.826083i
$71$	−5.85410	−	8.05748i	−0.694754	−	0.956247i	−0.999992	−	0.00397087i	$-0.998736\pi$
$71$	−5.85410	−	8.05748i	−0.694754	−	0.956247i	0.305238	−	0.952276i	$-0.401264\pi$
$72$	−2.87928	−	0.842471i	−0.339326	−	0.0992861i
$73$	2.35838	−	0.766285i	0.276028	−	0.0896869i	−0.167732	−	0.985833i	$-0.553644\pi$
$73$	2.35838	−	0.766285i	0.276028	−	0.0896869i	0.443760	+	0.896146i	$0.353644\pi$
$74$	−2.72744	+	8.39419i	−0.317058	+	0.975805i
$75$	0.411491	+	0.778968i	0.0475149	+	0.0899475i
$76$			0.240931i			0.0276367i
$77$		0			0
$78$	−1.44102	+	2.93439i	−0.163163	+	0.332254i
$79$	6.65877	−	9.16501i	0.749170	−	1.03114i	−0.248868	−	0.968537i	$-0.580059\pi$
$79$	6.65877	−	9.16501i	0.749170	−	1.03114i	0.998038	−	0.0626069i	$-0.0199414\pi$
$80$	2.01556	+	0.654895i	0.225346	+	0.0732195i
$81$	−8.98433	+	0.530822i	−0.998259	+	0.0589802i
$82$	−6.42001	+	4.66441i	−0.708972	+	0.515098i
$83$	−5.55630	+	4.03689i	−0.609883	+	0.443106i	−0.849373	−	0.527793i	$-0.823020\pi$
$83$	−5.55630	+	4.03689i	−0.609883	+	0.443106i	0.239490	+	0.970899i	$0.423020\pi$
$84$	−5.87928	−	0.842471i	−0.641482	−	0.0919211i
$85$	10.3958	+	3.37781i	1.12759	+	0.366375i
$86$	−3.82991	+	5.27142i	−0.412990	+	0.568432i
$87$	−6.48070	−	3.18254i	−0.694804	−	0.341204i
$88$		0			0
$89$		−	2.47254i		−	0.262088i	−0.991377	−	0.131044i	$-0.958167\pi$
$89$		−	2.47254i		−	0.262088i	0.991377	−	0.131044i	$-0.0418330\pi$
$90$	6.35509	−	0.187575i	0.669885	−	0.0197722i
$91$	−2.00000	+	6.15537i	−0.209657	+	0.645258i
$92$	4.72744	−	1.53604i	0.492869	−	0.160143i
$93$	11.1840	−	1.94093i	1.15973	−	0.201265i
$94$	1.98077	+	2.72629i	0.204301	+	0.281196i
$95$	−0.157785	−	0.485611i	−0.0161884	−	0.0498227i
$96$	−1.20654	+	1.24268i	−0.123142	+	0.126831i
$97$	10.6968	+	7.77169i	1.08610	+	0.789096i	0.978736	−	0.205124i	$-0.0657598\pi$
$97$	10.6968	+	7.77169i	1.08610	+	0.789096i	0.107361	+	0.994220i	$0.465760\pi$
$98$	−4.75856			−0.480687
$99$		0			0
$100$	0.508631			0.0508631
$101$	−1.99038	−	1.44610i	−0.198051	−	0.143892i	0.484340	−	0.874880i	$-0.339060\pi$
$101$	−1.99038	−	1.44610i	−0.198051	−	0.143892i	−0.682391	+	0.730988i	$0.739060\pi$
$102$	−6.22309	+	6.40948i	−0.616178	+	0.634633i
$103$	−1.42440	−	4.38387i	−0.140351	−	0.431955i	0.856033	−	0.516921i	$-0.172922\pi$
$103$	−1.42440	−	4.38387i	−0.140351	−	0.431955i	−0.996384	+	0.0849658i	$0.972922\pi$
$104$	1.10940	+	1.52696i	0.108786	+	0.149731i
$105$	12.4018	−	2.15226i	1.21029	−	0.210039i
$106$	−5.91040	+	1.92040i	−0.574069	+	0.186526i
$107$	−5.60407	+	17.2475i	−0.541766	+	1.66738i	0.186792	+	0.982399i	$0.440191\pi$
$107$	−5.60407	+	17.2475i	−0.541766	+	1.66738i	−0.728558	+	0.684984i	$0.759809\pi$
$108$	−2.15184	+	4.72965i	−0.207061	+	0.455111i
$109$			0.702783i			0.0673144i	0.999433	+	0.0336572i	$0.0107154\pi$
$109$			0.702783i			0.0673144i	−0.999433	+	0.0336572i	$0.989285\pi$
$110$		0			0
$111$	13.7221	+	6.73861i	1.30244	+	0.639601i
$112$	−2.01556	+	2.77418i	−0.190453	+	0.262135i
$113$	−4.07454	−	1.32390i	−0.383301	−	0.124542i	0.111027	−	0.993817i	$-0.464586\pi$
$113$	−4.07454	−	1.32390i	−0.383301	−	0.124542i	−0.494328	+	0.869275i	$0.664586\pi$
$114$	0.413086	+	0.0591931i	0.0386890	+	0.00554394i
$115$	−8.52249	+	6.19195i	−0.794726	+	0.577402i
$116$	−3.37235	+	2.45016i	−0.313115	+	0.227491i
$117$	4.67708	+	3.19161i	0.432397	+	0.295064i
$118$	−2.63628	−	0.856580i	−0.242689	−	0.0788546i
$119$	−10.3958	+	14.3086i	−0.952984	+	1.31167i
$120$	1.61803	−	3.29486i	0.147706	−	0.300778i
$121$		0			0
$122$		−	1.61899i		−	0.146576i
$123$	6.42001	+	12.1533i	0.578873	+	1.09583i
$124$	2.02518	−	6.23285i	0.181866	−	0.559727i
$125$	−11.1030	+	3.60758i	−0.993080	+	0.322671i
$126$	−2.88889	+	9.87326i	−0.257363	+	0.879580i
$127$	−10.3090	−	14.1891i	−0.914774	−	1.25908i	−0.965510	−	0.260366i	$-0.916157\pi$
$127$	−10.3090	−	14.1891i	−0.914774	−	1.25908i	0.0507363	−	0.998712i	$-0.483843\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	8.09710	+	7.86163i	0.712910	+	0.692178i
$130$	−3.23607	−	2.35114i	−0.283822	−	0.206209i
$131$	4.82298			0.421386			0.210693	−	0.977552i	$-0.432428\pi$
$131$	4.82298			0.421386			0.210693	+	0.977552i	$0.432428\pi$
$132$		0			0
$133$	0.826171			0.0716381
$134$	8.07719	+	5.86842i	0.697763	+	0.506954i
$135$	1.23974	−	10.9421i	0.106700	−	0.941748i
$136$	1.59384	+	4.90534i	0.136671	+	0.420630i
$137$	−10.6143	−	14.6093i	−0.906840	−	1.24816i	−0.968234	−	0.250045i	$-0.919555\pi$
$137$	−10.6143	−	14.6093i	−0.906840	−	1.24816i	0.0613939	−	0.998114i	$-0.480445\pi$
$138$	−1.47214	−	8.48275i	−0.125317	−	0.722100i
$139$	−0.940950	+	0.305733i	−0.0798103	+	0.0259319i	−0.348650	−	0.937253i	$-0.613360\pi$
$139$	−0.940950	+	0.305733i	−0.0798103	+	0.0259319i	0.268840	+	0.963185i	$0.413360\pi$
$140$	2.24568	−	6.91151i	0.189795	−	0.584129i
$141$	5.16097	−	2.72629i	0.434632	−	0.229595i
$142$			9.95959i			0.835790i
$143$		0			0
$144$	1.83419	+	2.37397i	0.152849	+	0.197831i
$145$	5.19258	−	7.14697i	0.431220	−	0.593524i
$146$	−2.35838	−	0.766285i	−0.195181	−	0.0634182i
$147$	−1.16910	+	8.15872i	−0.0964260	+	0.672920i
$148$	7.14052	−	5.18789i	0.586947	−	0.426442i
$149$	11.3158	−	8.22144i	0.927030	−	0.673526i	−0.0182342	−	0.999834i	$-0.505804\pi$
$149$	11.3158	−	8.22144i	0.927030	−	0.673526i	0.945264	+	0.326307i	$0.105804\pi$
$150$	0.124963	−	0.872067i	0.0102032	−	0.0712040i
$151$	6.01875	+	1.95561i	0.489799	+	0.159145i	0.543496	−	0.839412i	$-0.317100\pi$
$151$	6.01875	+	1.95561i	0.489799	+	0.159145i	−0.0536968	+	0.998557i	$0.517100\pi$
$152$	0.141616	−	0.194917i	0.0114866	−	0.0158099i
$153$	9.46037	+	12.2444i	0.764826	+	0.989903i
$154$		0			0
$155$			13.8890i			1.11559i
$156$	2.89060	−	1.52696i	0.231433	−	0.122255i
$157$	−1.14590	+	3.52671i	−0.0914526	+	0.281462i	−0.986313	−	0.164884i	$-0.947275\pi$
$157$	−1.14590	+	3.52671i	−0.0914526	+	0.281462i	0.894860	+	0.446346i	$0.147275\pi$
$158$	−10.7741	+	3.50072i	−0.857143	+	0.278503i
$159$	1.84051	+	10.6054i	0.145962	+	0.841064i
$160$	−1.24568	−	1.71454i	−0.0984800	−	0.135546i
$161$	−5.26719	−	16.2107i	−0.415113	−	1.27759i
$162$	7.58049	+	4.85141i	0.595579	+	0.381163i
$163$	−6.91743	−	5.02581i	−0.541815	−	0.393652i	0.282943	−	0.959137i	$-0.408689\pi$
$163$	−6.91743	−	5.02581i	−0.541815	−	0.393652i	−0.824759	+	0.565485i	$0.808689\pi$
$164$	7.93557			0.619664
$165$		0			0
$166$	6.86796			0.533057
$167$	−1.33161	−	0.967474i	−0.103043	−	0.0748654i	0.535070	−	0.844807i	$-0.320285\pi$
$167$	−1.33161	−	0.967474i	−0.103043	−	0.0748654i	−0.638114	+	0.769942i	$0.720285\pi$
$168$	4.26124	+	4.13733i	0.328762	+	0.319202i
$169$	2.91638	+	8.97570i	0.224337	+	0.690439i
$170$	−6.42497	−	8.84322i	−0.492773	−	0.678244i
$171$	0.202977	−	0.693708i	0.0155221	−	0.0530492i
$172$	6.19693	−	2.01350i	0.472511	−	0.153528i
$173$	−1.08423	+	3.33691i	−0.0824322	+	0.253700i	−0.983775	−	0.179406i	$-0.942582\pi$
$173$	−1.08423	+	3.33691i	−0.0824322	+	0.253700i	0.901343	+	0.433106i	$0.142582\pi$
$174$	3.37235	+	6.38399i	0.255657	+	0.483969i
$175$		−	1.74413i		−	0.131844i
$176$		0			0
$177$	−2.11633	+	4.30956i	−0.159073	+	0.323926i
$178$	−1.45332	+	2.00032i	−0.108931	+	0.149931i
$179$	12.6233	+	4.10155i	0.943507	+	0.306564i	0.740074	−	0.672525i	$-0.234790\pi$
$179$	12.6233	+	4.10155i	0.943507	+	0.306564i	0.203432	+	0.979089i	$0.434790\pi$
$180$	−5.25163	−	3.58367i	−0.391433	−	0.267111i
$181$	6.01386	−	4.36932i	0.447007	−	0.324769i	−0.341406	−	0.939916i	$-0.610903\pi$
$181$	6.01386	−	4.36932i	0.447007	−	0.324769i	0.788413	+	0.615147i	$0.210903\pi$
$182$	5.23607	−	3.80423i	0.388123	−	0.281988i
$183$	−2.77582	−	0.397761i	−0.205194	−	0.0294033i
$184$	−4.72744	−	1.53604i	−0.348511	−	0.113238i
$185$	−10.9946	+	15.1328i	−0.808341	+	1.11259i
$186$	−10.1889	−	5.00356i	−0.747087	−	0.366879i
$187$		0			0
$188$		−	3.36988i		−	0.245774i
$189$	16.2183	+	7.37883i	1.17971	+	0.536731i
$190$	−0.157785	+	0.485611i	−0.0114469	+	0.0352299i
$191$	2.46344	−	0.800420i	0.178248	−	0.0579163i	−0.218533	−	0.975830i	$-0.570127\pi$
$191$	2.46344	−	0.800420i	0.178248	−	0.0579163i	0.396781	+	0.917913i	$0.370127\pi$
$192$	1.70654	−	0.296161i	0.123159	−	0.0213736i
$193$	11.4770	+	15.7968i	0.826134	+	1.13708i	0.988630	+	0.150367i	$0.0480456\pi$
$193$	11.4770	+	15.7968i	0.826134	+	1.13708i	−0.162496	+	0.986709i	$0.551954\pi$
$194$	−4.08582	−	12.5749i	−0.293345	−	0.902823i
$195$	−4.82617	+	4.97072i	−0.345609	+	0.355961i
$196$	3.84975	+	2.79701i	0.274982	+	0.199786i
$197$	5.38713			0.383817			0.191908	−	0.981413i	$-0.438532\pi$
$197$	5.38713			0.383817			0.191908	+	0.981413i	$0.438532\pi$
$198$		0			0
$199$	7.38713			0.523659			0.261830	−	0.965114i	$-0.415674\pi$
$199$	7.38713			0.523659			0.261830	+	0.965114i	$0.415674\pi$
$200$	−0.411491	−	0.298966i	−0.0290968	−	0.0211401i
$201$	12.0461	−	12.4069i	0.849664	−	0.875113i
$202$	0.760259	+	2.33984i	0.0534916	+	0.164630i
$203$	8.40177	+	11.5640i	0.589688	+	0.811636i
$204$	8.80198	−	1.52754i	0.616262	−	0.106949i
$205$	−15.9946	+	5.19697i	−1.11711	+	0.362972i
$206$	−1.42440	+	4.38387i	−0.0992430	+	0.305438i
$207$	−14.9057	+	0.439953i	−1.03602	+	0.0305788i
$208$		−	1.88743i		−	0.130870i
$209$		0			0
$210$	−11.2983	−	5.54836i	−0.779657	−	0.382873i
$211$	−5.03276	+	6.92699i	−0.346469	+	0.476874i	−0.946317	−	0.323240i	$-0.895228\pi$
$211$	−5.03276	+	6.92699i	−0.346469	+	0.476874i	0.599848	+	0.800114i	$0.295228\pi$
$212$	5.91040	+	1.92040i	0.405928	+	0.131894i
$213$	17.0761	+	2.44692i	1.17003	+	0.167660i
$214$	14.6716	−	10.6596i	1.00293	−	0.728673i
$215$	−11.1716	+	8.11667i	−0.761900	+	0.553553i
$216$	4.52089	−	2.56155i	0.307608	−	0.174291i
$217$	−21.3729	−	6.94448i	−1.45089	−	0.471422i
$218$	0.413086	−	0.568564i	0.0279777	−	0.0385080i
$219$	−1.89324	+	3.85527i	−0.127934	+	0.260515i
$220$		0			0
$221$		−	9.73495i		−	0.654844i
$222$	−7.14052	−	13.5173i	−0.479240	−	0.907220i
$223$	0.0155598	−	0.0478882i	0.00104196	−	0.00320683i	−0.950534	−	0.310620i	$-0.899463\pi$
$223$	0.0155598	−	0.0478882i	0.00104196	−	0.00320683i	0.951576	+	0.307413i	$0.0994634\pi$
$224$	3.26124	−	1.05964i	0.217901	−	0.0708003i
$225$	−1.46449	−	0.428507i	−0.0976327	−	0.0285671i
$226$	2.51821	+	3.46601i	0.167509	+	0.230556i
$227$	4.41512	+	13.5884i	0.293042	+	0.901891i	0.983872	+	0.178873i	$0.0572453\pi$
$227$	4.41512	+	13.5884i	0.293042	+	0.901891i	−0.690830	+	0.723017i	$0.742755\pi$
$228$	−0.299400	−	0.290694i	−0.0198283	−	0.0192517i
$229$	24.4668	+	17.7761i	1.61681	+	1.17468i	0.831272	+	0.555866i	$0.187613\pi$
$229$	24.4668	+	17.7761i	1.61681	+	1.17468i	0.785537	+	0.618814i	$0.212387\pi$
$230$	10.5344			0.694616
$231$		0			0
$232$	4.16845			0.273672
$233$	2.28819	+	1.66247i	0.149904	+	0.108912i	0.660209	−	0.751082i	$-0.270468\pi$
$233$	2.28819	+	1.66247i	0.149904	+	0.108912i	−0.510305	+	0.859993i	$0.670468\pi$
$234$	−1.90786	−	5.33119i	−0.124721	−	0.348511i
$235$	2.20692	+	6.79220i	0.143964	+	0.443074i
$236$	1.62931	+	2.24256i	0.106059	+	0.145978i
$237$	3.35509	+	19.3327i	0.217936	+	1.25579i
$238$	16.8208	−	5.46541i	1.09033	−	0.354270i
$239$	0.350846	−	1.07979i	0.0226944	−	0.0698461i	−0.939068	−	0.343732i	$-0.888309\pi$
$239$	0.350846	−	1.07979i	0.0226944	−	0.0698461i	0.961762	+	0.273886i	$0.0883090\pi$
$240$	−3.24568	+	1.71454i	−0.209508	+	0.110673i
$241$		−	15.0464i		−	0.969223i	−0.874730	−	0.484611i	$-0.838961\pi$
$241$		−	15.0464i		−	0.969223i	0.874730	−	0.484611i	$-0.161039\pi$
$242$		0			0
$243$	10.1803	−	11.8051i	0.653069	−	0.757298i
$244$	−0.951618	+	1.30979i	−0.0609211	+	0.0838507i
$245$	−9.59116	−	3.11636i	−0.612756	−	0.199097i
$246$	1.94965	−	13.6058i	0.124305	−	0.867477i
$247$	−0.367893	+	0.267290i	−0.0234085	+	0.0170072i
$248$	−5.30198	+	3.85211i	−0.336676	+	0.244609i
$249$	1.68735	−	11.7754i	0.106932	−	0.746234i
$250$	11.1030	+	3.60758i	0.702214	+	0.228163i
$251$	5.66415	−	7.79603i	0.357518	−	0.492081i	−0.591937	−	0.805984i	$-0.701637\pi$
$251$	5.66415	−	7.79603i	0.357518	−	0.492081i	0.949455	+	0.313903i	$0.101637\pi$
$252$	8.14052	−	6.28959i	0.512805	−	0.396207i
$253$		0			0
$254$			17.5387i			1.10047i
$255$	−16.7405	+	8.84322i	−1.04833	+	0.553784i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	12.7022	−	4.12718i	0.792339	−	0.257446i	0.115239	−	0.993338i	$-0.463237\pi$
$257$	12.7022	−	4.12718i	0.792339	−	0.257446i	0.677100	+	0.735891i	$0.263237\pi$
$258$	−1.92974	−	11.1195i	−0.120140	−	0.692273i
$259$	−17.7897	−	24.4854i	−1.10540	−	1.52145i
$260$	1.23607	+	3.80423i	0.0766577	+	0.235928i
$261$	11.7741	−	4.21357i	0.728800	−	0.260814i
$262$	−3.90187	−	2.83488i	−0.241059	−	0.175139i
$263$	−9.33677			−0.575730			−0.287865	−	0.957671i	$-0.592945\pi$
$263$	−9.33677			−0.575730			−0.287865	+	0.957671i	$0.592945\pi$
$264$		0			0
$265$	−13.1704			−0.809053
$266$	−0.668387	−	0.485611i	−0.0409814	−	0.0297747i
$267$	3.07257	+	2.98322i	0.188038	+	0.182570i
$268$	−3.08521	−	9.49531i	−0.188459	−	0.580018i
$269$	8.00856	+	11.0228i	0.488291	+	0.672075i	0.980072	−	0.198644i	$-0.0636539\pi$
$269$	8.00856	+	11.0228i	0.488291	+	0.672075i	−0.491781	+	0.870719i	$0.663654\pi$
$270$	−7.43459	+	8.12366i	−0.452455	+	0.494390i
$271$	−4.46147	+	1.44962i	−0.271015	+	0.0880581i	−0.441372	−	0.897324i	$-0.645508\pi$
$271$	−4.46147	+	1.44962i	−0.271015	+	0.0880581i	0.170357	+	0.985382i	$0.445508\pi$
$272$	1.59384	−	4.90534i	0.0966409	−	0.297430i
$273$	−5.23607	−	9.91207i	−0.316901	−	0.599906i
$274$			18.0581i			1.09093i
$275$		0			0
$276$	−3.79505	+	7.72799i	−0.228435	+	0.465170i
$277$	−4.86796	+	6.70017i	−0.292487	+	0.402574i	−0.929820	−	0.368014i	$-0.880038\pi$
$277$	−4.86796	+	6.70017i	−0.292487	+	0.402574i	0.637333	+	0.770589i	$0.280038\pi$
$278$	0.940950	+	0.305733i	0.0564344	+	0.0183367i
$279$	−11.0820	+	16.2400i	−0.663464	+	0.972261i
$280$	−5.87928	+	4.27155i	−0.351354	+	0.255274i
$281$	10.2462	−	7.44429i	0.611236	−	0.444089i	−0.238613	−	0.971115i	$-0.576693\pi$
$281$	10.2462	−	7.44429i	0.611236	−	0.444089i	0.849849	+	0.527026i	$0.176693\pi$
$282$	−5.77779	−	0.827928i	−0.344062	−	0.0493024i
$283$	−21.5030	−	6.98676i	−1.27822	−	0.415320i	−0.410269	−	0.911965i	$-0.634565\pi$
$283$	−21.5030	−	6.98676i	−1.27822	−	0.415320i	−0.867954	+	0.496645i	$0.834565\pi$
$284$	5.85410	−	8.05748i	0.347377	−	0.478123i
$285$	0.793834	+	0.389835i	0.0470226	+	0.0230918i
$286$		0			0
$287$		−	27.2117i		−	1.60625i
$288$	−0.0885088	−	2.99869i	−0.00521543	−	0.176700i
$289$	2.96741	−	9.13275i	0.174554	−	0.537221i
$290$	−8.40177	+	2.72990i	−0.493369	+	0.160305i
$291$	−22.5639	+	3.91584i	−1.32272	+	0.229551i
$292$	1.45756	+	2.00616i	0.0852973	+	0.117402i
$293$	7.75383	+	23.8638i	0.452984	+	1.39414i	0.873486	+	0.486849i	$0.161854\pi$
$293$	7.75383	+	23.8638i	0.452984	+	1.39414i	−0.420502	+	0.907291i	$0.638146\pi$
$294$	5.74140	−	5.91336i	0.334845	−	0.344874i
$295$	−4.75261	−	3.45298i	−0.276708	−	0.201040i
$296$	−8.82617			−0.513011
$297$		0			0
$298$	−13.9871			−0.810254
$299$	7.59010	+	5.51453i	0.438947	+	0.318914i
$300$	−0.613685	+	0.632066i	−0.0354311	+	0.0364923i
$301$	−6.90445	−	21.2497i	−0.397966	−	1.22481i
$302$	−3.71979	−	5.11985i	−0.214050	−	0.294614i
$303$	4.19852	−	0.728631i	0.241199	−	0.0418588i
$304$	−0.229139	+	0.0744518i	−0.0131420	+	0.00427011i
$305$	1.06027	−	3.26317i	0.0607108	−	0.186849i
$306$	−0.456510	−	15.4666i	−0.0260969	−	0.884168i
$307$		−	16.0682i		−	0.917058i	−0.888679	−	0.458529i	$-0.848377\pi$
$307$		−	16.0682i		−	0.917058i	0.888679	−	0.458529i	$-0.151623\pi$
$308$		0			0
$309$	7.16635	+	3.51924i	0.407679	+	0.200203i
$310$	8.16373	−	11.2364i	0.463669	−	0.638185i
$311$	−9.15438	−	2.97444i	−0.519097	−	0.168665i	0.0377383	−	0.999288i	$-0.487985\pi$
$311$	−9.15438	−	2.97444i	−0.519097	−	0.168665i	−0.556836	+	0.830623i	$0.687985\pi$
$312$	−3.23607	−	0.463712i	−0.183206	−	0.0262525i
$313$	−16.2725	+	11.8227i	−0.919777	+	0.668257i	−0.943469	−	0.331462i	$-0.892458\pi$
$313$	−16.2725	+	11.8227i	−0.919777	+	0.668257i	0.0236913	+	0.999719i	$0.492458\pi$
$314$	3.00000	−	2.17963i	0.169300	−	0.123004i
$315$	−12.2887	+	18.0082i	−0.692389	+	1.01465i
$316$	10.7741	+	3.50072i	0.606091	+	0.196931i
$317$	10.8453	−	14.9273i	0.609134	−	0.838401i	−0.387372	−	0.921924i	$-0.626617\pi$
$317$	10.8453	−	14.9273i	0.609134	−	0.838401i	0.996506	+	0.0835226i	$0.0266171\pi$
$318$	4.74470	−	9.66179i	0.266070	−	0.541806i
$319$		0			0
$320$			2.11929i			0.118472i
$321$	−14.6716	−	27.7740i	−0.818891	−	1.55019i
$322$	−5.26719	+	16.2107i	−0.293529	+	0.903389i
$323$	−1.18185	+	0.384007i	−0.0657599	+	0.0213667i
$324$	−3.28115	−	8.38057i	−0.182286	−	0.465587i
$325$	0.564277	+	0.776660i	0.0313004	+	0.0430814i
$326$	2.64222	+	8.13193i	0.146339	+	0.450386i
$327$	−0.873335	−	0.847938i	−0.0482955	−	0.0468911i
$328$	−6.42001	−	4.66441i	−0.354486	−	0.257549i
$329$	−11.5556			−0.637080
$330$		0			0
$331$	−5.03641			−0.276826			−0.138413	−	0.990375i	$-0.544200\pi$
$331$	−5.03641			−0.276826			−0.138413	+	0.990375i	$0.544200\pi$
$332$	−5.55630	−	4.03689i	−0.304941	−	0.221553i
$333$	−24.9302	+	8.92171i	−1.36617	+	0.488907i
$334$	0.508631	+	1.56541i	0.0278311	+	0.0856552i
$335$	12.4369	+	17.1179i	0.679498	+	0.935249i
$336$	−1.01556	−	5.85186i	−0.0554033	−	0.319245i
$337$	−16.7902	+	5.45548i	−0.914622	+	0.297179i	−0.728259	−	0.685302i	$-0.759670\pi$
$337$	−16.7902	+	5.45548i	−0.914622	+	0.297179i	−0.186363	+	0.982481i	$0.559670\pi$
$338$	2.91638	−	8.97570i	0.158630	−	0.488214i
$339$	6.56130	−	3.46601i	0.356361	−	0.188248i
$340$			10.9308i			0.592807i
$341$		0			0
$342$	−0.571964	+	0.441914i	−0.0309282	+	0.0238960i
$343$	−4.51776	+	6.21817i	−0.243936	+	0.335750i
$344$	−6.19693	−	2.01350i	−0.334116	−	0.108561i
$345$	2.58813	−	18.0616i	0.139340	−	0.972403i
$346$	2.83854	−	2.06232i	0.152601	−	0.110871i
$347$	−12.1570	+	8.83255i	−0.652620	+	0.474156i	−0.864163	−	0.503213i	$-0.832151\pi$
$347$	−12.1570	+	8.83255i	−0.652620	+	0.474156i	0.211543	+	0.977369i	$0.432151\pi$
$348$	1.02412	−	7.14697i	0.0548988	−	0.383118i
$349$	−3.32413	−	1.08008i	−0.177937	−	0.0578152i	0.218694	−	0.975794i	$-0.429821\pi$
$349$	−3.32413	−	1.08008i	−0.177937	−	0.0578152i	−0.396630	+	0.917978i	$0.629821\pi$
$350$	−1.02518	+	1.41103i	−0.0547980	+	0.0754229i
$351$	−9.60925	+	1.96131i	−0.512904	+	0.104687i
$352$		0			0
$353$			25.2674i			1.34485i	0.740167	+	0.672423i	$0.234747\pi$
$353$			25.2674i			1.34485i	−0.740167	+	0.672423i	$0.765253\pi$
$354$	4.24524	−	2.24256i	0.225632	−	0.119190i
$355$	−6.52249	+	20.0742i	−0.346178	+	1.06543i
$356$	2.35152	−	0.764056i	0.124630	−	0.0404949i
$357$	−5.23804	−	30.1827i	−0.277226	−	1.59744i
$358$	−7.80160	−	10.7380i	−0.412328	−	0.567520i
$359$	−5.96229	−	18.3500i	−0.314677	−	0.968478i	−0.975887	−	0.218276i	$-0.929957\pi$
$359$	−5.96229	−	18.3500i	−0.314677	−	0.968478i	0.661210	−	0.750201i	$-0.270043\pi$
$360$	2.14222	+	5.98608i	0.112905	+	0.315494i
$361$	−15.3244	−	11.1338i	−0.806545	−	0.585989i
$362$	−7.43354			−0.390698
$363$		0			0
$364$	−6.47214			−0.339232
$365$	−4.25163	−	3.08899i	−0.222540	−	0.161685i
$366$	2.01189	+	1.95338i	0.105163	+	0.102105i
$367$	−0.277454	−	0.853917i	−0.0144830	−	0.0445741i	0.943554	−	0.331219i	$-0.107460\pi$
$367$	−0.277454	−	0.853917i	−0.0144830	−	0.0445741i	−0.958037	+	0.286645i	$0.907460\pi$
$368$	2.92172	+	4.02140i	0.152305	+	0.209630i
$369$	−22.8487	−	6.68549i	−1.18946	−	0.348033i
$370$	17.7897	−	5.78022i	0.924841	−	0.300499i
$371$	6.58521	−	20.2672i	0.341887	−	1.05222i
$372$	5.30198	+	10.0368i	0.274895	+	0.520386i
$373$			26.3407i			1.36387i	0.731413	+	0.681935i	$0.238861\pi$
$373$			26.3407i			1.36387i	−0.731413	+	0.681935i	$0.761139\pi$
$374$		0			0
$375$	8.91315	−	18.1501i	0.460273	−	0.937269i
$376$	−1.98077	+	2.72629i	−0.102150	+	0.140598i
$377$	−7.48259	−	2.43124i	−0.385373	−	0.125215i
$378$	−8.78373	−	15.5025i	−0.451786	−	0.797362i
$379$	2.15602	−	1.56644i	0.110747	−	0.0804625i	−0.531033	−	0.847351i	$-0.678196\pi$
$379$	2.15602	−	1.56644i	0.110747	−	0.0804625i	0.641780	+	0.766889i	$0.278196\pi$
$380$	0.413086	−	0.300124i	0.0211908	−	0.0153961i
$381$	30.0707	+	4.30898i	1.54057	+	0.220756i
$382$	−2.46344	−	0.800420i	−0.126040	−	0.0409530i
$383$	19.2253	−	26.4614i	0.982368	−	1.35211i	0.0468238	−	0.998903i	$-0.485090\pi$
$383$	19.2253	−	26.4614i	0.982368	−	1.35211i	0.935544	−	0.353210i	$-0.114910\pi$
$384$	−1.55470	−	0.763481i	−0.0793380	−	0.0389612i
$385$		0			0
$386$		−	19.5259i		−	0.993841i
$387$	−19.5390	+	0.576709i	−0.993223	+	0.0293158i
$388$	−4.08582	+	12.5749i	−0.207426	+	0.638392i
$389$	1.60221	−	0.520588i	0.0812350	−	0.0263949i	−0.268118	−	0.963386i	$-0.586402\pi$
$389$	1.60221	−	0.520588i	0.0812350	−	0.0263949i	0.349353	+	0.936991i	$0.386402\pi$
$390$	6.82617	−	1.18465i	0.345657	−	0.0599869i
$391$	15.0696	+	20.7415i	0.762102	+	1.04894i
$392$	−1.47047	−	4.52566i	−0.0742702	−	0.228580i
$393$	−5.81913	+	5.99343i	−0.293537	+	0.302328i
$394$	−4.35828	−	3.16647i	−0.219567	−	0.159525i
$395$	−24.0085			−1.20800
$396$		0			0
$397$	−8.89235			−0.446294			−0.223147	−	0.974785i	$-0.571633\pi$
$397$	−8.89235			−0.446294			−0.223147	+	0.974785i	$0.571633\pi$
$398$	−5.97631	−	4.34204i	−0.299565	−	0.217647i
$399$	−0.996811	+	1.02667i	−0.0499030	+	0.0513976i
$400$	0.157176	+	0.483737i	0.00785878	+	0.0241868i
$401$	11.4963	+	15.8233i	0.574099	+	0.790180i	0.993033	−	0.117837i	$-0.0375961\pi$
$401$	11.4963	+	15.8233i	0.574099	+	0.790180i	−0.418934	+	0.908017i	$0.637596\pi$
$402$	−17.0380	+	2.95686i	−0.849781	+	0.147475i
$403$	11.7641	−	3.82238i	0.586010	−	0.190406i
$404$	0.760259	−	2.33984i	0.0378243	−	0.116411i
$405$	12.1018	+	14.7427i	0.601341	+	0.732573i
$406$		−	14.2939i		−	0.709396i
$407$		0			0
$408$	−8.01882	−	3.93787i	−0.396991	−	0.194954i
$409$	14.5460	−	20.0208i	0.719252	−	0.989965i	−0.280297	−	0.959913i	$-0.590433\pi$
$409$	14.5460	−	20.0208i	0.719252	−	0.989965i	0.999548	−	0.0300515i	$-0.00956712\pi$
$410$	15.9946	+	5.19697i	0.789918	+	0.256660i
$411$	30.9613	+	4.43660i	1.52721	+	0.218841i
$412$	3.72914	−	2.70938i	0.183722	−	0.133481i
$413$	7.68989	−	5.58703i	0.378395	−	0.274920i
$414$	12.3175	+	8.40541i	0.605374	+	0.413103i
$415$	13.8428	+	4.49779i	0.679516	+	0.220788i
$416$	−1.10940	+	1.52696i	−0.0543930	+	0.0748655i
$417$	0.755368	−	1.53818i	0.0369905	−	0.0753250i
$418$		0			0
$419$			34.8462i			1.70235i	0.524883	+	0.851174i	$0.324109\pi$
$419$			34.8462i			1.70235i	−0.524883	+	0.851174i	$0.675891\pi$
$420$	5.87928	+	11.1297i	0.286879	+	0.543074i
$421$	5.42375	−	16.6926i	0.264338	−	0.813547i	−0.727508	−	0.686100i	$-0.759321\pi$
$421$	5.42375	−	16.6926i	0.264338	−	0.813547i	0.991845	−	0.127448i	$-0.0406786\pi$
$422$	8.14317	−	2.64588i	0.396403	−	0.128799i
$423$	−2.83903	+	9.70283i	−0.138038	+	0.471768i
$424$	−3.65283	−	5.02768i	−0.177397	−	0.244166i
$425$	0.810678	+	2.49501i	0.0393237	+	0.121026i
$426$	−12.3766	−	12.0167i	−0.599648	−	0.582210i
$427$	4.49137	+	3.26317i	0.217353	+	0.157916i
$428$	−18.1351			−0.876595
$429$		0			0
$430$	13.8089			0.665925
$431$	27.0376	+	19.6440i	1.30236	+	0.946218i	0.999976	−	0.00696946i	$-0.00221847\pi$
$431$	27.0376	+	19.6440i	1.30236	+	0.946218i	0.302381	+	0.953187i	$0.402218\pi$
$432$	−5.16312	−	0.584981i	−0.248411	−	0.0281449i
$433$	8.40143	+	25.8569i	0.403747	+	1.24261i	0.921937	+	0.387340i	$0.126606\pi$
$433$	8.40143	+	25.8569i	0.403747	+	1.24261i	−0.518190	+	0.855266i	$0.673394\pi$
$434$	13.2092	+	18.1809i	0.634061	+	0.872711i
$435$	2.61633	+	15.0758i	0.125444	+	0.722831i
$436$	−0.668387	+	0.217172i	−0.0320099	+	0.0104007i
$437$	0.370079	−	1.13899i	0.0177033	−	0.0544851i
$438$	3.79774	−	2.00616i	0.181463	−	0.0958581i
$439$		−	13.4068i		−	0.639873i	−0.947439	−	0.319936i	$-0.896338\pi$
$439$		−	13.4068i		−	0.639873i	0.947439	−	0.319936i	$-0.103662\pi$
$440$		0			0
$441$	−8.72811	−	11.2967i	−0.415624	−	0.537937i
$442$	−5.72206	+	7.87574i	−0.272171	+	0.374611i
$443$	17.5311	+	5.69619i	0.832927	+	0.270634i	0.694278	−	0.719707i	$-0.255724\pi$
$443$	17.5311	+	5.69619i	0.832927	+	0.270634i	0.138649	+	0.990342i	$0.455724\pi$
$444$	−2.16845	+	15.1328i	−0.102910	+	0.718171i
$445$	−4.23926	+	3.08000i	−0.200960	+	0.146006i
$446$	−0.0407361	+	0.0295965i	−0.00192891	+	0.00140144i
$447$	−3.43642	+	23.9815i	−0.162537	+	1.13429i
$448$	−3.26124	−	1.05964i	−0.154079	−	0.0500634i
$449$	17.8510	−	24.5698i	0.842443	−	1.15952i	−0.143035	−	0.989718i	$-0.545686\pi$
$449$	17.8510	−	24.5698i	0.842443	−	1.15952i	0.985478	−	0.169805i	$-0.0543138\pi$
$450$	0.932928	+	1.20748i	0.0439786	+	0.0569209i
$451$		0			0
$452$		−	4.28423i		−	0.201513i
$453$	−9.69208	+	5.11985i	−0.455373	+	0.240552i
$454$	4.41512	−	13.5884i	0.207212	−	0.637733i
$455$	13.0450	−	4.23857i	0.611558	−	0.198707i
$456$	0.0713545	+	0.411159i	0.00334148	+	0.0192543i
$457$	20.3890	+	28.0630i	0.953756	+	1.31273i	0.949839	+	0.312740i	$0.101247\pi$
$457$	20.3890	+	28.0630i	0.953756	+	1.31273i	0.00391756	+	0.999992i	$0.498753\pi$
$458$	−9.34547	−	28.7624i	−0.436685	−	1.34398i
$459$	−26.6303	−	3.01721i	−1.24299	−	0.140831i
$460$	−8.52249	−	6.19195i	−0.397363	−	0.288701i
$461$	20.8777			0.972370			0.486185	−	0.873856i	$-0.338388\pi$
$461$	20.8777			0.972370			0.486185	+	0.873856i	$0.338388\pi$
$462$		0			0
$463$	6.14371			0.285522			0.142761	−	0.989757i	$-0.454402\pi$
$463$	6.14371			0.285522			0.142761	+	0.989757i	$0.454402\pi$
$464$	−3.37235	−	2.45016i	−0.156557	−	0.113746i
$465$	−17.2595	−	16.7576i	−0.800392	−	0.777116i
$466$	−0.874011	−	2.68993i	−0.0404878	−	0.124609i
$467$	−20.4577	−	28.1576i	−0.946670	−	1.30298i	−0.952991	−	0.302999i	$-0.902012\pi$
$467$	−20.4577	−	28.1576i	−0.946670	−	1.30298i	0.00632072	−	0.999980i	$-0.497988\pi$
$468$	−1.59010	+	5.43443i	−0.0735026	+	0.251207i
$469$	−32.5601	+	10.5794i	−1.50349	+	0.488512i
$470$	2.20692	−	6.79220i	0.101798	−	0.313301i
$471$	−3.00000	−	5.67911i	−0.138233	−	0.261680i
$472$		−	2.77195i		−	0.127589i
$473$		0			0
$474$	8.64915	−	17.6126i	0.397269	−	0.808971i
$475$	0.0720302	−	0.0991411i	0.00330497	−	0.00454890i
$476$	−16.8208	−	5.46541i	−0.770980	−	0.250507i
$477$	−15.3998	−	10.5087i	−0.705108	−	0.481161i
$478$	−0.918528	+	0.667349i	−0.0420125	+	0.0305239i
$479$	28.1803	−	20.4742i	1.28759	−	0.935491i	0.287839	−	0.957679i	$-0.407063\pi$
$479$	28.1803	−	20.4742i	1.28759	−	0.935491i	0.999754	+	0.0221881i	$0.00706327\pi$
$480$	3.63359	+	0.520675i	0.165850	+	0.0237655i
$481$	15.8434	+	5.14784i	0.722398	+	0.234721i
$482$	−8.84404	+	12.1728i	−0.402835	+	0.554455i
$483$	26.4999	+	13.0135i	1.20578	+	0.592136i
$484$		0			0
$485$		−	28.0212i		−	1.27238i
$486$	−15.1749	+	3.56668i	−0.688349	+	0.161788i
$487$	−1.78176	+	5.48370i	−0.0807393	+	0.248490i	−0.983276	−	0.182124i	$-0.941703\pi$
$487$	−1.78176	+	5.48370i	−0.0807393	+	0.248490i	0.902536	+	0.430614i	$0.141703\pi$
$488$	1.53975	−	0.500295i	0.0697012	−	0.0226473i
$489$	14.5917	−	2.53230i	0.659858	−	0.114515i
$490$	5.92766	+	8.15872i	0.267784	+	0.368574i
$491$	3.21948	+	9.90855i	0.145293	+	0.447166i	0.997049	−	0.0767732i	$-0.0244617\pi$
$491$	3.21948	+	9.90855i	0.145293	+	0.447166i	−0.851755	+	0.523940i	$0.824462\pi$
$492$	−9.57461	+	9.86138i	−0.431657	+	0.444585i
$493$	−17.3939	−	12.6374i	−0.783380	−	0.569159i
$494$	0.454741			0.0204597
$495$		0			0
$496$	6.55361			0.294266
$497$	−27.6297	−	20.0742i	−1.23936	−	0.900449i
$498$	−8.28649	+	8.53468i	−0.371326	+	0.382448i
$499$	−6.76658	−	20.8254i	−0.302914	−	0.932272i	−0.980448	−	0.196781i	$-0.936951\pi$
$499$	−6.76658	−	20.8254i	−0.302914	−	0.932272i	0.677534	−	0.735492i	$-0.263049\pi$
$500$	−6.86202	−	9.44475i	−0.306879	−	0.422382i
$501$	2.80891	−	0.487471i	0.125493	−	0.0217786i
$502$	−9.16478	+	2.97782i	−0.409044	+	0.132907i
$503$	6.04830	−	18.6148i	0.269680	−	0.829991i	−0.720898	−	0.693041i	$-0.756270\pi$
$503$	6.04830	−	18.6148i	0.269680	−	0.829991i	0.990578	−	0.136949i	$-0.0437297\pi$
$504$	−10.2827	+	0.303503i	−0.458030	+	0.0135191i
$505$			5.21397i			0.232019i
$506$		0			0
$507$	−14.6727	−	7.20544i	−0.651636	−	0.320005i
$508$	10.3090	−	14.1891i	0.457387	−	0.629539i
$509$	34.4745	+	11.2014i	1.52805	+	0.496495i	0.948051	−	0.318120i	$-0.103051\pi$
$509$	34.4745	+	11.2014i	1.52805	+	0.496495i	0.580003	+	0.814614i	$0.303051\pi$
$510$	18.7413	+	2.68553i	0.829878	+	0.118917i
$511$	6.87928	−	4.99809i	0.304321	−	0.221102i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	0.617156	+	1.08922i	0.0272481	+	0.0480904i
$514$	−12.7022	−	4.12718i	−0.560268	−	0.182042i
$515$	−5.74194	+	7.90311i	−0.253020	+	0.348253i
$516$	−4.97472	+	10.1302i	−0.219000	+	0.445956i
$517$		0			0
$518$			30.2656i			1.32979i
$519$	−2.83854	−	5.37347i	−0.124598	−	0.235869i
$520$	1.23607	−	3.80423i	0.0542052	−	0.166826i
$521$	−17.2099	+	5.59184i	−0.753980	+	0.244983i	−0.660693	−	0.750656i	$-0.729737\pi$
$521$	−17.2099	+	5.59184i	−0.753980	+	0.244983i	−0.0932869	+	0.995639i	$0.529737\pi$
$522$	−12.0021	−	3.51180i	−0.525319	−	0.153707i
$523$	−14.7370	−	20.2838i	−0.644405	−	0.886947i	0.354436	−	0.935080i	$-0.384673\pi$
$523$	−14.7370	−	20.2838i	−0.644405	−	0.886947i	−0.998841	+	0.0481334i	$0.984673\pi$
$524$	1.49038	+	4.58693i	0.0651077	+	0.200381i
$525$	2.16740	+	2.10437i	0.0945931	+	0.0918423i
$526$	7.55361	+	5.48802i	0.329353	+	0.239289i
$527$	33.8021			1.47244
$528$		0			0
$529$	−1.70807			−0.0742639
$530$	10.6551	+	7.74138i	0.462828	+	0.336264i
$531$	−2.80195	−	7.82959i	−0.121594	−	0.339775i
$532$	0.255301	+	0.785736i	0.0110687	+	0.0340660i
$533$	8.80375	+	12.1173i	0.381333	+	0.524859i
$534$	−0.732270	−	4.21949i	−0.0316884	−	0.182595i
$535$	36.5525	−	11.8766i	1.58030	−	0.513471i
$536$	−3.08521	+	9.49531i	−0.133261	+	0.410135i
$537$	−20.3274	+	10.7380i	−0.877193	+	0.463378i
$538$		−	13.6250i		−	0.587415i
$539$		0			0
$540$	10.7897	−	2.20224i	0.464314	−	0.0947692i
$541$	−23.1545	+	31.8695i	−0.995490	+	1.37017i	−0.0674386	+	0.997723i	$0.521483\pi$
$541$	−23.1545	+	31.8695i	−0.995490	+	1.37017i	−0.928052	+	0.372451i	$0.878517\pi$
$542$	4.46147	+	1.44962i	0.191636	+	0.0622665i
$543$	−1.82630	+	12.7451i	−0.0783742	+	0.546944i
$544$	−4.17274	+	3.03167i	−0.178905	+	0.129982i
$545$	1.20495	−	0.875446i	0.0516143	−	0.0375000i
$546$	−1.59010	+	11.0967i	−0.0680501	+	0.474896i
$547$	−1.70862	−	0.555165i	−0.0730554	−	0.0237371i	0.272261	−	0.962223i	$-0.412228\pi$
$547$	−1.70862	−	0.555165i	−0.0730554	−	0.0237371i	−0.345317	+	0.938486i	$0.612228\pi$
$548$	10.6143	−	14.6093i	0.453420	−	0.624079i
$549$	3.84343	−	2.96954i	0.164034	−	0.126737i
$550$		0			0
$551$			1.00431i			0.0427851i
$552$	7.61266	−	4.02140i	0.324016	−	0.171162i
$553$	12.0042	−	36.9453i	0.510472	−	1.57107i
$554$	7.87652	−	2.55924i	0.334641	−	0.108732i
$555$	−5.53975	−	31.9212i	−0.235149	−	1.35498i
$556$	−0.581539	−	0.800420i	−0.0246627	−	0.0339454i
$557$	−13.2379	−	40.7422i	−0.560909	−	1.72630i	−0.679803	−	0.733395i	$-0.737935\pi$
$557$	−13.2379	−	40.7422i	−0.560909	−	1.72630i	0.118894	−	0.992907i	$-0.462065\pi$
$558$	18.5112	−	6.62455i	0.783640	−	0.280439i
$559$	9.94943	+	7.22869i	0.420816	+	0.305741i
$560$	7.26719			0.307095
$561$		0			0
$562$	−12.6650			−0.534240
$563$	13.9704	+	10.1501i	0.588784	+	0.427776i	0.841880	−	0.539665i	$-0.181449\pi$
$563$	13.9704	+	10.1501i	0.588784	+	0.427776i	−0.253096	+	0.967441i	$0.581449\pi$
$564$	4.18769	+	4.06591i	0.176333	+	0.171206i
$565$	2.80572	+	8.63512i	0.118038	+	0.363282i
$566$	13.2896	+	18.2916i	0.558604	+	0.768852i
$567$	−28.7376	+	11.2513i	−1.20687	+	0.472511i
$568$	−9.47214	+	3.07768i	−0.397442	+	0.129137i
$569$	1.68607	−	5.18918i	0.0706836	−	0.217542i	−0.909474	−	0.415760i	$-0.863516\pi$
$569$	1.68607	−	5.18918i	0.0706836	−	0.217542i	0.980158	+	0.198219i	$0.0635156\pi$
$570$	−0.413086	−	0.781987i	−0.0173023	−	0.0327538i
$571$			18.8259i			0.787838i	0.919145	+	0.393919i	$0.128881\pi$
$571$			18.8259i			0.787838i	−0.919145	+	0.393919i	$0.871119\pi$
$572$		0			0
$573$	−1.97758	+	4.02701i	−0.0826145	+	0.168231i
$574$	−15.9946	+	22.0147i	−0.667603	+	0.918876i
$575$	−2.40452	−	0.781276i	−0.100275	−	0.0325815i
$576$	−1.69098	+	2.47802i	−0.0704576	+	0.103251i
$577$	−12.6935	+	9.22238i	−0.528438	+	0.383933i	−0.819773	−	0.572688i	$-0.805901\pi$
$577$	−12.6935	+	9.22238i	−0.528438	+	0.383933i	0.291335	+	0.956621i	$0.405901\pi$
$578$	−7.76878	+	5.64435i	−0.323139	+	0.234774i
$579$	−33.4779	−	4.79721i	−1.39129	−	0.199365i
$580$	8.40177	+	2.72990i	0.348864	+	0.113353i
$581$	−13.8428	+	19.0530i	−0.574295	+	0.790450i
$582$	20.5563	+	10.0947i	0.852084	+	0.418441i
$583$		0			0
$584$		−	2.47975i		−	0.102613i
$585$	−0.354035	−	11.9948i	−0.0146376	−	0.495923i
$586$	7.75383	−	23.8638i	0.320308	−	0.985806i
$587$	2.82183	−	0.916868i	0.116469	−	0.0378432i	−0.250202	−	0.968194i	$-0.580497\pi$
$587$	2.82183	−	0.916868i	0.116469	−	0.0378432i	0.366672	+	0.930350i	$0.380497\pi$
$588$	−8.12068	+	1.40930i	−0.334891	+	0.0581186i
$589$	−0.928095	−	1.27741i	−0.0382415	−	0.0526349i
$590$	1.81534	+	5.58703i	0.0747362	+	0.230014i
$591$	−6.49980	+	6.69448i	−0.267366	+	0.275374i
$592$	7.14052	+	5.18789i	0.293474	+	0.213221i
$593$	−43.4839			−1.78567			−0.892836	−	0.450383i	$-0.851288\pi$
$593$	−43.4839			−1.78567			−0.892836	+	0.450383i	$0.851288\pi$
$594$		0			0
$595$	37.4826			1.53664
$596$	11.3158	+	8.22144i	0.463515	+	0.336763i
$597$	−8.91288	+	9.17984i	−0.364780	+	0.375706i
$598$	−2.89916	−	8.92270i	−0.118556	−	0.364876i
$599$	15.3131	+	21.0766i	0.625674	+	0.861167i	0.997751	−	0.0670354i	$-0.0213540\pi$
$599$	15.3131	+	21.0766i	0.625674	+	0.861167i	−0.372076	+	0.928202i	$0.621354\pi$
$600$	0.868001	−	0.150637i	0.0354360	−	0.00614973i
$601$	43.8829	−	14.2584i	1.79002	−	0.581613i	0.790498	−	0.612465i	$-0.209822\pi$
$601$	43.8829	−	14.2584i	1.79002	−	0.581613i	0.999524	+	0.0308513i	$0.00982183\pi$
$602$	−6.90445	+	21.2497i	−0.281405	+	0.866074i
$603$	0.883668	+	29.9388i	0.0359858	+	1.21920i
$604$			6.32849i			0.257502i
$605$		0			0
$606$	−3.82495	−	1.87835i	−0.155378	−	0.0763029i
$607$	−5.60812	+	7.71891i	−0.227626	+	0.313301i	−0.907519	−	0.420011i	$-0.862026\pi$
$607$	−5.60812	+	7.71891i	−0.227626	+	0.313301i	0.679893	+	0.733312i	$0.262026\pi$
$608$	0.229139	+	0.0744518i	0.00929282	+	0.00301942i
$609$	−24.5075	−	3.51180i	−0.993094	−	0.142305i
$610$	−2.77582	+	2.01675i	−0.112390	+	0.0816558i
$611$	5.14568	−	3.73856i	0.208172	−	0.151246i
$612$	−8.72173	+	12.7811i	−0.352555	+	0.516645i
$613$	9.96988	+	3.23941i	0.402680	+	0.130839i	0.503353	−	0.864081i	$-0.332100\pi$
$613$	9.96988	+	3.23941i	0.402680	+	0.130839i	−0.100673	+	0.994920i	$0.532100\pi$
$614$	−9.44462	+	12.9994i	−0.381154	+	0.524613i
$615$	12.8400	−	26.1466i	0.517760	−	1.05433i
$616$		0			0
$617$			26.7867i			1.07839i	0.842180	+	0.539196i	$0.181272\pi$
$617$			26.7867i			1.07839i	−0.842180	+	0.539196i	$0.818728\pi$
$618$	−3.72914	−	7.05940i	−0.150008	−	0.283971i
$619$	−2.48973	+	7.66261i	−0.100071	+	0.307986i	−0.988542	−	0.150946i	$-0.951768\pi$
$619$	−2.48973	+	7.66261i	−0.100071	+	0.307986i	0.888471	+	0.458932i	$0.151768\pi$
$620$	−13.2092	+	4.29193i	−0.530494	+	0.172368i
$621$	17.4376	−	19.0538i	0.699747	−	0.764603i
$622$	5.65772	+	7.78718i	0.226854	+	0.312238i
$623$	−2.62000	−	8.06355i	−0.104968	−	0.323059i
$624$	2.34547	+	2.27726i	0.0938940	+	0.0911635i
$625$	17.9587	+	13.0477i	0.718347	+	0.521910i
$626$	20.1139			0.803915
$627$		0			0
$628$	−3.70820			−0.147973
$629$	36.8293	+	26.7580i	1.46848	+	1.06691i
$630$	20.5267	−	7.34585i	0.817804	−	0.292666i
$631$	−6.32991	−	19.4815i	−0.251990	−	0.775545i	−0.994408	−	0.105608i	$-0.966321\pi$
$631$	−6.32991	−	19.4815i	−0.251990	−	0.775545i	0.742418	−	0.669937i	$-0.233679\pi$
$632$	−6.65877	−	9.16501i	−0.264872	−	0.364565i
$633$	−2.53580	−	14.6118i	−0.100789	−	0.580768i
$634$	−17.5481	+	5.70172i	−0.696924	+	0.226444i
$635$	−11.4860	+	35.3503i	−0.455808	+	1.40283i
$636$	−9.51760	+	5.02768i	−0.377397	+	0.199361i
$637$			8.98144i			0.355858i
$638$		0			0
$639$	−23.6438	+	18.2678i	−0.935333	+	0.722664i
$640$	1.24568	−	1.71454i	0.0492400	−	0.0677730i
$641$	−2.95338	−	0.959611i	−0.116651	−	0.0379024i	0.250110	−	0.968218i	$-0.419533\pi$
$641$	−2.95338	−	0.959611i	−0.116651	−	0.0379024i	−0.366761	+	0.930315i	$0.619533\pi$
$642$	−4.45552	+	31.0934i	−0.175846	+	1.22716i
$643$	31.7912	−	23.0977i	1.25372	−	0.910884i	0.255292	−	0.966864i	$-0.417828\pi$
$643$	31.7912	−	23.0977i	1.25372	−	0.910884i	0.998432	+	0.0559805i	$0.0178285\pi$
$644$	13.7897	−	10.0188i	0.543389	−	0.394795i
$645$	3.39263	−	23.6759i	0.133585	−	0.932237i
$646$	1.18185	+	0.384007i	0.0464993	+	0.0151085i
$647$	−21.0793	+	29.0131i	−0.828712	+	1.14062i	0.159449	+	0.987206i	$0.449028\pi$
$647$	−21.0793	+	29.0131i	−0.828712	+	1.14062i	−0.988161	+	0.153418i	$0.950972\pi$
$648$	−2.27147	+	8.70864i	−0.0892318	+	0.342108i
$649$		0			0
$650$		−	0.960005i		−	0.0376545i
$651$	34.4171	−	18.1809i	1.34891	−	0.712565i
$652$	2.64222	−	8.13193i	0.103478	−	0.318471i
$653$	−2.24293	+	0.728772i	−0.0877726	+	0.0285191i	−0.352574	−	0.935784i	$-0.614694\pi$
$653$	−2.24293	+	0.728772i	−0.0877726	+	0.0285191i	0.264801	+	0.964303i	$0.414694\pi$
$654$	0.208137	+	1.19933i	0.00813881	+	0.0468975i
$655$	−6.00791	−	8.26918i	−0.234749	−	0.323104i
$656$	2.45223	+	7.54718i	0.0957434	+	0.294668i
$657$	−2.50659	−	7.00425i	−0.0977915	−	0.273262i
$658$	9.34866	+	6.79220i	0.364449	+	0.264787i
$659$	−8.51039			−0.331518			−0.165759	−	0.986166i	$-0.553007\pi$
$659$	−8.51039			−0.331518			−0.165759	+	0.986166i	$0.553007\pi$
$660$		0			0
$661$	42.4546			1.65129			0.825646	−	0.564189i	$-0.190811\pi$
$661$	42.4546			1.65129			0.825646	+	0.564189i	$0.190811\pi$
$662$	4.07454	+	2.96033i	0.158362	+	0.115056i
$663$	12.0974	+	11.7456i	0.469825	+	0.456163i
$664$	2.12232	+	6.53182i	0.0823618	+	0.253484i
$665$	−1.02915	−	1.41650i	−0.0399087	−	0.0549296i
$666$	25.4130	+	7.43579i	0.984734	+	0.288131i
$667$	19.7061	−	6.40290i	0.763023	−	0.247921i
$668$	0.508631	−	1.56541i	0.0196795	−	0.0605674i
$669$	0.0407361	+	0.0771150i	0.00157495	+	0.00298144i
$670$		−	21.1588i		−	0.817438i
$671$		0			0
$672$	−2.61803	+	5.33119i	−0.100993	+	0.205655i
$673$	28.1092	−	38.6890i	1.08353	−	1.49135i	0.227958	−	0.973671i	$-0.426795\pi$
$673$	28.1092	−	38.6890i	1.08353	−	1.49135i	0.855573	−	0.517682i	$-0.173205\pi$
$674$	16.7902	+	5.45548i	0.646735	+	0.210137i
$675$	2.29947	−	1.30288i	0.0885065	−	0.0501479i
$676$	−7.63519	+	5.54729i	−0.293661	+	0.213357i
$677$	−4.45107	+	3.23389i	−0.171068	+	0.124288i	−0.670025	−	0.742338i	$-0.733717\pi$
$677$	−4.45107	+	3.23389i	−0.171068	+	0.124288i	0.498957	+	0.866627i	$0.333717\pi$
$678$	−7.34547	−	1.05257i	−0.282101	−	0.0404236i
$679$	43.1202	+	14.0106i	1.65480	+	0.537677i
$680$	6.42497	−	8.84322i	0.246386	−	0.339122i
$681$	−22.2130	−	10.9083i	−0.851205	−	0.418009i
$682$		0			0
$683$		−	40.1110i		−	1.53480i	−0.641166	−	0.767402i	$-0.721549\pi$
$683$		−	40.1110i		−	1.53480i	0.641166	−	0.767402i	$-0.278451\pi$
$684$	0.722479	−	0.0213245i	0.0276247	−	0.000815364i
$685$	−11.8262	+	36.3972i	−0.451855	+	1.39067i
$686$	7.30989	−	2.37513i	0.279093	−	0.0906828i
$687$	−51.6103	+	8.95669i	−1.96905	+	0.341719i
$688$	3.82991	+	5.27142i	0.146014	+	0.200971i
$689$	3.62463	+	11.1555i	0.138087	+	0.424989i
$690$	−12.7102	+	13.0909i	−0.483868	+	0.498361i
$691$	−25.5891	−	18.5916i	−0.973457	−	0.707258i	−0.0172201	−	0.999852i	$-0.505482\pi$
$691$	−25.5891	−	18.5916i	−0.973457	−	0.707258i	−0.956237	+	0.292594i	$0.905482\pi$
$692$	−3.50863			−0.133378
$693$		0			0
$694$	15.0268			0.570411
$695$	1.69632	+	1.23245i	0.0643450	+	0.0467494i
$696$	−5.02942	+	5.18005i	−0.190640	+	0.196349i
$697$	12.6481	+	38.9267i	0.479079	+	1.47445i
$698$	2.05443	+	2.82768i	0.0777612	+	0.107029i
$699$	−4.82671	+	0.837650i	−0.182563	+	0.0316829i
$700$	1.65877	−	0.538967i	0.0626956	−	0.0203710i
$701$	−4.85616	+	14.9457i	−0.183414	+	0.564492i	−0.999917	−	0.0128496i	$-0.995910\pi$
$701$	−4.85616	+	14.9457i	−0.183414	+	0.564492i	0.816503	+	0.577341i	$0.195910\pi$
$702$	8.92688	+	4.06145i	0.336923	+	0.153289i
$703$		−	2.12650i		−	0.0802025i
$704$		0			0
$705$	−11.1033	−	5.45258i	−0.418174	−	0.205356i
$706$	14.8518	−	20.4417i	0.558955	−	0.769335i
$707$	−8.02347	−	2.60698i	−0.301754	−	0.0980458i
$708$	−4.75261	−	0.681025i	−0.178614	−	0.0255945i
$709$	−4.80715	+	3.49260i	−0.180536	+	0.131167i	−0.674383	−	0.738382i	$-0.735590\pi$
$709$	−4.80715	+	3.49260i	−0.180536	+	0.131167i	0.493847	+	0.869549i	$0.335590\pi$
$710$	17.0761	−	12.4065i	0.640854	−	0.465608i
$711$	−28.0724	−	19.1564i	−1.05280	−	0.718422i
$712$	−2.35152	−	0.764056i	−0.0881270	−	0.0286342i
$713$	−19.1478	+	26.3547i	−0.717090	+	0.986990i
$714$	−13.5033	+	27.4971i	−0.505347	+	1.02905i
$715$		0			0
$716$			13.2729i			0.496031i
$717$	0.918528	+	1.73881i	0.0343030	+	0.0649370i
$718$	−5.96229	+	18.3500i	−0.222511	+	0.684817i
$719$	−29.3645	+	9.54110i	−1.09511	+	0.355823i	−0.800219	−	0.599708i	$-0.795284\pi$
$719$	−29.3645	+	9.54110i	−1.09511	+	0.355823i	−0.294892	+	0.955531i	$0.595284\pi$
$720$	1.78544	−	6.10201i	0.0665392	−	0.227409i
$721$	−9.29066	−	12.7875i	−0.346002	−	0.476231i
$722$	5.85339	+	18.0149i	0.217840	+	0.670444i
$723$	18.6978	+	18.1541i	0.695380	+	0.675158i
$724$	6.01386	+	4.36932i	0.223503	+	0.162385i
$725$	2.12020			0.0787424
$726$		0			0
$727$	−23.3566			−0.866249			−0.433124	−	0.901334i	$-0.642589\pi$
$727$	−23.3566			−0.866249			−0.433124	+	0.901334i	$0.642589\pi$
$728$	5.23607	+	3.80423i	0.194062	+	0.140994i
$729$	2.38697	+	26.8943i	0.0884061	+	0.996085i
$730$	1.62398	+	4.99809i	0.0601061	+	0.184988i
$731$	19.7539	+	27.1889i	0.730623	+	1.00562i
$732$	−0.479482	−	2.76288i	−0.0177222	−	0.102119i
$733$	−39.4398	+	12.8148i	−1.45674	+	0.473325i	−0.927074	−	0.374879i	$-0.877684\pi$
$733$	−39.4398	+	12.8148i	−1.45674	+	0.473325i	−0.529670	+	0.848204i	$0.677684\pi$
$734$	−0.277454	+	0.853917i	−0.0102410	+	0.0315186i
$735$	15.4448	−	8.15872i	0.569689	−	0.300939i
$736$		−	4.97072i		−	0.183223i
$737$		0			0
$738$	14.5554	+	18.8388i	0.535791	+	0.693466i
$739$	18.2713	−	25.1482i	0.672119	−	0.925092i	−0.327687	−	0.944786i	$-0.606269\pi$
$739$	18.2713	−	25.1482i	0.672119	−	0.925092i	0.999806	+	0.0196939i	$0.00626918\pi$
$740$	−17.7897	−	5.78022i	−0.653962	−	0.212485i
$741$	0.111723	−	0.779670i	0.00410424	−	0.0286419i
$742$	−17.2403	+	12.5258i	−0.632912	+	0.459837i
$743$	24.8174	−	18.0309i	0.910462	−	0.661489i	−0.0306698	−	0.999530i	$-0.509764\pi$
$743$	24.8174	−	18.0309i	0.910462	−	0.661489i	0.941132	+	0.338040i	$0.109764\pi$
$744$	1.61012	−	11.2364i	0.0590299	−	0.411947i
$745$	−28.1919	−	9.16011i	−1.03287	−	0.335601i
$746$	15.4827	−	21.3101i	0.566861	−	0.780217i
$747$	12.5972	+	16.3043i	0.460906	+	0.596544i
$748$		0			0
$749$			62.1868i			2.27226i
$750$	−17.8793	+	9.44475i	−0.652859	+	0.344874i
$751$	−2.30700	+	7.10023i	−0.0841838	+	0.259091i	−0.984284	−	0.176591i	$-0.943493\pi$
$751$	−2.30700	+	7.10023i	−0.0841838	+	0.259091i	0.900100	+	0.435682i	$0.143493\pi$
$752$	3.20495	−	1.04135i	0.116872	−	0.0379742i
$753$	2.85394	+	16.4450i	0.104003	+	0.599288i
$754$	4.62449	+	6.36507i	0.168414	+	0.231802i
$755$	−4.14450	−	12.7554i	−0.150834	−	0.464218i
$756$	−2.00594	+	17.7047i	−0.0729555	+	0.643915i
$757$	18.8904	+	13.7247i	0.686583	+	0.498831i	0.875535	−	0.483155i	$-0.160509\pi$
$757$	18.8904	+	13.7247i	0.686583	+	0.498831i	−0.188952	+	0.981986i	$0.560509\pi$
$758$	−2.66498			−0.0967965
$759$		0			0
$760$	−0.510602			−0.0185215
$761$	7.77691	+	5.65026i	0.281913	+	0.204822i	0.719751	−	0.694232i	$-0.244256\pi$
$761$	7.77691	+	5.65026i	0.281913	+	0.204822i	−0.437838	+	0.899054i	$0.644256\pi$
$762$	−21.7950	−	21.1612i	−0.789548	−	0.766588i
$763$	0.744699	+	2.29195i	0.0269599	+	0.0829741i
$764$	1.52249	+	2.09553i	0.0550817	+	0.0758135i
$765$	9.20889	−	31.4729i	0.332948	−	1.13790i
$766$	−31.1072	+	10.1073i	−1.12395	+	0.365193i
$767$	−1.61673	+	4.97579i	−0.0583769	+	0.179666i
$768$	0.809017	+	1.53150i	0.0291929	+	0.0552632i
$769$		−	34.6298i		−	1.24878i	−0.781112	−	0.624391i	$-0.785347\pi$
$769$		−	34.6298i		−	1.24878i	0.781112	−	0.624391i	$-0.214653\pi$
$770$		0			0
$771$	−10.1969	+	20.7643i	−0.367233	+	0.747809i
$772$	−11.4770	+	15.7968i	−0.413067	+	0.568538i
$773$	12.8941	+	4.18953i	0.463767	+	0.150687i	0.531575	−	0.847011i	$-0.321600\pi$
$773$	12.8941	+	4.18953i	0.463767	+	0.150687i	−0.0678078	+	0.997698i	$0.521600\pi$
$774$	16.1464	+	11.0182i	0.580369	+	0.396040i
$775$	−2.69675	+	1.95930i	−0.0968702	+	0.0703803i
$776$	10.6968	−	7.77169i	0.383993	−	0.278988i
$777$	51.8915	+	7.43579i	1.86160	+	0.266757i
$778$	−1.60221	−	0.520588i	−0.0574419	−	0.0186640i
$779$	1.12380	−	1.54678i	0.0402644	−	0.0554192i
$780$	−6.21881	−	3.05392i	−0.222669	−	0.109348i
$781$		0			0
$782$		−	25.6379i		−	0.916810i
$783$	−8.96985	+	19.7153i	−0.320556	+	0.704568i
$784$	−1.47047	+	4.52566i	−0.0525170	+	0.161631i
$785$	7.47411	−	2.42848i	0.266762	−	0.0866763i
$786$	8.23063	−	1.42838i	0.293577	−	0.0509487i
$787$	−10.8875	−	14.9854i	−0.388099	−	0.534172i	0.569609	−	0.821916i	$-0.307095\pi$
$787$	−10.8875	−	14.9854i	−0.388099	−	0.534172i	−0.957707	+	0.287744i	$0.907095\pi$
$788$	1.66471	+	5.12346i	0.0593030	+	0.182516i
$789$	11.2652	−	11.6026i	0.401052	−	0.413064i
$790$	19.4233	+	14.1118i	0.691049	+	0.502076i
$791$	−14.6909			−0.522350
$792$		0			0
$793$	−3.05573			−0.108512
$794$	7.19406	+	5.22679i	0.255308	+	0.185492i
$795$	15.8907	−	16.3666i	0.563584	−	0.580464i
$796$	2.28275	+	7.02557i	0.0809098	+	0.249015i
$797$	−30.2920	−	41.6933i	−1.07300	−	1.47685i	−0.867005	−	0.498300i	$-0.833958\pi$
$797$	−30.2920	−	41.6933i	−1.07300	−	1.47685i	−0.205992	−	0.978554i	$-0.566042\pi$
$798$	1.40990	−	0.244680i	0.0499098	−	0.00866158i
$799$	16.5304	−	5.37106i	0.584805	−	0.190015i
$800$	0.157176	−	0.483737i	0.00555700	−	0.0171027i
$801$	−7.41438	+	0.218841i	−0.261974	+	0.00773238i
$802$		−	19.5587i		−	0.690642i
$803$		0			0
$804$	15.5221	+	7.62256i	0.547421	+	0.268827i
$805$	−21.2327	+	29.2243i	−0.748353	+	1.03002i
$806$	−11.7641	−	3.82238i	−0.414372	−	0.134637i
$807$	−23.3605	−	3.34745i	−0.822330	−	0.117836i
$808$	−1.99038	+	1.44610i	−0.0700214	+	0.0508736i
$809$	−28.2831	+	20.5489i	−0.994382	+	0.722461i	−0.960876	−	0.276978i	$-0.910667\pi$
$809$	−28.2831	+	20.5489i	−0.994382	+	0.722461i	−0.0335059	+	0.999439i	$0.510667\pi$
$810$	−1.12496	−	19.0404i	−0.0395272	−	0.669010i
$811$	17.1154	+	5.56112i	0.601002	+	0.195277i	0.593687	−	0.804696i	$-0.297672\pi$
$811$	17.1154	+	5.56112i	0.601002	+	0.195277i	0.00731472	+	0.999973i	$0.497672\pi$
$812$	−8.40177	+	11.5640i	−0.294844	+	0.405818i
$813$	3.58154	−	7.29320i	0.125610	−	0.255784i
$814$		0			0
$815$			18.1208i			0.634743i
$816$	4.17274	+	7.89915i	0.146075	+	0.276525i
$817$	0.485116	−	1.49303i	0.0169721	−	0.0522346i
$818$	−23.5359	+	7.64727i	−0.822912	+	0.267380i
$819$	18.6351	+	5.45258i	0.651162	+	0.190529i
$820$	−9.88522	−	13.6058i	−0.345207	−	0.475137i
$821$	2.80515	+	8.63337i	0.0979005	+	0.301307i	0.987999	−	0.154462i	$-0.0493644\pi$
$821$	2.80515	+	8.63337i	0.0979005	+	0.301307i	−0.890098	+	0.455769i	$0.849364\pi$
$822$	−22.4405	−	21.7879i	−0.782701	−	0.759940i
$823$	0.622491	+	0.452266i	0.0216987	+	0.0157650i	0.598582	−	0.801062i	$-0.295731\pi$
$823$	0.622491	+	0.452266i	0.0216987	+	0.0157650i	−0.576883	+	0.816827i	$0.695731\pi$
$824$	−4.60947			−0.160578
$825$		0			0
$826$	−9.50523			−0.330729
$827$	−39.9982	−	29.0604i	−1.39087	−	1.01053i	−0.995769	−	0.0918931i	$-0.970708\pi$
$827$	−39.9982	−	29.0604i	−1.39087	−	1.01053i	−0.395105	−	0.918636i	$-0.629292\pi$
$828$	−5.02453	−	14.0402i	−0.174614	−	0.487930i
$829$	−5.42619	−	16.7001i	−0.188459	−	0.580018i	0.811531	−	0.584309i	$-0.198634\pi$
$829$	−5.42619	−	16.7001i	−0.188459	−	0.580018i	−0.999991	+	0.00429046i	$0.998634\pi$
$830$	−8.55531	−	11.7754i	−0.296959	−	0.408729i
$831$	−2.45277	−	14.1334i	−0.0850856	−	0.490281i
$832$	1.79505	−	0.583248i	0.0622322	−	0.0202205i
$833$	−7.58439	+	23.3424i	−0.262784	+	0.808765i
$834$	−1.51522	+	0.800420i	−0.0524679	+	0.0277163i
$835$			3.48827i			0.120717i
$836$		0			0
$837$	−6.81013	−	33.3656i	−0.235392	−	1.15329i
$838$	20.4821	−	28.1912i	0.707542	−	0.973848i
$839$	1.15241	+	0.374440i	0.0397856	+	0.0129271i	0.328842	−	0.944385i	$-0.393342\pi$
$839$	1.15241	+	0.374440i	0.0397856	+	0.0129271i	−0.289057	+	0.957312i	$0.593342\pi$
$840$	1.78544	−	12.4599i	0.0616034	−	0.429906i
$841$	9.40401	−	6.83241i	0.324276	−	0.235600i
$842$	−14.1996	+	10.3166i	−0.489350	+	0.355533i
$843$	−3.11159	+	21.7146i	−0.107169	+	0.747890i
$844$	−8.14317	−	2.64588i	−0.280299	−	0.0910748i
$845$	11.7563	−	16.1811i	0.404429	−	0.556648i
$846$	8.00000	−	6.18102i	0.275046	−	0.212508i
$847$		0			0
$848$			6.21456i			0.213409i
$849$	34.6266	−	18.2916i	1.18838	−	0.627765i
$850$	0.810678	−	2.49501i	0.0278060	−	0.0855782i
$851$	−41.7252	+	13.5573i	−1.43032	+	0.464739i
$852$	2.94965	+	16.9965i	0.101053	+	0.582290i
$853$	1.26195	+	1.73692i	0.0432082	+	0.0594710i	0.830074	−	0.557653i	$-0.188298\pi$
$853$	1.26195	+	1.73692i	0.0432082	+	0.0594710i	−0.786866	+	0.617124i	$0.788298\pi$
$854$	−1.71555	−	5.27992i	−0.0587049	−	0.180675i
$855$	−1.44223	+	0.516129i	−0.0493234	+	0.0176512i
$856$	14.6716	+	10.6596i	0.501466	+	0.364337i
$857$	55.7274			1.90361			0.951805	−	0.306704i	$-0.0992260\pi$
$857$	55.7274			1.90361			0.951805	+	0.306704i	$0.0992260\pi$
$858$		0			0
$859$	−36.2927			−1.23829			−0.619146	−	0.785276i	$-0.712521\pi$
$859$	−36.2927			−1.23829			−0.619146	+	0.785276i	$0.712521\pi$
$860$	−11.1716	−	8.11667i	−0.380950	−	0.276776i
$861$	33.8154	+	32.8321i	1.15243	+	1.11891i
$862$	−10.3275	−	31.7846i	−0.351755	−	1.08259i
$863$	−18.3274	−	25.2255i	−0.623871	−	0.858685i	0.373757	−	0.927527i	$-0.378070\pi$
$863$	−18.3274	−	25.2255i	−0.623871	−	0.858685i	−0.997628	+	0.0688420i	$0.978070\pi$
$864$	3.83321	+	3.50806i	0.130408	+	0.119347i
$865$	7.07186	−	2.29779i	0.240450	−	0.0781270i
$866$	8.40143	−	25.8569i	0.285492	−	0.878655i
$867$	7.76878	+	14.7066i	0.263842	+	0.499462i
$868$		−	22.4728i		−	0.762777i
$869$		0			0
$870$	6.74470	−	13.7345i	0.228667	−	0.465642i
$871$	11.0762	−	15.2451i	0.375304	−	0.516561i
$872$	0.668387	+	0.217172i	0.0226344	+	0.00735437i
$873$	22.3582	−	32.7643i	0.756709	−	1.10891i
$874$	−0.968880	+	0.703933i	−0.0327729	+	0.0238109i
$875$	−32.3868	+	23.5304i	−1.09487	+	0.795472i
$876$	−4.25163	−	0.609237i	−0.143649	−	0.0205842i
$877$	17.6284	+	5.72780i	0.595267	+	0.193414i	0.591129	−	0.806577i	$-0.298683\pi$
$877$	17.6284	+	5.72780i	0.595267	+	0.193414i	0.00413871	+	0.999991i	$0.498683\pi$
$878$	−7.88033	+	10.8463i	−0.265948	+	0.366046i
$879$	−39.0105	−	19.1572i	−1.31579	−	0.646157i
$880$		0			0
$881$		−	22.0893i		−	0.744207i	−0.928191	−	0.372103i	$-0.878637\pi$
$881$		−	22.0893i		−	0.744207i	0.928191	−	0.372103i	$-0.121363\pi$
$882$	0.421174	+	14.2695i	0.0141817	+	0.480478i
$883$	13.4960	−	41.5364i	0.454176	−	1.39781i	−0.417924	−	0.908482i	$-0.637242\pi$
$883$	13.4960	−	41.5364i	0.454176	−	1.39781i	0.872100	−	0.489328i	$-0.162758\pi$
$884$	9.25849	−	3.00827i	0.311397	−	0.101179i
$885$	10.0252	−	1.73982i	0.336993	−	0.0584833i
$886$	−10.8348	−	14.9128i	−0.364002	−	0.501006i
$887$	−2.60858	−	8.02839i	−0.0875877	−	0.269567i	0.897663	−	0.440682i	$-0.145263\pi$
$887$	−2.60858	−	8.02839i	−0.0875877	−	0.269567i	−0.985251	+	0.171114i	$0.945263\pi$
$888$	10.6492	−	10.9681i	0.357362	−	0.368066i
$889$	−48.6554	−	35.3503i	−1.63185	−	1.18561i
$890$	5.24001			0.175646
$891$		0			0
$892$	0.0503526			0.00168593
$893$	−0.656849	−	0.477229i	−0.0219806	−	0.0159698i
$894$	16.8761	−	17.3815i	0.564421	−	0.581326i
$895$	−8.69234	−	26.7523i	−0.290553	−	0.894230i
$896$	2.01556	+	2.77418i	0.0673351	+	0.0926789i
$897$	−16.0106	+	2.77855i	−0.534578	+	0.0927732i
$898$	−28.8836	+	9.38485i	−0.963858	+	0.313176i
$899$	8.44185	−	25.9814i	0.281552	−	0.866527i
$900$	−0.0450183	−	1.52523i	−0.00150061	−	0.0508410i
$901$			32.0534i			1.06785i
$902$		0			0
$903$	34.7371	+	17.0587i	1.15598	+	0.567677i
$904$	−2.51821	+	3.46601i	−0.0837543	+	0.115278i
$905$	−14.9827	−	4.86819i	−0.498043	−	0.161824i
$906$	10.8504	+	1.55481i	0.360481	+	0.0516551i
$907$	9.69876	−	7.04656i	0.322042	−	0.233977i	−0.415004	−	0.909819i	$-0.636220\pi$
$907$	9.69876	−	7.04656i	0.322042	−	0.233977i	0.737046	+	0.675842i	$0.236220\pi$
$908$	−11.5589	+	8.39806i	−0.383597	+	0.278700i
$909$	−4.16024	+	6.09654i	−0.137986	+	0.202210i
$910$	−13.0450	−	4.23857i	−0.432437	−	0.140507i
$911$	−16.7791	+	23.0945i	−0.555918	+	0.765155i	−0.990800	−	0.135332i	$-0.956790\pi$
$911$	−16.7791	+	23.0945i	−0.555918	+	0.765155i	0.434883	+	0.900487i	$0.356790\pi$
$912$	0.183946	−	0.374576i	0.00609108	−	0.0124035i
$913$		0			0
$914$		−	34.6878i		−	1.14737i
$915$	2.77582	+	5.25473i	0.0917657	+	0.173716i
$916$	−9.34547	+	28.7624i	−0.308783	+	0.950337i
$917$	15.7289	−	5.11064i	0.519415	−	0.168768i
$918$	19.7709	+	18.0938i	0.652536	+	0.597186i
$919$	32.3570	+	44.5356i	1.06736	+	1.46909i	0.872722	+	0.488217i	$0.162352\pi$
$919$	32.3570	+	44.5356i	1.06736	+	1.46909i	0.194636	+	0.980876i	$0.437648\pi$
$920$	3.25530	+	10.0188i	0.107324	+	0.330310i
$921$	19.9676	+	19.3869i	0.657954	+	0.638821i
$922$	−16.8904	−	12.2716i	−0.556255	−	0.404143i
$923$	18.7980			0.618745
$924$		0			0
$925$	−4.48926			−0.147606
$926$	−4.97037	−	3.61118i	−0.163336	−	0.118671i
$927$	−13.0198	+	4.65936i	−0.427626	+	0.153034i
$928$	1.28812	+	3.96443i	0.0422847	+	0.130139i
$929$	6.55781	+	9.02605i	0.215155	+	0.296135i	0.902929	−	0.429789i	$-0.141412\pi$
$929$	6.55781	+	9.02605i	0.215155	+	0.296135i	−0.687774	+	0.725924i	$0.741412\pi$
$930$	4.11338	+	23.7021i	0.134883	+	0.777223i
$931$	1.09037	−	0.354283i	0.0357355	−	0.0116112i
$932$	−0.874011	+	2.68993i	−0.0286292	+	0.0881115i
$933$	14.7414	−	7.78718i	0.482613	−	0.254941i
$934$			34.8047i			1.13885i
$935$		0			0
$936$	4.48070	−	3.46191i	0.146456	−	0.113156i
$937$	−18.5422	+	25.5211i	−0.605747	+	0.833739i	−0.996219	−	0.0868753i	$-0.972312\pi$
$937$	−18.5422	+	25.5211i	−0.605747	+	0.833739i	0.390472	+	0.920615i	$0.372312\pi$
$938$	32.5601	+	10.5794i	1.06313	+	0.345430i
$939$	4.94168	−	34.4861i	0.161266	−	1.12541i
$940$	−5.77779	+	4.19781i	−0.188451	+	0.136917i
$941$	−41.3518	+	30.0438i	−1.34803	+	0.979400i	−0.348922	+	0.937152i	$0.613452\pi$
$941$	−41.3518	+	30.0438i	−1.34803	+	0.979400i	−0.999107	+	0.0422486i	$0.986548\pi$
$942$	−0.911048	+	6.35786i	−0.0296836	+	0.207150i
$943$	−37.5149	−	12.1893i	−1.22165	−	0.396939i
$944$	−1.62931	+	2.24256i	−0.0530296	+	0.0729889i
$945$	−7.55164	−	36.9986i	−0.245655	−	1.20356i
$946$		0			0
$947$		−	23.9467i		−	0.778162i	−0.921204	−	0.389081i	$-0.872793\pi$
$947$		−	23.9467i		−	0.778162i	0.921204	−	0.389081i	$-0.127207\pi$
$948$	−17.3497	+	9.16501i	−0.563492	+	0.297666i
$949$	−1.44631	+	4.45128i	−0.0469492	+	0.144495i
$950$	−0.116547	+	0.0378685i	−0.00378129	+	0.00122862i
$951$	5.46452	+	31.4877i	0.177199	+	1.02106i
$952$	10.3958	+	14.3086i	0.336931	+	0.463745i
$953$	−6.18496	−	19.0353i	−0.200350	−	0.616615i	−0.999872	−	0.0159783i	$-0.994914\pi$
$953$	−6.18496	−	19.0353i	−0.200350	−	0.616615i	0.799522	−	0.600637i	$-0.205086\pi$
$954$	6.28183	+	17.5535i	0.203382	+	0.568316i
$955$	−4.44102	−	3.22659i	−0.143708	−	0.104410i
$956$	1.13536			0.0367203
$957$		0			0
$958$	−34.8328			−1.12540
$959$	−50.0965	−	36.3972i	−1.61770	−	1.17533i
$960$	−2.63359	−	2.55701i	−0.0849989	−	0.0825271i
$961$	3.69269	+	11.3649i	0.119119	+	0.366610i
$962$	−9.79178	−	13.4772i	−0.315700	−	0.434523i
$963$	52.2161	+	15.2783i	1.68264	+	0.492337i
$964$	14.3100	−	4.64959i	0.460893	−	0.149753i
$965$	12.7874	−	39.3556i	0.411641	−	1.26690i
$966$	−13.7897	−	26.1044i	−0.443676	−	0.839895i
$967$			48.8703i			1.57156i	0.618505	+	0.785781i	$0.287739\pi$
$967$			48.8703i			1.57156i	−0.618505	+	0.785781i	$0.712261\pi$
$968$		0			0
$969$	0.948756	−	1.93198i	0.0304784	−	0.0620642i
$970$	−16.4704	+	22.6696i	−0.528834	+	0.727877i
$971$	−25.9960	−	8.44660i	−0.834251	−	0.271064i	−0.139416	−	0.990234i	$-0.544522\pi$
$971$	−25.9960	−	8.44660i	−0.834251	−	0.271064i	−0.694835	+	0.719169i	$0.744522\pi$
$972$	14.3732	+	6.03410i	0.461021	+	0.193544i
$973$	−2.74470	+	1.99414i	−0.0879910	+	0.0639292i
$974$	4.66471	−	3.38911i	0.149467	−	0.108594i
$975$	−1.64596	−	0.235858i	−0.0527131	−	0.00755351i
$976$	−1.53975	−	0.500295i	−0.0492862	−	0.0160141i
$977$	9.09106	−	12.5128i	0.290849	−	0.400319i	−0.638441	−	0.769671i	$-0.720420\pi$
$977$	9.09106	−	12.5128i	0.290849	−	0.400319i	0.929290	+	0.369352i	$0.120420\pi$
$978$	−13.2933	−	6.52808i	−0.425074	−	0.208745i
$979$		0			0
$980$		−	10.0847i		−	0.322145i
$981$	2.10743	−	0.0622025i	0.0672851	−	0.00198597i
$982$	3.21948	−	9.90855i	0.102738	−	0.316194i
$983$	42.0482	−	13.6623i	1.34113	−	0.435759i	0.451429	−	0.892307i	$-0.350914\pi$
$983$	42.0482	−	13.6623i	1.34113	−	0.435759i	0.889699	+	0.456548i	$0.150914\pi$
$984$	13.5424	−	2.35021i	0.431716	−	0.0749220i
$985$	−6.71066	−	9.23643i	−0.213819	−	0.294297i
$986$	6.64386	+	20.4477i	0.211584	+	0.651187i
$987$	13.9423	−	14.3599i	0.443788	−	0.457080i
$988$	−0.367893	−	0.267290i	−0.0117042	−	0.00850362i
$989$	−32.3884			−1.02989
$990$		0			0
$991$	−36.1335			−1.14782			−0.573909	−	0.818919i	$-0.694574\pi$
$991$	−36.1335			−1.14782			−0.573909	+	0.818919i	$0.694574\pi$
$992$	−5.30198	−	3.85211i	−0.168338	−	0.122305i
$993$	6.07665	−	6.25865i	0.192837	−	0.198612i
$994$	10.5536	+	32.4807i	0.334740	+	1.03022i
$995$	−9.20203	−	12.6655i	−0.291724	−	0.401524i
$996$	11.7205	−	2.03402i	0.371377	−	0.0644505i
$997$	−7.72887	+	2.51126i	−0.244776	+	0.0795325i	−0.428836	−	0.903383i	$-0.641076\pi$
$997$	−7.72887	+	2.51126i	−0.244776	+	0.0795325i	0.184060	+	0.982915i	$0.441076\pi$
$998$	−6.76658	+	20.8254i	−0.214192	+	0.659216i
$999$	18.9925	−	41.7447i	0.600897	−	1.32074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.h.c.161.1		8
3.2	odd	2		726.2.h.f.161.2		8
11.2	odd	10		66.2.h.b.17.2	yes	8
11.3	even	5		726.2.h.a.239.2		8
11.4	even	5		66.2.h.a.35.2	yes	8
11.5	even	5		726.2.b.e.725.3		8
11.6	odd	10		726.2.b.c.725.3		8
11.7	odd	10		726.2.h.j.233.2		8
11.8	odd	10		726.2.h.f.239.2		8
11.9	even	5		726.2.h.d.215.2		8
11.10	odd	2		726.2.h.h.161.1		8
33.2	even	10		66.2.h.a.17.2	✓	8
33.5	odd	10		726.2.b.c.725.4		8
33.8	even	10	inner	726.2.h.c.239.1		8
33.14	odd	10		726.2.h.h.239.1		8
33.17	even	10		726.2.b.e.725.4		8
33.20	odd	10		726.2.h.j.215.2		8
33.26	odd	10		66.2.h.b.35.1	yes	8
33.29	even	10		726.2.h.d.233.1		8
33.32	even	2		726.2.h.a.161.2		8
44.15	odd	10		528.2.bn.b.497.1		8
44.35	even	10		528.2.bn.a.17.1		8
132.35	odd	10		528.2.bn.b.17.1		8
132.59	even	10		528.2.bn.a.497.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.h.a.17.2	✓	8	33.2	even	10
66.2.h.a.35.2	yes	8	11.4	even	5
66.2.h.b.17.2	yes	8	11.2	odd	10
66.2.h.b.35.1	yes	8	33.26	odd	10
528.2.bn.a.17.1		8	44.35	even	10
528.2.bn.a.497.2		8	132.59	even	10
528.2.bn.b.17.1		8	132.35	odd	10
528.2.bn.b.497.1		8	44.15	odd	10
726.2.b.c.725.3		8	11.6	odd	10
726.2.b.c.725.4		8	33.5	odd	10
726.2.b.e.725.3		8	11.5	even	5
726.2.b.e.725.4		8	33.17	even	10
726.2.h.a.161.2		8	33.32	even	2
726.2.h.a.239.2		8	11.3	even	5
726.2.h.c.161.1		8	1.1	even	1	trivial
726.2.h.c.239.1		8	33.8	even	10	inner
726.2.h.d.215.2		8	11.9	even	5
726.2.h.d.233.1		8	33.29	even	10
726.2.h.f.161.2		8	3.2	odd	2
726.2.h.f.239.2		8	11.8	odd	10
726.2.h.h.161.1		8	11.10	odd	2
726.2.h.h.239.1		8	33.14	odd	10
726.2.h.j.215.2		8	33.20	odd	10
726.2.h.j.233.2		8	11.7	odd	10

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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.20654 + 1.24268i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.24568 - 1.71454i) q^{5} +(1.70654 - 0.296161i) q^{6} +(3.26124 - 1.05964i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.0885088 - 2.99869i) q^{9} +2.11929i q^{10} +(-1.55470 - 0.763481i) q^{12} +(-1.10940 + 1.52696i) q^{13} +(-3.26124 - 1.05964i) q^{14} +(3.63359 + 0.520675i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.17274 + 3.03167i) q^{17} +(-1.69098 + 2.47802i) q^{18} +(0.229139 + 0.0744518i) q^{19} +(1.24568 - 1.71454i) q^{20} +(-2.61803 + 5.33119i) q^{21} -4.97072i q^{23} +(0.809017 + 1.53150i) q^{24} +(0.157176 - 0.483737i) q^{25} +(1.79505 - 0.583248i) q^{26} +(3.83321 + 3.50806i) q^{27} +(2.01556 + 2.77418i) q^{28} +(1.28812 + 3.96443i) q^{29} +(-2.63359 - 2.55701i) q^{30} +(-5.30198 - 3.85211i) q^{31} +1.00000 q^{32} +5.15778 q^{34} +(-5.87928 - 4.27155i) q^{35} +(2.82458 - 1.01082i) q^{36} +(-2.72744 - 8.39419i) q^{37} +(-0.141616 - 0.194917i) q^{38} +(-0.558984 - 3.22098i) q^{39} +(-2.01556 + 0.654895i) q^{40} +(2.45223 - 7.54718i) q^{41} +(5.25163 - 2.77418i) q^{42} -6.51583i q^{43} +(-5.03112 + 3.88718i) q^{45} +(-2.92172 + 4.02140i) q^{46} +(-3.20495 - 1.04135i) q^{47} +(0.245684 - 1.71454i) q^{48} +(3.84975 - 2.79701i) q^{49} +(-0.411491 + 0.298966i) q^{50} +(1.26719 - 8.84322i) q^{51} +(-1.79505 - 0.583248i) q^{52} +(3.65283 - 5.02768i) q^{53} +(-1.03914 - 5.09119i) q^{54} -3.42908i q^{56} +(-0.368986 + 0.194917i) q^{57} +(1.28812 - 3.96443i) q^{58} +(2.63628 - 0.856580i) q^{59} +(0.627650 + 3.61665i) q^{60} +(0.951618 + 1.30979i) q^{61} +(2.02518 + 6.23285i) q^{62} +(-3.46619 - 9.68569i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.00000 q^{65} -9.98396 q^{67} +(-4.17274 - 3.03167i) q^{68} +(6.17702 + 5.99739i) q^{69} +(2.24568 + 6.91151i) q^{70} +(-5.85410 - 8.05748i) q^{71} +(-2.87928 - 0.842471i) q^{72} +(2.35838 - 0.766285i) q^{73} +(-2.72744 + 8.39419i) q^{74} +(0.411491 + 0.778968i) q^{75} +0.240931i q^{76} +(-1.44102 + 2.93439i) q^{78} +(6.65877 - 9.16501i) q^{79} +(2.01556 + 0.654895i) q^{80} +(-8.98433 + 0.530822i) q^{81} +(-6.42001 + 4.66441i) q^{82} +(-5.55630 + 4.03689i) q^{83} +(-5.87928 - 0.842471i) q^{84} +(10.3958 + 3.37781i) q^{85} +(-3.82991 + 5.27142i) q^{86} +(-6.48070 - 3.18254i) q^{87} -2.47254i q^{89} +(6.35509 - 0.187575i) q^{90} +(-2.00000 + 6.15537i) q^{91} +(4.72744 - 1.53604i) q^{92} +(11.1840 - 1.94093i) q^{93} +(1.98077 + 2.72629i) q^{94} +(-0.157785 - 0.485611i) q^{95} +(-1.20654 + 1.24268i) q^{96} +(10.6968 + 7.77169i) q^{97} -4.75856 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 5 q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} + 2 q^{9} - 3 q^{12} + 10 q^{13} - 5 q^{14} + 4 q^{15} - 2 q^{16} - 15 q^{17} - 18 q^{18} + 10 q^{19} + 5 q^{20} - 12 q^{21} + 2 q^{24}+ \cdots + 22 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 5 * q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 + 2 * q^9 - 3 * q^12 + 10 * q^13 - 5 * q^14 + 4 * q^15 - 2 * q^16 - 15 * q^17 - 18 * q^18 + 10 * q^19 + 5 * q^20 - 12 * q^21 + 2 * q^24 - q^25 + 20 * q^27 + 22 * q^29 + 4 * q^30 - 2 * q^31 + 8 * q^32 + 10 * q^34 - 17 * q^35 + 2 * q^36 + 6 * q^37 - 15 * q^38 - 8 * q^39 + 3 * q^41 + 8 * q^42 - 8 * q^45 - 10 * q^46 - 40 * q^47 - 3 * q^48 + 7 * q^49 - 6 * q^50 - 40 * q^51 + 30 * q^53 - 15 * q^54 - 5 * q^57 + 22 * q^58 + 35 * q^59 + 9 * q^60 + 20 * q^61 + 13 * q^62 - 21 * q^63 - 2 * q^64 + 32 * q^65 - 2 * q^67 - 15 * q^68 + 44 * q^69 + 13 * q^70 - 20 * q^71 + 7 * q^72 + 5 * q^73 + 6 * q^74 + 6 * q^75 - 8 * q^78 + 25 * q^79 - 26 * q^81 - 2 * q^82 - 9 * q^83 - 17 * q^84 + 40 * q^85 - 10 * q^86 - 42 * q^87 + 27 * q^90 - 16 * q^91 + 10 * q^92 + 42 * q^93 - 10 * q^94 + 30 * q^95 + 2 * q^96 - q^97 + 22 * q^98

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