LMFDB - Embedded newform 507.2.e.k.484.1

Newspace parameters

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.e (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.04841538248$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			484.1
Root			$-0.623490 - 1.07992i$ of defining polynomial
Character	$\chi$	$=$	507.484
Dual form			507.2.e.k.22.1

$q$-expansion

$f(q)$	$=$	$q+(-0.623490 - 1.07992i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.222521 - 0.385418i) q^{4} -2.80194 q^{5} +(-0.623490 + 1.07992i) q^{6} +(2.40097 - 4.15860i) q^{7} -3.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.623490 - 1.07992i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.222521 - 0.385418i) q^{4} -2.80194 q^{5} +(-0.623490 + 1.07992i) q^{6} +(2.40097 - 4.15860i) q^{7} -3.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.74698 + 3.02586i) q^{10} +(-0.733406 - 1.27030i) q^{11} -0.445042 q^{12} -5.98792 q^{14} +(1.40097 + 2.42655i) q^{15} +(1.45593 + 2.52174i) q^{16} +(1.22252 - 2.11747i) q^{17} +1.24698 q^{18} +(-1.27144 + 2.20220i) q^{19} +(-0.623490 + 1.07992i) q^{20} -4.80194 q^{21} +(-0.914542 + 1.58403i) q^{22} +(1.75786 + 3.04471i) q^{23} +(1.52446 + 2.64044i) q^{24} +2.85086 q^{25} +1.00000 q^{27} +(-1.06853 - 1.85075i) q^{28} +(-0.925428 - 1.60289i) q^{29} +(1.74698 - 3.02586i) q^{30} -7.63102 q^{31} +(-1.23341 + 2.13632i) q^{32} +(-0.733406 + 1.27030i) q^{33} -3.04892 q^{34} +(-6.72737 + 11.6521i) q^{35} +(0.222521 + 0.385418i) q^{36} +(2.27748 + 3.94471i) q^{37} +3.17092 q^{38} +8.54288 q^{40} +(-0.623490 - 1.07992i) q^{41} +(2.99396 + 5.18569i) q^{42} +(-1.19202 + 2.06464i) q^{43} -0.652793 q^{44} +(1.40097 - 2.42655i) q^{45} +(2.19202 - 3.79669i) q^{46} +12.8170 q^{47} +(1.45593 - 2.52174i) q^{48} +(-8.02930 - 13.9072i) q^{49} +(-1.77748 - 3.07868i) q^{50} -2.44504 q^{51} -8.85086 q^{53} +(-0.623490 - 1.07992i) q^{54} +(2.05496 + 3.55929i) q^{55} +(-7.32036 + 12.6792i) q^{56} +2.54288 q^{57} +(-1.15399 + 1.99877i) q^{58} +(-1.08815 + 1.88472i) q^{59} +1.24698 q^{60} +(3.91454 - 6.78019i) q^{61} +(4.75786 + 8.24086i) q^{62} +(2.40097 + 4.15860i) q^{63} +8.89977 q^{64} +1.82908 q^{66} +(1.79105 + 3.10219i) q^{67} +(-0.544073 - 0.942362i) q^{68} +(1.75786 - 3.04471i) q^{69} +16.7778 q^{70} +(4.41939 - 7.65460i) q^{71} +(1.52446 - 2.64044i) q^{72} -7.69202 q^{73} +(2.83997 - 4.91897i) q^{74} +(-1.42543 - 2.46891i) q^{75} +(0.565843 + 0.980069i) q^{76} -7.04354 q^{77} -4.02177 q^{79} +(-4.07942 - 7.06576i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.777479 + 1.34663i) q^{82} -0.652793 q^{83} +(-1.06853 + 1.85075i) q^{84} +(-3.42543 + 5.93301i) q^{85} +2.97285 q^{86} +(-0.925428 + 1.60289i) q^{87} +(2.23609 + 3.87303i) q^{88} +(-3.14795 - 5.45241i) q^{89} -3.49396 q^{90} +1.56465 q^{92} +(3.81551 + 6.60866i) q^{93} +(-7.99127 - 13.8413i) q^{94} +(3.56249 - 6.17042i) q^{95} +2.46681 q^{96} +(5.01573 - 8.68750i) q^{97} +(-10.0124 + 17.3419i) q^{98} +1.46681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9	$ 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9} + q^{10} - q^{11} - 2 q^{12} + 2 q^{14} + 4 q^{15} + 5 q^{16} + 7 q^{17} - 2 q^{18} + 11 q^{19} + q^{20} - 20 q^{21} + 5 q^{22} - 2 q^{23} - 10 q^{25} + 6 q^{27} - q^{28} + 8 q^{29} + q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 18 q^{35} + q^{36} + 14 q^{37} + 40 q^{38} + 14 q^{40} + q^{41} - q^{42} + 3 q^{43} + 32 q^{44} + 4 q^{45} + 3 q^{46} + 18 q^{47} + 5 q^{48} - 17 q^{49} - 11 q^{50} - 14 q^{51} - 26 q^{53} + q^{54} + 13 q^{55} - 7 q^{56} - 22 q^{57} - 12 q^{58} - 14 q^{59} - 2 q^{60} + 13 q^{61} + 16 q^{62} + 10 q^{63} + 8 q^{64} - 10 q^{66} + 5 q^{67} - 7 q^{68} - 2 q^{69} + 16 q^{70} - 6 q^{71} - 36 q^{73} - 7 q^{74} + 5 q^{75} + q^{76} - 30 q^{77} - 18 q^{79} - 16 q^{80} - 3 q^{81} - 5 q^{82} + 32 q^{83} - q^{84} - 7 q^{85} + 30 q^{86} + 8 q^{87} + 7 q^{88} - 5 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} - 32 q^{94} - 3 q^{95} + 8 q^{96} + 5 q^{97} - 13 q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9 + q^10 - q^11 - 2 * q^12 + 2 * q^14 + 4 * q^15 + 5 * q^16 + 7 * q^17 - 2 * q^18 + 11 * q^19 + q^20 - 20 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^25 + 6 * q^27 - q^28 + 8 * q^29 + q^30 - 16 * q^31 - 4 * q^32 - q^33 - 18 * q^35 + q^36 + 14 * q^37 + 40 * q^38 + 14 * q^40 + q^41 - q^42 + 3 * q^43 + 32 * q^44 + 4 * q^45 + 3 * q^46 + 18 * q^47 + 5 * q^48 - 17 * q^49 - 11 * q^50 - 14 * q^51 - 26 * q^53 + q^54 + 13 * q^55 - 7 * q^56 - 22 * q^57 - 12 * q^58 - 14 * q^59 - 2 * q^60 + 13 * q^61 + 16 * q^62 + 10 * q^63 + 8 * q^64 - 10 * q^66 + 5 * q^67 - 7 * q^68 - 2 * q^69 + 16 * q^70 - 6 * q^71 - 36 * q^73 - 7 * q^74 + 5 * q^75 + q^76 - 30 * q^77 - 18 * q^79 - 16 * q^80 - 3 * q^81 - 5 * q^82 + 32 * q^83 - q^84 - 7 * q^85 + 30 * q^86 + 8 * q^87 + 7 * q^88 - 5 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 - 32 * q^94 - 3 * q^95 + 8 * q^96 + 5 * q^97 - 13 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.623490	−	1.07992i	−0.440874	−	0.763616i	0.556881	−	0.830593i	$-0.311998\pi$
$2$	−0.623490	−	1.07992i	−0.440874	−	0.763616i	−0.997755	+	0.0669766i	$0.978665\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.222521	−	0.385418i	0.111260	−	0.192709i
$5$	−2.80194			−1.25306			−0.626532	−	0.779395i	$-0.715526\pi$
$5$	−2.80194			−1.25306			−0.626532	+	0.779395i	$0.715526\pi$
$6$	−0.623490	+	1.07992i	−0.254539	+	0.440874i
$7$	2.40097	−	4.15860i	0.907481	−	1.57180i	0.0899290	−	0.995948i	$-0.471336\pi$
$7$	2.40097	−	4.15860i	0.907481	−	1.57180i	0.817552	−	0.575855i	$-0.195331\pi$
$8$	−3.04892			−1.07796
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.74698	+	3.02586i	0.552443	+	0.956860i
$11$	−0.733406	−	1.27030i	−0.221130	−	0.383009i	0.734021	−	0.679127i	$-0.237641\pi$
$11$	−0.733406	−	1.27030i	−0.221130	−	0.383009i	−0.955151	+	0.296118i	$0.904308\pi$
$12$	−0.445042			−0.128473
$13$		0			0
$13$		0			0
$14$	−5.98792			−1.60034
$15$	1.40097	+	2.42655i	0.361729	+	0.626532i
$16$	1.45593	+	2.52174i	0.363982	+	0.630435i
$17$	1.22252	−	2.11747i	0.296505	−	0.513562i	−0.678829	−	0.734296i	$-0.737512\pi$
$17$	1.22252	−	2.11747i	0.296505	−	0.513562i	0.975334	+	0.220735i	$0.0708456\pi$
$18$	1.24698			0.293916
$19$	−1.27144	+	2.20220i	−0.291688	+	0.505218i	−0.974209	−	0.225648i	$-0.927550\pi$
$19$	−1.27144	+	2.20220i	−0.291688	+	0.505218i	0.682521	+	0.730866i	$0.260884\pi$
$20$	−0.623490	+	1.07992i	−0.139417	+	0.241477i
$21$	−4.80194			−1.04787
$22$	−0.914542	+	1.58403i	−0.194981	+	0.337717i
$23$	1.75786	+	3.04471i	0.366540	+	0.634866i	0.989022	−	0.147768i	$-0.0472089\pi$
$23$	1.75786	+	3.04471i	0.366540	+	0.634866i	−0.622482	+	0.782634i	$0.713876\pi$
$24$	1.52446	+	2.64044i	0.311179	+	0.538978i
$25$	2.85086			0.570171
$26$		0			0
$27$	1.00000			0.192450
$28$	−1.06853	−	1.85075i	−0.201934	−	0.349759i
$29$	−0.925428	−	1.60289i	−0.171848	−	0.297649i	0.767218	−	0.641386i	$-0.221640\pi$
$29$	−0.925428	−	1.60289i	−0.171848	−	0.297649i	−0.939066	+	0.343737i	$0.888307\pi$
$30$	1.74698	−	3.02586i	0.318953	−	0.552443i
$31$	−7.63102			−1.37057			−0.685286	−	0.728274i	$-0.740323\pi$
$31$	−7.63102			−1.37057			−0.685286	+	0.728274i	$0.740323\pi$
$32$	−1.23341	+	2.13632i	−0.218037	+	0.377652i
$33$	−0.733406	+	1.27030i	−0.127670	+	0.221130i
$34$	−3.04892			−0.522885
$35$	−6.72737	+	11.6521i	−1.13713	+	1.96957i
$36$	0.222521	+	0.385418i	0.0370868	+	0.0642363i
$37$	2.27748	+	3.94471i	0.374415	+	0.648506i	0.990239	−	0.139377i	$-0.0445101\pi$
$37$	2.27748	+	3.94471i	0.374415	+	0.648506i	−0.615824	+	0.787884i	$0.711177\pi$
$38$	3.17092			0.514390
$39$		0			0
$40$	8.54288			1.35075
$41$	−0.623490	−	1.07992i	−0.0973727	−	0.168655i	0.813224	−	0.581951i	$-0.197711\pi$
$41$	−0.623490	−	1.07992i	−0.0973727	−	0.168655i	−0.910596	+	0.413297i	$0.864377\pi$
$42$	2.99396	+	5.18569i	0.461978	+	0.800169i
$43$	−1.19202	+	2.06464i	−0.181782	+	0.314855i	−0.942487	−	0.334242i	$-0.891520\pi$
$43$	−1.19202	+	2.06464i	−0.181782	+	0.314855i	0.760706	+	0.649097i	$0.224853\pi$
$44$	−0.652793			−0.0984122
$45$	1.40097	−	2.42655i	0.208844	−	0.361729i
$46$	2.19202	−	3.79669i	0.323196	−	0.559792i
$47$	12.8170			1.86955			0.934776	−	0.355238i	$-0.115600\pi$
$47$	12.8170			1.86955			0.934776	+	0.355238i	$0.115600\pi$
$48$	1.45593	−	2.52174i	0.210145	−	0.363982i
$49$	−8.02930	−	13.9072i	−1.14704	−	1.98674i
$50$	−1.77748	−	3.07868i	−0.251374	−	0.435392i
$51$	−2.44504			−0.342374
$52$		0			0
$53$	−8.85086			−1.21576			−0.607879	−	0.794030i	$-0.707980\pi$
$53$	−8.85086			−1.21576			−0.607879	+	0.794030i	$0.707980\pi$
$54$	−0.623490	−	1.07992i	−0.0848462	−	0.146958i
$55$	2.05496	+	3.55929i	0.277090	+	0.479935i
$56$	−7.32036	+	12.6792i	−0.978224	+	1.69433i
$57$	2.54288			0.336812
$58$	−1.15399	+	1.99877i	−0.151526	+	0.262451i
$59$	−1.08815	+	1.88472i	−0.141665	+	0.245370i	−0.928124	−	0.372272i	$-0.878579\pi$
$59$	−1.08815	+	1.88472i	−0.141665	+	0.245370i	0.786459	+	0.617642i	$0.211912\pi$
$60$	1.24698			0.160984
$61$	3.91454	−	6.78019i	0.501206	−	0.868114i	−0.498793	−	0.866721i	$-0.666223\pi$
$61$	3.91454	−	6.78019i	0.501206	−	0.868114i	0.999999	−	0.00139289i	$-0.000443372\pi$
$62$	4.75786	+	8.24086i	0.604249	+	1.04659i
$63$	2.40097	+	4.15860i	0.302494	+	0.523934i
$64$	8.89977			1.11247
$65$		0			0
$66$	1.82908			0.225145
$67$	1.79105	+	3.10219i	0.218812	+	0.378993i	0.954445	−	0.298387i	$-0.0964486\pi$
$67$	1.79105	+	3.10219i	0.218812	+	0.378993i	−0.735633	+	0.677380i	$0.763115\pi$
$68$	−0.544073	−	0.942362i	−0.0659785	−	0.114278i
$69$	1.75786	−	3.04471i	0.211622	−	0.366540i
$70$	16.7778			2.00533
$71$	4.41939	−	7.65460i	0.524485	−	0.908434i	−0.475109	−	0.879927i	$-0.657591\pi$
$71$	4.41939	−	7.65460i	0.524485	−	0.908434i	0.999594	−	0.0285072i	$-0.00907534\pi$
$72$	1.52446	−	2.64044i	0.179659	−	0.311179i
$73$	−7.69202			−0.900283			−0.450142	−	0.892957i	$-0.648626\pi$
$73$	−7.69202			−0.900283			−0.450142	+	0.892957i	$0.648626\pi$
$74$	2.83997	−	4.91897i	0.330140	−	0.571819i
$75$	−1.42543	−	2.46891i	−0.164594	−	0.285086i
$76$	0.565843	+	0.980069i	0.0649067	+	0.112422i
$77$	−7.04354			−0.802686
$78$		0			0
$79$	−4.02177			−0.452485			−0.226242	−	0.974071i	$-0.572644\pi$
$79$	−4.02177			−0.452485			−0.226242	+	0.974071i	$0.572644\pi$
$80$	−4.07942	−	7.06576i	−0.456093	−	0.789976i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.777479	+	1.34663i	−0.0858582	+	0.148711i
$83$	−0.652793			−0.0716533			−0.0358267	−	0.999358i	$-0.511406\pi$
$83$	−0.652793			−0.0716533			−0.0358267	+	0.999358i	$0.511406\pi$
$84$	−1.06853	+	1.85075i	−0.116586	+	0.201934i
$85$	−3.42543	+	5.93301i	−0.371540	+	0.643526i
$86$	2.97285			0.320571
$87$	−0.925428	+	1.60289i	−0.0992162	+	0.171848i
$88$	2.23609	+	3.87303i	0.238368	+	0.412866i
$89$	−3.14795	−	5.45241i	−0.333682	−	0.577954i	0.649549	−	0.760320i	$-0.274958\pi$
$89$	−3.14795	−	5.45241i	−0.333682	−	0.577954i	−0.983231	+	0.182366i	$0.941624\pi$
$90$	−3.49396			−0.368296
$91$		0			0
$92$	1.56465			0.163126
$93$	3.81551	+	6.60866i	0.395650	+	0.685286i
$94$	−7.99127	−	13.8413i	−0.824237	−	1.42762i
$95$	3.56249	−	6.17042i	0.365504	−	0.633071i
$96$	2.46681			0.251768
$97$	5.01573	−	8.68750i	0.509270	−	0.882082i	−0.490672	−	0.871344i	$-0.663249\pi$
$97$	5.01573	−	8.68750i	0.509270	−	0.882082i	0.999942	−	0.0107376i	$-0.00341793\pi$
$98$	−10.0124	+	17.3419i	−1.01140	+	1.75180i
$99$	1.46681			0.147420
$100$	0.634375	−	1.09877i	0.0634375	−	0.109877i
$101$	−6.94385	−	12.0271i	−0.690938	−	1.19674i	−0.971531	−	0.236913i	$-0.923864\pi$
$101$	−6.94385	−	12.0271i	−0.690938	−	1.19674i	0.280592	−	0.959827i	$-0.409469\pi$
$102$	1.52446	+	2.64044i	0.150944	+	0.261443i
$103$	−17.4034			−1.71481			−0.857405	−	0.514642i	$-0.827925\pi$
$103$	−17.4034			−1.71481			−0.857405	+	0.514642i	$0.827925\pi$
$104$		0			0
$105$	13.4547			1.31305
$106$	5.51842	+	9.55818i	0.535996	+	0.928373i
$107$	−5.27628	−	9.13879i	−0.510077	−	0.883480i	−0.999932	−	0.0116758i	$-0.996283\pi$
$107$	−5.27628	−	9.13879i	−0.510077	−	0.883480i	0.489854	−	0.871804i	$-0.337050\pi$
$108$	0.222521	−	0.385418i	0.0214121	−	0.0370868i
$109$	1.07069			0.102553			0.0512766	−	0.998684i	$-0.483671\pi$
$109$	1.07069			0.102553			0.0512766	+	0.998684i	$0.483671\pi$
$110$	2.56249	−	4.43836i	0.244324	−	0.423181i
$111$	2.27748	−	3.94471i	0.216169	−	0.374415i
$112$	13.9825			1.32123
$113$	8.26540	−	14.3161i	0.777543	−	1.34674i	−0.155811	−	0.987787i	$-0.549799\pi$
$113$	8.26540	−	14.3161i	0.777543	−	1.34674i	0.933354	−	0.358957i	$-0.116868\pi$
$114$	−1.58546	−	2.74609i	−0.148492	−	0.257195i
$115$	−4.92543	−	8.53109i	−0.459298	−	0.795528i
$116$	−0.823708			−0.0764794
$117$		0			0
$118$	2.71379			0.249825
$119$	−5.87047	−	10.1680i	−0.538145	−	0.932095i
$120$	−4.27144	−	7.39835i	−0.389927	−	0.675374i
$121$	4.42423	−	7.66299i	0.402203	−	0.696636i
$122$	−9.76271			−0.883874
$123$	−0.623490	+	1.07992i	−0.0562182	+	0.0973727i
$124$	−1.69806	+	2.94113i	−0.152490	+	0.264121i
$125$	6.02177			0.538604
$126$	2.99396	−	5.18569i	0.266723	−	0.461978i
$127$	4.76875	+	8.25972i	0.423158	+	0.732931i	0.996246	−	0.0865622i	$-0.0275881\pi$
$127$	4.76875	+	8.25972i	0.423158	+	0.732931i	−0.573088	+	0.819494i	$0.694255\pi$
$128$	−3.08211	−	5.33836i	−0.272422	−	0.471849i
$129$	2.38404			0.209903
$130$		0			0
$131$	−5.50902			−0.481326			−0.240663	−	0.970609i	$-0.577365\pi$
$131$	−5.50902			−0.481326			−0.240663	+	0.970609i	$0.577365\pi$
$132$	0.326396	+	0.565335i	0.0284092	+	0.0492061i
$133$	6.10537	+	10.5748i	0.529402	+	0.916952i
$134$	2.23341	−	3.86837i	0.192937	−	0.334177i
$135$	−2.80194			−0.241152
$136$	−3.72737	+	6.45599i	−0.319619	+	0.553596i
$137$	8.09179	−	14.0154i	0.691329	−	1.19742i	−0.280074	−	0.959978i	$-0.590359\pi$
$137$	8.09179	−	14.0154i	0.691329	−	1.19742i	0.971403	−	0.237438i	$-0.0763076\pi$
$138$	−4.38404			−0.373195
$139$	5.25451	−	9.10108i	0.445682	−	0.771944i	−0.552418	−	0.833568i	$-0.686295\pi$
$139$	5.25451	−	9.10108i	0.445682	−	0.771944i	0.998099	+	0.0616238i	$0.0196279\pi$
$140$	2.99396	+	5.18569i	0.253036	+	0.438271i
$141$	−6.40850	−	11.0999i	−0.539693	−	0.934776i
$142$	−11.0218			−0.924926
$143$		0			0
$144$	−2.91185			−0.242654
$145$	2.59299	+	4.49119i	0.215336	+	0.372973i
$146$	4.79590	+	8.30674i	0.396911	+	0.687470i
$147$	−8.02930	+	13.9072i	−0.662246	+	1.14704i
$148$	2.02715			0.166630
$149$	−7.17510	+	12.4276i	−0.587807	+	1.01811i	0.406712	+	0.913556i	$0.366675\pi$
$149$	−7.17510	+	12.4276i	−0.587807	+	1.01811i	−0.994519	+	0.104555i	$0.966658\pi$
$150$	−1.77748	+	3.07868i	−0.145131	+	0.251374i
$151$	1.96615			0.160003			0.0800014	−	0.996795i	$-0.474508\pi$
$151$	1.96615			0.160003			0.0800014	+	0.996795i	$0.474508\pi$
$152$	3.87651	−	6.71431i	0.314426	−	0.544603i
$153$	1.22252	+	2.11747i	0.0988350	+	0.171187i
$154$	4.39158	+	7.60643i	0.353883	+	0.612944i
$155$	21.3817			1.71742
$156$		0			0
$157$	10.7017			0.854089			0.427045	−	0.904231i	$-0.359555\pi$
$157$	10.7017			0.854089			0.427045	+	0.904231i	$0.359555\pi$
$158$	2.50753	+	4.34317i	0.199489	+	0.345524i
$159$	4.42543	+	7.66507i	0.350959	+	0.607879i
$160$	3.45593	−	5.98584i	0.273215	−	0.473222i
$161$	16.8823			1.33051
$162$	−0.623490	+	1.07992i	−0.0489860	+	0.0848462i
$163$	−1.94989	+	3.37730i	−0.152727	+	0.264531i	−0.932229	−	0.361869i	$-0.882139\pi$
$163$	−1.94989	+	3.37730i	−0.152727	+	0.264531i	0.779502	+	0.626400i	$0.215472\pi$
$164$	−0.554958			−0.0433349
$165$	2.05496	−	3.55929i	0.159978	−	0.277090i
$166$	0.407010	+	0.704961i	0.0315901	+	0.0547156i
$167$	−10.5097	−	18.2033i	−0.813264	−	1.40861i	−0.910568	−	0.413360i	$-0.864355\pi$
$167$	−10.5097	−	18.2033i	−0.813264	−	1.40861i	0.0973035	−	0.995255i	$-0.468978\pi$
$168$	14.6407			1.12956
$169$		0			0
$170$	8.54288			0.655209
$171$	−1.27144	−	2.20220i	−0.0972293	−	0.168406i
$172$	0.530499	+	0.918852i	0.0404502	+	0.0700618i
$173$	−6.61745	+	11.4618i	−0.503115	+	0.871421i	0.496878	+	0.867820i	$0.334480\pi$
$173$	−6.61745	+	11.4618i	−0.503115	+	0.871421i	−0.999994	+	0.00360102i	$0.998854\pi$
$174$	2.30798			0.174967
$175$	6.84481	−	11.8556i	0.517419	−	0.896197i
$176$	2.13557	−	3.69892i	0.160975	−	0.278816i
$177$	2.17629			0.163580
$178$	−3.92543	+	6.79904i	−0.294223	+	0.509610i
$179$	−4.26391	−	7.38530i	−0.318699	−	0.552003i	0.661518	−	0.749930i	$-0.269913\pi$
$179$	−4.26391	−	7.38530i	−0.318699	−	0.552003i	−0.980217	+	0.197926i	$0.936579\pi$
$180$	−0.623490	−	1.07992i	−0.0464722	−	0.0804922i
$181$	−3.63640			−0.270291			−0.135146	−	0.990826i	$-0.543150\pi$
$181$	−3.63640			−0.270291			−0.135146	+	0.990826i	$0.543150\pi$
$182$		0			0
$183$	−7.82908			−0.578743
$184$	−5.35958	−	9.28307i	−0.395114	−	0.684357i
$185$	−6.38135	−	11.0528i	−0.469167	−	0.812620i
$186$	4.75786	−	8.24086i	0.348864	−	0.604249i
$187$	−3.58642			−0.262265
$188$	2.85205	−	4.93990i	0.208007	−	0.360279i
$189$	2.40097	−	4.15860i	0.174645	−	0.302494i
$190$	−8.88471			−0.644564
$191$	−10.6908	+	18.5171i	−0.773561	+	1.33985i	0.162039	+	0.986784i	$0.448193\pi$
$191$	−10.6908	+	18.5171i	−0.773561	+	1.33985i	−0.935600	+	0.353062i	$0.885140\pi$
$192$	−4.44989	−	7.70743i	−0.321143	−	0.556236i
$193$	4.21379	+	7.29850i	0.303315	+	0.525358i	0.976885	−	0.213766i	$-0.0685731\pi$
$193$	4.21379	+	7.29850i	0.303315	+	0.525358i	−0.673569	+	0.739124i	$0.735240\pi$
$194$	−12.5090			−0.898096
$195$		0			0
$196$	−7.14675			−0.510482
$197$	13.2383	+	22.9293i	0.943186	+	1.63365i	0.759343	+	0.650691i	$0.225521\pi$
$197$	13.2383	+	22.9293i	0.943186	+	1.63365i	0.183844	+	0.982955i	$0.441146\pi$
$198$	−0.914542	−	1.58403i	−0.0649937	−	0.112572i
$199$	7.12618	−	12.3429i	0.505161	−	0.874965i	−0.494821	−	0.868995i	$-0.664766\pi$
$199$	7.12618	−	12.3429i	0.505161	−	0.874965i	0.999982	−	0.00597014i	$-0.00190036\pi$
$200$	−8.69202			−0.614619
$201$	1.79105	−	3.10219i	0.126331	−	0.218812i
$202$	−8.65883	+	14.9975i	−0.609233	+	1.05522i
$203$	−8.88769			−0.623794
$204$	−0.544073	+	0.942362i	−0.0380927	+	0.0659785i
$205$	1.74698	+	3.02586i	0.122014	+	0.211335i
$206$	10.8509	+	18.7942i	0.756015	+	1.30946i
$207$	−3.51573			−0.244360
$208$		0			0
$209$	3.72992			0.258004
$210$	−8.38889	−	14.5300i	−0.578888	−	1.00266i
$211$	−0.925428	−	1.60289i	−0.0637091	−	0.110347i	0.832412	−	0.554158i	$-0.186960\pi$
$211$	−0.925428	−	1.60289i	−0.0637091	−	0.110347i	−0.896121	+	0.443811i	$0.853626\pi$
$212$	−1.96950	+	3.41127i	−0.135266	+	0.234287i
$213$	−8.83877			−0.605623
$214$	−6.57942	+	11.3959i	−0.449760	+	0.779007i
$215$	3.33997	−	5.78500i	0.227784	−	0.394534i
$216$	−3.04892			−0.207453
$217$	−18.3218	+	31.7344i	−1.24377	+	2.15427i
$218$	−0.667563	−	1.15625i	−0.0452131	−	0.0783113i
$219$	3.84601	+	6.66149i	0.259889	+	0.450142i
$220$	1.82908			0.123317
$221$		0			0
$222$	−5.67994			−0.381213
$223$	−9.32520	−	16.1517i	−0.624462	−	1.08160i	−0.988645	−	0.150272i	$-0.951985\pi$
$223$	−9.32520	−	16.1517i	−0.624462	−	1.08160i	0.364183	−	0.931327i	$-0.381348\pi$
$224$	5.92274	+	10.2585i	0.395730	+	0.685424i
$225$	−1.42543	+	2.46891i	−0.0950285	+	0.164594i
$226$	−20.6136			−1.37119
$227$	−4.87867	+	8.45010i	−0.323808	+	0.560853i	−0.981270	−	0.192635i	$-0.938297\pi$
$227$	−4.87867	+	8.45010i	−0.323808	+	0.560853i	0.657462	+	0.753488i	$0.271630\pi$
$228$	0.565843	−	0.980069i	0.0374739	−	0.0649067i
$229$	−2.86294			−0.189188			−0.0945941	−	0.995516i	$-0.530155\pi$
$229$	−2.86294			−0.189188			−0.0945941	+	0.995516i	$0.530155\pi$
$230$	−6.14191	+	10.6381i	−0.404985	+	0.701455i
$231$	3.52177	+	6.09989i	0.231715	+	0.401343i
$232$	2.82155	+	4.88707i	0.185244	+	0.320852i
$233$	−5.78554			−0.379024			−0.189512	−	0.981878i	$-0.560691\pi$
$233$	−5.78554			−0.379024			−0.189512	+	0.981878i	$0.560691\pi$
$234$		0			0
$235$	−35.9124			−2.34267
$236$	0.484271	+	0.838781i	0.0315233	+	0.0546000i
$237$	2.01089	+	3.48296i	0.130621	+	0.226242i
$238$	−7.32036	+	12.6792i	−0.474508	+	0.821872i
$239$	7.09246			0.458773			0.229386	−	0.973335i	$-0.426328\pi$
$239$	7.09246			0.458773			0.229386	+	0.973335i	$0.426328\pi$
$240$	−4.07942	+	7.06576i	−0.263325	+	0.456093i
$241$	−1.94989	+	3.37730i	−0.125603	+	0.217551i	−0.921969	−	0.387265i	$-0.873420\pi$
$241$	−1.94989	+	3.37730i	−0.125603	+	0.217551i	0.796365	+	0.604816i	$0.206753\pi$
$242$	−11.0339			−0.709283
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.74214	−	3.01747i	−0.111529	−	0.193174i
$245$	22.4976	+	38.9670i	1.43732	+	2.48951i
$246$	1.55496			0.0991405
$247$		0			0
$248$	23.2664			1.47742
$249$	0.326396	+	0.565335i	0.0206845	+	0.0358267i
$250$	−3.75451	−	6.50301i	−0.237456	−	0.411286i
$251$	1.22252	−	2.11747i	0.0771648	−	0.133653i	−0.824861	−	0.565336i	$-0.808747\pi$
$251$	1.22252	−	2.11747i	0.0771648	−	0.133653i	0.902026	+	0.431682i	$0.142080\pi$
$252$	2.13706			0.134622
$253$	2.57846	−	4.46602i	0.162106	−	0.280776i
$254$	5.94653	−	10.2997i	0.373119	−	0.646261i
$255$	6.85086			0.429017
$256$	5.05645	−	8.75803i	0.316028	−	0.547377i
$257$	7.06518	+	12.2372i	0.440714	+	0.763339i	0.997743	−	0.0671545i	$-0.0213920\pi$
$257$	7.06518	+	12.2372i	0.440714	+	0.763339i	−0.557029	+	0.830493i	$0.688059\pi$
$258$	−1.48643	−	2.57457i	−0.0925409	−	0.160285i
$259$	21.8726			1.35910
$260$		0			0
$261$	1.85086			0.114565
$262$	3.43482	+	5.94928i	0.212204	+	0.367548i
$263$	11.8617	+	20.5451i	0.731426	+	1.26687i	0.956274	+	0.292473i	$0.0944783\pi$
$263$	11.8617	+	20.5451i	0.731426	+	1.26687i	−0.224847	+	0.974394i	$0.572188\pi$
$264$	2.23609	−	3.87303i	0.137622	−	0.238368i
$265$	24.7995			1.52342
$266$	7.61327	−	13.1866i	0.466799	−	0.808520i
$267$	−3.14795	+	5.45241i	−0.192651	+	0.333682i
$268$	1.59419			0.0973805
$269$	2.95808	−	5.12355i	0.180357	−	0.312388i	−0.761645	−	0.647995i	$-0.775608\pi$
$269$	2.95808	−	5.12355i	0.180357	−	0.312388i	0.942002	+	0.335606i	$0.108941\pi$
$270$	1.74698	+	3.02586i	0.106318	+	0.184148i
$271$	−1.59515	−	2.76287i	−0.0968982	−	0.167833i	0.813501	−	0.581563i	$-0.197559\pi$
$271$	−1.59515	−	2.76287i	−0.0968982	−	0.167833i	−0.910399	+	0.413731i	$0.864225\pi$
$272$	7.11960			0.431689
$273$		0			0
$274$	−20.1806			−1.21915
$275$	−2.09083	−	3.62143i	−0.126082	−	0.218381i
$276$	−0.782323	−	1.35502i	−0.0470903	−	0.0815629i
$277$	−10.9683	+	18.9977i	−0.659022	+	1.14146i	0.321848	+	0.946791i	$0.395696\pi$
$277$	−10.9683	+	18.9977i	−0.659022	+	1.14146i	−0.980869	+	0.194667i	$0.937637\pi$
$278$	−13.1045			−0.785958
$279$	3.81551	−	6.60866i	0.228429	−	0.395650i
$280$	20.5112	−	35.5264i	1.22578	−	2.12311i
$281$	−11.9903			−0.715282			−0.357641	−	0.933859i	$-0.616419\pi$
$281$	−11.9903			−0.715282			−0.357641	+	0.933859i	$0.616419\pi$
$282$	−7.99127	+	13.8413i	−0.475873	+	0.824237i
$283$	7.18329	+	12.4418i	0.427002	+	0.739590i	0.996605	−	0.0823303i	$-0.0262362\pi$
$283$	7.18329	+	12.4418i	0.427002	+	0.739590i	−0.569603	+	0.821920i	$0.692903\pi$
$284$	−1.96681	−	3.40662i	−0.116709	−	0.202146i
$285$	−7.12498			−0.422047
$286$		0			0
$287$	−5.98792			−0.353456
$288$	−1.23341	−	2.13632i	−0.0726791	−	0.125884i
$289$	5.51089	+	9.54513i	0.324170	+	0.561478i
$290$	3.23341	−	5.60042i	0.189872	−	0.328868i
$291$	−10.0315			−0.588055
$292$	−1.71164	+	2.96464i	−0.100166	+	0.173492i
$293$	9.37920	−	16.2452i	0.547939	−	0.949058i	−0.450477	−	0.892788i	$-0.648746\pi$
$293$	9.37920	−	16.2452i	0.547939	−	0.949058i	0.998416	−	0.0562695i	$-0.0179206\pi$
$294$	20.0248			1.16787
$295$	3.04892	−	5.28088i	0.177515	−	0.307465i
$296$	−6.94385	−	12.0271i	−0.403603	−	0.699061i
$297$	−0.733406	−	1.27030i	−0.0425565	−	0.0737101i
$298$	17.8944			1.03659
$299$		0			0
$300$	−1.26875			−0.0732513
$301$	5.72401	+	9.91428i	0.329927	+	0.571450i
$302$	−1.22587	−	2.12327i	−0.0705411	−	0.122181i
$303$	−6.94385	+	12.0271i	−0.398913	+	0.690938i
$304$	−7.40449			−0.424676
$305$	−10.9683	+	18.9977i	−0.628043	+	1.08780i
$306$	1.52446	−	2.64044i	0.0871475	−	0.150944i
$307$	−25.6262			−1.46257			−0.731283	−	0.682074i	$-0.761078\pi$
$307$	−25.6262			−1.46257			−0.731283	+	0.682074i	$0.761078\pi$
$308$	−1.56734	+	2.71470i	−0.0893072	+	0.154685i
$309$	8.70171	+	15.0718i	0.495023	+	0.857405i
$310$	−13.3312	−	23.0904i	−0.757164	−	1.31145i
$311$	11.3817			0.645394			0.322697	−	0.946502i	$-0.395410\pi$
$311$	11.3817			0.645394			0.322697	+	0.946502i	$0.395410\pi$
$312$		0			0
$313$	27.5743			1.55859			0.779297	−	0.626655i	$-0.215576\pi$
$313$	27.5743			1.55859			0.779297	+	0.626655i	$0.215576\pi$
$314$	−6.67241	−	11.5569i	−0.376546	−	0.652196i
$315$	−6.72737	−	11.6521i	−0.379044	−	0.656524i
$316$	−0.894928	+	1.55006i	−0.0503436	+	0.0871977i
$317$	11.2597			0.632405			0.316203	−	0.948692i	$-0.397592\pi$
$317$	11.2597			0.632405			0.316203	+	0.948692i	$0.397592\pi$
$318$	5.51842	−	9.55818i	0.309458	−	0.535996i
$319$	−1.35743	+	2.35113i	−0.0760014	+	0.131638i
$320$	−24.9366			−1.39400
$321$	−5.27628	+	9.13879i	−0.294493	+	0.510077i
$322$	−10.5260	−	18.2315i	−0.586588	−	1.01600i
$323$	3.10872	+	5.38446i	0.172974	+	0.299599i
$324$	−0.445042			−0.0247245
$325$		0			0
$326$	4.86294			0.269333
$327$	−0.535344	−	0.927243i	−0.0296046	−	0.0512766i
$328$	1.90097	+	3.29257i	0.104963	+	0.181802i
$329$	30.7732	−	53.3008i	1.69658	−	2.93857i
$330$	−5.12498			−0.282121
$331$	−5.95324	+	10.3113i	−0.327220	+	0.566761i	−0.981959	−	0.189094i	$-0.939445\pi$
$331$	−5.95324	+	10.3113i	−0.327220	+	0.566761i	0.654739	+	0.755855i	$0.272778\pi$
$332$	−0.145260	+	0.251598i	−0.00797218	+	0.0138082i
$333$	−4.55496			−0.249610
$334$	−13.1054	+	22.6992i	−0.717094	+	1.24204i
$335$	−5.01842	−	8.69215i	−0.274185	−	0.474903i
$336$	−6.99127	−	12.1092i	−0.381405	−	0.660613i
$337$	17.1672			0.935157			0.467578	−	0.883952i	$-0.345127\pi$
$337$	17.1672			0.935157			0.467578	+	0.883952i	$0.345127\pi$
$338$		0			0
$339$	−16.5308			−0.897830
$340$	1.52446	+	2.64044i	0.0826754	+	0.143198i
$341$	5.59664	+	9.69366i	0.303075	+	0.524941i
$342$	−1.58546	+	2.74609i	−0.0857317	+	0.148492i
$343$	−43.4989			−2.34872
$344$	3.63437	−	6.29492i	0.195952	−	0.339399i
$345$	−4.92543	+	8.53109i	−0.265176	+	0.459298i
$346$	16.5036			0.887242
$347$	12.1380	−	21.0237i	0.651603	−	1.12861i	−0.331131	−	0.943585i	$-0.607430\pi$
$347$	12.1380	−	21.0237i	0.651603	−	1.12861i	0.982734	−	0.185025i	$-0.0592366\pi$
$348$	0.411854	+	0.713352i	0.0220777	+	0.0382397i
$349$	−2.28621	−	3.95983i	−0.122378	−	0.211965i	0.798327	−	0.602224i	$-0.205719\pi$
$349$	−2.28621	−	3.95983i	−0.122378	−	0.211965i	−0.920705	+	0.390259i	$0.872385\pi$
$350$	−17.0707			−0.912467
$351$		0			0
$352$	3.61835			0.192859
$353$	−3.03803	−	5.26203i	−0.161698	−	0.280069i	0.773780	−	0.633455i	$-0.218364\pi$
$353$	−3.03803	−	5.26203i	−0.161698	−	0.280069i	−0.935478	+	0.353385i	$0.885030\pi$
$354$	−1.35690	−	2.35021i	−0.0721182	−	0.124912i
$355$	−12.3828	+	21.4477i	−0.657213	+	1.13833i
$356$	−2.80194			−0.148502
$357$	−5.87047	+	10.1680i	−0.310698	+	0.538145i
$358$	−5.31700	+	9.20932i	−0.281012	+	0.486728i
$359$	14.9661			0.789883			0.394942	−	0.918706i	$-0.370765\pi$
$359$	14.9661			0.789883			0.394942	+	0.918706i	$0.370765\pi$
$360$	−4.27144	+	7.39835i	−0.225125	+	0.389927i
$361$	6.26689	+	10.8546i	0.329836	+	0.571293i
$362$	2.26726	+	3.92701i	0.119164	+	0.206399i
$363$	−8.84846			−0.464424
$364$		0			0
$365$	21.5526			1.12811
$366$	4.88135	+	8.45475i	0.255152	+	0.441937i
$367$	−18.5417	−	32.1151i	−0.967868	−	1.67640i	−0.701704	−	0.712468i	$-0.747577\pi$
$367$	−18.5417	−	32.1151i	−0.967868	−	1.67640i	−0.266164	−	0.963928i	$-0.585756\pi$
$368$	−5.11865	+	8.86575i	−0.266828	+	0.462159i
$369$	1.24698			0.0649152
$370$	−7.95742	+	13.7827i	−0.413687	+	0.716526i
$371$	−21.2506	+	36.8072i	−1.10328	+	1.91093i
$372$	3.39612			0.176081
$373$	18.2545	−	31.6177i	0.945183	−	1.63710i	0.189798	−	0.981823i	$-0.439217\pi$
$373$	18.2545	−	31.6177i	0.945183	−	1.63710i	0.755385	−	0.655282i	$-0.227450\pi$
$374$	2.23609	+	3.87303i	0.115626	+	0.200270i
$375$	−3.01089	−	5.21501i	−0.155481	−	0.269302i
$376$	−39.0780			−2.01529
$377$		0			0
$378$	−5.98792			−0.307985
$379$	−13.2925	−	23.0234i	−0.682792	−	1.18263i	−0.974125	−	0.226009i	$-0.927432\pi$
$379$	−13.2925	−	23.0234i	−0.682792	−	1.18263i	0.291333	−	0.956622i	$-0.405901\pi$
$380$	−1.58546	−	2.74609i	−0.0813323	−	0.140872i
$381$	4.76875	−	8.25972i	0.244310	−	0.423158i
$382$	26.6625			1.36417
$383$	−7.17510	+	12.4276i	−0.366630	+	0.635022i	−0.989036	−	0.147672i	$-0.952822\pi$
$383$	−7.17510	+	12.4276i	−0.366630	+	0.635022i	0.622406	+	0.782694i	$0.286155\pi$
$384$	−3.08211	+	5.33836i	−0.157283	+	0.272422i
$385$	19.7356			1.00582
$386$	5.25451	−	9.10108i	0.267448	−	0.463233i
$387$	−1.19202	−	2.06464i	−0.0605939	−	0.104952i
$388$	−2.23221	−	3.86630i	−0.113323	−	0.196282i
$389$	−22.6582			−1.14881			−0.574407	−	0.818570i	$-0.694767\pi$
$389$	−22.6582			−1.14881			−0.574407	+	0.818570i	$0.694767\pi$
$390$		0			0
$391$	8.59611			0.434724
$392$	24.4807	+	42.4018i	1.23646	+	2.14161i
$393$	2.75451	+	4.77096i	0.138947	+	0.240663i
$394$	16.5078	−	28.5924i	0.831652	−	1.44046i
$395$	11.2687			0.566992
$396$	0.326396	−	0.565335i	0.0164020	−	0.0284092i
$397$	3.95377	−	6.84813i	0.198434	−	0.343698i	−0.749587	−	0.661906i	$-0.769748\pi$
$397$	3.95377	−	6.84813i	0.198434	−	0.343698i	0.948021	+	0.318208i	$0.103081\pi$
$398$	−17.7724			−0.890850
$399$	6.10537	−	10.5748i	0.305651	−	0.529402i
$400$	4.15064	+	7.18911i	0.207532	+	0.359456i
$401$	1.46830	+	2.54318i	0.0733236	+	0.127000i	0.900356	−	0.435154i	$-0.143306\pi$
$401$	1.46830	+	2.54318i	0.0733236	+	0.127000i	−0.827032	+	0.562154i	$0.809973\pi$
$402$	−4.46681			−0.222784
$403$		0			0
$404$	−6.18060			−0.307497
$405$	1.40097	+	2.42655i	0.0696147	+	0.120576i
$406$	5.54138	+	9.59796i	0.275014	+	0.476339i
$407$	3.34063	−	5.78615i	0.165589	−	0.286809i
$408$	7.45473			0.369064
$409$	5.87747	−	10.1801i	0.290622	−	0.503372i	−0.683335	−	0.730105i	$-0.739471\pi$
$409$	5.87747	−	10.1801i	0.290622	−	0.503372i	0.973957	+	0.226733i	$0.0728044\pi$
$410$	2.17845	−	3.77318i	0.107586	−	0.186344i
$411$	−16.1836			−0.798278
$412$	−3.87263	+	6.70758i	−0.190791	+	0.330459i
$413$	5.22521	+	9.05033i	0.257116	+	0.445338i
$414$	2.19202	+	3.79669i	0.107732	+	0.186597i
$415$	1.82908			0.0897862
$416$		0			0
$417$	−10.5090			−0.514629
$418$	−2.32557	−	4.02800i	−0.113747	−	0.197016i
$419$	−3.67092	−	6.35821i	−0.179336	−	0.310619i	0.762317	−	0.647203i	$-0.224062\pi$
$419$	−3.67092	−	6.35821i	−0.179336	−	0.310619i	−0.941653	+	0.336584i	$0.890728\pi$
$420$	2.99396	−	5.18569i	0.146090	−	0.253036i
$421$	−25.6963			−1.25236			−0.626181	−	0.779677i	$-0.715383\pi$
$421$	−25.6963			−1.25236			−0.626181	+	0.779677i	$0.715383\pi$
$422$	−1.15399	+	1.99877i	−0.0561753	+	0.0972985i
$423$	−6.40850	+	11.0999i	−0.311592	+	0.539693i
$424$	26.9855			1.31053
$425$	3.48523	−	6.03660i	0.169058	−	0.292818i
$426$	5.51089	+	9.54513i	0.267003	+	0.462463i
$427$	−18.7974	−	32.5580i	−0.909669	−	1.57559i
$428$	−4.69633			−0.227006
$429$		0			0
$430$	−8.32975			−0.401696
$431$	4.47099	+	7.74399i	0.215360	+	0.373015i	0.953384	−	0.301760i	$-0.0975741\pi$
$431$	4.47099	+	7.74399i	0.215360	+	0.373015i	−0.738024	+	0.674775i	$0.764241\pi$
$432$	1.45593	+	2.52174i	0.0700483	+	0.121327i
$433$	−1.45742	+	2.52432i	−0.0700391	+	0.121311i	−0.898918	−	0.438116i	$-0.855646\pi$
$433$	−1.45742	+	2.52432i	−0.0700391	+	0.121311i	0.828879	+	0.559428i	$0.188979\pi$
$434$	45.6939			2.19338
$435$	2.59299	−	4.49119i	0.124324	−	0.215336i
$436$	0.238250	−	0.412662i	0.0114101	−	0.0197629i
$437$	−8.94007			−0.427661
$438$	4.79590	−	8.30674i	0.229157	−	0.396911i
$439$	−4.52930	−	7.84498i	−0.216172	−	0.374421i	0.737463	−	0.675388i	$-0.236024\pi$
$439$	−4.52930	−	7.84498i	−0.216172	−	0.374421i	−0.953634	+	0.300967i	$0.902690\pi$
$440$	−6.26540	−	10.8520i	−0.298691	−	0.517348i
$441$	16.0586			0.764696
$442$		0			0
$443$	11.2325			0.533672			0.266836	−	0.963742i	$-0.414022\pi$
$443$	11.2325			0.533672			0.266836	+	0.963742i	$0.414022\pi$
$444$	−1.01357	−	1.75556i	−0.0481021	−	0.0833152i
$445$	8.82036	+	15.2773i	0.418125	+	0.724214i
$446$	−11.6283	+	20.1409i	−0.550618	+	0.953698i
$447$	14.3502			0.678741
$448$	21.3681	−	37.0106i	1.00955	−	1.74859i
$449$	14.3790	−	24.9051i	0.678585	−	1.17534i	−0.296822	−	0.954933i	$-0.595927\pi$
$449$	14.3790	−	24.9051i	0.678585	−	1.17534i	0.975407	−	0.220411i	$-0.0707399\pi$
$450$	3.55496			0.167582
$451$	−0.914542	+	1.58403i	−0.0430641	+	0.0745892i
$452$	−3.67845	−	6.37126i	−0.173020	−	0.299679i
$453$	−0.983074	−	1.70273i	−0.0461888	−	0.0800014i
$454$	12.1672			0.571035
$455$		0			0
$456$	−7.75302			−0.363068
$457$	−9.53803	−	16.5204i	−0.446170	−	0.772790i	0.551963	−	0.833869i	$-0.313879\pi$
$457$	−9.53803	−	16.5204i	−0.446170	−	0.772790i	−0.998133	+	0.0610792i	$0.980546\pi$
$458$	1.78501	+	3.09173i	0.0834081	+	0.144467i
$459$	1.22252	−	2.11747i	0.0570624	−	0.0988350i
$460$	−4.38404			−0.204407
$461$	15.8666	−	27.4817i	0.738981	−	1.27995i	−0.213974	−	0.976839i	$-0.568641\pi$
$461$	15.8666	−	27.4817i	0.738981	−	1.27995i	0.952955	−	0.303113i	$-0.0980258\pi$
$462$	4.39158	−	7.60643i	0.204315	−	0.353883i
$463$	36.4784			1.69530			0.847648	−	0.530559i	$-0.178018\pi$
$463$	36.4784			1.69530			0.847648	+	0.530559i	$0.178018\pi$
$464$	2.69471	−	4.66737i	0.125099	−	0.216677i
$465$	−10.6908	−	18.5171i	−0.495775	−	0.858708i
$466$	3.60723	+	6.24790i	0.167102	+	0.289428i
$467$	13.0000			0.601568			0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000			0.601568			0.300784	+	0.953692i	$0.402752\pi$
$468$		0			0
$469$	17.2010			0.794271
$470$	22.3910	+	38.7824i	1.03282	+	1.78890i
$471$	−5.35086	−	9.26795i	−0.246554	−	0.427045i
$472$	3.31767	−	5.74637i	0.152708	−	0.264498i
$473$	3.49694			0.160790
$474$	2.50753	−	4.34317i	0.115175	−	0.199489i
$475$	−3.62469	+	6.27814i	−0.166312	+	0.288061i
$476$	−5.22521			−0.239497
$477$	4.42543	−	7.66507i	0.202626	−	0.350959i
$478$	−4.42208	−	7.65926i	−0.202261	−	0.350326i
$479$	2.80827	+	4.86407i	0.128313	+	0.222245i	0.923023	−	0.384744i	$-0.125710\pi$
$479$	2.80827	+	4.86407i	0.128313	+	0.222245i	−0.794710	+	0.606989i	$0.792377\pi$
$480$	−6.91185			−0.315482
$481$		0			0
$482$	4.86294			0.221501
$483$	−8.44116	−	14.6205i	−0.384086	−	0.665256i
$484$	−1.96897	−	3.41035i	−0.0894985	−	0.155016i
$485$	−14.0538	+	24.3418i	−0.638148	+	1.10531i
$486$	1.24698			0.0565641
$487$	−4.87867	+	8.45010i	−0.221073	+	0.382910i	−0.955134	−	0.296173i	$-0.904289\pi$
$487$	−4.87867	+	8.45010i	−0.221073	+	0.382910i	0.734061	+	0.679084i	$0.237623\pi$
$488$	−11.9351	+	20.6722i	−0.540277	+	0.935788i
$489$	3.89977			0.176354
$490$	28.0541	−	48.5911i	1.26735	−	2.19512i
$491$	3.69418	+	6.39850i	0.166716	+	0.288760i	0.937263	−	0.348622i	$-0.113350\pi$
$491$	3.69418	+	6.39850i	0.166716	+	0.288760i	−0.770547	+	0.637383i	$0.780017\pi$
$492$	0.277479	+	0.480608i	0.0125097	+	0.0216675i
$493$	−4.52542			−0.203815
$494$		0			0
$495$	−4.10992			−0.184727
$496$	−11.1102	−	19.2435i	−0.498863	−	0.864056i
$497$	−21.2216	−	36.7569i	−0.951920	−	1.64877i
$498$	0.407010	−	0.704961i	0.0182385	−	0.0315901i
$499$	43.2814			1.93754			0.968771	−	0.247956i	$-0.0797589\pi$
$499$	43.2814			1.93754			0.968771	+	0.247956i	$0.0797589\pi$
$500$	1.33997	−	2.32090i	0.0599253	−	0.103794i
$501$	−10.5097	+	18.2033i	−0.469538	+	0.813264i
$502$	−3.04892			−0.136080
$503$	−5.38351	+	9.32451i	−0.240039	+	0.415760i	−0.960725	−	0.277502i	$-0.910494\pi$
$503$	−5.38351	+	9.32451i	−0.240039	+	0.415760i	0.720686	+	0.693261i	$0.243827\pi$
$504$	−7.32036	−	12.6792i	−0.326075	−	0.564778i
$505$	19.4562	+	33.6992i	0.865791	+	1.49959i
$506$	−6.43057			−0.285874
$507$		0			0
$508$	4.24459			0.188323
$509$	−20.7724	−	35.9788i	−0.920720	−	1.59473i	−0.798303	−	0.602256i	$-0.794269\pi$
$509$	−20.7724	−	35.9788i	−0.920720	−	1.59473i	−0.122417	−	0.992479i	$-0.539065\pi$
$510$	−4.27144	−	7.39835i	−0.189142	−	0.327604i
$511$	−18.4683	+	31.9880i	−0.816990	+	1.41507i
$512$	−24.9390			−1.10216
$513$	−1.27144	+	2.20220i	−0.0561354	+	0.0972293i
$514$	8.81013	−	15.2596i	0.388598	−	0.673072i
$515$	48.7633			2.14877
$516$	0.530499	−	0.918852i	0.0233539	−	0.0404502i
$517$	−9.40007	−	16.2814i	−0.413415	−	0.716055i
$518$	−13.6374	−	23.6206i	−0.599191	−	1.03783i
$519$	13.2349			0.580948
$520$		0			0
$521$	25.7198			1.12680			0.563402	−	0.826183i	$-0.309492\pi$
$521$	25.7198			1.12680			0.563402	+	0.826183i	$0.309492\pi$
$522$	−1.15399	−	1.99877i	−0.0505087	−	0.0874837i
$523$	−4.29643	−	7.44163i	−0.187870	−	0.325400i	0.756670	−	0.653797i	$-0.226825\pi$
$523$	−4.29643	−	7.44163i	−0.187870	−	0.325400i	−0.944540	+	0.328397i	$0.893492\pi$
$524$	−1.22587	+	2.12327i	−0.0535525	+	0.0927557i
$525$	−13.6896			−0.597464
$526$	14.7913	−	25.6194i	0.644933	−	1.11706i
$527$	−9.32908	+	16.1584i	−0.406381	+	0.703873i
$528$	−4.27114			−0.185878
$529$	5.31982	−	9.21420i	0.231297	−	0.400618i
$530$	−15.4623	−	26.7814i	−0.671638	−	1.16331i
$531$	−1.08815	−	1.88472i	−0.0472215	−	0.0817901i
$532$	5.43429			0.235606
$533$		0			0
$534$	7.85086			0.339740
$535$	14.7838	+	25.6063i	0.639160	+	1.10706i
$536$	−5.46077	−	9.45833i	−0.235869	−	0.408538i
$537$	−4.26391	+	7.38530i	−0.184001	+	0.318699i
$538$	−7.37734			−0.318060
$539$	−11.7775	+	20.3992i	−0.507292	+	0.878655i
$540$	−0.623490	+	1.07992i	−0.0268307	+	0.0464722i
$541$	−31.3534			−1.34799			−0.673995	−	0.738736i	$-0.735423\pi$
$541$	−31.3534			−1.34799			−0.673995	+	0.738736i	$0.735423\pi$
$542$	−1.98911	+	3.44525i	−0.0854398	+	0.147986i
$543$	1.81820	+	3.14921i	0.0780264	+	0.135146i
$544$	3.01573	+	5.22340i	0.129298	+	0.223951i
$545$	−3.00000			−0.128506
$546$		0			0
$547$	19.9342			0.852325			0.426163	−	0.904647i	$-0.359865\pi$
$547$	19.9342			0.852325			0.426163	+	0.904647i	$0.359865\pi$
$548$	−3.60119	−	6.23744i	−0.153835	−	0.266450i
$549$	3.91454	+	6.78019i	0.167069	+	0.289371i
$550$	−2.60723	+	4.51585i	−0.111173	+	0.192557i
$551$	4.70650			0.200503
$552$	−5.35958	+	9.28307i	−0.228119	+	0.395114i
$553$	−9.65615	+	16.7249i	−0.410621	+	0.711217i
$554$	27.3545			1.16218
$555$	−6.38135	+	11.0528i	−0.270873	+	0.469167i
$556$	−2.33848	−	4.05036i	−0.0991736	−	0.171774i
$557$	16.6174	+	28.7823i	0.704104	+	1.21954i	0.967014	+	0.254723i	$0.0819844\pi$
$557$	16.6174	+	28.7823i	0.704104	+	1.21954i	−0.262910	+	0.964820i	$0.584682\pi$
$558$	−9.51573			−0.402833
$559$		0			0
$560$	−39.1782			−1.65558
$561$	1.79321	+	3.10593i	0.0757093	+	0.131132i
$562$	7.47584	+	12.9485i	0.315349	+	0.546201i
$563$	−1.93565	+	3.35264i	−0.0815779	+	0.141297i	−0.903928	−	0.427685i	$-0.859329\pi$
$563$	−1.93565	+	3.35264i	−0.0815779	+	0.141297i	0.822350	+	0.568982i	$0.192663\pi$
$564$	−5.70410			−0.240186
$565$	−23.1591	+	40.1128i	−0.974312	+	1.68756i
$566$	8.95742	−	15.5147i	0.376508	−	0.652132i
$567$	−4.80194			−0.201662
$568$	−13.4743	+	23.3382i	−0.565371	+	0.979251i
$569$	−10.0728	−	17.4467i	−0.422276	−	0.731403i	0.573886	−	0.818935i	$-0.305435\pi$
$569$	−10.0728	−	17.4467i	−0.422276	−	0.731403i	−0.996162	+	0.0875324i	$0.972102\pi$
$570$	4.44235	+	7.69438i	0.186070	+	0.322282i
$571$	−32.1269			−1.34447			−0.672234	−	0.740338i	$-0.734665\pi$
$571$	−32.1269			−1.34447			−0.672234	+	0.740338i	$0.734665\pi$
$572$		0			0
$573$	21.3817			0.893231
$574$	3.73341	+	6.46645i	0.155829	+	0.269904i
$575$	5.01142	+	8.68003i	0.208991	+	0.361982i
$576$	−4.44989	+	7.70743i	−0.185412	+	0.321143i
$577$	16.7506			0.697338			0.348669	−	0.937246i	$-0.386634\pi$
$577$	16.7506			0.697338			0.348669	+	0.937246i	$0.386634\pi$
$578$	6.87196	−	11.9026i	0.285836	−	0.495082i
$579$	4.21379	−	7.29850i	0.175119	−	0.303315i
$580$	2.30798			0.0958336
$581$	−1.56734	+	2.71470i	−0.0650240	+	0.112625i
$582$	6.25451	+	10.8331i	0.259258	+	0.449048i
$583$	6.49127	+	11.2432i	0.268841	+	0.465646i
$584$	23.4523			0.970465
$585$		0			0
$586$	−23.3913			−0.966287
$587$	−3.36898	−	5.83524i	−0.139053	−	0.240846i	0.788086	−	0.615566i	$-0.211072\pi$
$587$	−3.36898	−	5.83524i	−0.139053	−	0.240846i	−0.927138	+	0.374719i	$0.877739\pi$
$588$	3.57338	+	6.18927i	0.147364	+	0.255241i
$589$	9.70237	−	16.8050i	0.399779	−	0.692438i
$590$	−7.60388			−0.313047
$591$	13.2383	−	22.9293i	0.544549	−	0.943186i
$592$	−6.63169	+	11.4864i	−0.272561	+	0.472089i
$593$	−18.1172			−0.743985			−0.371992	−	0.928236i	$-0.621325\pi$
$593$	−18.1172			−0.743985			−0.371992	+	0.928236i	$0.621325\pi$
$594$	−0.914542	+	1.58403i	−0.0375241	+	0.0649937i
$595$	16.4487	+	28.4900i	0.674331	+	1.16797i
$596$	3.19322	+	5.53082i	0.130799	+	0.226551i
$597$	−14.2524			−0.583310
$598$		0			0
$599$	−26.7851			−1.09441			−0.547204	−	0.836999i	$-0.684308\pi$
$599$	−26.7851			−1.09441			−0.547204	+	0.836999i	$0.684308\pi$
$600$	4.34601	+	7.52751i	0.177425	+	0.307309i
$601$	2.35086	+	4.07180i	0.0958934	+	0.166092i	0.909981	−	0.414650i	$-0.136096\pi$
$601$	2.35086	+	4.07180i	0.0958934	+	0.166092i	−0.814088	+	0.580742i	$0.802763\pi$
$602$	7.13773	−	12.3629i	0.290912	−	0.503874i
$603$	−3.58211			−0.145875
$604$	0.437509	−	0.757788i	0.0178020	−	0.0308340i
$605$	−12.3964	+	21.4712i	−0.503986	+	0.872930i
$606$	17.3177			0.703482
$607$	−13.8198	+	23.9366i	−0.560929	+	0.971558i	0.436486	+	0.899711i	$0.356223\pi$
$607$	−13.8198	+	23.9366i	−0.560929	+	0.971558i	−0.997416	+	0.0718472i	$0.977111\pi$
$608$	−3.13640	−	5.43240i	−0.127198	−	0.220313i
$609$	4.44385	+	7.69697i	0.180074	+	0.311897i
$610$	27.3545			1.10755
$611$		0			0
$612$	1.08815			0.0439857
$613$	24.0891	+	41.7236i	0.972950	+	1.68520i	0.686541	+	0.727091i	$0.259128\pi$
$613$	24.0891	+	41.7236i	0.972950	+	1.68520i	0.286409	+	0.958108i	$0.407539\pi$
$614$	15.9777	+	27.6742i	0.644807	+	1.11684i
$615$	1.74698	−	3.02586i	0.0704450	−	0.122014i
$616$	21.4752			0.865259
$617$	15.1521	−	26.2443i	0.610002	−	1.05655i	−0.381238	−	0.924477i	$-0.624502\pi$
$617$	15.1521	−	26.2443i	0.610002	−	1.05655i	0.991239	−	0.132077i	$-0.0421646\pi$
$618$	10.8509	−	18.7942i	0.436485	−	0.756015i
$619$	10.9041			0.438272			0.219136	−	0.975694i	$-0.429676\pi$
$619$	10.9041			0.438272			0.219136	+	0.975694i	$0.429676\pi$
$620$	4.75786	−	8.24086i	0.191080	−	0.330961i
$621$	1.75786	+	3.04471i	0.0705407	+	0.122180i
$622$	−7.09634	−	12.2912i	−0.284537	−	0.492833i
$623$	−30.2325			−1.21124
$624$		0			0
$625$	−31.1269			−1.24508
$626$	−17.1923	−	29.7780i	−0.687143	−	1.19017i
$627$	−1.86496	−	3.23021i	−0.0744794	−	0.129002i
$628$	2.38135	−	4.12463i	0.0950264	−	0.164591i
$629$	11.1371			0.444064
$630$	−8.38889	+	14.5300i	−0.334221	+	0.578888i
$631$	−5.22617	+	9.05199i	−0.208050	+	0.360354i	−0.951100	−	0.308882i	$-0.900045\pi$
$631$	−5.22617	+	9.05199i	−0.208050	+	0.360354i	0.743050	+	0.669236i	$0.233379\pi$
$632$	12.2620			0.487758
$633$	−0.925428	+	1.60289i	−0.0367824	+	0.0637091i
$634$	−7.02028	−	12.1595i	−0.278811	−	0.482915i
$635$	−13.3617	−	23.1432i	−0.530244	−	0.918410i
$636$	3.93900			0.156192
$637$		0			0
$638$	3.38537			0.134028
$639$	4.41939	+	7.65460i	0.174828	+	0.302811i
$640$	8.63587	+	14.9578i	0.341363	+	0.591257i
$641$	8.79709	−	15.2370i	0.347464	−	0.601826i	−0.638334	−	0.769760i	$-0.720376\pi$
$641$	8.79709	−	15.2370i	0.347464	−	0.601826i	0.985798	+	0.167934i	$0.0537095\pi$
$642$	13.1588			0.519338
$643$	11.3029	−	19.5772i	0.445743	−	0.772049i	−0.552361	−	0.833605i	$-0.686273\pi$
$643$	11.3029	−	19.5772i	0.445743	−	0.772049i	0.998104	+	0.0615560i	$0.0196063\pi$
$644$	3.75667	−	6.50674i	0.148033	−	0.256401i
$645$	−6.67994			−0.263022
$646$	3.87651	−	6.71431i	0.152519	−	0.264171i
$647$	12.3959	+	21.4703i	0.487333	+	0.844085i	0.999894	−	0.0145658i	$-0.00463659\pi$
$647$	12.3959	+	21.4703i	0.487333	+	0.844085i	−0.512561	+	0.858651i	$0.671303\pi$
$648$	1.52446	+	2.64044i	0.0598864	+	0.103726i
$649$	3.19221			0.125305
$650$		0			0
$651$	36.6437			1.43618
$652$	0.867781	+	1.50304i	0.0339849	+	0.0588636i
$653$	10.9053	+	18.8885i	0.426757	+	0.739164i	0.996583	−	0.0826012i	$-0.0263228\pi$
$653$	10.9053	+	18.8885i	0.426757	+	0.739164i	−0.569826	+	0.821765i	$0.692989\pi$
$654$	−0.667563	+	1.15625i	−0.0261038	+	0.0452131i
$655$	15.4359			0.603132
$656$	1.81551	−	3.14456i	0.0708838	−	0.122774i
$657$	3.84601	−	6.66149i	0.150047	−	0.259889i
$658$	−76.7472			−2.99192
$659$	−8.27628	+	14.3349i	−0.322398	+	0.558410i	−0.980982	−	0.194097i	$-0.937822\pi$
$659$	−8.27628	+	14.3349i	−0.322398	+	0.558410i	0.658584	+	0.752507i	$0.271156\pi$
$660$	−0.914542	−	1.58403i	−0.0355985	−	0.0616584i
$661$	−7.97703	−	13.8166i	−0.310271	−	0.537405i	0.668150	−	0.744026i	$-0.267086\pi$
$661$	−7.97703	−	13.8166i	−0.310271	−	0.537405i	−0.978421	+	0.206622i	$0.933753\pi$
$662$	14.8471			0.577050
$663$		0			0
$664$	1.99031			0.0772391
$665$	−17.1069	−	29.6299i	−0.663376	−	1.14900i
$666$	2.83997	+	4.91897i	0.110047	+	0.190606i
$667$	3.25355	−	5.63532i	0.125978	−	0.218200i
$668$	−9.35450			−0.361937
$669$	−9.32520	+	16.1517i	−0.360533	+	0.624462i
$670$	−6.25786	+	10.8389i	−0.241762	+	0.418745i
$671$	−11.4838			−0.443327
$672$	5.92274	−	10.2585i	0.228475	−	0.395730i
$673$	3.69418	+	6.39850i	0.142400	+	0.246644i	0.928400	−	0.371583i	$-0.121185\pi$
$673$	3.69418	+	6.39850i	0.142400	+	0.246644i	−0.786000	+	0.618227i	$0.787851\pi$
$674$	−10.7036	−	18.5391i	−0.412286	−	0.714101i
$675$	2.85086			0.109729
$676$		0			0
$677$	−22.1454			−0.851118			−0.425559	−	0.904931i	$-0.639922\pi$
$677$	−22.1454			−0.851118			−0.425559	+	0.904931i	$0.639922\pi$
$678$	10.3068	+	17.8519i	0.395830	+	0.685597i
$679$	−24.0852	−	41.7168i	−0.924306	−	1.60094i
$680$	10.4438	−	18.0893i	0.400503	−	0.693692i
$681$	9.75733			0.373902
$682$	6.97889	−	12.0878i	0.267236	−	0.462866i
$683$	4.55011	−	7.88103i	0.174105	−	0.301559i	−0.765746	−	0.643143i	$-0.777630\pi$
$683$	4.55011	−	7.88103i	0.174105	−	0.301559i	0.939851	+	0.341584i	$0.110963\pi$
$684$	−1.13169			−0.0432711
$685$	−22.6727	+	39.2703i	−0.866279	+	1.50044i
$686$	27.1211	+	46.9751i	1.03549	+	1.79352i
$687$	1.43147	+	2.47938i	0.0546139	+	0.0945941i
$688$	−6.94198			−0.264661
$689$		0			0
$690$	12.2838			0.467637
$691$	6.88553	+	11.9261i	0.261938	+	0.453690i	0.966757	−	0.255697i	$-0.0823050\pi$
$691$	6.88553	+	11.9261i	0.261938	+	0.453690i	−0.704819	+	0.709387i	$0.748972\pi$
$692$	2.94504	+	5.10096i	0.111954	+	0.193909i
$693$	3.52177	−	6.09989i	0.133781	−	0.231715i
$694$	−30.2717			−1.14910
$695$	−14.7228	+	25.5007i	−0.558468	+	0.967295i
$696$	2.82155	−	4.88707i	0.106951	−	0.185244i
$697$	−3.04892			−0.115486
$698$	−2.85086	+	4.93783i	−0.107906	+	0.186899i
$699$	2.89277	+	5.01043i	0.109415	+	0.189512i
$700$	−3.04623	−	5.27622i	−0.115137	−	0.199422i
$701$	46.5090			1.75662			0.878311	−	0.478090i	$-0.158671\pi$
$701$	46.5090			1.75662			0.878311	+	0.478090i	$0.158671\pi$
$702$		0			0
$703$	−11.5827			−0.436850
$704$	−6.52715	−	11.3054i	−0.246001	−	0.426086i
$705$	17.9562	+	31.1011i	0.676270	+	1.17133i
$706$	−3.78836	+	6.56164i	−0.142577	+	0.246951i
$707$	−66.6878			−2.50805
$708$	0.484271	−	0.838781i	0.0182000	−	0.0315233i
$709$	3.62283	−	6.27492i	0.136058	−	0.235660i	−0.789943	−	0.613180i	$-0.789890\pi$
$709$	3.62283	−	6.27492i	0.136058	−	0.235660i	0.926001	+	0.377521i	$0.123223\pi$
$710$	30.8823			1.15899
$711$	2.01089	−	3.48296i	0.0754141	−	0.130621i
$712$	9.59783	+	16.6239i	0.359694	+	0.623008i
$713$	−13.4143	−	23.2343i	−0.502370	−	0.870130i
$714$	14.6407			0.547915
$715$		0			0
$716$	−3.79523			−0.141835
$717$	−3.54623	−	6.14225i	−0.132436	−	0.229386i
$718$	−9.33124	−	16.1622i	−0.348239	−	0.603167i
$719$	−12.7573	+	22.0963i	−0.475768	+	0.824055i	−0.999615	−	0.0277580i	$-0.991163\pi$
$719$	−12.7573	+	22.0963i	−0.475768	+	0.824055i	0.523846	+	0.851813i	$0.324497\pi$
$720$	8.15883			0.304062
$721$	−41.7851	+	72.3739i	−1.55616	+	2.69534i
$722$	7.81468	−	13.5354i	0.290832	−	0.503736i
$723$	3.89977			0.145034
$724$	−0.809175	+	1.40153i	−0.0300728	+	0.0520875i
$725$	−2.63826	−	4.56960i	−0.0979825	−	0.169711i
$726$	5.51693	+	9.55560i	0.204752	+	0.354641i
$727$	−14.4873			−0.537303			−0.268651	−	0.963238i	$-0.586578\pi$
$727$	−14.4873			−0.537303			−0.268651	+	0.963238i	$0.586578\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−13.4378	−	23.2750i	−0.497355	−	0.861445i
$731$	2.91454	+	5.04814i	0.107798	+	0.186712i
$732$	−1.74214	+	3.01747i	−0.0643912	+	0.111529i
$733$	−37.5036			−1.38523			−0.692614	−	0.721308i	$-0.743541\pi$
$733$	−37.5036			−1.38523			−0.692614	+	0.721308i	$0.743541\pi$
$734$	−23.1211	+	40.0469i	−0.853415	+	1.47816i
$735$	22.4976	−	38.9670i	0.829837	−	1.43732i
$736$	−8.67264			−0.319678
$737$	2.62714	−	4.55034i	0.0967719	−	0.167614i
$738$	−0.777479	−	1.34663i	−0.0286194	−	0.0495703i
$739$	21.5938	+	37.4016i	0.794341	+	1.37584i	0.923257	+	0.384184i	$0.125517\pi$
$739$	21.5938	+	37.4016i	0.794341	+	1.37584i	−0.128915	+	0.991656i	$0.541149\pi$
$740$	−5.67994			−0.208799
$741$		0			0
$742$	52.9982			1.94563
$743$	6.73825	+	11.6710i	0.247202	+	0.428167i	0.962749	−	0.270398i	$-0.0871554\pi$
$743$	6.73825	+	11.6710i	0.247202	+	0.428167i	−0.715546	+	0.698566i	$0.753822\pi$
$744$	−11.6332	−	20.1493i	−0.426493	−	0.738708i
$745$	20.1042	−	34.8214i	0.736560	−	1.27576i
$746$	−45.5260			−1.66683
$747$	0.326396	−	0.565335i	0.0119422	−	0.0206845i
$748$	−0.798053	+	1.38227i	−0.0291797	+	0.0505407i
$749$	−50.6728			−1.85154
$750$	−3.75451	+	6.50301i	−0.137095	+	0.237456i
$751$	−17.7947	−	30.8213i	−0.649338	−	1.12469i	−0.983281	−	0.182093i	$-0.941713\pi$
$751$	−17.7947	−	30.8213i	−0.649338	−	1.12469i	0.333943	−	0.942593i	$-0.391621\pi$
$752$	18.6606	+	32.3211i	0.680483	+	1.17863i
$753$	−2.44504			−0.0891023
$754$		0			0
$755$	−5.50902			−0.200494
$756$	−1.06853	−	1.85075i	−0.0388621	−	0.0673112i
$757$	6.10537	+	10.5748i	0.221903	+	0.384348i	0.955386	−	0.295360i	$-0.0954397\pi$
$757$	6.10537	+	10.5748i	0.221903	+	0.384348i	−0.733483	+	0.679708i	$0.762106\pi$
$758$	−16.5755	+	28.7097i	−0.602050	+	1.04278i
$759$	−5.15691			−0.187184
$760$	−10.8617	+	18.8131i	−0.393997	+	0.682422i
$761$	15.4535	−	26.7663i	0.560190	−	0.970278i	−0.437289	−	0.899321i	$-0.644061\pi$
$761$	15.4535	−	26.7663i	0.560190	−	0.970278i	0.997479	−	0.0709569i	$-0.0226053\pi$
$762$	−11.8931			−0.430840
$763$	2.57069	−	4.45256i	0.0930651	−	0.161194i
$764$	4.75786	+	8.24086i	0.172134	+	0.298144i
$765$	−3.42543	−	5.93301i	−0.123847	−	0.214509i
$766$	17.8944			0.646551
$767$		0			0
$768$	−10.1129			−0.364918
$769$	5.99462	+	10.3830i	0.216172	+	0.374420i	0.953634	−	0.300968i	$-0.0973096\pi$
$769$	5.99462	+	10.3830i	0.216172	+	0.374420i	−0.737463	+	0.675388i	$0.763976\pi$
$770$	−12.3049	−	21.3127i	−0.443439	−	0.768058i
$771$	7.06518	−	12.2372i	0.254446	−	0.440714i
$772$	3.75063			0.134988
$773$	21.9831	−	38.0758i	0.790676	−	1.36949i	−0.134873	−	0.990863i	$-0.543062\pi$
$773$	21.9831	−	38.0758i	0.790676	−	1.36949i	0.925549	−	0.378628i	$-0.123604\pi$
$774$	−1.48643	+	2.57457i	−0.0534285	+	0.0925409i
$775$	−21.7549			−0.781460
$776$	−15.2925	+	26.4875i	−0.548970	+	0.950845i
$777$	−10.9363	−	18.9422i	−0.392338	−	0.679549i
$778$	14.1271	+

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.623490 - 1.07992i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.222521 - 0.385418i) q^{4} -2.80194 q^{5} +(-0.623490 + 1.07992i) q^{6} +(2.40097 - 4.15860i) q^{7} -3.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.623490 - 1.07992i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.222521 - 0.385418i) q^{4} -2.80194 q^{5} +(-0.623490 + 1.07992i) q^{6} +(2.40097 - 4.15860i) q^{7} -3.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.74698 + 3.02586i) q^{10} +(-0.733406 - 1.27030i) q^{11} -0.445042 q^{12} -5.98792 q^{14} +(1.40097 + 2.42655i) q^{15} +(1.45593 + 2.52174i) q^{16} +(1.22252 - 2.11747i) q^{17} +1.24698 q^{18} +(-1.27144 + 2.20220i) q^{19} +(-0.623490 + 1.07992i) q^{20} -4.80194 q^{21} +(-0.914542 + 1.58403i) q^{22} +(1.75786 + 3.04471i) q^{23} +(1.52446 + 2.64044i) q^{24} +2.85086 q^{25} +1.00000 q^{27} +(-1.06853 - 1.85075i) q^{28} +(-0.925428 - 1.60289i) q^{29} +(1.74698 - 3.02586i) q^{30} -7.63102 q^{31} +(-1.23341 + 2.13632i) q^{32} +(-0.733406 + 1.27030i) q^{33} -3.04892 q^{34} +(-6.72737 + 11.6521i) q^{35} +(0.222521 + 0.385418i) q^{36} +(2.27748 + 3.94471i) q^{37} +3.17092 q^{38} +8.54288 q^{40} +(-0.623490 - 1.07992i) q^{41} +(2.99396 + 5.18569i) q^{42} +(-1.19202 + 2.06464i) q^{43} -0.652793 q^{44} +(1.40097 - 2.42655i) q^{45} +(2.19202 - 3.79669i) q^{46} +12.8170 q^{47} +(1.45593 - 2.52174i) q^{48} +(-8.02930 - 13.9072i) q^{49} +(-1.77748 - 3.07868i) q^{50} -2.44504 q^{51} -8.85086 q^{53} +(-0.623490 - 1.07992i) q^{54} +(2.05496 + 3.55929i) q^{55} +(-7.32036 + 12.6792i) q^{56} +2.54288 q^{57} +(-1.15399 + 1.99877i) q^{58} +(-1.08815 + 1.88472i) q^{59} +1.24698 q^{60} +(3.91454 - 6.78019i) q^{61} +(4.75786 + 8.24086i) q^{62} +(2.40097 + 4.15860i) q^{63} +8.89977 q^{64} +1.82908 q^{66} +(1.79105 + 3.10219i) q^{67} +(-0.544073 - 0.942362i) q^{68} +(1.75786 - 3.04471i) q^{69} +16.7778 q^{70} +(4.41939 - 7.65460i) q^{71} +(1.52446 - 2.64044i) q^{72} -7.69202 q^{73} +(2.83997 - 4.91897i) q^{74} +(-1.42543 - 2.46891i) q^{75} +(0.565843 + 0.980069i) q^{76} -7.04354 q^{77} -4.02177 q^{79} +(-4.07942 - 7.06576i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.777479 + 1.34663i) q^{82} -0.652793 q^{83} +(-1.06853 + 1.85075i) q^{84} +(-3.42543 + 5.93301i) q^{85} +2.97285 q^{86} +(-0.925428 + 1.60289i) q^{87} +(2.23609 + 3.87303i) q^{88} +(-3.14795 - 5.45241i) q^{89} -3.49396 q^{90} +1.56465 q^{92} +(3.81551 + 6.60866i) q^{93} +(-7.99127 - 13.8413i) q^{94} +(3.56249 - 6.17042i) q^{95} +2.46681 q^{96} +(5.01573 - 8.68750i) q^{97} +(-10.0124 + 17.3419i) q^{98} +1.46681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9	\( 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9} + q^{10} - q^{11} - 2 q^{12} + 2 q^{14} + 4 q^{15} + 5 q^{16} + 7 q^{17} - 2 q^{18} + 11 q^{19} + q^{20} - 20 q^{21} + 5 q^{22} - 2 q^{23} - 10 q^{25} + 6 q^{27} - q^{28} + 8 q^{29} + q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 18 q^{35} + q^{36} + 14 q^{37} + 40 q^{38} + 14 q^{40} + q^{41} - q^{42} + 3 q^{43} + 32 q^{44} + 4 q^{45} + 3 q^{46} + 18 q^{47} + 5 q^{48} - 17 q^{49} - 11 q^{50} - 14 q^{51} - 26 q^{53} + q^{54} + 13 q^{55} - 7 q^{56} - 22 q^{57} - 12 q^{58} - 14 q^{59} - 2 q^{60} + 13 q^{61} + 16 q^{62} + 10 q^{63} + 8 q^{64} - 10 q^{66} + 5 q^{67} - 7 q^{68} - 2 q^{69} + 16 q^{70} - 6 q^{71} - 36 q^{73} - 7 q^{74} + 5 q^{75} + q^{76} - 30 q^{77} - 18 q^{79} - 16 q^{80} - 3 q^{81} - 5 q^{82} + 32 q^{83} - q^{84} - 7 q^{85} + 30 q^{86} + 8 q^{87} + 7 q^{88} - 5 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} - 32 q^{94} - 3 q^{95} + 8 q^{96} + 5 q^{97} - 13 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9 + q^10 - q^11 - 2 * q^12 + 2 * q^14 + 4 * q^15 + 5 * q^16 + 7 * q^17 - 2 * q^18 + 11 * q^19 + q^20 - 20 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^25 + 6 * q^27 - q^28 + 8 * q^29 + q^30 - 16 * q^31 - 4 * q^32 - q^33 - 18 * q^35 + q^36 + 14 * q^37 + 40 * q^38 + 14 * q^40 + q^41 - q^42 + 3 * q^43 + 32 * q^44 + 4 * q^45 + 3 * q^46 + 18 * q^47 + 5 * q^48 - 17 * q^49 - 11 * q^50 - 14 * q^51 - 26 * q^53 + q^54 + 13 * q^55 - 7 * q^56 - 22 * q^57 - 12 * q^58 - 14 * q^59 - 2 * q^60 + 13 * q^61 + 16 * q^62 + 10 * q^63 + 8 * q^64 - 10 * q^66 + 5 * q^67 - 7 * q^68 - 2 * q^69 + 16 * q^70 - 6 * q^71 - 36 * q^73 - 7 * q^74 + 5 * q^75 + q^76 - 30 * q^77 - 18 * q^79 - 16 * q^80 - 3 * q^81 - 5 * q^82 + 32 * q^83 - q^84 - 7 * q^85 + 30 * q^86 + 8 * q^87 + 7 * q^88 - 5 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 - 32 * q^94 - 3 * q^95 + 8 * q^96 + 5 * q^97 - 13 * q^98 + 2 * q^99

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