LMFDB - Embedded newform 1014.2.e.n.991.2

Newspace parameters

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.e (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$0.222521 - 0.385418i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.n.529.2

$q$-expansion

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.13706 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.0244587 + 0.0423637i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.13706 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.0244587 + 0.0423637i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.06853 - 1.85075i) q^{10} +(3.14795 + 5.45241i) q^{11} -1.00000 q^{12} -0.0489173 q^{14} +(-1.06853 - 1.85075i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.44504 - 2.50289i) q^{17} -1.00000 q^{18} +(-3.60388 + 6.24210i) q^{19} +(1.06853 - 1.85075i) q^{20} -0.0489173 q^{21} +(-3.14795 + 5.45241i) q^{22} +(-1.35690 - 2.35021i) q^{23} +(-0.500000 - 0.866025i) q^{24} -0.432960 q^{25} -1.00000 q^{27} +(-0.0244587 - 0.0423637i) q^{28} +(-2.45593 - 4.25379i) q^{29} +(1.06853 - 1.85075i) q^{30} -9.00969 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.14795 + 5.45241i) q^{33} +2.89008 q^{34} +(0.0522697 - 0.0905338i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.0881460 - 0.152673i) q^{37} -7.20775 q^{38} +2.13706 q^{40} +(-4.29590 - 7.44071i) q^{41} +(-0.0244587 - 0.0423637i) q^{42} +(-3.35690 + 5.81431i) q^{43} -6.29590 q^{44} +(1.06853 - 1.85075i) q^{45} +(1.35690 - 2.35021i) q^{46} -7.20775 q^{47} +(0.500000 - 0.866025i) q^{48} +(3.49880 + 6.06011i) q^{49} +(-0.216480 - 0.374955i) q^{50} +2.89008 q^{51} +9.34481 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-6.72737 - 11.6521i) q^{55} +(0.0244587 - 0.0423637i) q^{56} -7.20775 q^{57} +(2.45593 - 4.25379i) q^{58} +(-2.13437 + 3.69685i) q^{59} +2.13706 q^{60} +(-3.55496 + 6.15737i) q^{61} +(-4.50484 - 7.80262i) q^{62} +(-0.0244587 - 0.0423637i) q^{63} +1.00000 q^{64} -6.29590 q^{66} +(2.69202 + 4.66272i) q^{67} +(1.44504 + 2.50289i) q^{68} +(1.35690 - 2.35021i) q^{69} +0.104539 q^{70} +(-4.35690 + 7.54637i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.9487 q^{73} +(0.0881460 - 0.152673i) q^{74} +(-0.216480 - 0.374955i) q^{75} +(-3.60388 - 6.24210i) q^{76} -0.307979 q^{77} +13.8291 q^{79} +(1.06853 + 1.85075i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.29590 - 7.44071i) q^{82} +11.1347 q^{83} +(0.0244587 - 0.0423637i) q^{84} +(-3.08815 + 5.34883i) q^{85} -6.71379 q^{86} +(2.45593 - 4.25379i) q^{87} +(-3.14795 - 5.45241i) q^{88} +(1.96077 + 3.39616i) q^{89} +2.13706 q^{90} +2.71379 q^{92} +(-4.50484 - 7.80262i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(7.70171 - 13.3398i) q^{95} +1.00000 q^{96} +(-1.23945 + 2.14678i) q^{97} +(-3.49880 + 6.06011i) q^{98} -6.29590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 5 q^{11} - 6 q^{12} + 18 q^{14} - q^{15} - 3 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + q^{20} + 18 q^{21} - 5 q^{22} - 3 q^{24} + 36 q^{25} - 6 q^{27} + 9 q^{28} - 11 q^{29} + q^{30} - 10 q^{31} + 3 q^{32} - 5 q^{33} + 16 q^{34} + 4 q^{35} - 3 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{40} + 2 q^{41} + 9 q^{42} - 12 q^{43} - 10 q^{44} + q^{45} - 8 q^{47} + 3 q^{48} - 20 q^{49} + 18 q^{50} + 16 q^{51} + 10 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 8 q^{57} + 11 q^{58} - 5 q^{59} + 2 q^{60} - 22 q^{61} - 5 q^{62} + 9 q^{63} + 6 q^{64} - 10 q^{66} + 6 q^{67} + 8 q^{68} + 8 q^{70} - 18 q^{71} + 3 q^{72} + 26 q^{73} + 8 q^{74} + 18 q^{75} - 4 q^{76} - 12 q^{77} + 62 q^{79} + q^{80} - 3 q^{81} - 2 q^{82} - 26 q^{83} - 9 q^{84} - 26 q^{85} - 24 q^{86} + 11 q^{87} - 5 q^{88} - 14 q^{89} + 2 q^{90} - 5 q^{93} - 4 q^{94} - 8 q^{95} + 6 q^{96} - 23 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 5 * q^11 - 6 * q^12 + 18 * q^14 - q^15 - 3 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + q^20 + 18 * q^21 - 5 * q^22 - 3 * q^24 + 36 * q^25 - 6 * q^27 + 9 * q^28 - 11 * q^29 + q^30 - 10 * q^31 + 3 * q^32 - 5 * q^33 + 16 * q^34 + 4 * q^35 - 3 * q^36 - 8 * q^37 - 8 * q^38 + 2 * q^40 + 2 * q^41 + 9 * q^42 - 12 * q^43 - 10 * q^44 + q^45 - 8 * q^47 + 3 * q^48 - 20 * q^49 + 18 * q^50 + 16 * q^51 + 10 * q^53 - 3 * q^54 - 18 * q^55 - 9 * q^56 - 8 * q^57 + 11 * q^58 - 5 * q^59 + 2 * q^60 - 22 * q^61 - 5 * q^62 + 9 * q^63 + 6 * q^64 - 10 * q^66 + 6 * q^67 + 8 * q^68 + 8 * q^70 - 18 * q^71 + 3 * q^72 + 26 * q^73 + 8 * q^74 + 18 * q^75 - 4 * q^76 - 12 * q^77 + 62 * q^79 + q^80 - 3 * q^81 - 2 * q^82 - 26 * q^83 - 9 * q^84 - 26 * q^85 - 24 * q^86 + 11 * q^87 - 5 * q^88 - 14 * q^89 + 2 * q^90 - 5 * q^93 - 4 * q^94 - 8 * q^95 + 6 * q^96 - 23 * q^97 + 20 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.13706			−0.955724			−0.477862	−	0.878435i	$-0.658588\pi$
$5$	−2.13706			−0.955724			−0.477862	+	0.878435i	$0.658588\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.0244587	+	0.0423637i	−0.00924451	+	0.0160120i	−0.870611	−	0.491973i	$-0.836276\pi$
$7$	−0.0244587	+	0.0423637i	−0.00924451	+	0.0160120i	0.861366	+	0.507985i	$0.169609\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.06853	−	1.85075i	−0.337899	−	0.585259i
$11$	3.14795	+	5.45241i	0.949142	+	1.64396i	0.747237	+	0.664557i	$0.231380\pi$
$11$	3.14795	+	5.45241i	0.949142	+	1.64396i	0.201905	+	0.979405i	$0.435287\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−0.0489173			−0.0130737
$15$	−1.06853	−	1.85075i	−0.275894	−	0.477862i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.44504	−	2.50289i	0.350474	−	0.607039i	−0.635858	−	0.771806i	$-0.719354\pi$
$17$	1.44504	−	2.50289i	0.350474	−	0.607039i	0.986333	+	0.164767i	$0.0526871\pi$
$18$	−1.00000			−0.235702
$19$	−3.60388	+	6.24210i	−0.826786	+	1.43203i	0.0737611	+	0.997276i	$0.476500\pi$
$19$	−3.60388	+	6.24210i	−0.826786	+	1.43203i	−0.900547	+	0.434759i	$0.856834\pi$
$20$	1.06853	−	1.85075i	0.238931	−	0.413841i
$21$	−0.0489173			−0.0106746
$22$	−3.14795	+	5.45241i	−0.671145	+	1.16246i
$23$	−1.35690	−	2.35021i	−0.282932	−	0.490053i	0.689173	−	0.724597i	$-0.257974\pi$
$23$	−1.35690	−	2.35021i	−0.282932	−	0.490053i	−0.972106	+	0.234543i	$0.924641\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.432960			−0.0865921
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−0.0244587	−	0.0423637i	−0.00462225	−	0.00800598i
$29$	−2.45593	−	4.25379i	−0.456054	−	0.789909i	0.542694	−	0.839931i	$-0.317404\pi$
$29$	−2.45593	−	4.25379i	−0.456054	−	0.789909i	−0.998748	+	0.0500215i	$0.984071\pi$
$30$	1.06853	−	1.85075i	0.195086	−	0.337899i
$31$	−9.00969			−1.61819			−0.809094	−	0.587679i	$-0.800042\pi$
$31$	−9.00969			−1.61819			−0.809094	+	0.587679i	$0.800042\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.14795	+	5.45241i	−0.547987	+	0.949142i
$34$	2.89008			0.495645
$35$	0.0522697	−	0.0905338i	0.00883520	−	0.0153030i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.0881460	−	0.152673i	−0.0144911	−	0.0250993i	0.858689	−	0.512497i	$-0.171279\pi$
$37$	−0.0881460	−	0.152673i	−0.0144911	−	0.0250993i	−0.873180	+	0.487398i	$0.837946\pi$
$38$	−7.20775			−1.16925
$39$		0			0
$40$	2.13706			0.337899
$41$	−4.29590	−	7.44071i	−0.670906	−	1.16204i	−0.977647	−	0.210251i	$-0.932572\pi$
$41$	−4.29590	−	7.44071i	−0.670906	−	1.16204i	0.306741	−	0.951793i	$-0.400761\pi$
$42$	−0.0244587	−	0.0423637i	−0.00377405	−	0.00653685i
$43$	−3.35690	+	5.81431i	−0.511922	+	0.886675i	0.487983	+	0.872853i	$0.337733\pi$
$43$	−3.35690	+	5.81431i	−0.511922	+	0.886675i	−0.999904	+	0.0138213i	$0.995600\pi$
$44$	−6.29590			−0.949142
$45$	1.06853	−	1.85075i	0.159287	−	0.275894i
$46$	1.35690	−	2.35021i	0.200063	−	0.346520i
$47$	−7.20775			−1.05136			−0.525679	−	0.850683i	$-0.676189\pi$
$47$	−7.20775			−1.05136			−0.525679	+	0.850683i	$0.676189\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	3.49880	+	6.06011i	0.499829	+	0.865729i
$50$	−0.216480	−	0.374955i	−0.0306149	−	0.0530266i
$51$	2.89008			0.404693
$52$		0			0
$53$	9.34481			1.28361			0.641804	−	0.766868i	$-0.278186\pi$
$53$	9.34481			1.28361			0.641804	+	0.766868i	$0.278186\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−6.72737	−	11.6521i	−0.907118	−	1.57117i
$56$	0.0244587	−	0.0423637i	0.00326843	−	0.00566108i
$57$	−7.20775			−0.954690
$58$	2.45593	−	4.25379i	0.322479	−	0.558550i
$59$	−2.13437	+	3.69685i	−0.277872	+	0.481288i	−0.970856	−	0.239665i	$-0.922962\pi$
$59$	−2.13437	+	3.69685i	−0.277872	+	0.481288i	0.692984	+	0.720953i	$0.256296\pi$
$60$	2.13706			0.275894
$61$	−3.55496	+	6.15737i	−0.455166	+	0.788370i	−0.998698	−	0.0510183i	$-0.983753\pi$
$61$	−3.55496	+	6.15737i	−0.455166	+	0.788370i	0.543532	+	0.839388i	$0.317087\pi$
$62$	−4.50484	−	7.80262i	−0.572116	−	0.990934i
$63$	−0.0244587	−	0.0423637i	−0.00308150	−	0.00533732i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.29590			−0.774971
$67$	2.69202	+	4.66272i	0.328883	+	0.569642i	0.982290	−	0.187365i	$-0.0599946\pi$
$67$	2.69202	+	4.66272i	0.328883	+	0.569642i	−0.653408	+	0.757006i	$0.726661\pi$
$68$	1.44504	+	2.50289i	0.175237	+	0.303520i
$69$	1.35690	−	2.35021i	0.163351	−	0.282932i
$70$	0.104539			0.0124949
$71$	−4.35690	+	7.54637i	−0.517068	+	0.895589i	0.482735	+	0.875766i	$0.339643\pi$
$71$	−4.35690	+	7.54637i	−0.517068	+	0.895589i	−0.999804	+	0.0198223i	$0.993690\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	14.9487			1.74961			0.874806	−	0.484474i	$-0.160989\pi$
$73$	14.9487			1.74961			0.874806	+	0.484474i	$0.160989\pi$
$74$	0.0881460	−	0.152673i	0.0102468	−	0.0177479i
$75$	−0.216480	−	0.374955i	−0.0249970	−	0.0432960i
$76$	−3.60388	−	6.24210i	−0.413393	−	0.716017i
$77$	−0.307979			−0.0350974
$78$		0			0
$79$	13.8291			1.55589			0.777947	−	0.628330i	$-0.216261\pi$
$79$	13.8291			1.55589			0.777947	+	0.628330i	$0.216261\pi$
$80$	1.06853	+	1.85075i	0.119465	+	0.206920i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.29590	−	7.44071i	0.474402	−	0.821689i
$83$	11.1347			1.22219			0.611094	−	0.791558i	$-0.290730\pi$
$83$	11.1347			1.22219			0.611094	+	0.791558i	$0.290730\pi$
$84$	0.0244587	−	0.0423637i	0.00266866	−	0.00462225i
$85$	−3.08815	+	5.34883i	−0.334956	+	0.580162i
$86$	−6.71379			−0.723967
$87$	2.45593	−	4.25379i	0.263303	−	0.456054i
$88$	−3.14795	−	5.45241i	−0.335572	−	0.581229i
$89$	1.96077	+	3.39616i	0.207841	+	0.359992i	0.951034	−	0.309085i	$-0.100023\pi$
$89$	1.96077	+	3.39616i	0.207841	+	0.359992i	−0.743193	+	0.669077i	$0.766690\pi$
$90$	2.13706			0.225266
$91$		0			0
$92$	2.71379			0.282932
$93$	−4.50484	−	7.80262i	−0.467131	−	0.809094i
$94$	−3.60388	−	6.24210i	−0.371711	−	0.643823i
$95$	7.70171	−	13.3398i	0.790179	−	1.36863i
$96$	1.00000			0.102062
$97$	−1.23945	+	2.14678i	−0.125847	+	0.217973i	−0.922064	−	0.387038i	$-0.873498\pi$
$97$	−1.23945	+	2.14678i	−0.125847	+	0.217973i	0.796217	+	0.605011i	$0.206831\pi$
$98$	−3.49880	+	6.06011i	−0.353433	+	0.612163i
$99$	−6.29590			−0.632761
$100$	0.216480	−	0.374955i	0.0216480	−	0.0374955i
$101$	−0.826396	−	1.43136i	−0.0822295	−	0.142426i	0.821978	−	0.569520i	$-0.192871\pi$
$101$	−0.826396	−	1.43136i	−0.0822295	−	0.142426i	−0.904207	+	0.427094i	$0.859537\pi$
$102$	1.44504	+	2.50289i	0.143080	+	0.247823i
$103$	−8.23490			−0.811409			−0.405704	−	0.914004i	$-0.632974\pi$
$103$	−8.23490			−0.811409			−0.405704	+	0.914004i	$0.632974\pi$
$104$		0			0
$105$	0.104539			0.0102020
$106$	4.67241	+	8.09285i	0.453824	+	0.786047i
$107$	4.18329	+	7.24567i	0.404414	+	0.700466i	0.994253	−	0.107055i	$-0.0341421\pi$
$107$	4.18329	+	7.24567i	0.404414	+	0.700466i	−0.589839	+	0.807521i	$0.700809\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	17.4276			1.66926			0.834630	−	0.550811i	$-0.185682\pi$
$109$	17.4276			1.66926			0.834630	+	0.550811i	$0.185682\pi$
$110$	6.72737	−	11.6521i	0.641429	−	1.11099i
$111$	0.0881460	−	0.152673i	0.00836645	−	0.0144911i
$112$	0.0489173			0.00462225
$113$	6.98792	−	12.1034i	0.657368	−	1.13859i	−0.323926	−	0.946082i	$-0.605003\pi$
$113$	6.98792	−	12.1034i	0.657368	−	1.13859i	0.981294	−	0.192513i	$-0.0616636\pi$
$114$	−3.60388	−	6.24210i	−0.337534	−	0.584626i
$115$	2.89977	+	5.02255i	0.270405	+	0.468355i
$116$	4.91185			0.456054
$117$		0			0
$118$	−4.26875			−0.392970
$119$	0.0706876	+	0.122435i	0.00647992	+	0.0112236i
$120$	1.06853	+	1.85075i	0.0975431	+	0.168950i
$121$	−14.3192	+	24.8015i	−1.30174	+	2.25468i
$122$	−7.10992			−0.643702
$123$	4.29590	−	7.44071i	0.387348	−	0.670906i
$124$	4.50484	−	7.80262i	0.404547	−	0.700696i
$125$	11.6106			1.03848
$126$	0.0244587	−	0.0423637i	0.00217895	−	0.00377405i
$127$	3.76055	+	6.51347i	0.333695	+	0.577977i	0.983233	−	0.182352i	$-0.0583711\pi$
$127$	3.76055	+	6.51347i	0.333695	+	0.577977i	−0.649538	+	0.760329i	$0.725038\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.71379			−0.591116
$130$		0			0
$131$	5.12498			0.447772			0.223886	−	0.974615i	$-0.428126\pi$
$131$	5.12498			0.447772			0.223886	+	0.974615i	$0.428126\pi$
$132$	−3.14795	−	5.45241i	−0.273994	−	0.474571i
$133$	−0.176292	−	0.305347i	−0.0152865	−	0.0264769i
$134$	−2.69202	+	4.66272i	−0.232555	+	0.402797i
$135$	2.13706			0.183929
$136$	−1.44504	+	2.50289i	−0.123911	+	0.214621i
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$	2.71379			0.231013
$139$	−4.34481	+	7.52544i	−0.368522	+	0.638299i	−0.989335	−	0.145660i	$-0.953470\pi$
$139$	−4.34481	+	7.52544i	−0.368522	+	0.638299i	0.620812	+	0.783959i	$0.286803\pi$
$140$	0.0522697	+	0.0905338i	0.00441760	+	0.00765150i
$141$	−3.60388	−	6.24210i	−0.303501	−	0.525679i
$142$	−8.71379			−0.731245
$143$		0			0
$144$	1.00000			0.0833333
$145$	5.24847	+	9.09062i	0.435862	+	0.754935i
$146$	7.47434	+	12.9459i	0.618581	+	1.07141i
$147$	−3.49880	+	6.06011i	−0.288576	+	0.499829i
$148$	0.176292			0.0144911
$149$	−2.43416	+	4.21608i	−0.199414	+	0.345395i	−0.948339	−	0.317260i	$-0.897237\pi$
$149$	−2.43416	+	4.21608i	−0.199414	+	0.345395i	0.748925	+	0.662655i	$0.230570\pi$
$150$	0.216480	−	0.374955i	0.0176755	−	0.0306149i
$151$	−14.7463			−1.20004			−0.600019	−	0.799986i	$-0.704840\pi$
$151$	−14.7463			−1.20004			−0.600019	+	0.799986i	$0.704840\pi$
$152$	3.60388	−	6.24210i	0.292313	−	0.506301i
$153$	1.44504	+	2.50289i	0.116825	+	0.202346i
$154$	−0.153989	−	0.266717i	−0.0124088	−	0.0214927i
$155$	19.2543			1.54654
$156$		0			0
$157$	−16.7138			−1.33391			−0.666953	−	0.745100i	$-0.732402\pi$
$157$	−16.7138			−1.33391			−0.666953	+	0.745100i	$0.732402\pi$
$158$	6.91454	+	11.9763i	0.550091	+	0.952786i
$159$	4.67241	+	8.09285i	0.370546	+	0.641804i
$160$	−1.06853	+	1.85075i	−0.0844748	+	0.146315i
$161$	0.132751			0.0104623
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	2.77479	−	4.80608i	0.217338	−	0.376441i	−0.736655	−	0.676269i	$-0.763596\pi$
$163$	2.77479	−	4.80608i	0.217338	−	0.376441i	0.953993	+	0.299828i	$0.0969292\pi$
$164$	8.59179			0.670906
$165$	6.72737	−	11.6521i	0.523725	−	0.907118i
$166$	5.56734	+	9.64291i	0.432109	+	0.748435i
$167$	−1.96077	−	3.39616i	−0.151729	−	0.262802i	0.780134	−	0.625612i	$-0.215151\pi$
$167$	−1.96077	−	3.39616i	−0.151729	−	0.262802i	−0.931863	+	0.362810i	$0.881817\pi$
$168$	0.0489173			0.00377405
$169$		0			0
$170$	−6.17629			−0.473700
$171$	−3.60388	−	6.24210i	−0.275595	−	0.477345i
$172$	−3.35690	−	5.81431i	−0.255961	−	0.443337i
$173$	1.74214	−	3.01747i	0.132452	−	0.229414i	−0.792169	−	0.610302i	$-0.791048\pi$
$173$	1.74214	−	3.01747i	0.132452	−	0.229414i	0.924621	+	0.380888i	$0.124382\pi$
$174$	4.91185			0.372367
$175$	0.0105896	−	0.0183418i	0.000800501	−	0.00138651i
$176$	3.14795	−	5.45241i	0.237286	−	0.410991i
$177$	−4.26875			−0.320859
$178$	−1.96077	+	3.39616i	−0.146966	+	0.254553i
$179$	−1.79440	−	3.10800i	−0.134120	−	0.232303i	0.791141	−	0.611634i	$-0.209487\pi$
$179$	−1.79440	−	3.10800i	−0.134120	−	0.232303i	−0.925261	+	0.379331i	$0.876154\pi$
$180$	1.06853	+	1.85075i	0.0796436	+	0.137947i
$181$	5.50604			0.409261			0.204630	−	0.978839i	$-0.434401\pi$
$181$	5.50604			0.409261			0.204630	+	0.978839i	$0.434401\pi$
$182$		0			0
$183$	−7.10992			−0.525580
$184$	1.35690	+	2.35021i	0.100032	+	0.173260i
$185$	0.188374	+	0.326273i	0.0138495	+	0.0239880i
$186$	4.50484	−	7.80262i	0.330311	−	0.572116i
$187$	18.1957			1.33060
$188$	3.60388	−	6.24210i	0.262840	−	0.455252i
$189$	0.0244587	−	0.0423637i	0.00177911	−	0.00308150i
$190$	15.4034			1.11748
$191$	2.82908	−	4.90012i	0.204705	−	0.354560i	−0.745333	−	0.666692i	$-0.767710\pi$
$191$	2.82908	−	4.90012i	0.204705	−	0.354560i	0.950039	+	0.312132i	$0.101043\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−6.70171	−	11.6077i	−0.482400	−	0.835541i	0.517396	−	0.855746i	$-0.326901\pi$
$193$	−6.70171	−	11.6077i	−0.482400	−	0.835541i	−0.999796	+	0.0202053i	$0.993568\pi$
$194$	−2.47889			−0.177974
$195$		0			0
$196$	−6.99761			−0.499829
$197$	−9.99061	−	17.3042i	−0.711801	−	1.23288i	−0.964180	−	0.265248i	$-0.914546\pi$
$197$	−9.99061	−	17.3042i	−0.711801	−	1.23288i	0.252379	−	0.967628i	$-0.418787\pi$
$198$	−3.14795	−	5.45241i	−0.223715	−	0.387486i
$199$	3.12080	−	5.40539i	0.221228	−	0.383178i	−0.733953	−	0.679200i	$-0.762327\pi$
$199$	3.12080	−	5.40539i	0.221228	−	0.383178i	0.955181	+	0.296022i	$0.0956603\pi$
$200$	0.432960			0.0306149
$201$	−2.69202	+	4.66272i	−0.189881	+	0.328883i
$202$	0.826396	−	1.43136i	0.0581450	−	0.100710i
$203$	0.240275			0.0168640
$204$	−1.44504	+	2.50289i	−0.101173	+	0.175237i
$205$	9.18060	+	15.9013i	0.641201	+	1.11059i
$206$	−4.11745	−	7.13163i	−0.286876	−	0.496884i
$207$	2.71379			0.188622
$208$		0			0
$209$	−45.3793			−3.13895
$210$	0.0522697	+	0.0905338i	0.00360695	+	0.00624743i
$211$	2.54288	+	4.40439i	0.175059	+	0.303211i	0.940182	−	0.340674i	$-0.110655\pi$
$211$	2.54288	+	4.40439i	0.175059	+	0.303211i	−0.765123	+	0.643884i	$0.777322\pi$
$212$	−4.67241	+	8.09285i	−0.320902	+	0.555819i
$213$	−8.71379			−0.597059
$214$	−4.18329	+	7.24567i	−0.285964	+	0.495304i
$215$	7.17390	−	12.4256i	0.489256	−	0.847416i
$216$	1.00000			0.0680414
$217$	0.220365	−	0.381683i	0.0149594	−	0.0259104i
$218$	8.71379	+	15.0927i	0.590172	+	1.02221i
$219$	7.47434	+	12.9459i	0.505069	+	0.874806i
$220$	13.4547			0.907118
$221$		0			0
$222$	0.176292			0.0118319
$223$	10.2741	+	17.7953i	0.688006	+	1.19166i	0.972482	+	0.232979i	$0.0748473\pi$
$223$	10.2741	+	17.7953i	0.688006	+	1.19166i	−0.284475	+	0.958683i	$0.591819\pi$
$224$	0.0244587	+	0.0423637i	0.00163421	+	0.00283054i
$225$	0.216480	−	0.374955i	0.0144320	−	0.0249970i
$226$	13.9758			0.929659
$227$	−2.20560	+	3.82020i	−0.146390	+	0.253556i	−0.929891	−	0.367836i	$-0.880099\pi$
$227$	−2.20560	+	3.82020i	−0.146390	+	0.253556i	0.783500	+	0.621391i	$0.213432\pi$
$228$	3.60388	−	6.24210i	0.238672	−	0.413393i
$229$	0.230586			0.0152376			0.00761878	−	0.999971i	$-0.497575\pi$
$229$	0.230586			0.0152376			0.00761878	+	0.999971i	$0.497575\pi$
$230$	−2.89977	+	5.02255i	−0.191205	+	0.331177i
$231$	−0.153989	−	0.266717i	−0.0101317	−	0.0175487i
$232$	2.45593	+	4.25379i	0.161240	+	0.279275i
$233$	−7.82371			−0.512548			−0.256274	−	0.966604i	$-0.582495\pi$
$233$	−7.82371			−0.512548			−0.256274	+	0.966604i	$0.582495\pi$
$234$		0			0
$235$	15.4034			1.00481
$236$	−2.13437	−	3.69685i	−0.138936	−	0.240644i
$237$	6.91454	+	11.9763i	0.449148	+	0.777947i
$238$	−0.0706876	+	0.122435i	−0.00458200	+	0.00793625i
$239$	11.1535			0.721457			0.360729	−	0.932671i	$-0.382528\pi$
$239$	11.1535			0.721457			0.360729	+	0.932671i	$0.382528\pi$
$240$	−1.06853	+	1.85075i	−0.0689734	+	0.119465i
$241$	1.77263	−	3.07029i	0.114185	−	0.197775i	−0.803268	−	0.595617i	$-0.796908\pi$
$241$	1.77263	−	3.07029i	0.114185	−	0.197775i	0.917454	+	0.397842i	$0.130241\pi$
$242$	−28.6383			−1.84094
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.55496	−	6.15737i	−0.227583	−	0.394185i
$245$	−7.47716	−	12.9508i	−0.477699	−	0.827398i
$246$	8.59179			0.547793
$247$		0			0
$248$	9.00969			0.572116
$249$	5.56734	+	9.64291i	0.352816	+	0.611094i
$250$	5.80529	+	10.0551i	0.367159	+	0.635938i
$251$	2.08546	−	3.61212i	0.131633	−	0.227995i	−0.792673	−	0.609647i	$-0.791311\pi$
$251$	2.08546	−	3.61212i	0.131633	−	0.227995i	0.924306	+	0.381652i	$0.124645\pi$
$252$	0.0489173			0.00308150
$253$	8.54288	−	14.7967i	0.537086	−	0.930260i
$254$	−3.76055	+	6.51347i	−0.235958	+	0.408691i
$255$	−6.17629			−0.386774
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.44504	+	9.43109i	0.339652	+	0.588295i	0.984367	−	0.176128i	$-0.0563572\pi$
$257$	5.44504	+	9.43109i	0.339652	+	0.588295i	−0.644715	+	0.764423i	$0.723024\pi$
$258$	−3.35690	−	5.81431i	−0.208991	−	0.361983i
$259$	0.00862374			0.000535853
$260$		0			0
$261$	4.91185			0.304036
$262$	2.56249	+	4.43836i	0.158311	+	0.274203i
$263$	15.6136	+	27.0435i	0.962774	+	1.66757i	0.715481	+	0.698632i	$0.246207\pi$
$263$	15.6136	+	27.0435i	0.962774	+	1.66757i	0.247292	+	0.968941i	$0.420459\pi$
$264$	3.14795	−	5.45241i	0.193743	−	0.335572i
$265$	−19.9705			−1.22678
$266$	0.176292	−	0.305347i	0.0108092	−	0.0187220i
$267$	−1.96077	+	3.39616i	−0.119997	+	0.207841i
$268$	−5.38404			−0.328883
$269$	−7.95862	+	13.7847i	−0.485245	+	0.840470i	−0.999856	−	0.0169542i	$-0.994603\pi$
$269$	−7.95862	+	13.7847i	−0.485245	+	0.840470i	0.514611	+	0.857424i	$0.327936\pi$
$270$	1.06853	+	1.85075i	0.0650288	+	0.112633i
$271$	−1.76055	−	3.04937i	−0.106946	−	0.185236i	0.807586	−	0.589750i	$-0.200774\pi$
$271$	−1.76055	−	3.04937i	−0.106946	−	0.185236i	−0.914532	+	0.404514i	$0.867441\pi$
$272$	−2.89008			−0.175237
$273$		0			0
$274$	−4.00000			−0.241649
$275$	−1.36294	−	2.36068i	−0.0821882	−	0.142354i
$276$	1.35690	+	2.35021i	0.0816755	+	0.141466i
$277$	4.29052	−	7.43140i	0.257792	−	0.446509i	−0.707858	−	0.706355i	$-0.750338\pi$
$277$	4.29052	−	7.43140i	0.257792	−	0.446509i	0.965650	+	0.259845i	$0.0836716\pi$
$278$	−8.68963			−0.521169
$279$	4.50484	−	7.80262i	0.269698	−	0.467131i
$280$	−0.0522697	+	0.0905338i	−0.00312371	+	0.00541043i
$281$	−8.07846			−0.481920			−0.240960	−	0.970535i	$-0.577462\pi$
$281$	−8.07846			−0.481920			−0.240960	+	0.970535i	$0.577462\pi$
$282$	3.60388	−	6.24210i	0.214608	−	0.371711i
$283$	8.70171	+	15.0718i	0.517263	+	0.895926i	0.999799	+	0.0200496i	$0.00638242\pi$
$283$	8.70171	+	15.0718i	0.517263	+	0.895926i	−0.482536	+	0.875876i	$0.660284\pi$
$284$	−4.35690	−	7.54637i	−0.258534	−	0.447794i
$285$	15.4034			0.912420
$286$		0			0
$287$	0.420288			0.0248088
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	4.32371	+	7.48888i	0.254336	+	0.440522i
$290$	−5.24847	+	9.09062i	−0.308201	+	0.533820i
$291$	−2.47889			−0.145315
$292$	−7.47434	+	12.9459i	−0.437403	+	0.757604i
$293$	9.68545	−	16.7757i	0.565830	−	0.980046i	−0.431142	−	0.902284i	$-0.641889\pi$
$293$	9.68545	−	16.7757i	0.565830	−	0.980046i	0.996972	−	0.0777621i	$-0.0247775\pi$
$294$	−6.99761			−0.408109
$295$	4.56129	−	7.90039i	0.265569	−	0.459979i
$296$	0.0881460	+	0.152673i	0.00512338	+	0.00887396i
$297$	−3.14795	−	5.45241i	−0.182662	−	0.316381i
$298$	−4.86831			−0.282014
$299$		0			0
$300$	0.432960			0.0249970
$301$	−0.164210	−	0.284421i	−0.00946493	−	0.0163937i
$302$	−7.37316	−	12.7707i	−0.424278	−	0.734870i
$303$	0.826396	−	1.43136i	0.0474752	−	0.0822295i
$304$	7.20775			0.413393
$305$	7.59717	−	13.1587i	0.435013	−	0.753464i
$306$	−1.44504	+	2.50289i	−0.0826075	+	0.143080i
$307$	−12.4263			−0.709204			−0.354602	−	0.935017i	$-0.615384\pi$
$307$	−12.4263			−0.709204			−0.354602	+	0.935017i	$0.615384\pi$
$308$	0.153989	−	0.266717i	0.00877435	−	0.0151976i
$309$	−4.11745	−	7.13163i	−0.234233	−	0.405704i
$310$	9.62714	+	16.6747i	0.546785	+	0.947059i
$311$	2.71379			0.153885			0.0769425	−	0.997036i	$-0.475484\pi$
$311$	2.71379			0.153885			0.0769425	+	0.997036i	$0.475484\pi$
$312$		0			0
$313$	15.3884			0.869801			0.434901	−	0.900478i	$-0.356783\pi$
$313$	15.3884			0.869801			0.434901	+	0.900478i	$0.356783\pi$
$314$	−8.35690	−	14.4746i	−0.471607	−	0.816847i
$315$	0.0522697	+	0.0905338i	0.00294507	+	0.00510100i
$316$	−6.91454	+	11.9763i	−0.388973	+	0.673722i
$317$	25.6528			1.44080			0.720402	−	0.693557i	$-0.243957\pi$
$317$	25.6528			1.44080			0.720402	+	0.693557i	$0.243957\pi$
$318$	−4.67241	+	8.09285i	−0.262016	+	0.453824i
$319$	15.4623	−	26.7814i	0.865721	−	1.49947i
$320$	−2.13706			−0.119465
$321$	−4.18329	+	7.24567i	−0.233489	+	0.404414i
$322$	0.0663757	+	0.114966i	0.00369898	+	0.00640681i
$323$	10.4155	+	18.0402i	0.579534	+	1.00378i
$324$	1.00000			0.0555556
$325$		0			0
$326$	5.54958			0.307363
$327$	8.71379	+	15.0927i	0.481874	+	0.834630i
$328$	4.29590	+	7.44071i	0.237201	+	0.410845i
$329$	0.176292	−	0.305347i	0.00971929	−	0.0168343i
$330$	13.4547			0.740659
$331$	1.91185	−	3.31143i	0.105085	−	0.182013i	−0.808688	−	0.588238i	$-0.799822\pi$
$331$	1.91185	−	3.31143i	0.105085	−	0.182013i	0.913773	+	0.406225i	$0.133155\pi$
$332$	−5.56734	+	9.64291i	−0.305547	+	0.529223i
$333$	0.176292			0.00966074
$334$	1.96077	−	3.39616i	0.107289	−	0.185829i
$335$	−5.75302	−	9.96452i	−0.314321	−	0.544420i
$336$	0.0244587	+	0.0423637i	0.00133433	+	0.00231113i
$337$	20.1304			1.09657			0.548285	−	0.836291i	$-0.315281\pi$
$337$	20.1304			1.09657			0.548285	+	0.836291i	$0.315281\pi$
$338$		0			0
$339$	13.9758			0.759063
$340$	−3.08815	−	5.34883i	−0.167478	−	0.290081i
$341$	−28.3620	−	49.1245i	−1.53589	−	2.66024i
$342$	3.60388	−	6.24210i	0.194875	−	0.337534i
$343$	−0.684726			−0.0369717
$344$	3.35690	−	5.81431i	0.180992	−	0.313487i
$345$	−2.89977	+	5.02255i	−0.156118	+	0.270405i
$346$	3.48427			0.187316
$347$	−1.46950	+	2.54525i	−0.0788869	+	0.136636i	−0.902770	−	0.430124i	$-0.858470\pi$
$347$	−1.46950	+	2.54525i	−0.0788869	+	0.136636i	0.823883	+	0.566760i	$0.191803\pi$
$348$	2.45593	+	4.25379i	0.131652	+	0.228027i
$349$	−3.68664	−	6.38546i	−0.197342	−	0.341806i	0.750324	−	0.661070i	$-0.229897\pi$
$349$	−3.68664	−	6.38546i	−0.197342	−	0.341806i	−0.947666	+	0.319265i	$0.896564\pi$
$350$	0.0211793			0.00113208
$351$		0			0
$352$	6.29590			0.335572
$353$	1.00538	+	1.74136i	0.0535108	+	0.0926834i	0.891540	−	0.452942i	$-0.149626\pi$
$353$	1.00538	+	1.74136i	0.0535108	+	0.0926834i	−0.838029	+	0.545625i	$0.816292\pi$
$354$	−2.13437	−	3.69685i	−0.113441	−	0.196485i
$355$	9.31096	−	16.1271i	0.494175	−	0.855935i
$356$	−3.92154			−0.207841
$357$	−0.0706876	+	0.122435i	−0.00374118	+	0.00647992i
$358$	1.79440	−	3.10800i	0.0948373	−	0.164263i
$359$	31.4577			1.66027			0.830137	−	0.557559i	$-0.188262\pi$
$359$	31.4577			1.66027			0.830137	+	0.557559i	$0.188262\pi$
$360$	−1.06853	+	1.85075i	−0.0563166	+	0.0975431i
$361$	−16.4758	−	28.5370i	−0.867149	−	1.50195i
$362$	2.75302	+	4.76837i	0.144696	+	0.250620i
$363$	−28.6383			−1.50312
$364$		0			0
$365$	−31.9463			−1.67215
$366$	−3.55496	−	6.15737i	−0.185821	−	0.321851i
$367$	2.24967	+	3.89654i	0.117432	+	0.203398i	0.918749	−	0.394842i	$-0.129201\pi$
$367$	2.24967	+	3.89654i	0.117432	+	0.203398i	−0.801317	+	0.598239i	$0.795867\pi$
$368$	−1.35690	+	2.35021i	−0.0707331	+	0.122513i
$369$	8.59179			0.447271
$370$	−0.188374	+	0.326273i	−0.00979308	+	0.0169621i
$371$	−0.228562	+	0.395881i	−0.0118663	+	0.0205531i
$372$	9.00969			0.467131
$373$	−18.9148	+	32.7615i	−0.979373	+	1.69632i	−0.314698	+	0.949192i	$0.601903\pi$
$373$	−18.9148	+	32.7615i	−0.979373	+	1.69632i	−0.664676	+	0.747132i	$0.731430\pi$
$374$	9.09783	+	15.7579i	0.470438	+	0.814822i
$375$	5.80529	+	10.0551i	0.299784	+	0.519241i
$376$	7.20775			0.371711
$377$		0			0
$378$	0.0489173			0.00251604
$379$	4.21983	+	7.30896i	0.216758	+	0.375436i	0.953815	−	0.300395i	$-0.0971183\pi$
$379$	4.21983	+	7.30896i	0.216758	+	0.375436i	−0.737057	+	0.675831i	$0.763785\pi$
$380$	7.70171	+	13.3398i	0.395089	+	0.684315i
$381$	−3.76055	+	6.51347i	−0.192659	+	0.333695i
$382$	5.65817			0.289497
$383$	−0.643104	+	1.11389i	−0.0328611	+	0.0569171i	−0.881988	−	0.471271i	$-0.843795\pi$
$383$	−0.643104	+	1.11389i	−0.0328611	+	0.0569171i	0.849127	+	0.528188i	$0.177129\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	0.658170			0.0335434
$386$	6.70171	−	11.6077i	0.341108	−	0.590817i
$387$	−3.35690	−	5.81431i	−0.170641	−	0.295558i
$388$	−1.23945	−	2.14678i	−0.0629234	−	0.108986i
$389$	23.3924			1.18604			0.593021	−	0.805187i	$-0.297935\pi$
$389$	23.3924			1.18604			0.593021	+	0.805187i	$0.297935\pi$
$390$		0			0
$391$	−7.84309			−0.396642
$392$	−3.49880	−	6.06011i	−0.176716	−	0.306082i
$393$	2.56249	+	4.43836i	0.129261	+	0.223886i
$394$	9.99061	−	17.3042i	0.503320	−	0.871775i
$395$	−29.5536			−1.48700
$396$	3.14795	−	5.45241i	0.158190	−	0.273994i
$397$	−18.5429	+	32.1172i	−0.930640	+	1.61192i	−0.148411	+	0.988926i	$0.547416\pi$
$397$	−18.5429	+	32.1172i	−0.930640	+	1.61192i	−0.782229	+	0.622990i	$0.785918\pi$
$398$	6.24160			0.312863
$399$	0.176292	−	0.305347i	0.00882564	−	0.0152865i
$400$	0.216480	+	0.374955i	0.0108240	+	0.0187477i
$401$	−2.43296	−	4.21401i	−0.121496	−	0.210438i	0.798862	−	0.601515i	$-0.205436\pi$
$401$	−2.43296	−	4.21401i	−0.121496	−	0.210438i	−0.920358	+	0.391077i	$0.872103\pi$
$402$	−5.38404			−0.268532
$403$		0			0
$404$	1.65279			0.0822295
$405$	1.06853	+	1.85075i	0.0530958	+	0.0919646i
$406$	0.120137	+	0.208084i	0.00596232	+	0.0103270i
$407$	0.554958	−	0.961216i	0.0275083	−	0.0476457i
$408$	−2.89008			−0.143080
$409$	0.222521	−	0.385418i	0.0110030	−	0.0190577i	−0.860472	−	0.509499i	$-0.829831\pi$
$409$	0.222521	−	0.385418i	0.0110030	−	0.0190577i	0.871474	+	0.490441i	$0.163164\pi$
$410$	−9.18060	+	15.9013i	−0.453398	+	0.785308i
$411$	−4.00000			−0.197305
$412$	4.11745	−	7.13163i	0.202852	−	0.351350i
$413$	−0.104408	−	0.180840i	−0.00513758	−	0.00889855i
$414$	1.35690	+	2.35021i	0.0666878	+	0.115507i
$415$	−23.7955			−1.16807
$416$		0			0
$417$	−8.68963			−0.425533
$418$	−22.6896	−	39.2996i	−1.10979	−	1.92221i
$419$	−8.99343	−	15.5771i	−0.439358	−	0.760990i	0.558282	−	0.829651i	$-0.311461\pi$
$419$	−8.99343	−	15.5771i	−0.439358	−	0.760990i	−0.997640	+	0.0686612i	$0.978127\pi$
$420$	−0.0522697	+	0.0905338i	−0.00255050	+	0.00441760i
$421$	−21.2814			−1.03719			−0.518597	−	0.855019i	$-0.673545\pi$
$421$	−21.2814			−1.03719			−0.518597	+	0.855019i	$0.673545\pi$
$422$	−2.54288	+	4.40439i	−0.123785	+	0.214402i
$423$	3.60388	−	6.24210i	0.175226	−	0.303501i
$424$	−9.34481			−0.453824
$425$	−0.625646	+	1.08365i	−0.0303483	+	0.0525648i
$426$	−4.35690	−	7.54637i	−0.211092	−	0.365623i
$427$	−0.173899	−	0.301202i	−0.00841557	−	0.0145762i
$428$	−8.36658			−0.404414
$429$		0			0
$430$	14.3478			0.691912
$431$	12.3569	+	21.4028i	0.595211	+	1.03094i	0.993517	+	0.113683i	$0.0362648\pi$
$431$	12.3569	+	21.4028i	0.595211	+	1.03094i	−0.398306	+	0.917252i	$0.630402\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−16.1087	+	27.9011i	−0.774136	+	1.34084i	0.161143	+	0.986931i	$0.448482\pi$
$433$	−16.1087	+	27.9011i	−0.774136	+	1.34084i	−0.935279	+	0.353911i	$0.884851\pi$
$434$	0.440730			0.0211557
$435$	−5.24847	+	9.09062i	−0.251645	+	0.435862i
$436$	−8.71379	+	15.0927i	−0.417315	+	0.722811i
$437$	19.5603			0.935698
$438$	−7.47434	+	12.9459i	−0.357138	+	0.618581i
$439$	−16.0438	−	27.7887i	−0.765731	−	1.32628i	−0.939859	−	0.341561i	$-0.889044\pi$
$439$	−16.0438	−	27.7887i	−0.765731	−	1.32628i	0.174129	−	0.984723i	$-0.444289\pi$
$440$	6.72737	+	11.6521i	0.320715	+	0.555494i
$441$	−6.99761			−0.333219
$442$		0			0
$443$	20.5109			0.974504			0.487252	−	0.873261i	$-0.337999\pi$
$443$	20.5109			0.974504			0.487252	+	0.873261i	$0.337999\pi$
$444$	0.0881460	+	0.152673i	0.00418322	+	0.00724556i
$445$	−4.19029	−	7.25780i	−0.198639	−	0.344053i
$446$	−10.2741	+	17.7953i	−0.486494	+	0.842632i
$447$	−4.86831			−0.230263
$448$	−0.0244587	+	0.0423637i	−0.00115556	+	0.00200149i
$449$	−7.65817	+	13.2643i	−0.361411	+	0.625983i	−0.988193	−	0.153212i	$-0.951038\pi$
$449$	−7.65817	+	13.2643i	−0.361411	+	0.625983i	0.626782	+	0.779195i	$0.284372\pi$
$450$	0.432960			0.0204099
$451$	27.0465	−	46.8460i	1.27357	−	2.20589i
$452$	6.98792	+	12.1034i	0.328684	+	0.569297i
$453$	−7.37316	−	12.7707i	−0.346421	−	0.600019i
$454$	−4.41119			−0.207027
$455$		0			0
$456$	7.20775			0.337534
$457$	−9.59299	−	16.6155i	−0.448741	−	0.777242i	0.549563	−	0.835452i	$-0.314794\pi$
$457$	−9.59299	−	16.6155i	−0.448741	−	0.777242i	−0.998304	+	0.0582096i	$0.981461\pi$
$458$	0.115293	+	0.199693i	0.00538729	+	0.00933106i
$459$	−1.44504	+	2.50289i	−0.0674488	+	0.116825i
$460$	−5.79954			−0.270405
$461$	4.15615	−	7.19865i	0.193571	−	0.335275i	−0.752860	−	0.658181i	$-0.771326\pi$
$461$	4.15615	−	7.19865i	0.193571	−	0.335275i	0.946431	+	0.322906i	$0.104660\pi$
$462$	0.153989	−	0.266717i	0.00716423	−	0.0124088i
$463$	6.32842			0.294107			0.147053	−	0.989129i	$-0.453021\pi$
$463$	6.32842			0.294107			0.147053	+	0.989129i	$0.453021\pi$
$464$	−2.45593	+	4.25379i	−0.114014	+	0.197477i
$465$	9.62714	+	16.6747i	0.446448	+	0.773270i
$466$	−3.91185	−	6.77553i	−0.181213	−	0.313870i
$467$	−31.1879			−1.44320			−0.721602	−	0.692308i	$-0.756594\pi$
$467$	−31.1879			−1.44320			−0.721602	+	0.692308i	$0.756594\pi$
$468$		0			0
$469$	−0.263373			−0.0121614
$470$	7.70171	+	13.3398i	0.355253	+	0.615317i
$471$	−8.35690	−	14.4746i	−0.385065	−	0.666953i
$472$	2.13437	−	3.69685i	0.0982426	−	0.170161i
$473$	−42.2693			−1.94355
$474$	−6.91454	+	11.9763i	−0.317595	+	0.550091i
$475$	1.56033	−	2.70258i	0.0715931	−	0.124003i
$476$	−0.141375			−0.00647992
$477$	−4.67241	+	8.09285i	−0.213935	+	0.370546i
$478$	5.57673	+	9.65918i	0.255074	+	0.441800i
$479$	−8.96615	−	15.5298i	−0.409674	−	0.709576i	0.585179	−	0.810904i	$-0.301024\pi$
$479$	−8.96615	−	15.5298i	−0.409674	−	0.709576i	−0.994853	+	0.101328i	$0.967691\pi$
$480$	−2.13706			−0.0975431
$481$		0			0
$482$	3.54527			0.161483
$483$	0.0663757	+	0.114966i	0.00302020	+	0.00523114i
$484$	−14.3192	−	24.8015i	−0.650871	−	1.12734i
$485$	2.64878	−	4.58782i	0.120275	−	0.208322i
$486$	1.00000			0.0453609
$487$	15.1640	−	26.2648i	0.687145	−	1.19017i	−0.285612	−	0.958345i	$-0.592197\pi$
$487$	15.1640	−	26.2648i	0.687145	−	1.19017i	0.972757	−	0.231825i	$-0.0744697\pi$
$488$	3.55496	−	6.15737i	0.160925	−	0.278731i
$489$	5.54958			0.250961
$490$	7.47716	−	12.9508i	0.337784	−	0.585059i
$491$	−15.0477	−	26.0634i	−0.679094	−	1.17623i	−0.975254	−	0.221087i	$-0.929039\pi$
$491$	−15.0477	−	26.0634i	−0.679094	−	1.17623i	0.296160	−	0.955138i	$-0.404294\pi$
$492$	4.29590	+	7.44071i	0.193674	+	0.335453i
$493$	−14.1957			−0.639341
$494$		0			0
$495$	13.4547			0.604745
$496$	4.50484	+	7.80262i	0.202273	+	0.350348i
$497$	−0.213128	−	0.369148i	−0.00956009	−	0.0165586i
$498$	−5.56734	+	9.64291i	−0.249478	+	0.432109i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−5.80529	+	10.0551i	−0.259620	+	0.449676i
$501$	1.96077	−	3.39616i	0.0876008	−	0.151729i
$502$	4.17092			0.186157
$503$	−16.8756	+	29.2294i	−0.752446	+	1.30328i	0.194188	+	0.980964i	$0.437793\pi$
$503$	−16.8756	+	29.2294i	−0.752446	+	1.30328i	−0.946634	+	0.322311i	$0.895540\pi$
$504$	0.0244587	+	0.0423637i	0.00108948	+	0.00188703i
$505$	1.76606	+	3.05891i	0.0785887	+	0.136120i
$506$	17.0858			0.759554
$507$		0			0
$508$	−7.52111			−0.333695
$509$	−7.37196	−	12.7686i	−0.326756	−	0.565959i	0.655110	−	0.755534i	$-0.272622\pi$
$509$	−7.37196	−	12.7686i	−0.326756	−	0.565959i	−0.981866	+	0.189575i	$0.939289\pi$
$510$	−3.08815	−	5.34883i	−0.136745	−	0.236850i
$511$	−0.365625	+	0.633281i	−0.0161743	+	0.0280147i
$512$	−1.00000			−0.0441942
$513$	3.60388	−	6.24210i	0.159115	−	0.275595i
$514$	−5.44504	+	9.43109i	−0.240171	+	0.415988i
$515$	17.5985			0.775483
$516$	3.35690	−	5.81431i	0.147779	−	0.255961i
$517$	−22.6896	−	39.2996i	−0.997889	−	1.72839i
$518$	0.00431187	+	0.00746837i	0.000189453	+	0.000328142i
$519$	3.48427			0.152943
$520$		0			0
$521$	22.1086			0.968595			0.484297	−	0.874903i	$-0.339075\pi$
$521$	22.1086			0.968595			0.484297	+	0.874903i	$0.339075\pi$
$522$	2.45593	+	4.25379i	0.107493	+	0.186183i
$523$	8.67994	+	15.0341i	0.379547	+	0.657395i	0.990996	−	0.133889i	$-0.0427464\pi$
$523$	8.67994	+	15.0341i	0.379547	+	0.657395i	−0.611449	+	0.791284i	$0.709413\pi$
$524$	−2.56249	+	4.43836i	−0.111943	+	0.193891i
$525$	0.0211793			0.000924339
$526$	−15.6136	+	27.0435i	−0.680784	+	1.17915i
$527$	−13.0194	+	22.5502i	−0.567133	+	0.982303i
$528$	6.29590			0.273994
$529$	7.81767	−	13.5406i	0.339899	−	0.588722i
$530$	−9.98523	−	17.2949i	−0.433731	−	0.751244i
$531$	−2.13437	−	3.69685i	−0.0926240	−	0.160429i
$532$	0.352584			0.0152865
$533$		0			0
$534$	−3.92154			−0.169702
$535$	−8.93996	−	15.4845i	−0.386508	−	0.669452i
$536$	−2.69202	−	4.66272i	−0.116278	−	0.201399i
$537$	1.79440	−	3.10800i	0.0774343	−	0.134120i
$538$	−15.9172			−0.686241
$539$	−22.0281	+	38.1538i	−0.948818	+	1.64340i
$540$	−1.06853	+	1.85075i	−0.0459823	+	0.0796436i
$541$	8.83579			0.379880			0.189940	−	0.981796i	$-0.439171\pi$
$541$	8.83579			0.379880			0.189940	+	0.981796i	$0.439171\pi$
$542$	1.76055	−	3.04937i	0.0756222	−	0.130982i
$543$	2.75302	+	4.76837i	0.118143	+	0.204630i
$544$	−1.44504	−	2.50289i	−0.0619557	−	0.107310i
$545$	−37.2438			−1.59535
$546$		0			0
$547$	−8.10859			−0.346698			−0.173349	−	0.984860i	$-0.555459\pi$
$547$	−8.10859			−0.346698			−0.173349	+	0.984860i	$0.555459\pi$
$548$	−2.00000	−	3.46410i	−0.0854358	−	0.147979i
$549$	−3.55496	−	6.15737i	−0.151722	−	0.262790i
$550$	1.36294	−	2.36068i	0.0581158	−	0.100660i
$551$	35.4034			1.50824
$552$	−1.35690	+	2.35021i	−0.0577533	+	0.100032i
$553$	−0.338241	+	0.585851i	−0.0143835	+	0.0249129i
$554$	8.58104			0.364573
$555$	−0.188374	+	0.326273i	−0.00799601	+	0.0138495i
$556$	−4.34481	−	7.52544i	−0.184261	−	0.319150i
$557$	−4.78017	−	8.27949i	−0.202542	−	0.350813i	0.746805	−	0.665043i	$-0.231587\pi$
$557$	−4.78017	−	8.27949i	−0.202542	−	0.350813i	−0.949347	+	0.314230i	$0.898254\pi$
$558$	9.00969			0.381411
$559$		0			0
$560$	−0.104539			−0.00441760
$561$	9.09783	+	15.7579i	0.384111	+	0.665300i
$562$	−4.03923	−	6.99615i	−0.170385	−	0.295115i
$563$	22.5819	−	39.1129i	0.951712	−	1.64841i	0.209994	−	0.977703i	$-0.432656\pi$
$563$	22.5819	−	39.1129i	0.951712	−	1.64841i	0.741719	−	0.670711i	$-0.234011\pi$
$564$	7.20775			0.303501
$565$	−14.9336	+	25.8658i	−0.628262	+	1.08818i
$566$	−8.70171	+	15.0718i	−0.365760	+	0.633515i
$567$	0.0489173			0.00205434
$568$	4.35690	−	7.54637i	0.182811	−	0.316638i
$569$	1.60388	+	2.77799i	0.0672380	+	0.116460i	0.897685	−	0.440639i	$-0.145248\pi$
$569$	1.60388	+	2.77799i	0.0672380	+	0.116460i	−0.830447	+	0.557098i	$0.811915\pi$
$570$	7.70171	+	13.3398i	0.322589	+	0.558741i
$571$	0.0241632			0.00101120			0.000505599	−	1.00000i	$-0.499839\pi$
$571$	0.0241632			0.00101120			0.000505599		1.00000i	$0.499839\pi$
$572$		0			0
$573$	5.65817			0.236373
$574$	0.210144	+	0.363980i	0.00877123	+	0.0151922i
$575$	0.587482	+	1.01755i	0.0244997	+	0.0424347i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−46.0200			−1.91584			−0.957918	−	0.287041i	$-0.907328\pi$
$577$	−46.0200			−1.91584			−0.957918	+	0.287041i	$0.907328\pi$
$578$	−4.32371	+	7.48888i	−0.179843	+	0.311496i
$579$	6.70171	−	11.6077i	0.278514	−	0.482400i
$580$	−10.4969			−0.435862
$581$	−0.272339	+	0.471705i	−0.0112985	+	0.0195696i
$582$	−1.23945	−	2.14678i	−0.0513767	−	0.0889871i
$583$	29.4170	+	50.9517i	1.21833	+	2.11020i
$584$	−14.9487			−0.618581
$585$		0			0
$586$	19.3709			0.800204
$587$	12.9693	+	22.4634i	0.535299	+	0.927165i	0.999149	+	0.0412510i	$0.0131343\pi$
$587$	12.9693	+	22.4634i	0.535299	+	0.927165i	−0.463850	+	0.885914i	$0.653532\pi$
$588$	−3.49880	−	6.06011i	−0.144288	−	0.249915i
$589$	32.4698	−	56.2393i	1.33789	−	2.31730i
$590$	9.12259			0.375571
$591$	9.99061	−	17.3042i	0.410959	−	0.711801i
$592$	−0.0881460	+	0.152673i	−0.00362278	+	0.00627484i
$593$	−8.30691			−0.341124			−0.170562	−	0.985347i	$-0.554558\pi$
$593$	−8.30691			−0.341124			−0.170562	+	0.985347i	$0.554558\pi$
$594$	3.14795	−	5.45241i	0.129162	−	0.223715i
$595$	−0.151064	−	0.261650i	−0.00619302	−	0.0107266i
$596$	−2.43416	−	4.21608i	−0.0997069	−	0.172697i
$597$	6.24160			0.255452
$598$		0			0
$599$	37.1702			1.51873			0.759366	−	0.650664i	$-0.225509\pi$
$599$	37.1702			1.51873			0.759366	+	0.650664i	$0.225509\pi$
$600$	0.216480	+	0.374955i	0.00883776	+	0.0153075i
$601$	6.28501	+	10.8860i	0.256371	+	0.444048i	0.965267	−	0.261265i	$-0.0841398\pi$
$601$	6.28501	+	10.8860i	0.256371	+	0.444048i	−0.708896	+	0.705313i	$0.750806\pi$
$602$	0.164210	−	0.284421i	0.00669272	−	0.0115921i
$603$	−5.38404			−0.219255
$604$	7.37316	−	12.7707i	0.300010	−	0.519632i
$605$	30.6010	−	53.0024i	1.24411	−	2.15485i
$606$	1.65279			0.0671401
$607$	−4.02446	+	6.97057i	−0.163348	+	0.282927i	−0.936067	−	0.351821i	$-0.885563\pi$
$607$	−4.02446	+	6.97057i	−0.163348	+	0.282927i	0.772720	+	0.634748i	$0.218896\pi$
$608$	3.60388	+	6.24210i	0.146156	+	0.253150i
$609$	0.120137	+	0.208084i	0.00486821	+	0.00843199i
$610$	15.1943			0.615201
$611$		0			0
$612$	−2.89008			−0.116825
$613$	−15.2295	−	26.3783i	−0.615115	−	1.06541i	−0.990364	−	0.138486i	$-0.955776\pi$
$613$	−15.2295	−	26.3783i	−0.615115	−	1.06541i	0.375250	−	0.926924i	$-0.377557\pi$
$614$	−6.21313	−	10.7615i	−0.250741	−	0.434297i
$615$	−9.18060	+	15.9013i	−0.370198	+	0.641201i
$616$	0.307979			0.0124088
$617$	−2.36658	+	4.09904i	−0.0952751	+	0.165021i	−0.909723	−	0.415215i	$-0.863706\pi$
$617$	−2.36658	+	4.09904i	−0.0952751	+	0.165021i	0.814448	+	0.580236i	$0.197040\pi$
$618$	4.11745	−	7.13163i	0.165628	−	0.286876i
$619$	−24.9095			−1.00120			−0.500598	−	0.865680i	$-0.666886\pi$
$619$	−24.9095			−1.00120			−0.500598	+	0.865680i	$0.666886\pi$
$620$	−9.62714	+	16.6747i	−0.386635	+	0.669672i
$621$	1.35690	+	2.35021i	0.0544504	+	0.0943108i
$622$	1.35690	+	2.35021i	0.0544066	+	0.0942349i
$623$	−0.191831			−0.00768556
$624$		0			0
$625$	−22.6477			−0.905910
$626$	7.69418	+	13.3267i	0.307521	+	0.532642i
$627$	−22.6896	−	39.2996i	−0.906136	−	1.56947i
$628$	8.35690	−	14.4746i	0.333476	−	0.577598i
$629$	−0.509499			−0.0203150
$630$	−0.0522697	+	0.0905338i	−0.00208248	+	0.00360695i
$631$	−12.2148	+	21.1566i	−0.486262	+	0.842230i	−0.999875	−	0.0157918i	$-0.994973\pi$
$631$	−12.2148	+	21.1566i	−0.486262	+	0.842230i	0.513614	+	0.858022i	$0.328306\pi$
$632$	−13.8291			−0.550091
$633$	−2.54288	+	4.40439i	−0.101070	+	0.175059i
$634$	12.8264	+	22.2160i	0.509401	+	0.882309i
$635$	−8.03654	−	13.9197i	−0.318920	−	0.552386i
$636$	−9.34481			−0.370546
$637$		0			0
$638$	30.9245			1.22431
$639$	−4.35690	−	7.54637i	−0.172356	−	0.298530i
$640$	−1.06853	−	1.85075i	−0.0422374	−	0.0731574i
$641$	−24.3991	+	42.2605i	−0.963707	+	1.66919i	−0.250657	+	0.968076i	$0.580647\pi$
$641$	−24.3991	+	42.2605i	−0.963707	+	1.66919i	−0.713050	+	0.701113i	$0.752687\pi$
$642$	−8.36658			−0.330203
$643$	14.1347	−	24.4820i	0.557417	−	0.965475i	−0.440294	−	0.897854i	$-0.645126\pi$
$643$	14.1347	−	24.4820i	0.557417	−	0.965475i	0.997711	−	0.0676209i	$-0.0215408\pi$
$644$	−0.0663757	+	0.114966i	−0.00261557	+	0.00453030i
$645$	14.3478			0.564944
$646$	−10.4155	+	18.0402i	−0.409792	+	0.709781i
$647$	−17.4480	−	30.2209i	−0.685953	−	1.18810i	−0.973136	−	0.230229i	$-0.926052\pi$
$647$	−17.4480	−	30.2209i	−0.685953	−	1.18810i	0.287184	−	0.957876i	$-0.407281\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−26.8756			−1.05496
$650$		0			0
$651$	0.440730			0.0172736
$652$	2.77479	+	4.80608i	0.108669	+	0.188221i
$653$	5.85786	+	10.1461i	0.229236	+	0.397048i	0.957582	−	0.288162i	$-0.0930440\pi$
$653$	5.85786	+	10.1461i	0.229236	+	0.397048i	−0.728346	+	0.685209i	$0.759711\pi$
$654$	−8.71379	+	15.0927i	−0.340736	+	0.590172i
$655$	−10.9524			−0.427946
$656$	−4.29590	+	7.44071i	−0.167727	+	0.290511i
$657$	−7.47434	+	12.9459i	−0.291602	+	0.505069i
$658$	0.352584			0.0137452
$659$	3.56734	−	6.17881i	0.138964	−	0.240692i	−0.788141	−	0.615495i	$-0.788956\pi$
$659$	3.56734	−	6.17881i	0.138964	−	0.240692i	0.927105	+	0.374803i	$0.122290\pi$
$660$	6.72737	+	11.6521i	0.261862	+	0.453559i
$661$	4.26444	+	7.38622i	0.165867	+	0.287291i	0.936963	−	0.349429i	$-0.113624\pi$
$661$	4.26444	+	7.38622i	0.165867	+	0.287291i	−0.771096	+	0.636719i	$0.780291\pi$
$662$	3.82371			0.148613
$663$		0			0
$664$	−11.1347			−0.432109
$665$	0.376747	+	0.652545i	0.0146096	+	0.0253046i
$666$	0.0881460	+	0.152673i	0.00341559	+	0.00591597i
$667$	−6.66487	+	11.5439i	−0.258065	+	0.446982i
$668$	3.92154			0.151729
$669$	−10.2741	+	17.7953i	−0.397221	+	0.688006i
$670$	5.75302	−	9.96452i	0.222259	−	0.384963i
$671$	−44.7633			−1.72807
$672$	−0.0244587	+	0.0423637i	−0.000943514	+	0.00163421i
$673$	15.7969	+	27.3610i	0.608924	+	1.05469i	0.991418	+	0.130729i	$0.0417319\pi$
$673$	15.7969	+	27.3610i	0.608924	+	1.05469i	−0.382494	+	0.923958i	$0.624935\pi$
$674$	10.0652	+	17.4334i	0.387696	+	0.671510i
$675$	0.432960			0.0166646
$676$		0			0
$677$	−17.3002			−0.664901			−0.332451	−	0.943121i	$-0.607875\pi$
$677$	−17.3002			−0.664901			−0.332451	+	0.943121i	$0.607875\pi$
$678$	6.98792	+	12.1034i	0.268369	+	0.464829i
$679$	−0.0606304	−	0.105015i	−0.00232678	−	0.00403011i
$680$	3.08815	−	5.34883i	0.118425	−	0.205118i
$681$	−4.41119			−0.169037
$682$	28.3620	−	49.1245i	1.08604	−	1.88107i
$683$	−15.1978	+	26.3234i	−0.581529	+	1.00724i	0.413770	+	0.910382i	$0.364212\pi$
$683$	−15.1978	+	26.3234i	−0.581529	+	1.00724i	−0.995298	+	0.0968556i	$0.969122\pi$
$684$	7.20775			0.275595
$685$	4.27413	−	7.40300i	0.163306	−	0.282854i
$686$	−0.342363	−	0.592990i	−0.0130715	−	0.0226405i
$687$	0.115293	+	0.199693i	0.00439871	+	0.00761878i
$688$	6.71379			0.255961
$689$		0			0
$690$	−5.79954			−0.220785
$691$	−17.8659	−	30.9447i	−0.679652	−	1.17719i	−0.975086	−	0.221828i	$-0.928798\pi$
$691$	−17.8659	−	30.9447i	−0.679652	−	1.17719i	0.295434	−	0.955363i	$-0.404536\pi$
$692$	1.74214	+	3.01747i	0.0662260	+	0.114707i
$693$	0.153989	−	0.266717i	0.00584957	−	0.0101317i
$694$	−2.93900			−0.111563
$695$	9.28514	−	16.0823i	0.352206	−	0.610038i
$696$	−2.45593	+	4.25379i	−0.0930917	+	0.161240i
$697$	−24.8310			−0.940541
$698$	3.68664	−	6.38546i	0.139542	−	0.241693i
$699$	−3.91185	−	6.77553i	−0.147960	−	0.256274i
$700$	0.0105896	+	0.0183418i	0.000400250	+	0.000693254i
$701$	20.1328			0.760404			0.380202	−	0.924904i	$-0.375855\pi$
$701$	20.1328			0.760404			0.380202	+	0.924904i	$0.375855\pi$
$702$		0			0
$703$	1.27067			0.0479242
$704$	3.14795	+	5.45241i	0.118643	+	0.205495i
$705$	7.70171	+	13.3398i	0.290063	+	0.502404i
$706$	−1.00538	+	1.74136i	−0.0378379	+	0.0655371i
$707$	0.0808502			0.00304069
$708$	2.13437	−	3.69685i	0.0802147	−	0.138936i
$709$	−8.30798	+	14.3898i	−0.312013	+	0.540422i	−0.978798	−	0.204828i	$-0.934336\pi$
$709$	−8.30798	+	14.3898i	−0.312013	+	0.540422i	0.666785	+	0.745250i	$0.267670\pi$
$710$	18.6219			0.698868
$711$	−6.91454	+	11.9763i	−0.259316	+	0.449148i
$712$	−1.96077	−	3.39616i	−0.0734830	−	0.127276i
$713$	12.2252	+	21.1747i	0.457838	+	0.792998i
$714$	−0.141375			−0.00529083
$715$		0			0
$716$	3.58881			0.134120
$717$	5.57673	+	9.65918i	0.208267	+	0.360729i
$718$	15.7289	+	27.2432i	0.586996	+	1.01671i
$719$	−1.02416	+	1.77390i	−0.0381948	+	0.0661554i	−0.884491	−	0.466557i	$-0.845494\pi$
$719$	−1.02416	+	1.77390i	−0.0381948	+	0.0661554i	0.846296	+	0.532713i	$0.178827\pi$
$720$	−2.13706			−0.0796436
$721$	0.201415	−	0.348860i	0.00750107	−	0.0129922i
$722$	16.4758	−	28.5370i	0.613167	−	1.06204i
$723$	3.54527			0.131850
$724$	−2.75302	+	4.76837i	−0.102315	+	0.177215i
$725$	1.06332	+	1.84172i	0.0394907	+	0.0683998i
$726$	−14.3192	−	24.8015i	−0.531434	−	0.920470i
$727$	29.9377			1.11033			0.555163	−	0.831741i	$-0.312656\pi$
$727$	29.9377			1.11033			0.555163	+	0.831741i	$0.312656\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−15.9731	−	27.6663i	−0.591193	−	1.02398i
$731$	9.70171	+	16.8039i	0.358831	+	0.621513i
$732$	3.55496	−	6.15737i	0.131395	−	0.227583i
$733$	−1.46250			−0.0540187			−0.0270093	−	0.999635i	$-0.508598\pi$
$733$	−1.46250			−0.0540187			−0.0270093	+	0.999635i	$0.508598\pi$
$734$	−2.24967	+	3.89654i	−0.0830368	+	0.143824i
$735$	7.47716	−	12.9508i	0.275799	−	0.477699i
$736$	−2.71379			−0.100032
$737$	−16.9487	+	29.3560i	−0.624313	+	1.08134i
$738$	4.29590	+	7.44071i	0.158134	+	0.273896i
$739$	−20.1933	−	34.9758i	−0.742822	−	1.28660i	−0.951206	−	0.308558i	$-0.900154\pi$
$739$	−20.1933	−	34.9758i	−0.742822	−	1.28660i	0.208384	−	0.978047i	$-0.433180\pi$
$740$	−0.376747			−0.0138495
$741$		0			0
$742$	−0.457123			−0.0167815
$743$	4.88769	+	8.46573i	0.179312	+	0.310577i	0.941645	−	0.336607i	$-0.109280\pi$
$743$	4.88769	+	8.46573i	0.179312	+	0.310577i	−0.762333	+	0.647185i	$0.775946\pi$
$744$	4.50484	+	7.80262i	0.165156	+	0.286058i
$745$	5.20195	−	9.01004i	0.190585	−	0.330102i
$746$	−37.8297			−1.38504
$747$	−5.56734	+	9.64291i	−0.203698	+	0.352816i
$748$	−9.09783	+	15.7579i	−0.332650	+	0.576166i
$749$	−0.409271			−0.0149544
$750$	−5.80529	+	10.0551i	−0.211979	+	0.367159i
$751$	−17.2729	−	29.9176i	−0.630298	−	1.09171i	−0.987491	−	0.157678i	$-0.949599\pi$
$751$	−17.2729	−	29.9176i	−0.630298	−	1.09171i	0.357192	−	0.934031i	$-0.383734\pi$
$752$	3.60388	+	6.24210i	0.131420	+	0.227626i
$753$	4.17092			0.151997
$754$		0			0
$755$	31.5138			1.14690
$756$	0.0244587	+	0.0423637i	0.000889553	+	0.00154075i
$757$	2.57242	+	4.45556i	0.0934961	+	0.161940i	0.908980	−	0.416840i	$-0.136862\pi$
$757$	2.57242	+	4.45556i	0.0934961	+	0.161940i	−0.815484	+	0.578780i	$0.803529\pi$
$758$	−4.21983	+	7.30896i	−0.153271	+	0.265474i
$759$	17.0858			0.620174
$760$	−7.70171	+	13.3398i	−0.279370	+	0.483884i
$761$	9.75600	−	16.8979i	0.353655	−	0.612548i	−0.633232	−	0.773962i	$-0.718272\pi$
$761$	9.75600	−	16.8979i	0.353655	−	0.612548i	0.986887	+	0.161414i	$0.0516054\pi$
$762$	−7.52111			−0.272461
$763$	−0.426256	+	0.738296i	−0.0154315	+	0.0267281i
$764$	2.82908	+	4.90012i	0.102353	+	0.177280i
$765$	−3.08815	−	5.34883i	−0.111652	−	0.193387i
$766$	−1.28621			−0.0464726
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	−2.87800	−	4.98485i	−0.103783	−	0.179758i	0.809457	−	0.587179i	$-0.199762\pi$
$769$	−2.87800	−	4.98485i	−0.103783	−	0.179758i	−0.913241	+	0.407421i	$0.866428\pi$
$770$	0.329085	+	0.569992i	0.0118594	+	0.0205411i
$771$	−5.44504	+	9.43109i	−0.196098	+	0.339652i
$772$	13.4034			0.482400
$773$	2.06369	−	3.57441i	0.0742257	−	0.128563i	−0.826524	−	0.562902i	$-0.809685\pi$
$773$	2.06369	−	3.57441i	0.0742257	−	0.128563i	0.900749	+	0.434339i	$0.143018\pi$
$774$	3.35690	−	5.81431i	0.120661	−	0.208991i
$775$	3.90084			0.140122
$776$	1.23945	−	2.14678i	0.0444935	−	0.0770651i
$777$	0.00431187	+	0.00746837i	0.000154687	+	0.000267926i
$778$	11.6962	+	20.2584i	0.419329	+	0.726299i
$779$	61.9275

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.13706 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.0244587 + 0.0423637i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.13706 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.0244587 + 0.0423637i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.06853 - 1.85075i) q^{10} +(3.14795 + 5.45241i) q^{11} -1.00000 q^{12} -0.0489173 q^{14} +(-1.06853 - 1.85075i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.44504 - 2.50289i) q^{17} -1.00000 q^{18} +(-3.60388 + 6.24210i) q^{19} +(1.06853 - 1.85075i) q^{20} -0.0489173 q^{21} +(-3.14795 + 5.45241i) q^{22} +(-1.35690 - 2.35021i) q^{23} +(-0.500000 - 0.866025i) q^{24} -0.432960 q^{25} -1.00000 q^{27} +(-0.0244587 - 0.0423637i) q^{28} +(-2.45593 - 4.25379i) q^{29} +(1.06853 - 1.85075i) q^{30} -9.00969 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.14795 + 5.45241i) q^{33} +2.89008 q^{34} +(0.0522697 - 0.0905338i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.0881460 - 0.152673i) q^{37} -7.20775 q^{38} +2.13706 q^{40} +(-4.29590 - 7.44071i) q^{41} +(-0.0244587 - 0.0423637i) q^{42} +(-3.35690 + 5.81431i) q^{43} -6.29590 q^{44} +(1.06853 - 1.85075i) q^{45} +(1.35690 - 2.35021i) q^{46} -7.20775 q^{47} +(0.500000 - 0.866025i) q^{48} +(3.49880 + 6.06011i) q^{49} +(-0.216480 - 0.374955i) q^{50} +2.89008 q^{51} +9.34481 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-6.72737 - 11.6521i) q^{55} +(0.0244587 - 0.0423637i) q^{56} -7.20775 q^{57} +(2.45593 - 4.25379i) q^{58} +(-2.13437 + 3.69685i) q^{59} +2.13706 q^{60} +(-3.55496 + 6.15737i) q^{61} +(-4.50484 - 7.80262i) q^{62} +(-0.0244587 - 0.0423637i) q^{63} +1.00000 q^{64} -6.29590 q^{66} +(2.69202 + 4.66272i) q^{67} +(1.44504 + 2.50289i) q^{68} +(1.35690 - 2.35021i) q^{69} +0.104539 q^{70} +(-4.35690 + 7.54637i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.9487 q^{73} +(0.0881460 - 0.152673i) q^{74} +(-0.216480 - 0.374955i) q^{75} +(-3.60388 - 6.24210i) q^{76} -0.307979 q^{77} +13.8291 q^{79} +(1.06853 + 1.85075i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.29590 - 7.44071i) q^{82} +11.1347 q^{83} +(0.0244587 - 0.0423637i) q^{84} +(-3.08815 + 5.34883i) q^{85} -6.71379 q^{86} +(2.45593 - 4.25379i) q^{87} +(-3.14795 - 5.45241i) q^{88} +(1.96077 + 3.39616i) q^{89} +2.13706 q^{90} +2.71379 q^{92} +(-4.50484 - 7.80262i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(7.70171 - 13.3398i) q^{95} +1.00000 q^{96} +(-1.23945 + 2.14678i) q^{97} +(-3.49880 + 6.06011i) q^{98} -6.29590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 5 q^{11} - 6 q^{12} + 18 q^{14} - q^{15} - 3 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + q^{20} + 18 q^{21} - 5 q^{22} - 3 q^{24} + 36 q^{25} - 6 q^{27} + 9 q^{28} - 11 q^{29} + q^{30} - 10 q^{31} + 3 q^{32} - 5 q^{33} + 16 q^{34} + 4 q^{35} - 3 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{40} + 2 q^{41} + 9 q^{42} - 12 q^{43} - 10 q^{44} + q^{45} - 8 q^{47} + 3 q^{48} - 20 q^{49} + 18 q^{50} + 16 q^{51} + 10 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 8 q^{57} + 11 q^{58} - 5 q^{59} + 2 q^{60} - 22 q^{61} - 5 q^{62} + 9 q^{63} + 6 q^{64} - 10 q^{66} + 6 q^{67} + 8 q^{68} + 8 q^{70} - 18 q^{71} + 3 q^{72} + 26 q^{73} + 8 q^{74} + 18 q^{75} - 4 q^{76} - 12 q^{77} + 62 q^{79} + q^{80} - 3 q^{81} - 2 q^{82} - 26 q^{83} - 9 q^{84} - 26 q^{85} - 24 q^{86} + 11 q^{87} - 5 q^{88} - 14 q^{89} + 2 q^{90} - 5 q^{93} - 4 q^{94} - 8 q^{95} + 6 q^{96} - 23 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 5 * q^11 - 6 * q^12 + 18 * q^14 - q^15 - 3 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + q^20 + 18 * q^21 - 5 * q^22 - 3 * q^24 + 36 * q^25 - 6 * q^27 + 9 * q^28 - 11 * q^29 + q^30 - 10 * q^31 + 3 * q^32 - 5 * q^33 + 16 * q^34 + 4 * q^35 - 3 * q^36 - 8 * q^37 - 8 * q^38 + 2 * q^40 + 2 * q^41 + 9 * q^42 - 12 * q^43 - 10 * q^44 + q^45 - 8 * q^47 + 3 * q^48 - 20 * q^49 + 18 * q^50 + 16 * q^51 + 10 * q^53 - 3 * q^54 - 18 * q^55 - 9 * q^56 - 8 * q^57 + 11 * q^58 - 5 * q^59 + 2 * q^60 - 22 * q^61 - 5 * q^62 + 9 * q^63 + 6 * q^64 - 10 * q^66 + 6 * q^67 + 8 * q^68 + 8 * q^70 - 18 * q^71 + 3 * q^72 + 26 * q^73 + 8 * q^74 + 18 * q^75 - 4 * q^76 - 12 * q^77 + 62 * q^79 + q^80 - 3 * q^81 - 2 * q^82 - 26 * q^83 - 9 * q^84 - 26 * q^85 - 24 * q^86 + 11 * q^87 - 5 * q^88 - 14 * q^89 + 2 * q^90 - 5 * q^93 - 4 * q^94 - 8 * q^95 + 6 * q^96 - 23 * q^97 + 20 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more