LMFDB - Embedded newform 931.2.x.a.226.1

Newspace parameters

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.x (of order $9$, degree $6$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			226.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	931.226
Dual form			931.2.x.a.655.1

$q$-expansion

$f(q)$	$=$	$q+(-1.03209 - 0.866025i) q^{2} +(-0.500000 + 2.83564i) q^{3} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(2.97178 - 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(-4.97178 - 1.80958i) q^{9} +O(q^{10})$	\(q+(-1.03209 - 0.866025i) q^{2} +(-0.500000 + 2.83564i) q^{3} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(2.97178 - 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(-4.97178 - 1.80958i) q^{9} +(-0.907604 + 0.761570i) q^{10} -2.22668 q^{11} +0.532089 q^{12} +(1.97178 - 1.65452i) q^{13} +(2.37939 + 0.866025i) q^{15} +(3.37939 - 1.23000i) q^{16} +(-0.439693 + 0.160035i) q^{17} +(3.56418 + 6.17334i) q^{18} +(1.52094 - 4.08494i) q^{19} -0.162504 q^{20} +(2.29813 + 1.92836i) q^{22} +(-2.06418 + 1.73205i) q^{23} +(-6.49273 - 5.44804i) q^{24} +(3.97178 + 1.44561i) q^{25} -3.46791 q^{26} +(3.29813 - 5.71253i) q^{27} +(-1.19459 - 6.77487i) q^{29} +(-1.70574 - 2.95442i) q^{30} +(3.55303 - 6.15403i) q^{31} +(0.979055 + 0.356347i) q^{32} +(1.11334 - 6.31407i) q^{33} +(0.592396 + 0.215615i) q^{34} +(-0.169778 + 0.962858i) q^{36} +(-2.47178 + 4.28125i) q^{37} +(-5.10741 + 2.89884i) q^{38} +(3.70574 + 6.41852i) q^{39} +(1.98293 + 1.66387i) q^{40} +(1.89646 + 1.59132i) q^{41} +(-3.66637 + 1.33445i) q^{43} +(0.0714517 + 0.405223i) q^{44} +(-2.32635 + 4.02936i) q^{45} +3.63041 q^{46} +(6.85117 + 2.49362i) q^{47} +(1.79813 + 10.1977i) q^{48} +(-2.84730 - 4.93166i) q^{50} +(-0.233956 - 1.32683i) q^{51} +(-0.364370 - 0.305743i) q^{52} +(-0.492726 - 2.79439i) q^{53} +(-8.35117 + 3.03958i) q^{54} +(-0.340022 + 1.92836i) q^{55} +(10.8229 + 6.35532i) q^{57} +(-4.63429 + 8.02682i) q^{58} +(5.92514 - 2.15658i) q^{59} +(0.0812519 - 0.460802i) q^{60} +(6.99273 - 5.86759i) q^{61} +(-8.99660 + 3.27449i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(-1.13176 - 1.96026i) q^{65} +(-6.61721 + 5.55250i) q^{66} +(5.87939 - 4.93339i) q^{67} +(0.0432332 + 0.0748822i) q^{68} +(-3.87939 - 6.71929i) q^{69} +(8.74422 - 3.18264i) q^{71} +(11.9304 - 10.0108i) q^{72} +(0.241230 - 1.36808i) q^{73} +(6.25877 - 2.27801i) q^{74} +(-6.08512 + 10.5397i) q^{75} +(-0.792204 - 0.145708i) q^{76} +(1.73396 - 9.83375i) q^{78} +(11.1309 - 4.05131i) q^{79} +(-0.549163 - 3.11446i) q^{80} +(2.39053 + 2.00589i) q^{81} +(-0.579193 - 3.28476i) q^{82} +(7.41534 + 12.8438i) q^{83} +(0.0714517 + 0.405223i) q^{85} +(4.93969 + 1.79790i) q^{86} +19.8084 q^{87} +(3.27719 - 5.67626i) q^{88} +(-1.78699 - 10.1345i) q^{89} +(5.89053 - 2.14398i) q^{90} +(0.381445 + 0.320070i) q^{92} +(15.6741 + 13.1521i) q^{93} +(-4.91147 - 8.50692i) q^{94} +(-3.30541 - 1.94096i) q^{95} +(-1.50000 + 2.59808i) q^{96} +(1.64156 - 9.30975i) q^{97} +(11.0706 + 4.02936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9	$ 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} - 9 q^{10} - 6 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{23} - 21 q^{24} + 9 q^{25} - 30 q^{26} + 6 q^{27} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 24 q^{36} + 3 q^{38} + 12 q^{39} - 9 q^{40} + 21 q^{41} - 3 q^{43} - 15 q^{45} + 36 q^{46} + 15 q^{47} - 3 q^{48} - 15 q^{50} - 6 q^{51} - 21 q^{52} + 15 q^{53} - 24 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 12 q^{62} - 12 q^{64} - 12 q^{65} - 9 q^{66} + 24 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 15 q^{79} - 15 q^{80} - 3 q^{81} + 45 q^{82} + 24 q^{86} + 42 q^{87} + 9 q^{88} - 3 q^{89} + 18 q^{90} + 42 q^{92} + 27 q^{93} - 9 q^{94} - 24 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 - 9 * q^10 - 6 * q^12 - 3 * q^13 + 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^23 - 21 * q^24 + 9 * q^25 - 30 * q^26 + 6 * q^27 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^36 + 3 * q^38 + 12 * q^39 - 9 * q^40 + 21 * q^41 - 3 * q^43 - 15 * q^45 + 36 * q^46 + 15 * q^47 - 3 * q^48 - 15 * q^50 - 6 * q^51 - 21 * q^52 + 15 * q^53 - 24 * q^54 + 18 * q^55 + 24 * q^57 - 18 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 12 * q^62 - 12 * q^64 - 12 * q^65 - 9 * q^66 + 24 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 - 15 * q^75 + 36 * q^76 + 15 * q^78 + 15 * q^79 - 15 * q^80 - 3 * q^81 + 45 * q^82 + 24 * q^86 + 42 * q^87 + 9 * q^88 - 3 * q^89 + 18 * q^90 + 42 * q^92 + 27 * q^93 - 9 * q^94 - 24 * q^95 - 9 * q^96 + 18 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−1.03209	−	0.866025i	−0.729797	−	0.612372i	0.200279	−	0.979739i	$-0.435815\pi$
$2$	−1.03209	−	0.866025i	−0.729797	−	0.612372i	−0.930076	+	0.367366i	$0.880260\pi$
$3$	−0.500000	+	2.83564i	−0.288675	+	1.63716i	0.403179	+	0.915121i	$0.367905\pi$
$3$	−0.500000	+	2.83564i	−0.288675	+	1.63716i	−0.691854	+	0.722037i	$0.743206\pi$
$4$	−0.0320889	−	0.181985i	−0.0160444	−	0.0909926i
$5$	0.152704	−	0.866025i	0.0682911	−	0.387298i	−0.931435	−	0.363907i	$-0.881443\pi$
$5$	0.152704	−	0.866025i	0.0682911	−	0.387298i	0.999726	−	0.0233912i	$-0.00744633\pi$
$6$	2.97178	−	2.49362i	1.21322	−	1.01802i
$7$		0			0
$7$		0			0
$8$	−1.47178	+	2.54920i	−0.520353	+	0.901278i
$9$	−4.97178	−	1.80958i	−1.65726	−	0.603193i
$10$	−0.907604	+	0.761570i	−0.287010	+	0.240830i
$11$	−2.22668			−0.671370			−0.335685	−	0.941974i	$-0.608968\pi$
$11$	−2.22668			−0.671370			−0.335685	+	0.941974i	$0.608968\pi$
$12$	0.532089			0.153601
$13$	1.97178	−	1.65452i	0.546874	−	0.458882i	−0.327007	−	0.945022i	$-0.606040\pi$
$13$	1.97178	−	1.65452i	0.546874	−	0.458882i	0.873881	+	0.486140i	$0.161596\pi$
$14$		0			0
$15$	2.37939	+	0.866025i	0.614355	+	0.223607i
$16$	3.37939	−	1.23000i	0.844846	−	0.307499i
$17$	−0.439693	+	0.160035i	−0.106641	+	0.0388142i	−0.394790	−	0.918772i	$-0.629183\pi$
$17$	−0.439693	+	0.160035i	−0.106641	+	0.0388142i	0.288149	+	0.957586i	$0.406960\pi$
$18$	3.56418	+	6.17334i	0.840085	+	1.45507i
$19$	1.52094	−	4.08494i	0.348929	−	0.937149i
$19$	1.52094	−	4.08494i	0.348929	−	0.937149i
$20$	−0.162504			−0.0363370
$21$		0			0
$22$	2.29813	+	1.92836i	0.489964	+	0.411128i
$23$	−2.06418	+	1.73205i	−0.430411	+	0.361158i	−0.832107	−	0.554616i	$-0.812865\pi$
$23$	−2.06418	+	1.73205i	−0.430411	+	0.361158i	0.401696	+	0.915773i	$0.368421\pi$
$24$	−6.49273	−	5.44804i	−1.32532	−	1.11208i
$25$	3.97178	+	1.44561i	0.794356	+	0.289122i
$26$	−3.46791			−0.680113
$27$	3.29813	−	5.71253i	0.634726	−	1.09938i
$28$		0			0
$29$	−1.19459	−	6.77487i	−0.221830	−	1.25806i	−0.868653	−	0.495421i	$-0.835014\pi$
$29$	−1.19459	−	6.77487i	−0.221830	−	1.25806i	0.646822	−	0.762641i	$-0.276097\pi$
$30$	−1.70574	−	2.95442i	−0.311424	−	0.539401i
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	−0.347696	−	0.937607i	$-0.613036\pi$
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	0.985840	−	0.167690i	$-0.0536307\pi$
$32$	0.979055	+	0.356347i	0.173074	+	0.0629939i
$33$	1.11334	−	6.31407i	0.193808	−	1.09914i
$34$	0.592396	+	0.215615i	0.101595	+	0.0369776i
$35$		0			0
$36$	−0.169778	+	0.962858i	−0.0282963	+	0.160476i
$37$	−2.47178	+	4.28125i	−0.406358	+	0.703833i	−0.994479	−	0.104940i	$-0.966535\pi$
$37$	−2.47178	+	4.28125i	−0.406358	+	0.703833i	0.588120	+	0.808774i	$0.299868\pi$
$38$	−5.10741	+	2.89884i	−0.828531	+	0.470255i
$39$	3.70574	+	6.41852i	0.593393	+	1.02779i
$40$	1.98293	+	1.66387i	0.313528	+	0.263081i
$41$	1.89646	+	1.59132i	0.296177	+	0.248522i	0.778751	−	0.627333i	$-0.215854\pi$
$41$	1.89646	+	1.59132i	0.296177	+	0.248522i	−0.482574	+	0.875855i	$0.660298\pi$
$42$		0			0
$43$	−3.66637	+	1.33445i	−0.559117	+	0.203502i	−0.606093	−	0.795394i	$-0.707264\pi$
$43$	−3.66637	+	1.33445i	−0.559117	+	0.203502i	0.0469757	+	0.998896i	$0.485042\pi$
$44$	0.0714517	+	0.405223i	0.0107718	+	0.0610897i
$45$	−2.32635	+	4.02936i	−0.346792	+	0.600661i
$46$	3.63041			0.535275
$47$	6.85117	+	2.49362i	0.999345	+	0.363732i	0.789332	−	0.613967i	$-0.210427\pi$
$47$	6.85117	+	2.49362i	0.999345	+	0.363732i	0.210013	+	0.977699i	$0.432649\pi$
$48$	1.79813	+	10.1977i	0.259538	+	1.47191i
$49$		0			0
$50$	−2.84730	−	4.93166i	−0.402669	−	0.697442i
$51$	−0.233956	−	1.32683i	−0.0327603	−	0.185793i
$52$	−0.364370	−	0.305743i	−0.0505291	−	0.0423989i
$53$	−0.492726	−	2.79439i	−0.0676811	−	0.383839i	−0.999767	−	0.0216005i	$-0.993124\pi$
$53$	−0.492726	−	2.79439i	−0.0676811	−	0.383839i	0.932086	−	0.362238i	$-0.117987\pi$
$54$	−8.35117	+	3.03958i	−1.13645	+	0.413634i
$55$	−0.340022	+	1.92836i	−0.0458486	+	0.260020i
$56$		0			0
$57$	10.8229	+	6.35532i	1.43353	+	0.841783i
$58$	−4.63429	+	8.02682i	−0.608511	+	1.05397i
$59$	5.92514	−	2.15658i	0.771388	−	0.280762i	0.0738112	−	0.997272i	$-0.476484\pi$
$59$	5.92514	−	2.15658i	0.771388	−	0.280762i	0.697577	+	0.716510i	$0.254262\pi$
$60$	0.0812519	−	0.460802i	0.0104896	−	0.0594893i
$61$	6.99273	−	5.86759i	0.895327	−	0.751268i	−0.0739445	−	0.997262i	$-0.523559\pi$
$61$	6.99273	−	5.86759i	0.895327	−	0.751268i	0.969271	+	0.245994i	$0.0791143\pi$
$62$	−8.99660	+	3.27449i	−1.14257	+	0.415861i
$63$		0			0
$64$	−4.29813	−	7.44459i	−0.537267	−	0.930573i
$65$	−1.13176	−	1.96026i	−0.140377	−	0.243141i
$66$	−6.61721	+	5.55250i	−0.814522	+	0.683465i
$67$	5.87939	−	4.93339i	0.718281	−	0.602710i	−0.208628	−	0.977995i	$-0.566900\pi$
$67$	5.87939	−	4.93339i	0.718281	−	0.602710i	0.926909	+	0.375286i	$0.122455\pi$
$68$	0.0432332	+	0.0748822i	0.00524280	+	0.00908080i
$69$	−3.87939	−	6.71929i	−0.467023	−	0.808908i
$70$		0			0
$71$	8.74422	−	3.18264i	1.03775	−	0.377709i	0.233722	−	0.972303i	$-0.424909\pi$
$71$	8.74422	−	3.18264i	1.03775	−	0.377709i	0.804026	+	0.594594i	$0.202687\pi$
$72$	11.9304	−	10.0108i	1.40601	−	1.17978i
$73$	0.241230	−	1.36808i	0.0282338	−	0.160122i	−0.967431	−	0.253134i	$-0.918539\pi$
$73$	0.241230	−	1.36808i	0.0282338	−	0.160122i	0.995665	+	0.0930125i	$0.0296497\pi$
$74$	6.25877	−	2.27801i	0.727567	−	0.264813i
$75$	−6.08512	+	10.5397i	−0.702649	+	1.21702i
$76$	−0.792204	−	0.145708i	−0.0908720	−	0.0167139i
$77$		0			0
$78$	1.73396	−	9.83375i	0.196332	−	1.11345i
$79$	11.1309	−	4.05131i	1.25232	−	0.455808i	0.371136	−	0.928578i	$-0.378968\pi$
$79$	11.1309	−	4.05131i	1.25232	−	0.455808i	0.881186	+	0.472770i	$0.156746\pi$
$80$	−0.549163	−	3.11446i	−0.0613983	−	0.348207i
$81$	2.39053	+	2.00589i	0.265614	+	0.222877i
$82$	−0.579193	−	3.28476i	−0.0639611	−	0.362742i
$83$	7.41534	+	12.8438i	0.813940	+	1.40979i	0.910087	+	0.414418i	$0.136015\pi$
$83$	7.41534	+	12.8438i	0.813940	+	1.40979i	−0.0961469	+	0.995367i	$0.530652\pi$
$84$		0			0
$85$	0.0714517	+	0.405223i	0.00775003	+	0.0439526i
$86$	4.93969	+	1.79790i	0.532661	+	0.193873i
$87$	19.8084			2.12368
$88$	3.27719	−	5.67626i	0.349349	−	0.605091i
$89$	−1.78699	−	10.1345i	−0.189420	−	1.07426i	−0.920143	−	0.391582i	$-0.871928\pi$
$89$	−1.78699	−	10.1345i	−0.189420	−	1.07426i	0.730723	−	0.682674i	$-0.239183\pi$
$90$	5.89053	−	2.14398i	0.620916	−	0.225995i
$91$		0			0
$92$	0.381445	+	0.320070i	0.0397684	+	0.0333696i
$93$	15.6741	+	13.1521i	1.62533	+	1.36381i
$94$	−4.91147	−	8.50692i	−0.506580	−	0.877422i
$95$	−3.30541	−	1.94096i	−0.339128	−	0.199138i
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$	1.64156	−	9.30975i	0.166675	−	0.945261i	−0.780645	−	0.624974i	$-0.785109\pi$
$97$	1.64156	−	9.30975i	0.166675	−	0.945261i	0.947320	−	0.320287i	$-0.103779\pi$
$98$		0			0
$99$	11.0706	+	4.02936i	1.11263	+	0.404966i
$100$	0.135630	−	0.769193i	0.0135630	−	0.0769193i
$101$	8.69119	+	3.16333i	0.864806	+	0.314764i	0.736062	−	0.676914i	$-0.236683\pi$
$101$	8.69119	+	3.16333i	0.864806	+	0.314764i	0.128744	+	0.991678i	$0.458905\pi$
$102$	−0.907604	+	1.57202i	−0.0898662	+	0.155653i
$103$	2.75490	+	4.77163i	0.271448	+	0.470162i	0.969233	−	0.246145i	$-0.0791640\pi$
$103$	2.75490	+	4.77163i	0.271448	+	0.470162i	−0.697785	+	0.716308i	$0.745831\pi$
$104$	1.31567	+	7.46156i	0.129012	+	0.731666i
$105$		0			0
$106$	−1.91147	+	3.31077i	−0.185659	+	0.321570i
$107$	10.2344			0.989399			0.494699	−	0.869064i	$-0.335278\pi$
$107$	10.2344			0.989399			0.494699	+	0.869064i	$0.335278\pi$
$108$	−1.14543	−	0.416902i	−0.110219	−	0.0401164i
$109$	−1.39646	−	1.17177i	−0.133757	−	0.112235i	0.573455	−	0.819237i	$-0.305603\pi$
$109$	−1.39646	−	1.17177i	−0.133757	−	0.112235i	−0.707212	+	0.707002i	$0.750047\pi$
$110$	2.02094	−	1.69577i	0.192690	−	0.161686i
$111$	−10.9042	−	9.14971i	−1.03498	−	0.868452i
$112$		0			0
$113$	−17.6878			−1.66393			−0.831963	−	0.554830i	$-0.812783\pi$
$113$	−17.6878			−1.66393			−0.831963	+	0.554830i	$0.812783\pi$
$114$	−5.66637	−	15.9322i	−0.530705	−	1.49219i
$115$	1.18479	+	2.05212i	0.110482	+	0.191361i
$116$	−1.19459	+	0.434796i	−0.110915	+	0.0403698i
$117$	−12.7973	+	4.65782i	−1.18311	+	0.430616i
$118$	−7.98293	−	2.90555i	−0.734888	−	0.267477i
$119$		0			0
$120$	−5.70961	+	4.79093i	−0.521213	+	0.437350i
$121$	−6.04189			−0.549263
$122$	−12.2986			−1.11346
$123$	−5.46064	+	4.58202i	−0.492369	+	0.413147i
$124$	−1.23396	−	0.449123i	−0.110812	−	0.0403324i
$125$	4.05690	−	7.02676i	0.362861	−	0.628493i
$126$		0			0
$127$	8.88919	−	7.45891i	0.788788	−	0.661871i	−0.156657	−	0.987653i	$-0.550072\pi$
$127$	8.88919	−	7.45891i	0.788788	−	0.661871i	0.945445	+	0.325782i	$0.105627\pi$
$128$	−1.64930	+	9.35365i	−0.145779	+	0.826753i
$129$	−1.95084	−	11.0637i	−0.171762	−	0.974109i
$130$	−0.529563	+	3.00330i	−0.0464457	+	0.263407i
$131$	1.41353	+	1.18610i	0.123501	+	0.103630i	0.702446	−	0.711737i	$-0.252091\pi$
$131$	1.41353	+	1.18610i	0.123501	+	0.103630i	−0.578945	+	0.815366i	$0.696536\pi$
$132$	−1.18479			−0.103123
$133$		0			0
$134$	−10.3405			−0.893282
$135$	−4.44356	−	3.72859i	−0.382441	−	0.320906i
$136$	0.239170	−	1.35640i	0.0205087	−	0.116310i
$137$	0.0444153	+	0.251892i	0.00379465	+	0.0215206i	0.986646	−	0.162878i	$-0.0520775\pi$
$137$	0.0444153	+	0.251892i	0.00379465	+	0.0215206i	−0.982852	+	0.184398i	$0.940966\pi$
$138$	−1.81521	+	10.2946i	−0.154521	+	0.876331i
$139$	3.26604	−	2.74054i	0.277022	−	0.232449i	−0.493682	−	0.869643i	$-0.664349\pi$
$139$	3.26604	−	2.74054i	0.277022	−	0.232449i	0.770704	+	0.637193i	$0.219905\pi$
$140$		0			0
$141$	−10.4966	+	18.1806i	−0.883973	+	1.53109i
$142$	−11.7811	−	4.28795i	−0.988645	−	0.359837i
$143$	−4.39053	+	3.68409i	−0.367155	+	0.308079i
$144$	−19.0273			−1.58561
$145$	−6.04963			−0.502394
$146$	−1.43376	+	1.20307i	−0.118659	+	0.0995668i
$147$		0			0
$148$	0.858441	+	0.312447i	0.0705634	+	0.0256830i
$149$	−15.5608	+	5.66366i	−1.27479	+	0.463985i	−0.888705	−	0.458479i	$-0.848394\pi$
$149$	−15.5608	+	5.66366i	−1.27479	+	0.463985i	−0.386083	+	0.922464i	$0.626172\pi$
$150$	15.4081	−	5.60808i	1.25806	−	0.457898i
$151$	2.18092	+	3.77747i	0.177481	+	0.307406i	0.941017	−	0.338359i	$-0.109872\pi$
$151$	2.18092	+	3.77747i	0.177481	+	0.307406i	−0.763536	+	0.645765i	$0.776539\pi$
$152$	8.17483	+	9.88933i	0.663066	+	0.802131i
$153$	2.47565			0.200145
$154$		0			0
$155$	−4.78699	−	4.01676i	−0.384500	−	0.322634i
$156$	1.04916	−	0.880352i	0.0840003	−	0.0704846i
$157$	−7.36824	−	6.18269i	−0.588050	−	0.493432i	0.299530	−	0.954087i	$-0.403170\pi$
$157$	−7.36824	−	6.18269i	−0.588050	−	0.493432i	−0.887579	+	0.460655i	$0.847615\pi$
$158$	−14.9966	−	5.45831i	−1.19307	−	0.434240i
$159$	8.17024			0.647943
$160$	0.458111	−	0.793471i	0.0362168	−	0.0627294i
$161$		0			0
$162$	−0.730085	−	4.14052i	−0.0573609	−	0.325310i
$163$	−4.17752	−	7.23567i	−0.327209	−	0.566742i	0.654748	−	0.755847i	$-0.272775\pi$
$163$	−4.17752	−	7.23567i	−0.327209	−	0.566742i	−0.981957	+	0.189105i	$0.939441\pi$
$164$	0.228741	−	0.396191i	0.0178617	−	0.0309373i
$165$	−5.29813	−	1.92836i	−0.412459	−	0.150123i
$166$	3.46972	−	19.6778i	0.269303	−	1.52729i
$167$	−3.79174	−	1.38008i	−0.293413	−	0.106794i	0.191120	−	0.981567i	$-0.438788\pi$
$167$	−3.79174	−	1.38008i	−0.293413	−	0.106794i	−0.484533	+	0.874773i	$0.661010\pi$
$168$		0			0
$169$	−1.10694	+	6.27779i	−0.0851496	+	0.482907i
$170$	0.277189	−	0.480105i	0.0212594	−	0.0368224i
$171$	−14.9538	+	17.5572i	−1.14355	+	1.34263i
$172$	0.360500	+	0.624404i	0.0274879	+	0.0476104i
$173$	−15.4311	−	12.9482i	−1.17320	−	0.984434i	−0.173203	−	0.984886i	$-0.555412\pi$
$173$	−15.4311	−	12.9482i	−1.17320	−	0.984434i	−1.00000		0.000452057i	$0.999856\pi$
$174$	−20.4440	−	17.1546i	−1.54986	−	1.30049i
$175$		0			0
$176$	−7.52481	+	2.73881i	−0.567204	+	0.206445i
$177$	3.15270	+	17.8799i	0.236972	+	1.34393i
$178$	−6.93242	+	12.0073i	−0.519607	+	0.899985i
$179$	−11.5125			−0.860484			−0.430242	−	0.902714i	$-0.641572\pi$
$179$	−11.5125			−0.860484			−0.430242	+	0.902714i	$0.641572\pi$
$180$	0.807934	+	0.294064i	0.0602198	+	0.0219182i
$181$	1.48246	+	8.40744i	0.110190	+	0.624920i	0.989020	+	0.147784i	$0.0472141\pi$
$181$	1.48246	+	8.40744i	0.110190	+	0.624920i	−0.878829	+	0.477136i	$0.841675\pi$
$182$		0			0
$183$	13.1420	+	22.7627i	0.971487	+	1.68266i
$184$	−1.37733	−	7.81120i	−0.101538	−	0.575850i
$185$	3.33022	+	2.79439i	0.244843	+	0.205448i
$186$	−4.78699	−	27.1484i	−0.350999	−	1.99061i
$187$	0.979055	−	0.356347i	0.0715956	−	0.0260587i
$188$	0.233956	−	1.32683i	0.0170630	−	0.0967689i
$189$		0			0
$190$	1.73055	+	4.86581i	0.125547	+	0.353003i
$191$	−9.16772	+	15.8790i	−0.663353	+	1.14896i	0.316376	+	0.948634i	$0.397534\pi$
$191$	−9.16772	+	15.8790i	−0.663353	+	1.14896i	−0.979729	+	0.200327i	$0.935800\pi$
$192$	23.2592	−	8.46567i	1.67859	−	0.610957i
$193$	0.0516892	−	0.293144i	0.00372067	−	0.0211010i	−0.982891	−	0.184189i	$-0.941034\pi$
$193$	0.0516892	−	0.293144i	0.00372067	−	0.0211010i	0.986612	+	0.163088i	$0.0521454\pi$
$194$	−9.75671	+	8.18685i	−0.700491	+	0.587782i
$195$	6.12449	−	2.22913i	0.438583	−	0.159631i
$196$		0			0
$197$	−6.57057	−	11.3806i	−0.468134	−	0.810832i	0.531203	−	0.847245i	$-0.321740\pi$
$197$	−6.57057	−	11.3806i	−0.468134	−	0.810832i	−0.999337	+	0.0364128i	$0.988407\pi$
$198$	−7.93629	−	13.7461i	−0.564008	−	0.976890i
$199$	−0.196652	+	0.165011i	−0.0139403	+	0.0116973i	−0.649731	−	0.760164i	$-0.725119\pi$
$199$	−0.196652	+	0.165011i	−0.0139403	+	0.0116973i	0.635791	+	0.771861i	$0.280674\pi$
$200$	−9.53074	+	7.99724i	−0.673925	+	0.565491i
$201$	11.0496	+	19.1385i	0.779381	+	1.34993i
$202$	−6.23055	−	10.7916i	−0.438380	−	0.759297i
$203$		0			0
$204$	−0.233956	+	0.0851529i	−0.0163802	+	0.00596189i
$205$	1.66772	−	1.39938i	0.116479	−	0.0977371i
$206$	1.28905	−	7.31056i	0.0898123	−	0.509351i
$207$	13.3969	−	4.87608i	0.931151	−	0.338911i
$208$	4.62836	−	8.01655i	0.320919	−	0.555848i
$209$	−3.38666	+	9.09586i	−0.234260	+	0.629174i
$210$		0			0
$211$	0.425145	−	2.41112i	0.0292682	−	0.165988i	−0.966670	−	0.256024i	$-0.917587\pi$
$211$	0.425145	−	2.41112i	0.0292682	−	0.165988i	0.995938	+	0.0900364i	$0.0286983\pi$
$212$	−0.492726	+	0.179338i	−0.0338406	+	0.0123170i
$213$	4.65270	+	26.3868i	0.318798	+	1.80799i
$214$	−10.5628	−	8.86327i	−0.722060	−	0.605881i
$215$	0.595800	+	3.37895i	0.0406332	+	0.230442i
$216$	9.70826	+	16.8152i	0.660564	+	1.14413i
$217$		0			0
$218$	0.426489	+	2.41874i	0.0288855	+	0.163818i
$219$	3.75877	+	1.36808i	0.253994	+	0.0924463i
$220$	0.361844			0.0243955
$221$	−0.602196	+	1.04303i	−0.0405081	+	0.0701621i
$222$	3.33022	+	18.8866i	0.223510	+	1.26759i
$223$	7.99660	−	2.91052i	0.535492	−	0.194903i	−0.0600971	−	0.998193i	$-0.519141\pi$
$223$	7.99660	−	2.91052i	0.535492	−	0.194903i	0.595589	+	0.803289i	$0.296919\pi$
$224$		0			0
$225$	−17.1309	−	14.3745i	−1.14206	−	0.958301i
$226$	18.2554	+	15.3181i	1.21433	+	1.01894i
$227$	7.07532	+	12.2548i	0.469606	+	0.813381i	0.999396	−	0.0347477i	$-0.0110628\pi$
$227$	7.07532	+	12.2548i	0.469606	+	0.813381i	−0.529790	+	0.848129i	$0.677729\pi$
$228$	0.809278	−	2.17355i	0.0535957	−	0.143947i
$229$	10.2665	−	17.7821i	0.678430	−	1.17508i	−0.297023	−	0.954870i	$-0.595994\pi$
$229$	10.2665	−	17.7821i	0.678430	−	1.17508i	0.975454	−	0.220205i	$-0.0706727\pi$
$230$	0.554378	−	3.14403i	0.0365546	−	0.207311i
$231$		0			0
$232$	19.0287	+	6.92588i	1.24929	+	0.454706i
$233$	3.06506	−	17.3828i	0.200798	−	1.13878i	−0.703117	−	0.711074i	$-0.748209\pi$
$233$	3.06506	−	17.3828i	0.200798	−	1.13878i	0.903916	−	0.427711i	$-0.140680\pi$
$234$	17.2417	+	6.27546i	1.12712	+	0.410240i
$235$	3.20574	−	5.55250i	0.209119	−	0.362205i
$236$	−0.582596	−	1.00909i	−0.0379238	−	0.0656859i
$237$	5.92262	+	33.5888i	0.384715	+	2.18183i
$238$		0			0
$239$	−1.17617	+	2.03719i	−0.0760804	+	0.131775i	−0.901556	−	0.432663i	$-0.857574\pi$
$239$	−1.17617	+	2.03719i	−0.0760804	+	0.131775i	0.825475	+	0.564438i	$0.190907\pi$
$240$	9.10607			0.587794
$241$	−12.9684	−	4.72010i	−0.835367	−	0.304049i	−0.111307	−	0.993786i	$-0.535504\pi$
$241$	−12.9684	−	4.72010i	−0.835367	−	0.304049i	−0.724060	+	0.689737i	$0.757726\pi$
$242$	6.23577	+	5.23243i	0.400850	+	0.336353i
$243$	8.27584	−	6.94426i	0.530896	−	0.445474i
$244$	−1.29220	−	1.08429i	−0.0827249	−	0.0694144i
$245$		0			0
$246$	9.60401			0.612329
$247$	−3.75965	−	10.5710i	−0.239221	−	0.672619i
$248$	10.4586	+	18.1148i	0.664120	+	1.15029i
$249$	−40.1279	+	14.6054i	−2.54301	+	0.925578i
$250$	−10.2724	+	3.73886i	−0.649686	+	0.236466i
$251$	3.91400	+	1.42458i	0.247050	+	0.0899187i	0.462577	−	0.886579i	$-0.346925\pi$
$251$	3.91400	+	1.42458i	0.247050	+	0.0899187i	−0.215528	+	0.976498i	$0.569147\pi$
$252$		0			0
$253$	4.59627	−	3.85673i	0.288965	−	0.242470i
$254$	−15.6340			−0.980967
$255$	−1.18479			−0.0741946
$256$	−3.36753	+	2.82569i	−0.210470	+	0.176606i
$257$	−0.627011	−	0.228213i	−0.0391119	−	0.0142356i	0.322390	−	0.946607i	$-0.395514\pi$
$257$	−0.627011	−	0.228213i	−0.0391119	−	0.0142356i	−0.361502	+	0.932371i	$0.617736\pi$
$258$	−7.56805	+	13.1082i	−0.471166	+	0.816084i
$259$		0			0
$260$	−0.320422	+	0.268866i	−0.0198717	+	0.0166744i
$261$	−6.32042	+	35.8449i	−0.391224	+	2.21874i
$262$	−0.431703	−	2.44831i	−0.0266707	−	0.151257i
$263$	1.97952	−	11.2264i	0.122063	−	0.692251i	−0.860947	−	0.508695i	$-0.830128\pi$
$263$	1.97952	−	11.2264i	0.122063	−	0.692251i	0.983009	−	0.183556i	$-0.0587609\pi$
$264$	14.4572	+	12.1311i	0.889781	+	0.746615i
$265$	−2.49525			−0.153282
$266$		0			0
$267$	29.6313			1.81341
$268$	−1.08647	−	0.911654i	−0.0663665	−	0.0556881i
$269$	3.36706	−	19.0955i	0.205293	−	1.16428i	−0.691684	−	0.722200i	$-0.743131\pi$
$269$	3.36706	−	19.0955i	0.205293	−	1.16428i	0.896978	−	0.442076i	$-0.145758\pi$
$270$	1.35710	+	7.69648i	0.0825903	+	0.468393i
$271$	−2.32588	+	13.1907i	−0.141287	+	0.801281i	0.828986	+	0.559269i	$0.188918\pi$
$271$	−2.32588	+	13.1907i	−0.141287	+	0.801281i	−0.970273	+	0.242011i	$0.922193\pi$
$272$	−1.28905	+	1.08164i	−0.0781600	+	0.0655841i
$273$		0			0
$274$	0.172304	−	0.298439i	0.0104093	−	0.0180294i
$275$	−8.84389	−	3.21891i	−0.533307	−	0.194108i
$276$	−1.09833	+	0.921605i	−0.0661115	+	0.0554741i
$277$	17.7469			1.06631			0.533154	−	0.846018i	$-0.321007\pi$
$277$	17.7469			1.06631			0.533154	+	0.846018i	$0.321007\pi$
$278$	−5.74422			−0.344516
$279$	−28.8011	+	24.1670i	−1.72428	+	1.44684i
$280$		0			0
$281$	−17.1766	−	6.25179i	−1.02467	−	0.372950i	−0.225622	−	0.974215i	$-0.572442\pi$
$281$	−17.1766	−	6.25179i	−1.02467	−	0.372950i	−0.799050	+	0.601265i	$0.794664\pi$
$282$	26.5783	−	9.67372i	1.58272	−	0.576061i
$283$	−7.22416	+	2.62938i	−0.429431	+	0.156300i	−0.547688	−	0.836683i	$-0.684492\pi$
$283$	−7.22416	+	2.62938i	−0.429431	+	0.156300i	0.118256	+	0.992983i	$0.462270\pi$
$284$	−0.859785	−	1.48919i	−0.0510188	−	0.0883672i
$285$	7.15657	−	8.40247i	0.423919	−	0.497719i
$286$	7.72193			0.456608
$287$		0			0
$288$	−4.22281	−	3.54336i	−0.248832	−	0.208794i
$289$	−12.8550	+	10.7867i	−0.756179	+	0.634509i
$290$	6.24376	+	5.23913i	0.366646	+	0.307652i
$291$	25.5783	+	9.30975i	1.49943	+	0.545747i
$292$	−0.256711			−0.0150229
$293$	5.25150	−	9.09586i	0.306796	−	0.531386i	−0.670864	−	0.741581i	$-0.734076\pi$
$293$	5.25150	−	9.09586i	0.306796	−	0.531386i	0.977660	+	0.210195i	$0.0674098\pi$
$294$		0			0
$295$	−0.962859	−	5.46064i	−0.0560598	−	0.317931i
$296$	−7.27584	−	12.6021i	−0.422900	−	0.732484i
$297$	−7.34389	+	12.7200i	−0.426136	+	0.738089i
$298$	20.9650	+	7.63063i	1.21447	+	0.442030i
$299$	−1.20439	+	6.83045i	−0.0696518	+	0.395015i
$300$	2.11334	+	0.769193i	0.122014	+	0.0444094i
$301$		0			0
$302$	1.02048	−	5.78742i	0.0587219	−	0.333028i
$303$	−13.3157	+	23.0634i	−0.764966	+	1.32496i
$304$	0.115400	−	15.6753i	0.00661865	−	0.899042i
$305$	−4.01367	−	6.95188i	−0.229822	−	0.398064i
$306$	−2.55509	−	2.14398i	−0.146065	−	0.122563i
$307$	−8.95929	−	7.51774i	−0.511334	−	0.429060i	0.350264	−	0.936651i	$-0.386092\pi$
$307$	−8.95929	−	7.51774i	−0.511334	−	0.429060i	−0.861598	+	0.507591i	$0.830536\pi$
$308$		0			0
$309$	−14.9081	+	5.42609i	−0.848091	+	0.308680i
$310$	1.46198	+	8.29131i	0.0830350	+	0.470915i
$311$	−7.98293	+	13.8268i	−0.452670	+	0.784048i	−0.998551	−	0.0538151i	$-0.982862\pi$
$311$	−7.98293	+	13.8268i	−0.452670	+	0.784048i	0.545881	+	0.837863i	$0.316195\pi$
$312$	−21.8161			−1.23510
$313$	25.0228	+	9.10754i	1.41437	+	0.514788i	0.932409	−	0.361404i	$-0.117703\pi$
$313$	25.0228	+	9.10754i	1.41437	+	0.514788i	0.481961	+	0.876193i	$0.339925\pi$
$314$	2.25031	+	12.7622i	0.126993	+	0.720211i
$315$		0			0
$316$	−1.09446	−	1.89565i	−0.0615679	−	0.106639i
$317$	5.12819	+	29.0834i	0.288028	+	1.63349i	0.694264	+	0.719720i	$0.255730\pi$
$317$	5.12819	+	29.0834i	0.288028	+	1.63349i	−0.406236	+	0.913768i	$0.633159\pi$
$318$	−8.43242	−	7.07564i	−0.472867	−	0.396782i
$319$	2.65998	+	15.0855i	0.148930	+	0.844625i
$320$	−7.10354	+	2.58548i	−0.397100	+	0.144533i
$321$	−5.11721	+	29.0211i	−0.285615	+	1.61980i
$322$		0			0
$323$	−0.0150147	+	2.03952i	−0.000835443	+	0.113482i
$324$	0.288333	−	0.499408i	0.0160185	−	0.0277449i
$325$	10.2233	−	3.72097i	0.567085	−	0.206402i
$326$	−1.95471	+	11.0857i	−0.108261	+	0.613980i
$327$	4.02094	−	3.37397i	0.222359	−	0.186581i
$328$	−6.84776	+	2.49238i	−0.378104	+	0.137619i
$329$		0			0
$330$	3.79813	+	6.57856i	0.209080	+	0.362138i
$331$	−13.8327	−	23.9590i	−0.760317	−	1.31691i	−0.942687	−	0.333677i	$-0.891710\pi$
$331$	−13.8327	−	23.9590i	−0.760317	−	1.31691i	0.182371	−	0.983230i	$-0.441623\pi$
$332$	2.09942	−	1.76162i	0.115221	−	0.0966817i
$333$	20.0364	−	16.8126i	1.09799	−	0.921322i
$334$	2.71823	+	4.70810i	0.148735	+	0.257616i
$335$	−3.37464	−	5.84504i	−0.184376	−	0.319349i
$336$		0			0
$337$	−16.7827	+	6.10841i	−0.914212	+	0.332746i	−0.755934	−	0.654648i	$-0.772817\pi$
$337$	−16.7827	+	6.10841i	−0.914212	+	0.332746i	−0.158279	+	0.987394i	$0.550594\pi$
$338$	6.57919	−	5.52060i	0.357861	−	0.300281i
$339$	8.84389	−	50.1562i	0.480334	−	2.72411i
$340$	0.0714517	−	0.0260063i	0.00387501	−	0.00141039i
$341$	−7.91147	+	13.7031i	−0.428430	+	0.742063i
$342$	30.6386	−	5.17015i	1.65675	−	0.279569i
$343$		0			0
$344$	1.99432	−	11.3103i	0.107526	−	0.609813i
$345$	−6.41147	+	2.33359i	−0.345182	+	0.125636i
$346$	4.71276	+	26.7274i	0.253360	+	1.43687i
$347$	−4.44356	−	3.72859i	−0.238543	−	0.200161i	0.515677	−	0.856783i	$-0.327540\pi$
$347$	−4.44356	−	3.72859i	−0.238543	−	0.200161i	−0.754220	+	0.656622i	$0.771985\pi$
$348$	−0.635630	−	3.60483i	−0.0340733	−	0.193239i
$349$	−2.68614	−	4.65253i	−0.143786	−	0.249044i	0.785134	−	0.619326i	$-0.212594\pi$
$349$	−2.68614	−	4.65253i	−0.143786	−	0.249044i	−0.928919	+	0.370282i	$0.879261\pi$
$350$		0			0
$351$	−2.94831	−	16.7207i	−0.157369	−	0.892485i
$352$	−2.18004	−	0.793471i	−0.116197	−	0.0422922i
$353$	−25.2344			−1.34309			−0.671546	−	0.740963i	$-0.734370\pi$
$353$	−25.2344			−1.34309			−0.671546	+	0.740963i	$0.734370\pi$
$354$	12.2306	−	21.1839i	0.650047	−	1.12591i
$355$	−1.42097	−	8.05872i	−0.0754172	−	0.427712i
$356$	−1.78699	+	0.650411i	−0.0947102	+	0.0344717i
$357$		0			0
$358$	11.8819	+	9.97011i	0.627979	+	0.526937i
$359$	5.12243	+	4.29823i	0.270351	+	0.226852i	0.767877	−	0.640598i	$-0.221313\pi$
$359$	5.12243	+	4.29823i	0.270351	+	0.226852i	−0.497525	+	0.867449i	$0.665758\pi$
$360$	−6.84776	−	11.8607i	−0.360909	−	0.625112i
$361$	−14.3735	−	12.4259i	−0.756498	−	0.653996i
$362$	5.75103	−	9.96108i	0.302267	−	0.523543i
$363$	3.02094	−	17.1326i	0.158558	−	0.899230i
$364$		0			0
$365$	−1.14796	−	0.417822i	−0.0600868	−	0.0218698i
$366$	6.14930	−	34.8744i	0.321429	−	1.82291i
$367$	−7.62923	−	2.77681i	−0.398243	−	0.144948i	0.135132	−	0.990828i	$-0.456854\pi$
$367$	−7.62923	−	2.77681i	−0.398243	−	0.144948i	−0.533375	+	0.845879i	$0.679076\pi$
$368$	−4.84524	+	8.39220i	−0.252575	+	0.437473i
$369$	−6.54916	−	11.3435i	−0.340936	−	0.590518i
$370$	−1.01707	−	5.76811i	−0.0528752	−	0.299870i
$371$		0			0
$372$	1.89053	−	3.27449i	0.0980194	−	0.169775i
$373$	34.8976			1.80693			0.903463	−	0.428665i	$-0.141016\pi$
$373$	34.8976			1.80693			0.903463	+	0.428665i	$0.141016\pi$
$374$	−1.31908	−	0.480105i	−0.0682079	−	0.0248256i
$375$	17.8969	+	15.0173i	0.924193	+	0.775490i
$376$	−16.4402	+	13.7949i	−0.847836	+	0.711419i
$377$	−13.5646	−	11.3821i	−0.698615	−	0.586207i
$378$		0			0
$379$	1.70140			0.0873950			0.0436975	−	0.999045i	$-0.486086\pi$
$379$	1.70140			0.0873950			0.0436975	+	0.999045i	$0.486086\pi$
$380$	−0.247159	+	0.663818i	−0.0126790	+	0.0340532i
$381$	16.7062	+	28.9360i	0.855885	+	1.48244i
$382$	23.2135	−	8.44901i	1.18770	−	0.432289i
$383$	−2.75965	+	1.00443i	−0.141011	+	0.0513240i	−0.411562	−	0.911382i	$-0.635017\pi$
$383$	−2.75965	+	1.00443i	−0.141011	+	0.0513240i	0.270550	+	0.962706i	$0.412794\pi$
$384$	−25.6989	−	9.35365i	−1.31144	−	0.477326i
$385$		0			0
$386$	−0.307218	+	0.257787i	−0.0156370	+	0.0131210i
$387$	20.6432			1.04935
$388$	−1.74691			−0.0886860
$389$	−18.8195	+	15.7915i	−0.954189	+	0.800659i	−0.979998	−	0.199007i	$-0.936228\pi$
$389$	−18.8195	+	15.7915i	−0.954189	+	0.800659i	0.0258092	+	0.999667i	$0.491784\pi$
$390$	−8.25150	−	3.00330i	−0.417831	−	0.152078i
$391$	0.630415	−	1.09191i	0.0318815	−	0.0552203i
$392$		0			0
$393$	−4.07011	+	3.41523i	−0.205310	+	0.172275i
$394$	−3.07444	+	17.4360i	−0.154888	+	0.878415i
$395$	−1.80881	−	10.2583i	−0.0910112	−	0.516150i
$396$	0.378041	−	2.14398i	0.0189973	−	0.107739i
$397$	−24.3876	−	20.4636i	−1.22398	−	1.02704i	−0.998607	−	0.0527667i	$-0.983196\pi$
$397$	−24.3876	−	20.4636i	−1.22398	−	1.02704i	−0.225371	−	0.974273i	$-0.572360\pi$
$398$	0.345866			0.0173367
$399$		0			0
$400$	15.2003			0.760014
$401$	−0.0662372	−	0.0555796i	−0.00330773	−	0.00277551i	0.641132	−	0.767430i	$-0.278465\pi$
$401$	−0.0662372	−	0.0555796i	−0.00330773	−	0.00277551i	−0.644440	+	0.764655i	$0.722909\pi$
$402$	5.17024	−	29.3219i	0.257868	−	1.46244i
$403$	−3.17617	−	18.0130i	−0.158217	−	0.897290i
$404$	0.296789	−	1.68317i	0.0147658	−	0.0837411i
$405$	2.10220	−	1.76395i	0.104459	−	0.0876515i
$406$		0			0
$407$	5.50387	−	9.53298i	0.272817	−	0.472532i
$408$	3.72668	+	1.35640i	0.184498	+	0.0671519i
$409$	15.3255	−	12.8596i	0.757796	−	0.635866i	−0.179756	−	0.983711i	$-0.557531\pi$
$409$	15.3255	−	12.8596i	0.757796	−	0.635866i	0.937552	+	0.347845i	$0.113086\pi$
$410$	−2.93313			−0.144857
$411$	−0.736482			−0.0363280
$412$	0.779963	−	0.654467i	0.0384260	−	0.0322433i
$413$		0			0
$414$	−18.0496	−	6.56953i	−0.887091	−	0.322875i
$415$	12.2554	−	4.46059i	0.601592	−	0.218962i
$416$	2.52007	−	0.917229i	0.123556	−	0.0449709i
$417$	6.13816	+	10.6316i	0.300587	+	0.520632i
$418$	11.3726	−	6.45480i	0.556251	−	0.315715i
$419$	25.4097			1.24135			0.620673	−	0.784070i	$-0.286859\pi$
$419$	25.4097			1.24135			0.620673	+	0.784070i	$0.286859\pi$
$420$		0			0
$421$	3.34730	+	2.80872i	0.163137	+	0.136888i	0.720702	−	0.693245i	$-0.243820\pi$
$421$	3.34730	+	2.80872i	0.163137	+	0.136888i	−0.557565	+	0.830134i	$0.688264\pi$
$422$	−2.52687	+	2.12030i	−0.123006	+	0.103215i
$423$	−29.5501	−	24.7955i	−1.43677	−	1.20560i
$424$	7.84864	+	2.85667i	0.381164	+	0.138732i
$425$	−1.97771			−0.0959331
$426$	18.0496	−	31.2629i	0.874507	−	1.51469i
$427$		0			0
$428$	−0.328411	−	1.86251i	−0.0158744	−	0.0900279i
$429$	−8.25150	−	14.2920i	−0.398386	−	0.690025i
$430$	2.31134	−	4.00335i	0.111463	−	0.193059i
$431$	35.9962	+	13.1015i	1.73388	+	0.631079i	0.998894	−	0.0470089i	$-0.0149689\pi$
$431$	35.9962	+	13.1015i	1.73388	+	0.631079i	0.734981	+	0.678088i	$0.237191\pi$
$432$	4.11927	−	23.3615i	0.198188	−	1.12398i
$433$	17.0376	+	6.20118i	0.818775	+	0.298010i	0.717244	−	0.696823i	$-0.245403\pi$
$433$	17.0376	+	6.20118i	0.818775	+	0.298010i	0.101532	+	0.994832i	$0.467626\pi$
$434$		0			0
$435$	3.02481	−	17.1546i	0.145029	−	0.822499i
$436$	−0.168434	+	0.291736i	−0.00806651	+	0.0139716i
$437$	3.93582	+	11.0664i	0.188276	+	0.529377i
$438$	−2.69459	−	4.66717i	−0.128753	−	0.223006i
$439$	−4.66566	−	3.91495i	−0.222680	−	0.186850i	0.524622	−	0.851335i	$-0.324207\pi$
$439$	−4.66566	−	3.91495i	−0.222680	−	0.186850i	−0.747302	+	0.664485i	$0.768651\pi$
$440$	−4.41534	−	3.70491i	−0.210493	−	0.176625i
$441$		0			0
$442$	1.52481	−	0.554987i	0.0725280	−	0.0263981i
$443$	−5.19088	−	29.4390i	−0.246626	−	1.39869i	−0.816685	−	0.577084i	$-0.804191\pi$
$443$	−5.19088	−	29.4390i	−0.246626	−	1.39869i	0.570059	−	0.821604i	$-0.306920\pi$
$444$	−1.31521	+	2.27801i	−0.0624170	+	0.108109i
$445$	−9.04963			−0.428994
$446$	−10.7738	−	3.92134i	−0.510154	−	0.185681i
$447$	−8.27972	−	46.9566i	−0.391617	−	2.22097i
$448$		0			0
$449$	5.62495	+	9.74270i	0.265458	+	0.459787i	0.967683	−	0.252168i	$-0.0811435\pi$
$449$	5.62495	+	9.74270i	0.265458	+	0.459787i	−0.702226	+	0.711955i	$0.747810\pi$
$450$	5.23190	+	29.6716i	0.246634	+	1.39873i
$451$	−4.22281	−	3.54336i	−0.198844	−	0.166850i
$452$	0.567581	+	3.21891i	0.0266968	+	0.151405i
$453$	−11.8020	+	4.29558i	−0.554507	+	0.201824i
$454$	3.31062	−	18.7755i	0.155375	−	0.881176i
$455$		0			0
$456$	−32.1300	+	18.2362i	−1.50463	+	0.853989i
$457$	11.6951	−	20.2564i	0.547072	−	0.947556i	−0.451402	−	0.892321i	$-0.649076\pi$
$457$	11.6951	−	20.2564i	0.547072	−	0.947556i	0.998473	−	0.0552352i	$-0.0175909\pi$
$458$	−25.9957	+	9.46167i	−1.21470	+	0.442115i
$459$	−0.535959	+	3.03958i	−0.0250164	+	0.141875i
$460$	0.335437	−	0.281465i	0.0156398	−	0.0131234i
$461$	34.4149	−	12.5260i	1.60286	−	0.583395i	0.622853	−	0.782339i	$-0.285974\pi$
$461$	34.4149	−	12.5260i	1.60286	−	0.583395i	0.980011	+	0.198945i	$0.0637514\pi$
$462$		0			0
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.540534	+	0.841322i	$0.318222\pi$
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.458340	+	0.888777i	$0.348444\pi$
$464$	−12.3701	−	21.4256i	−0.574265	−	0.994657i
$465$	13.7836	−	11.5658i	0.639198	−	0.536351i
$466$	−18.2173	+	15.2862i	−0.843902	+	0.708118i
$467$	−12.7981	−	22.1670i	−0.592227	−	1.02577i	−0.993932	−	0.109998i	$-0.964916\pi$
$467$	−12.7981	−	22.1670i	−0.592227	−	1.02577i	0.401705	−	0.915769i	$-0.368418\pi$
$468$	1.25830	+	2.17945i	0.0581651	+	0.100745i
$469$		0			0
$470$	−8.11721	+	2.95442i	−0.374419	+	0.136277i
$471$	21.2160	−	17.8023i	0.977582	−	0.820289i
$472$	−3.22297	+	18.2784i	−0.148349	+	0.841331i
$473$	8.16385	−	2.97140i	0.375374	−	0.136625i
$474$	22.9761	−	39.7958i	1.05533	−	1.82788i
$475$	11.9461	−	14.0258i	0.548124	−	0.643548i
$476$		0			0
$477$	−2.60694	+	14.7847i	−0.119364	+	0.676946i
$478$	2.97818	−	1.08397i	0.136219	−	0.0495796i
$479$	6.62923	+	37.5962i	0.302897	+	1.71782i	0.633240	+	0.773955i	$0.281725\pi$
$479$	6.62923	+	37.5962i	0.302897	+	1.71782i	−0.330343	+	0.943861i	$0.607164\pi$
$480$	2.02094	+	1.69577i	0.0922431	+	0.0774011i
$481$	2.20961	+	12.5313i	0.100749	+	0.571378i
$482$	9.29679	+	16.1025i	0.423457	+	0.733449i
$483$		0			0
$484$	0.193877	+	1.09953i	0.00881261	+	0.0499788i
$485$	−7.81180	−	2.84326i	−0.354716	−	0.129106i
$486$	−14.5553			−0.660242
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	−0.940475	−	0.339864i	$-0.889619\pi$
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	0.764568	+	0.644543i	$0.222952\pi$
$488$	4.66591	+	26.4617i	0.211216	+	1.19786i
$489$	22.6065	−	8.22811i	1.02230	−	0.372088i
$490$		0			0
$491$	−28.1313	−	23.6050i	−1.26955	−	1.06528i	−0.994596	−	0.103822i	$-0.966893\pi$
$491$	−28.1313	−	23.6050i	−1.26955	−	1.06528i	−0.274954	−	0.961457i	$-0.588663\pi$
$492$	1.00908	+	0.846723i	0.0454931	+	0.0381732i
$493$	1.60947	+	2.78768i	0.0724869	+	0.125551i
$494$	−5.27450	+	14.1662i	−0.237311	+	0.637368i
$495$	5.18004	−	8.97210i	0.232826	−	0.403266i
$496$	4.43763	−	25.1671i	0.199256	−	1.13003i
$497$		0			0
$498$	54.0642	+	19.6778i	2.42268	+	0.881782i
$499$	0.855448	−	4.85148i	0.0382951	−	0.217182i	−0.959655	−	0.281180i	$-0.909274\pi$
$499$	0.855448	−	4.85148i	0.0382951	−	0.217182i	0.997950	+	0.0639981i	$0.0203852\pi$
$500$	−1.40895	−	0.512815i	−0.0630101	−	0.0229338i
$501$	5.80928	−	10.0620i	0.259539	−	0.449535i
$502$	−2.80587	−	4.85992i	−0.125232	−	0.216909i
$503$	5.72163	+	32.4490i	0.255115	+	1.44683i	0.795778	+	0.605589i	$0.207062\pi$
$503$	5.72163	+	32.4490i	0.255115	+	1.44683i	−0.540663	+	0.841239i	$0.681827\pi$
$504$		0			0
$505$	4.06670	−	7.04374i	0.180966	−	0.313442i
$506$	−8.08378			−0.359368
$507$	−17.2481	−	6.27779i	−0.766015	−	0.278807i
$508$	−1.64266	−	1.37835i	−0.0728810	−	0.0611544i
$509$	−28.2939	+	23.7414i	−1.25410	+	1.05232i	−0.257819	+	0.966193i	$0.583004\pi$
$509$	−28.2939	+	23.7414i	−1.25410	+	1.05232i	−0.996284	+	0.0861240i	$0.972552\pi$
$510$	1.22281	+	1.02606i	0.0541470	+	0.0454347i
$511$		0			0
$512$	24.9186			1.10126
$513$	−18.3191	−	22.1611i	−0.808807	−	0.978437i
$514$	0.449493	+	0.778544i	0.0198263	+	0.0343401i
$515$	4.55303	−	1.65717i	0.200631	−	0.0730236i
$516$	−1.95084	+	0.710047i	−0.0858808	+	0.0312581i
$517$	−15.2554	−	5.55250i	−0.670930	−	0.244199i
$518$		0			0
$519$	44.4320	−	37.2829i	1.95035	−	1.63654i
$520$	6.66281			0.292183
$521$	9.29179			0.407081			0.203540	−	0.979067i	$-0.434755\pi$
$521$	9.29179			0.407081			0.203540	+	0.979067i	$0.434755\pi$
$522$	37.5658	−	31.5215i	1.64421	−	1.37966i
$523$	26.7015	+	9.71854i	1.16757	+	0.424962i	0.851797	−	0.523872i	$-0.175513\pi$
$523$	26.7015	+	9.71854i	1.16757	+	0.424962i	0.315776	+	0.948834i	$0.397735\pi$
$524$	0.170493	−	0.295303i	0.00744802	−	0.0129004i
$525$		0			0
$526$	−11.7654	+	9.87236i	−0.512996	+	0.430455i
$527$	−0.577382	+	3.27449i	−0.0251511	+	0.142639i
$528$	−4.00387	−	22.7071i	−0.174246	−	0.988199i
$529$	−2.73308	+	15.5001i	−0.118829	+	0.673916i
$530$	2.57532	+	2.16095i	0.111865	+	0.0938657i
$531$	−33.3610			−1.44775
$532$		0			0
$533$	6.37227			0.276014
$534$	−30.5822	−	25.6615i	−1.32342	−	1.11048i
$535$	1.56283	−	8.86327i	0.0675672	−	0.383193i
$536$	3.92303	+	22.2486i	0.169449	+	0.960993i
$537$	5.75624	−	32.6453i	0.248400	−	1.40875i
$538$	−20.0123	+	16.7923i	−0.862793	+	0.723969i
$539$		0			0
$540$	−0.535959	+	0.928309i	−0.0230640	+	0.0399480i
$541$	−14.0817	−	5.12533i	−0.605420	−	0.220355i	0.0210779	−	0.999778i	$-0.493290\pi$
$541$	−14.0817	−	5.12533i	−0.605420	−	0.220355i	−0.626498	+	0.779423i	$0.715512\pi$
$542$	13.8240	−	11.5998i	0.593794	−	0.498252i
$543$	−24.5817			−1.05490
$544$	−0.487511			−0.0209019
$545$	−1.22803	+	1.03044i	−0.0526028	+	0.0441390i
$546$		0			0
$547$	3.65270	+	1.32948i	0.156178	+	0.0568443i	0.418926	−	0.908020i	$-0.362407\pi$
$547$	3.65270	+	1.32948i	0.156178	+	0.0568443i	−0.262748	+	0.964864i	$0.584629\pi$
$548$	0.0444153	−	0.0161658i	0.00189733	−	0.000690571i
$549$	−45.3842	+	16.5185i	−1.93695	+	0.704992i
$550$	6.34002	+	10.9812i	0.270339	+	0.468242i
$551$	−29.4918	−	5.42437i	−1.25639	−	0.231086i
$552$	22.8384			0.972068
$553$		0			0
$554$	−18.3164	−	15.3693i	−0.778189	−	0.652978i
$555$	−9.58899	+	8.04612i	−0.407030	+	0.341539i
$556$	−0.603541	−	0.506431i	−0.0255958	−	0.0214774i
$557$	−12.4081	−	4.51617i	−0.525747	−	0.191356i	0.0654914	−	0.997853i	$-0.479138\pi$
$557$	−12.4081	−	4.51617i	−0.525747	−	0.191356i	−0.591238	+	0.806497i	$0.701361\pi$
$558$	50.6546			2.14438
$559$	−5.02141	+	8.69734i	−0.212383	+	0.367858i
$560$		0			0
$561$	0.520945	+	2.95442i	0.0219943	+	0.124736i
$562$	12.3136	+	21.3278i	0.519418	+	0.899659i
$563$	−5.35638	+	9.27752i	−0.225745	+	0.391001i	−0.956543	−	0.291593i	$-0.905815\pi$
$563$	−5.35638	+	9.27752i	−0.225745	+	0.391001i	0.730798	+	0.682594i	$0.239148\pi$
$564$	3.64543	+	1.32683i	0.153500	+	0.0558695i
$565$	−2.70099	+	15.3181i	−0.113631	+	0.644436i
$566$	9.73308	+	3.54255i	0.409112	+	0.148905i
$567$		0			0
$568$	−4.75641	+	26.9749i	−0.199574	+	1.13184i
$569$	6.73530	−	11.6659i	0.282358	−	0.489059i	−0.689607	−	0.724184i	$-0.742217\pi$
$569$	6.73530	−	11.6659i	0.282358	−	0.489059i	0.971965	+	0.235125i	$0.0755499\pi$
$570$	−14.6630	+	2.47432i	−0.614164	+	0.103638i
$571$	−6.33275	−	10.9686i	−0.265017	−	0.459023i	0.702551	−	0.711634i	$-0.252044\pi$
$571$	−6.33275	−	10.9686i	−0.265017	−	0.459023i	−0.967568	+	0.252610i	$0.918711\pi$
$572$	0.811337	+	0.680793i	0.0339237	+	0.0284654i
$573$	−40.4432	−	33.9358i	−1.68954	−	1.41769i
$574$		0			0
$575$	−10.7023	+	3.89533i	−0.446318	+	0.162447i
$576$	7.89780	+	44.7907i	0.329075	+	1.86628i
$577$	5.27719	−	9.14036i	0.219692	−	0.380518i	−0.735022	−	0.678044i	$-0.762828\pi$
$577$	5.27719	−	9.14036i	0.219692	−	0.380518i	0.954714	+	0.297526i	$0.0961613\pi$
$578$	22.6091			0.940413
$579$	0.805407	+	0.293144i	0.0334716	+	0.0121827i
$580$	0.194126	+	1.10094i	0.00806064	+	0.0457142i
$581$		0			0
$582$	−18.3366	−	31.7600i	−0.760077	−	1.31649i
$583$	1.09714	+	6.22221i	0.0454391	+	0.257698i
$584$	3.13247	+	2.62846i	0.129623	+	0.108766i
$585$	2.07960	+	11.7940i	0.0859810	+	0.487623i
$586$	−13.2973	+	4.83981i	−0.549305	+	0.199931i
$587$	−3.32619	+	18.8638i	−0.137287	+	0.778591i	0.835954	+	0.548800i	$0.184915\pi$
$587$	−3.32619	+	18.8638i	−0.137287	+	0.778591i	−0.973240	+	0.229791i	$0.926196\pi$
$588$		0			0
$589$	−19.7349	−	23.8739i	−0.813162	−	0.983706i
$590$	−3.73530	+	6.46973i	−0.153780	+	0.266355i
$591$	35.5565	−	12.9415i	1.46260	−	0.532342i
$592$	−3.08718	+	17.5083i	−0.126882	+	0.719586i
$593$	−6.66044	+	5.58878i	−0.273512	+	0.229504i	−0.769218	−	0.638987i	$-0.779354\pi$
$593$	−6.66044	+	5.58878i	−0.273512	+	0.229504i	0.495706	+	0.868490i	$0.334909\pi$
$594$	18.5954	−	6.76817i	0.762978	−	0.277701i
$595$		0			0
$596$	1.53003	+	2.65009i	0.0626724	+	0.108552i
$597$	−0.369585	−	0.640140i	−0.0151261	−	0.0261992i
$598$	7.15839	−	6.00660i	0.292728	−	0.245628i
$599$	15.1919	−	12.7475i	0.620724	−	0.520850i	−0.277307	−	0.960781i	$-0.589442\pi$
$599$	15.1919	−	12.7475i	0.620724	−	0.520850i	0.898031	+	0.439932i	$0.144997\pi$
$600$	−17.9119	−	31.0244i	−0.731252	−	1.26657i
$601$	16.8807	+	29.2383i	0.688579	+	1.19265i	0.972298	+	0.233747i	$0.0750986\pi$
$601$	16.8807	+	29.2383i	0.688579	+	1.19265i	−0.283718	+	0.958908i	$0.591568\pi$
$602$		0			0
$603$	−38.1584	+	13.8885i	−1.55393	+	0.565584i
$604$	0.617460	−	0.518110i	0.0251241	−	0.0210816i
$605$	−0.922618	+	5.23243i	−0.0375098	+	0.212729i
$606$	33.7165	−	12.2718i	1.36964	−	0.498507i
$607$	−17.6425	+	30.5577i	−0.716087	+	1.24030i	0.246452	+	0.969155i	$0.420735\pi$
$607$	−17.6425	+	30.5577i	−0.716087	+	1.24030i	−0.962539	+	0.271144i	$0.912598\pi$
$608$	2.94475	−	3.45740i	0.119425	−	0.140216i
$609$		0			0
$610$	−1.87804	+	10.6509i	−0.0760397	+	0.431242i
$611$	17.6348	−	6.41852i	0.713426	−	0.259666i
$612$	−0.0794409	−	0.450532i	−0.00321121	−	0.0182117i
$613$	14.1361	+	11.8616i	0.570952	+	0.479085i	0.881962	−	0.471321i	$-0.156223\pi$
$613$	14.1361	+	11.8616i	0.570952	+	0.479085i	−0.311010	+	0.950407i	$0.600667\pi$
$614$	2.73623	+	15.5180i	0.110425	+	0.626254i
$615$	3.13429	+	5.42874i	0.126387	+	0.218908i
$616$		0			0
$617$	−6.19671	−	35.1433i	−0.249470	−	1.41482i	−0.809878	−	0.586598i	$-0.800467\pi$
$617$	−6.19671	−	35.1433i	−0.249470	−	1.41482i	0.560408	−	0.828217i	$-0.310644\pi$
$618$	20.0856	+	7.31056i	0.807961	+	0.294074i
$619$	3.65951			0.147088			0.0735441	−	0.997292i	$-0.476569\pi$
$619$	3.65951			0.147088			0.0735441	+	0.997292i	$0.476569\pi$
$620$	−0.577382	+	1.00005i	−0.0231882	+	0.0401631i
$621$	3.08647	+	17.5042i	0.123856	+	0.702420i
$622$	20.2135	−	7.35710i	0.810487	−	0.294993i
$623$		0			0
$624$	20.4179	+	17.1326i	0.817369	+	0.685854i
$625$	10.7233	+	8.99790i	0.428931	+	0.359916i
$626$	−17.9383	−	31.0701i	−0.716961	−	1.24181i
$627$	−24.0993	−	14.1513i	−0.962432	−	0.565148i
$628$	−0.888719	+	1.53931i	−0.0354637	+	0.0614250i
$629$	0.401674	−	2.27801i	0.0160158	−	0.0908301i
$630$		0			0
$631$	0.745977	+	0.271514i	0.0296969	+	0.0108088i	0.356826	−	0.934171i	$-0.383859\pi$
$631$	0.745977	+	0.271514i	0.0296969	+	0.0108088i	−0.327129	+	0.944980i	$0.606081\pi$
$632$	−6.05463	+	34.3375i	−0.240840	+	1.36587i
$633$	6.62449	+	2.41112i	0.263300	+	0.0958332i
$634$	19.8942	−	34.4578i	0.790101	−	1.36850i
$635$	−5.10220	−	8.83726i	−0.202474	−	0.350696i
$636$	−0.262174	−	1.48686i	−0.0103959	−	0.0589579i
$637$		0			0
$638$	10.3191	−	17.8732i	0.408536	−	0.707605i
$639$	−49.2336			−1.94765
$640$	7.84864	+	2.85667i	0.310245	+	0.112920i
$641$	22.5082	+	18.8866i	0.889021	+	0.745977i	0.968013	−	0.250898i	$-0.0807259\pi$
$641$	22.5082	+	18.8866i	0.889021	+	0.745977i	−0.0789927	+	0.996875i	$0.525170\pi$
$642$	30.4145	−	25.5208i	1.20036	−	1.00722i
$643$	17.0168	+	14.2788i	0.671078	+	0.563101i	0.913384	−	0.407098i	$-0.133459\pi$
$643$	17.0168	+	14.2788i	0.671078	+	0.563101i	−0.242306	+	0.970200i	$0.577904\pi$
$644$		0			0
$645$	−9.87939			−0.389000
$646$	1.78177	−	2.09196i	0.0701030	−	0.0823073i
$647$	−5.62954	−	9.75065i	−0.221320	−	0.383337i	0.733889	−	0.679269i	$-0.237703\pi$
$647$	−5.62954	−	9.75065i	−0.221320	−	0.383337i	−0.955209	+	0.295932i	$0.904370\pi$
$648$	−8.63176	+	3.14170i	−0.339088	+	0.123418i
$649$	−13.1934	+	4.80201i	−0.517887	+	0.188495i
$650$	−13.7738	−	5.01325i	−0.540252	−	0.196636i
$651$		0			0
$652$	−1.18273	+	0.992431i	−0.0463194	+	0.0388666i
$653$	27.0000			1.05659			0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000			1.05659			0.528296	+	0.849060i	$0.322831\pi$
$654$	−7.07192			−0.276534
$655$	1.24304	−	1.04303i	0.0485696	−	0.0407547i
$656$	8.36618	+	3.04504i	0.326645	+	0.118889i
$657$	−3.67499	+	6.36527i	−0.143375	+	0.248333i
$658$		0			0
$659$	21.4691	−	18.0147i	0.836317	−	0.701753i	−0.120415	−	0.992724i	$-0.538423\pi$
$659$	21.4691	−	18.0147i	0.836317	−	0.701753i	0.956732	+	0.290970i	$0.0939781\pi$
$660$	−0.180922	+	1.02606i	−0.00704238	+	0.0399393i
$661$	1.97400	+	11.1951i	0.0767798	+	0.435440i	0.998830	+	0.0483686i	$0.0154022\pi$
$661$	1.97400	+	11.1951i	0.0767798	+	0.435440i	−0.922050	+	0.387071i	$0.873487\pi$
$662$	−6.47250	+	36.7074i	−0.251561	+	1.42667i
$663$	−2.65657	−	2.22913i	−0.103173	−	0.0865722i
$664$	−43.6551			−1.69415
$665$		0			0
$666$	−35.2395			−1.36550
$667$	14.2003	+	11.9154i	0.549837	+	0.461368i
$668$	−0.129481	+	0.734325i	−0.00500978	+	0.0284119i
$669$	4.25490	+	24.1307i	0.164504	+	0.932948i
$670$	−1.57903	+	8.95513i	−0.0610033	+	0.345967i
$671$	−15.5706	+	13.0653i	−0.601095	+	0.504379i
$672$		0			0
$673$	8.28359	−	14.3476i	0.319309	−	0.553059i	−0.661035	−	0.750355i	$-0.729883\pi$
$673$	8.28359	−	14.3476i	0.319309	−	0.553059i	0.980344	+	0.197296i	$0.0632160\pi$
$674$	22.6113	+	8.22983i	0.870954	+	0.317001i
$675$	21.3576	−	17.9211i	0.822053	−	0.689784i
$676$	1.17799			0.0453071
$677$	−9.04963			−0.347806			−0.173903	−	0.984763i	$-0.555638\pi$
$677$	−9.04963			−0.347806			−0.173903	+	0.984763i	$0.555638\pi$
$678$	−52.5642	+	44.1066i	−2.01872	+	1.69390i
$679$		0			0
$680$	−1.13816	−	0.414255i	−0.0436463	−	0.0158859i
$681$	−38.2879	+	13.9357i	−1.46720	+	0.534016i
$682$	20.0326	−	7.29125i	0.767086	−	0.279197i
$683$	−4.36571	−	7.56164i	−0.167049	−	0.289338i	0.770332	−	0.637643i	$-0.220091\pi$
$683$	−4.36571	−	7.56164i	−0.167049	−	0.289338i	−0.937381	+	0.348305i	$0.886757\pi$
$684$	3.67499	+	2.15799i	0.140517	+	0.0825126i
$685$	0.224927			0.00859402
$686$		0			0
$687$	45.2904	+	38.0032i	1.72794	+	1.44991i
$688$	−10.7487	+	9.01925i	−0.409791	+	0.343856i
$689$	−5.59492	−	4.69470i	−0.213150	−	0.178854i
$690$	8.63816	+	3.14403i	0.328849	+	0.119691i
$691$	34.7202			1.32082			0.660409	−	0.750906i	$-0.270383\pi$
$691$	34.7202			1.32082			0.660409	+	0.750906i	$0.270383\pi$
$692$	−1.86122	+	3.22372i	−0.0707528	+	0.122547i
$693$		0			0
$694$	1.35710	+	7.69648i	0.0515147	+	0.292154i
$695$	−1.87464	−	3.24697i	−0.0711091	−	0.123164i
$696$	−29.1536	+	50.4956i	−1.10507	+	1.91403i
$697$	−1.08853	−	0.396191i	−0.0412309	−	0.0150068i
$698$	−1.25687	+	7.12808i	−0.0475734	+	0.269802i
$699$	47.7588	+	17.3828i	1.80640	+	0.657478i
$700$		0			0
$701$	6.84436	−	38.8163i	0.258508	−	1.46607i	−0.528397	−	0.848997i	$-0.677207\pi$
$701$	6.84436	−	38.8163i	0.258508	−	1.46607i	0.786905	−	0.617074i	$-0.211682\pi$
$702$	−11.4376	+	19.8106i	−0.431686	+	0.747701i
$703$	13.7292	+	16.6086i	0.517807	+	0.626406i
$704$	9.57057	+	16.5767i	0.360705	+	0.624759i
$705$	14.1420	+	11.8666i	0.532620	+	0.446921i
$706$	26.0442	+	21.8537i	0.980185	+	0.822473i
$707$		0			0
$708$	3.15270	−	1.14749i	0.118486	−	0.0431253i
$709$	−7.14068	−	40.4968i	−0.268174	−	1.52089i	−0.759842	−	0.650107i	$-0.774724\pi$
$709$	−7.14068	−	40.4968i	−0.268174	−	1.52089i	0.491668	−	0.870783i	$-0.336387\pi$
$710$	−5.51249	+	9.54791i	−0.206880	+	0.358327i
$711$	−62.6715			−2.35036
$712$	28.4650	+	10.3604i	1.06677	+	0.388273i
$713$	3.32501	+	18.8571i	0.124523	+	0.706202i
$714$		0			0
$715$	2.52007	+	4.36488i	0.0942452	+	0.163237i
$716$	0.369423	+	2.09510i	0.0138060	+	0.0782976i
$717$	−5.18866	−	4.35381i	−0.193774	−	0.162596i
$718$	−1.56443	−	8.87230i	−0.0583839	−	0.331111i
$719$	39.8387	−	14.5001i	1.48573	−	0.540763i	0.533411	−	0.845856i	$-0.320910\pi$
$719$	39.8387	−	14.5001i	1.48573	−	0.540763i	0.952323	+	0.305093i	$0.0986875\pi$
$720$	−2.90554	+	16.4782i	−0.108283	+	0.614105i
$721$		0			0
$722$	4.07351	+	25.2724i	0.151600	+	0.940543i
$723$	19.8687	−	34.4136i	0.738925	−	1.27986i
$724$	1.48246	−	0.539571i	0.0550952	−	0.0200530i
$725$	5.04916	−	28.6352i	0.187521	−	1.06349i
$726$	−17.9552	+	15.0662i	−0.666379	+	0.559158i
$727$	−48.5411	+	17.6675i	−1.80029	+	0.655251i	−0.801965	+	0.597371i	$0.796212\pi$
$727$	−48.5411	+	17.6675i	−1.80029	+	0.655251i	−0.998324	+	0.0578805i	$0.981566\pi$
$728$		0			0
$729$	20.2344	+	35.0470i	0.749423	+	1.29804i
$730$	0.822948	+	1.42539i	0.0304587	+	0.0527560i
$731$	1.39852	−	1.17350i	0.0517261	−	0.0434033i
$732$	3.72075	−	3.12208i	0.137523	−	0.115395i
$733$	11.4581	+	19.8460i	0.423215	+	0.733030i	0.996252	−	0.0864997i	$-0.0275682\pi$
$733$	11.4581	+	19.8460i	0.423215	+	0.733030i	−0.573037	+	0.819530i	$0.694235\pi$
$734$	5.46926	+	9.47303i	0.201874	+	0.349656i
$735$		0			0
$736$	−2.63816	+	0.960210i	−0.0972437	+	0.0353938i
$737$	−13.0915	+	10.9851i	−0.482232	+	0.404641i
$738$	−3.06443	+	17.3792i	−0.112803	+	0.639738i
$739$	−26.4304	+	9.61986i	−0.972256	+	0.353872i	−0.778825	−	0.627241i	$-0.784184\pi$
$739$	−26.4304	+	9.61986i	−0.972256	+	0.353872i	−0.193432	+	0.981114i	$0.561962\pi$
$740$	0.401674	−	0.695720i	0.0147658	−	0.0255752i
$741$	31.8555	−	5.37549i	1.17024	−	0.197474i
$742$		0			0
$743$	1.06489	−	6.03931i	0.0390671	−	0.221561i	−0.959024	−	0.283326i	$-0.908562\pi$
$743$	1.06489	−	6.03931i	0.0390671	−	0.221561i	0.998091	+	0.0617657i	$0.0196731\pi$
$744$	−56.5963	+	20.5994i	−2.07492	+	0.755210i
$745$	2.52869	+	14.3409i	0.0926439	+	0.525409i
$746$	−36.0174	−	30.2222i	−1.31869	−	1.10651i
$747$	−13.6257	−	77.2750i	−0.498537	−	2.82734i
$748$	−0.0962667	−	0.166739i	−0.00351986	−	0.00609657i
$749$		0			0
$750$	−5.46585	−	30.9984i	−0.199585	−	1.13190i
$751$	−5.30066	−	1.92928i	−0.193424	−	0.0704005i	0.243492	−	0.969903i	$-0.421707\pi$
$751$	−5.30066	−	1.92928i	−0.193424	−	0.0704005i	−0.436916	+	0.899502i	$0.643929\pi$
$752$	26.2199			0.956140
$753$	−5.99660	+	10.3864i	−0.218528	+	0.378502i
$754$	4.14274	+	23.4947i	0.150870	+	0.855625i
$755$	3.60442	−	1.31190i	0.131178	−	0.0477450i
$756$		0			0
$757$	12.0207	+	10.0866i	0.436900	+	0.366602i	0.834548	−	0.550936i	$-0.185729\pi$
$757$	12.0207	+	10.0866i	0.436900	+	0.366602i	−0.397648	+	0.917538i	$0.630173\pi$
$758$	−1.75600	−	1.47346i	−0.0637806	−	0.0535183i
$759$	8.63816	+	14.9617i	0.313545	+	0.543076i
$760$	9.81274	−	5.56947i	0.355945	−	0.202026i
$761$	−2.43242	+	4.21307i	−0.0881751	+	0.152724i	−0.906740	−	0.421691i	$-0.861437\pi$
$761$	−2.43242	+	4.21307i	−0.0881751	+	0.152724i	0.818565	+	0.574414i	$0.194770\pi$
$762$	7.81702	−	44.3325i	0.283181	−	1.60600i
$763$		0			0
$764$	3.18392	+	1.15885i	0.115190	+	0.0419257i
$765$	0.378041	−	2.14398i	0.0136681	−	0.0775157i
$766$	3.71806	+	1.35326i	0.134339	+	0.0488954i
$767$	8.11499	−	14.0556i	0.293015	−	0.507517i
$768$	−6.32888	−	10.9619i	−0.228374	−	0.395555i
$769$	3.91266	+	22.1898i	0.141094	+	0.800184i	0.970421	+	0.241420i	$0.0776131\pi$
$769$	3.91266	+	22.1898i	0.141094	+	0.800184i	−0.829327	+	0.558764i	$0.811276\pi$
$770$		0			0
$771$	0.960637	−	1.66387i	0.0345965	−	0.0599229i
$772$	−0.0550065			−0.00197973
$773$	24.8380	+	9.04028i	0.893359	+	0.325156i	0.747589	−	0.664162i	$-0.231212\pi$
$773$	24.8380	+	9.04028i	0.893359	+	0.325156i	0.145771	+	0.989318i	$0.453434\pi$
$774$	−21.3056	−	17.8775i

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.x (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.03209 - 0.866025i) q^{2} +(-0.500000 + 2.83564i) q^{3} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(2.97178 - 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(-4.97178 - 1.80958i) q^{9} +O(q^{10})\)	\(q+(-1.03209 - 0.866025i) q^{2} +(-0.500000 + 2.83564i) q^{3} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(2.97178 - 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(-4.97178 - 1.80958i) q^{9} +(-0.907604 + 0.761570i) q^{10} -2.22668 q^{11} +0.532089 q^{12} +(1.97178 - 1.65452i) q^{13} +(2.37939 + 0.866025i) q^{15} +(3.37939 - 1.23000i) q^{16} +(-0.439693 + 0.160035i) q^{17} +(3.56418 + 6.17334i) q^{18} +(1.52094 - 4.08494i) q^{19} -0.162504 q^{20} +(2.29813 + 1.92836i) q^{22} +(-2.06418 + 1.73205i) q^{23} +(-6.49273 - 5.44804i) q^{24} +(3.97178 + 1.44561i) q^{25} -3.46791 q^{26} +(3.29813 - 5.71253i) q^{27} +(-1.19459 - 6.77487i) q^{29} +(-1.70574 - 2.95442i) q^{30} +(3.55303 - 6.15403i) q^{31} +(0.979055 + 0.356347i) q^{32} +(1.11334 - 6.31407i) q^{33} +(0.592396 + 0.215615i) q^{34} +(-0.169778 + 0.962858i) q^{36} +(-2.47178 + 4.28125i) q^{37} +(-5.10741 + 2.89884i) q^{38} +(3.70574 + 6.41852i) q^{39} +(1.98293 + 1.66387i) q^{40} +(1.89646 + 1.59132i) q^{41} +(-3.66637 + 1.33445i) q^{43} +(0.0714517 + 0.405223i) q^{44} +(-2.32635 + 4.02936i) q^{45} +3.63041 q^{46} +(6.85117 + 2.49362i) q^{47} +(1.79813 + 10.1977i) q^{48} +(-2.84730 - 4.93166i) q^{50} +(-0.233956 - 1.32683i) q^{51} +(-0.364370 - 0.305743i) q^{52} +(-0.492726 - 2.79439i) q^{53} +(-8.35117 + 3.03958i) q^{54} +(-0.340022 + 1.92836i) q^{55} +(10.8229 + 6.35532i) q^{57} +(-4.63429 + 8.02682i) q^{58} +(5.92514 - 2.15658i) q^{59} +(0.0812519 - 0.460802i) q^{60} +(6.99273 - 5.86759i) q^{61} +(-8.99660 + 3.27449i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(-1.13176 - 1.96026i) q^{65} +(-6.61721 + 5.55250i) q^{66} +(5.87939 - 4.93339i) q^{67} +(0.0432332 + 0.0748822i) q^{68} +(-3.87939 - 6.71929i) q^{69} +(8.74422 - 3.18264i) q^{71} +(11.9304 - 10.0108i) q^{72} +(0.241230 - 1.36808i) q^{73} +(6.25877 - 2.27801i) q^{74} +(-6.08512 + 10.5397i) q^{75} +(-0.792204 - 0.145708i) q^{76} +(1.73396 - 9.83375i) q^{78} +(11.1309 - 4.05131i) q^{79} +(-0.549163 - 3.11446i) q^{80} +(2.39053 + 2.00589i) q^{81} +(-0.579193 - 3.28476i) q^{82} +(7.41534 + 12.8438i) q^{83} +(0.0714517 + 0.405223i) q^{85} +(4.93969 + 1.79790i) q^{86} +19.8084 q^{87} +(3.27719 - 5.67626i) q^{88} +(-1.78699 - 10.1345i) q^{89} +(5.89053 - 2.14398i) q^{90} +(0.381445 + 0.320070i) q^{92} +(15.6741 + 13.1521i) q^{93} +(-4.91147 - 8.50692i) q^{94} +(-3.30541 - 1.94096i) q^{95} +(-1.50000 + 2.59808i) q^{96} +(1.64156 - 9.30975i) q^{97} +(11.0706 + 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} - 9 q^{10} - 6 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{23} - 21 q^{24} + 9 q^{25} - 30 q^{26} + 6 q^{27} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 24 q^{36} + 3 q^{38} + 12 q^{39} - 9 q^{40} + 21 q^{41} - 3 q^{43} - 15 q^{45} + 36 q^{46} + 15 q^{47} - 3 q^{48} - 15 q^{50} - 6 q^{51} - 21 q^{52} + 15 q^{53} - 24 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 12 q^{62} - 12 q^{64} - 12 q^{65} - 9 q^{66} + 24 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 15 q^{79} - 15 q^{80} - 3 q^{81} + 45 q^{82} + 24 q^{86} + 42 q^{87} + 9 q^{88} - 3 q^{89} + 18 q^{90} + 42 q^{92} + 27 q^{93} - 9 q^{94} - 24 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 - 9 * q^10 - 6 * q^12 - 3 * q^13 + 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^23 - 21 * q^24 + 9 * q^25 - 30 * q^26 + 6 * q^27 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^36 + 3 * q^38 + 12 * q^39 - 9 * q^40 + 21 * q^41 - 3 * q^43 - 15 * q^45 + 36 * q^46 + 15 * q^47 - 3 * q^48 - 15 * q^50 - 6 * q^51 - 21 * q^52 + 15 * q^53 - 24 * q^54 + 18 * q^55 + 24 * q^57 - 18 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 12 * q^62 - 12 * q^64 - 12 * q^65 - 9 * q^66 + 24 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 - 15 * q^75 + 36 * q^76 + 15 * q^78 + 15 * q^79 - 15 * q^80 - 3 * q^81 + 45 * q^82 + 24 * q^86 + 42 * q^87 + 9 * q^88 - 3 * q^89 + 18 * q^90 + 42 * q^92 + 27 * q^93 - 9 * q^94 - 24 * q^95 - 9 * q^96 + 18 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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