LMFDB - Embedded newform 78.2.e.b.55.1

Newspace parameters

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.e (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	78.55
Dual form			78.2.e.b.61.1

$q$-expansion

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} -1.00000 q^{12} +(2.50000 - 2.59808i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} -1.00000 q^{18} +(1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.00000 q^{25} +(3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(4.50000 + 7.79423i) q^{29} +(0.500000 - 0.866025i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} -5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.50000 + 9.52628i) q^{37} +2.00000 q^{38} +(3.50000 + 0.866025i) q^{39} +1.00000 q^{40} +(-2.50000 - 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} +2.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{46} +2.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{50} -5.00000 q^{51} +(1.00000 + 3.46410i) q^{52} -1.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.00000 + 1.73205i) q^{56} +2.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(4.00000 - 6.92820i) q^{59} +1.00000 q^{60} +(5.50000 - 9.52628i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +2.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(3.00000 - 5.19615i) q^{69} -2.00000 q^{70} +(7.00000 - 12.1244i) q^{71} +(0.500000 - 0.866025i) q^{72} -13.0000 q^{73} +(-5.50000 + 9.52628i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(1.00000 + 1.73205i) q^{76} -4.00000 q^{77} +(1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(2.50000 - 4.33013i) q^{85} -10.0000 q^{86} +(-4.50000 + 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-1.00000 - 1.73205i) q^{89} +1.00000 q^{90} +(-2.00000 - 6.92820i) q^{91} +6.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-1.00000 + 1.73205i) q^{95} +1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +(-1.50000 + 2.59808i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - q^{10} - 2 q^{11} - 2 q^{12} + 5 q^{13} + 4 q^{14} - q^{15} - q^{16} - 5 q^{17} - 2 q^{18} + 2 q^{19} + q^{20} + 4 q^{21} + 2 q^{22} - 6 q^{23} - q^{24} - 8 q^{25} + 7 q^{26} - 2 q^{27} + 2 q^{28} + 9 q^{29} + q^{30} - 8 q^{31} + q^{32} + 2 q^{33} - 10 q^{34} - 2 q^{35} - q^{36} + 11 q^{37} + 4 q^{38} + 7 q^{39} + 2 q^{40} - 5 q^{41} + 2 q^{42} - 10 q^{43} + 4 q^{44} + q^{45} + 6 q^{46} + 4 q^{47} + q^{48} + 3 q^{49} - 4 q^{50} - 10 q^{51} + 2 q^{52} - 2 q^{53} - q^{54} + 2 q^{55} - 2 q^{56} + 4 q^{57} - 9 q^{58} + 8 q^{59} + 2 q^{60} + 11 q^{61} - 4 q^{62} + 2 q^{63} + 2 q^{64} - 5 q^{65} + 4 q^{66} - 2 q^{67} - 5 q^{68} + 6 q^{69} - 4 q^{70} + 14 q^{71} + q^{72} - 26 q^{73} - 11 q^{74} - 4 q^{75} + 2 q^{76} - 8 q^{77} + 2 q^{78} - 8 q^{79} + q^{80} - q^{81} + 5 q^{82} + 12 q^{83} - 2 q^{84} + 5 q^{85} - 20 q^{86} - 9 q^{87} + 2 q^{88} - 2 q^{89} + 2 q^{90} - 4 q^{91} + 12 q^{92} - 4 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} + 2 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9 - q^10 - 2 * q^11 - 2 * q^12 + 5 * q^13 + 4 * q^14 - q^15 - q^16 - 5 * q^17 - 2 * q^18 + 2 * q^19 + q^20 + 4 * q^21 + 2 * q^22 - 6 * q^23 - q^24 - 8 * q^25 + 7 * q^26 - 2 * q^27 + 2 * q^28 + 9 * q^29 + q^30 - 8 * q^31 + q^32 + 2 * q^33 - 10 * q^34 - 2 * q^35 - q^36 + 11 * q^37 + 4 * q^38 + 7 * q^39 + 2 * q^40 - 5 * q^41 + 2 * q^42 - 10 * q^43 + 4 * q^44 + q^45 + 6 * q^46 + 4 * q^47 + q^48 + 3 * q^49 - 4 * q^50 - 10 * q^51 + 2 * q^52 - 2 * q^53 - q^54 + 2 * q^55 - 2 * q^56 + 4 * q^57 - 9 * q^58 + 8 * q^59 + 2 * q^60 + 11 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 - 5 * q^65 + 4 * q^66 - 2 * q^67 - 5 * q^68 + 6 * q^69 - 4 * q^70 + 14 * q^71 + q^72 - 26 * q^73 - 11 * q^74 - 4 * q^75 + 2 * q^76 - 8 * q^77 + 2 * q^78 - 8 * q^79 + q^80 - q^81 + 5 * q^82 + 12 * q^83 - 2 * q^84 + 5 * q^85 - 20 * q^86 - 9 * q^87 + 2 * q^88 - 2 * q^89 + 2 * q^90 - 4 * q^91 + 12 * q^92 - 4 * q^93 + 2 * q^94 - 2 * q^95 + 2 * q^96 + 2 * q^97 - 3 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	−1.00000			−0.288675
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$	2.00000			0.534522
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$	−1.00000			−0.235702
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	2.00000			0.436436
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.00000			−0.800000
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$	−1.00000			−0.192450
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	0.893517	+	0.449029i	$0.148230\pi$
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	−0.0578882	+	0.998323i	$0.518437\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$	−5.00000			−0.857493
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.821995	+	0.569495i	$0.192861\pi$
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.0821995	+	0.996616i	$0.473806\pi$
$38$	2.00000			0.324443
$39$	3.50000	+	0.866025i	0.560449	+	0.138675i
$40$	1.00000			0.158114
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	0.602072	−	0.798441i	$-0.294342\pi$
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	−0.992507	+	0.122189i	$0.961009\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	0.179069	+	0.983836i	$0.442691\pi$
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	−0.941562	+	0.336840i	$0.890642\pi$
$44$	2.00000			0.301511
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	−5.00000			−0.700140
$52$	1.00000	+	3.46410i	0.138675	+	0.480384i
$53$	−1.00000			−0.137361			−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000			−0.137361			−0.0686803	+	0.997639i	$0.521879\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$	2.00000			0.264906
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$	1.00000			0.129099
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	1.00000	+	1.73205i	0.125988	+	0.218218i
$64$	1.00000			0.125000
$65$	−2.50000	+	2.59808i	−0.310087	+	0.322252i
$66$	2.00000			0.246183
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	−2.00000			−0.239046
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	−0.0666994	−	0.997773i	$-0.521247\pi$
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	0.897447	−	0.441123i	$-0.145420\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−13.0000			−1.52153			−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000			−1.52153			−0.760767	+	0.649025i	$0.775177\pi$
$74$	−5.50000	+	9.52628i	−0.639362	+	1.10741i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$	−4.00000			−0.455842
$78$	1.00000	+	3.46410i	0.113228	+	0.392232i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.50000	−	4.33013i	0.276079	−	0.478183i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$	2.50000	−	4.33013i	0.271163	−	0.469668i
$86$	−10.0000			−1.07833
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	0.808146	−	0.588982i	$-0.200471\pi$
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	−0.914146	+	0.405385i	$0.867138\pi$
$90$	1.00000			0.105409
$91$	−2.00000	−	6.92820i	−0.209657	−	0.726273i
$92$	6.00000			0.625543
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$	1.00000			0.102062
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	−1.50000	+	2.59808i	−0.151523	+	0.262445i
$99$	2.00000			0.201008
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	0.963182	−	0.268851i	$-0.0866439\pi$
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	−0.714423	+	0.699715i	$0.753311\pi$
$102$	−2.50000	−	4.33013i	−0.247537	−	0.428746i
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$	−2.00000			−0.195180
$106$	−0.500000	−	0.866025i	−0.0485643	−	0.0841158i
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.861931	+	0.507026i	$0.169255\pi$
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.00813215	+	0.999967i	$0.497411\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$	−5.50000	+	9.52628i	−0.522037	+	0.904194i
$112$	−2.00000			−0.188982
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	−0.786806	−	0.617200i	$-0.788267\pi$
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	0.927914	+	0.372794i	$0.121600\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	3.00000	+	5.19615i	0.279751	+	0.484544i
$116$	−9.00000			−0.835629
$117$	1.00000	+	3.46410i	0.0924500	+	0.320256i
$118$	8.00000			0.736460
$119$	5.00000	+	8.66025i	0.458349	+	0.793884i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	11.0000			0.995893
$123$	2.50000	−	4.33013i	0.225417	−	0.390434i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	9.00000			0.804984
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	6.00000	+	10.3923i	0.532414	+	0.922168i	0.999284	+	0.0378419i	$0.0120483\pi$
$127$	6.00000	+	10.3923i	0.532414	+	0.922168i	−0.466870	+	0.884326i	$0.654618\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−10.0000			−0.880451
$130$	−3.50000	−	0.866025i	−0.306970	−	0.0759555i
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	1.00000	+	1.73205i	0.0870388	+	0.150756i
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$	1.00000			0.0860663
$136$	2.50000	−	4.33013i	0.214373	−	0.371305i
$137$	−8.50000	+	14.7224i	−0.726204	+	1.25782i	0.232273	+	0.972651i	$0.425384\pi$
$137$	−8.50000	+	14.7224i	−0.726204	+	1.25782i	−0.958477	+	0.285171i	$0.907949\pi$
$138$	6.00000			0.510754
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	−0.491033	−	0.871141i	$-0.663381\pi$
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	0.999947	−	0.0103230i	$-0.00328598\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$	1.00000	+	1.73205i	0.0842152	+	0.145865i
$142$	14.0000			1.17485
$143$	−7.00000	−	1.73205i	−0.585369	−	0.144841i
$144$	1.00000			0.0833333
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$	−6.50000	−	11.2583i	−0.537944	−	0.931746i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$	−11.0000			−0.904194
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	−6.00000			−0.488273			−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000			−0.488273			−0.244137	+	0.969741i	$0.578505\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$	−2.50000	−	4.33013i	−0.202113	−	0.350070i
$154$	−2.00000	−	3.46410i	−0.161165	−	0.279145i
$155$	4.00000			0.321288
$156$	−2.50000	+	2.59808i	−0.200160	+	0.208013i
$157$	−7.00000			−0.558661			−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000			−0.558661			−0.279330	+	0.960195i	$0.590112\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$	−0.500000	−	0.866025i	−0.0396526	−	0.0686803i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−12.0000			−0.945732
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	5.00000			0.390434
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	−12.0000	−	20.7846i	−0.928588	−	1.60836i	−0.785687	−	0.618624i	$-0.787690\pi$
$167$	−12.0000	−	20.7846i	−0.928588	−	1.60836i	−0.142901	−	0.989737i	$-0.545643\pi$
$168$	−2.00000			−0.154303
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	5.00000			0.383482
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	−0.0566411	−	0.998395i	$-0.518039\pi$
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	0.892956	−	0.450145i	$-0.148628\pi$
$174$	−9.00000			−0.682288
$175$	−4.00000	+	6.92820i	−0.302372	+	0.523723i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	8.00000			0.601317
$178$	1.00000	−	1.73205i	0.0749532	−	0.129823i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	5.00000	−	5.19615i	0.370625	−	0.385164i
$183$	11.0000			0.813143
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	−5.50000	−	9.52628i	−0.404368	−	0.700386i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	10.0000			0.731272
$188$	−1.00000	+	1.73205i	−0.0729325	+	0.126323i
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$	−2.00000			−0.145095
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	−0.929267	−	0.369410i	$-0.879560\pi$
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	0.784552	+	0.620063i	$0.212893\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	8.50000	+	14.7224i	0.611843	+	1.05974i	0.990930	+	0.134382i	$0.0429051\pi$
$193$	8.50000	+	14.7224i	0.611843	+	1.05974i	−0.379086	+	0.925361i	$0.623762\pi$
$194$	2.00000			0.143592
$195$	−3.50000	−	0.866025i	−0.250640	−	0.0620174i
$196$	−3.00000			−0.214286
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$	4.00000			0.282843
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	−2.50000	+	4.33013i	−0.175899	+	0.304667i
$203$	18.0000			1.26335
$204$	2.50000	−	4.33013i	0.175035	−	0.303170i
$205$	2.50000	+	4.33013i	0.174608	+	0.302429i
$206$	5.00000	+	8.66025i	0.348367	+	0.603388i
$207$	6.00000			0.417029
$208$	−3.50000	−	0.866025i	−0.242681	−	0.0600481i
$209$	−4.00000			−0.276686
$210$	−1.00000	−	1.73205i	−0.0690066	−	0.119523i
$211$	−12.0000	−	20.7846i	−0.826114	−	1.43087i	−0.901065	−	0.433684i	$-0.857213\pi$
$211$	−12.0000	−	20.7846i	−0.826114	−	1.43087i	0.0749508	−	0.997187i	$-0.476120\pi$
$212$	0.500000	−	0.866025i	0.0343401	−	0.0594789i
$213$	14.0000			0.959264
$214$	−9.00000	+	15.5885i	−0.615227	+	1.06561i
$215$	5.00000	−	8.66025i	0.340997	−	0.590624i
$216$	1.00000			0.0680414
$217$	−4.00000	+	6.92820i	−0.271538	+	0.470317i
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$	−6.50000	−	11.2583i	−0.439229	−	0.760767i
$220$	−2.00000			−0.134840
$221$	5.00000	+	17.3205i	0.336336	+	1.16510i
$222$	−11.0000			−0.738272
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	0.999128	+	0.0417488i	$0.0132929\pi$
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	−0.463409	+	0.886145i	$0.653374\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$	3.00000			0.199557
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	−0.999184	−	0.0403978i	$-0.987137\pi$
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	0.534577	+	0.845120i	$0.320471\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	−3.00000	+	5.19615i	−0.197814	+	0.342624i
$231$	−2.00000	−	3.46410i	−0.131590	−	0.227921i
$232$	−4.50000	−	7.79423i	−0.295439	−	0.511716i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$	−2.50000	+	2.59808i	−0.163430	+	0.169842i
$235$	−2.00000			−0.130466
$236$	4.00000	+	6.92820i	0.260378	+	0.450988i
$237$	−2.00000	−	3.46410i	−0.129914	−	0.225018i
$238$	−5.00000	+	8.66025i	−0.324102	+	0.561361i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	−0.956456	−	0.291877i	$-0.905720\pi$
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	0.731001	+	0.682376i	$0.239053\pi$
$242$	7.00000			0.449977
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	5.50000	+	9.52628i	0.352101	+	0.609858i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	5.00000			0.318788
$247$	−2.00000	−	6.92820i	−0.127257	−	0.440831i
$248$	4.00000			0.254000
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	−2.00000	+	3.46410i	−0.126239	+	0.218652i	−0.922217	−	0.386674i	$-0.873624\pi$
$251$	−2.00000	+	3.46410i	−0.126239	+	0.218652i	0.795978	+	0.605326i	$0.206957\pi$
$252$	−2.00000			−0.125988
$253$	−6.00000	+	10.3923i	−0.377217	+	0.653359i
$254$	−6.00000	+	10.3923i	−0.376473	+	0.652071i
$255$	5.00000			0.313112
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$	−5.00000	−	8.66025i	−0.311286	−	0.539164i
$259$	22.0000			1.36701
$260$	−1.00000	−	3.46410i	−0.0620174	−	0.214834i
$261$	−9.00000			−0.557086
$262$	−4.00000	−	6.92820i	−0.247121	−	0.428026i
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	0.565376	−	0.824833i	$-0.308731\pi$
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	−0.997015	+	0.0772134i	$0.975398\pi$
$264$	−1.00000	+	1.73205i	−0.0615457	+	0.106600i
$265$	1.00000			0.0614295
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	1.00000	−	1.73205i	0.0611990	−	0.106000i
$268$	2.00000			0.122169
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	−0.569789	−	0.821791i	$-0.692975\pi$
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	0.996586	+	0.0825561i	$0.0263084\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	0.718580	−	0.695444i	$-0.244792\pi$
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	−0.961563	+	0.274586i	$0.911459\pi$
$272$	5.00000			0.303170
$273$	5.00000	−	5.19615i	0.302614	−	0.314485i
$274$	−17.0000			−1.02701
$275$	4.00000	+	6.92820i	0.241209	+	0.417786i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	−0.652140	−	0.758099i	$-0.726128\pi$
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	0.982603	+	0.185720i	$0.0594618\pi$
$278$	12.0000			0.719712
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$	1.00000	−	1.73205i	0.0597614	−	0.103510i
$281$	25.0000			1.49137			0.745687	−	0.666296i	$-0.232121\pi$
$281$	25.0000			1.49137			0.745687	+	0.666296i	$0.232121\pi$
$282$	−1.00000	+	1.73205i	−0.0595491	+	0.103142i
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	−0.936039	−	0.351895i	$-0.885537\pi$
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	0.163270	−	0.986581i	$-0.447796\pi$
$284$	7.00000	+	12.1244i	0.415374	+	0.719448i
$285$	−2.00000			−0.118470
$286$	−2.00000	−	6.92820i	−0.118262	−	0.409673i
$287$	−10.0000			−0.590281
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	4.50000	−	7.79423i	0.264249	−	0.457693i
$291$	2.00000			0.117242
$292$	6.50000	−	11.2583i	0.380384	−	0.658844i
$293$	0.500000	−	0.866025i	0.0292103	−	0.0505937i	−0.851051	−	0.525084i	$-0.824034\pi$
$293$	0.500000	−	0.866025i	0.0292103	−	0.0505937i	0.880261	+	0.474490i	$0.157367\pi$
$294$	−3.00000			−0.174964
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	−5.50000	−	9.52628i	−0.319681	−	0.553704i
$297$	1.00000	+	1.73205i	0.0580259	+	0.100504i
$298$	−3.00000			−0.173785
$299$	−21.0000	−	5.19615i	−1.21446	−	0.300501i
$300$	4.00000			0.230940
$301$	10.0000	+	17.3205i	0.576390	+	0.998337i
$302$	−3.00000	−	5.19615i	−0.172631	−	0.299005i
$303$	−2.50000	+	4.33013i	−0.143621	+	0.248759i
$304$	−2.00000			−0.114708
$305$	−5.50000	+	9.52628i	−0.314929	+	0.545473i
$306$	2.50000	−	4.33013i	0.142915	−	0.247537i
$307$	−14.0000			−0.799022			−0.399511	−	0.916728i	$-0.630820\pi$
$307$	−14.0000			−0.799022			−0.399511	+	0.916728i	$0.630820\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$	5.00000	+	8.66025i	0.284440	+	0.492665i
$310$	2.00000	+	3.46410i	0.113592	+	0.196748i
$311$	6.00000			0.340229			0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000			0.340229			0.170114	+	0.985424i	$0.445586\pi$
$312$	−3.50000	−	0.866025i	−0.198148	−	0.0490290i
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	−3.50000	−	6.06218i	−0.197516	−	0.342108i
$315$	−1.00000	−	1.73205i	−0.0563436	−	0.0975900i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−33.0000			−1.85346			−0.926732	−	0.375722i	$-0.877395\pi$
$317$	−33.0000			−1.85346			−0.926732	+	0.375722i	$0.877395\pi$
$318$	0.500000	−	0.866025i	0.0280386	−	0.0485643i
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$	−1.00000			−0.0559017
$321$	−9.00000	+	15.5885i	−0.502331	+	0.870063i
$322$	−6.00000	−	10.3923i	−0.334367	−	0.579141i
$323$	5.00000	+	8.66025i	0.278207	+	0.481869i
$324$	1.00000			0.0555556
$325$	−10.0000	+	10.3923i	−0.554700	+	0.576461i
$326$	−20.0000			−1.10770
$327$	−1.00000	−	1.73205i	−0.0553001	−	0.0957826i
$328$	2.50000	+	4.33013i	0.138039	+	0.239091i
$329$	2.00000	−	3.46410i	0.110264	−	0.190982i
$330$	−2.00000			−0.110096
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	−11.0000			−0.602796
$334$	12.0000	−	20.7846i	0.656611	−	1.13728i
$335$	1.00000	+	1.73205i	0.0546358	+	0.0946320i
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$	−9.00000			−0.490261			−0.245131	−	0.969490i	$-0.578831\pi$
$337$	−9.00000			−0.490261			−0.245131	+	0.969490i	$0.578831\pi$
$338$	11.0000	−	6.92820i	0.598321	−	0.376845i
$339$	3.00000			0.162938
$340$	2.50000	+	4.33013i	0.135582	+	0.234834i
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	−1.00000	+	1.73205i	−0.0540738	+	0.0936586i
$343$	20.0000			1.07990
$344$	5.00000	−	8.66025i	0.269582	−	0.466930i
$345$	−3.00000	+	5.19615i	−0.161515	+	0.279751i
$346$	22.0000			1.18273
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	−0.935245	−	0.354001i	$-0.884821\pi$
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	0.774197	+	0.632945i	$0.218154\pi$
$348$	−4.50000	−	7.79423i	−0.241225	−	0.417815i
$349$	−3.00000	−	5.19615i	−0.160586	−	0.278144i	0.774493	−	0.632583i	$-0.218005\pi$
$349$	−3.00000	−	5.19615i	−0.160586	−	0.278144i	−0.935079	+	0.354439i	$0.884672\pi$
$350$	−8.00000			−0.427618
$351$	−2.50000	+	2.59808i	−0.133440	+	0.138675i
$352$	−2.00000			−0.106600
$353$	−8.50000	−	14.7224i	−0.452409	−	0.783596i	0.546126	−	0.837703i	$-0.316102\pi$
$353$	−8.50000	−	14.7224i	−0.452409	−	0.783596i	−0.998535	+	0.0541072i	$0.982769\pi$
$354$	4.00000	+	6.92820i	0.212598	+	0.368230i
$355$	−7.00000	+	12.1244i	−0.371521	+	0.643494i
$356$	2.00000			0.106000
$357$	−5.00000	+	8.66025i	−0.264628	+	0.458349i
$358$	−3.00000	+	5.19615i	−0.158555	+	0.274625i
$359$	−30.0000			−1.58334			−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000			−1.58334			−0.791670	+	0.610949i	$0.790788\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	2.50000	+	4.33013i	0.131397	+	0.227586i
$363$	7.00000			0.367405
$364$	7.00000	+	1.73205i	0.366900	+	0.0907841i
$365$	13.0000			0.680451
$366$	5.50000	+	9.52628i	0.287490	+	0.497947i
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	0.890945	−	0.454112i	$-0.150043\pi$
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	−0.838745	+	0.544524i	$0.816710\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$	5.00000			0.260290
$370$	5.50000	−	9.52628i	0.285931	−	0.495248i
$371$	−1.00000	+	1.73205i	−0.0519174	+	0.0899236i
$372$	4.00000			0.207390
$373$	−4.50000	+	7.79423i	−0.233001	+	0.403570i	−0.958690	−	0.284453i	$-0.908188\pi$
$373$	−4.50000	+	7.79423i	−0.233001	+	0.403570i	0.725689	+	0.688023i	$0.241521\pi$
$374$	5.00000	+	8.66025i	0.258544	+	0.447811i
$375$	4.50000	+	7.79423i	0.232379	+	0.402492i
$376$	−2.00000			−0.103142
$377$	31.5000	+	7.79423i	1.62233	+	0.401423i
$378$	−2.00000			−0.102869
$379$	−6.00000	−	10.3923i	−0.308199	−	0.533817i	0.669769	−	0.742569i	$-0.266393\pi$
$379$	−6.00000	−	10.3923i	−0.308199	−	0.533817i	−0.977969	+	0.208752i	$0.933060\pi$
$380$	−1.00000	−	1.73205i	−0.0512989	−	0.0888523i
$381$	−6.00000	+	10.3923i	−0.307389	+	0.532414i
$382$	−4.00000			−0.204658
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	4.00000			0.203859
$386$	−8.50000	+	14.7224i	−0.432639	+	0.749352i
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	19.0000			0.963338			0.481669	−	0.876353i	$-0.340031\pi$
$389$	19.0000			0.963338			0.481669	+	0.876353i	$0.340031\pi$
$390$	−1.00000	−	3.46410i	−0.0506370	−	0.175412i
$391$	30.0000			1.51717
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$	−4.00000	−	6.92820i	−0.201773	−	0.349482i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$	4.00000			0.201262
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	−0.546795	−	0.837267i	$-0.684152\pi$
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	0.998492	+	0.0549046i	$0.0174855\pi$
$398$	−10.0000			−0.501255
$399$	2.00000	−	3.46410i	0.100125	−	0.173422i
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$	2.00000			0.0997509
$403$	−10.0000	+	10.3923i	−0.498135	+	0.517678i
$404$	−5.00000			−0.248759
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	9.00000	+	15.5885i	0.446663	+	0.773642i
$407$	11.0000	−	19.0526i	0.545250	−	0.944400i
$408$	5.00000			0.247537
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	0.428063	+	0.903749i	$0.359196\pi$
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	−0.996701	+	0.0811615i	$0.974137\pi$
$410$	−2.50000	+	4.33013i	−0.123466	+	0.213850i
$411$	−17.0000			−0.838548
$412$	−5.00000	+	8.66025i	−0.246332	+	0.426660i
$413$	−8.00000	−	13.8564i	−0.393654	−	0.681829i
$414$	3.00000	+	5.19615i	0.147442	+	0.255377i
$415$	−6.00000			−0.294528
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$	12.0000			0.587643
$418$	−2.00000	−	3.46410i	−0.0978232	−	0.169435i
$419$	16.0000	+	27.7128i	0.781651	+	1.35386i	0.930979	+	0.365072i	$0.118956\pi$
$419$	16.0000	+	27.7128i	0.781651	+	1.35386i	−0.149328	+	0.988788i	$0.547711\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	−23.0000			−1.12095			−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000			−1.12095			−0.560476	+	0.828171i	$0.689382\pi$
$422$	12.0000	−	20.7846i	0.584151	−	1.01178i
$423$	−1.00000	+	1.73205i	−0.0486217	+	0.0842152i
$424$	1.00000			0.0485643
$425$	10.0000	−	17.3205i	0.485071	−	0.840168i
$426$	7.00000	+	12.1244i	0.339151	+	0.587427i
$427$	−11.0000	−	19.0526i	−0.532327	−	0.922018i
$428$	−18.0000			−0.870063
$429$	−2.00000	−	6.92820i	−0.0965609	−	0.334497i
$430$	10.0000			0.482243
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	10.5000	−	18.1865i	0.504598	−	0.873989i	−0.495388	−	0.868672i	$-0.664974\pi$
$433$	10.5000	−	18.1865i	0.504598	−	0.873989i	0.999986	−	0.00531724i	$-0.00169254\pi$
$434$	−8.00000			−0.384012
$435$	4.50000	−	7.79423i	0.215758	−	0.373705i
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−12.0000			−0.574038
$438$	6.50000	−	11.2583i	0.310582	−	0.537944i
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$	−1.00000	−	1.73205i	−0.0476731	−	0.0825723i
$441$	−3.00000			−0.142857
$442$	−12.5000	+	12.9904i	−0.594564	+	0.617889i
$443$	20.0000			0.950229			0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000			0.950229			0.475114	+	0.879924i	$0.342407\pi$
$444$	−5.50000	−	9.52628i	−0.261018	−	0.452097i
$445$	1.00000	+	1.73205i	0.0474045	+	0.0821071i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	−3.00000			−0.141895
$448$	1.00000	−	1.73205i	0.0472456	−	0.0818317i
$449$	15.0000	−	25.9808i	0.707894	−	1.22611i	−0.257743	−	0.966213i	$-0.582979\pi$
$449$	15.0000	−	25.9808i	0.707894	−	1.22611i	0.965637	−	0.259895i	$-0.0836878\pi$
$450$	4.00000			0.188562
$451$	−5.00000	+	8.66025i	−0.235441	+	0.407795i
$452$	1.50000	+	2.59808i	0.0705541	+	0.122203i
$453$	−3.00000	−	5.19615i	−0.140952	−	0.244137i
$454$	−14.0000			−0.657053
$455$	2.00000	+	6.92820i	0.0937614	+	0.324799i
$456$	−2.00000			−0.0936586
$457$	−1.50000	−	2.59808i	−0.0701670	−	0.121533i	0.828807	−	0.559534i	$-0.189020\pi$
$457$	−1.50000	−	2.59808i	−0.0701670	−	0.121533i	−0.898974	+	0.438001i	$0.855687\pi$
$458$	5.00000	+	8.66025i	0.233635	+	0.404667i
$459$	2.50000	−	4.33013i	0.116690	−	0.202113i
$460$	−6.00000			−0.279751
$461$	−1.50000	+	2.59808i	−0.0698620	+	0.121004i	−0.898840	−	0.438276i	$-0.855589\pi$
$461$	−1.50000	+	2.59808i	−0.0698620	+	0.121004i	0.828978	+	0.559281i	$0.188923\pi$
$462$	2.00000	−	3.46410i	0.0930484	−	0.161165i
$463$	−14.0000			−0.650635			−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000			−0.650635			−0.325318	+	0.945605i	$0.605471\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$	2.00000	+	3.46410i	0.0927478	+	0.160644i
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−22.0000			−1.01804			−0.509019	−	0.860755i	$-0.669992\pi$
$467$	−22.0000			−1.01804			−0.509019	+	0.860755i	$0.669992\pi$
$468$	−3.50000	−	0.866025i	−0.161788	−	0.0400320i
$469$	−4.00000			−0.184703
$470$	−1.00000	−	1.73205i	−0.0461266	−	0.0798935i
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	−4.00000	+	6.92820i	−0.184115	+	0.318896i
$473$	20.0000			0.919601
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$	−4.00000	+	6.92820i	−0.183533	+	0.317888i
$476$	−10.0000			−0.458349
$477$	0.500000	−	0.866025i	0.0228934	−	0.0396526i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	−16.0000	−	27.7128i	−0.731059	−	1.26623i	−0.956431	−	0.291958i	$-0.905693\pi$
$479$	−16.0000	−	27.7128i	−0.731059	−	1.26623i	0.225372	−	0.974273i	$-0.427640\pi$
$480$	−1.00000			−0.0456435
$481$	38.5000	+	9.52628i	1.75545	+	0.434361i
$482$	−7.00000			−0.318841
$483$	−6.00000	−	10.3923i	−0.273009	−	0.472866i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	1.00000			0.0453609
$487$	13.0000	−	22.5167i	0.589086	−	1.02033i	−0.405266	−	0.914199i	$-0.632821\pi$
$487$	13.0000	−	22.5167i	0.589086	−	1.02033i	0.994352	−	0.106129i	$-0.0338455\pi$
$488$	−5.50000	+	9.52628i	−0.248973	+	0.431234i
$489$	−20.0000			−0.904431
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	0.975898	+	0.218229i	$0.0700279\pi$
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	−0.298957	+	0.954267i	$0.596639\pi$
$492$	2.50000	+	4.33013i	0.112709	+	0.195217i
$493$	−45.0000			−2.02670
$494$	5.00000	−	5.19615i	0.224961	−	0.233786i
$495$	−2.00000			−0.0898933
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−14.0000	−	24.2487i	−0.627986	−	1.08770i
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$	−4.00000			−0.178529
$503$	7.00000	−	12.1244i	0.312115	−	0.540598i	−0.666705	−	0.745321i	$-0.732296\pi$
$503$	7.00000	−	12.1244i	0.312115	−	0.540598i	0.978820	+	0.204723i	$0.0656294\pi$
$504$	−1.00000	−	1.73205i	−0.0445435	−	0.0771517i
$505$	−2.50000	−	4.33013i	−0.111249	−	0.192688i
$506$	−12.0000			−0.533465
$507$	11.0000	−	6.92820i	0.488527	−	0.307692i
$508$	−12.0000			−0.532414
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$	2.50000	+	4.33013i	0.110702	+	0.191741i
$511$	−13.0000	+	22.5167i	−0.575086	+	0.996078i
$512$	−1.00000			−0.0441942
$513$	−1.00000	+	1.73205i	−0.0441511	+	0.0764719i
$514$	−1.50000	+	2.59808i	−0.0661622	+	0.114596i
$515$	−10.0000			−0.440653
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	−2.00000	−	3.46410i	−0.0879599	−	0.152351i
$518$	11.0000	+	19.0526i	0.483312	+	0.837121i
$519$	22.0000			0.965693
$520$	2.50000	−	2.59808i	0.109632	−	0.113933i
$521$	25.0000			1.09527			0.547635	−	0.836717i	$-0.315528\pi$
$521$	25.0000			1.09527			0.547635	+	0.836717i	$0.315528\pi$
$522$	−4.50000	−	7.79423i	−0.196960	−	0.341144i
$523$	19.0000	+	32.9090i	0.830812	+	1.43901i	0.897395	+	0.441228i	$0.145457\pi$
$523$	19.0000	+	32.9090i	0.830812	+	1.43901i	−0.0665832	+	0.997781i	$0.521210\pi$
$524$	4.00000	−	6.92820i	0.174741	−	0.302660i
$525$	−8.00000			−0.349149
$526$	7.00000	−	12.1244i	0.305215	−	0.528647i
$527$	10.0000	−	17.3205i	0.435607	−	0.754493i
$528$	−2.00000			−0.0870388
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	0.500000	+	0.866025i	0.0217186	+	0.0376177i
$531$	4.00000	+	6.92820i	0.173585	+	0.300658i
$532$	4.00000			0.173422
$533$	−17.5000	−	4.33013i	−0.758009	−	0.187559i
$534$	2.00000			0.0865485
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	−3.00000	+	5.19615i	−0.129460	+	0.224231i
$538$	14.0000			0.603583
$539$	3.00000	−	5.19615i	0.129219	−	0.223814i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−7.00000			−0.300954			−0.150477	−	0.988614i	$-0.548081\pi$
$541$	−7.00000			−0.300954			−0.150477	+	0.988614i	$0.548081\pi$
$542$	4.00000	−	6.92820i	0.171815	−	0.297592i
$543$	2.50000	+	4.33013i	0.107285	+	0.185824i
$544$	2.50000	+	4.33013i	0.107187	+	0.185653i
$545$	2.00000			0.0856706
$546$	7.00000	+	1.73205i	0.299572	+	0.0741249i
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	−8.50000	−	14.7224i	−0.363102	−	0.628911i
$549$	5.50000	+	9.52628i	0.234734	+	0.406572i
$550$	−4.00000	+	6.92820i	−0.170561	+	0.295420i
$551$	18.0000			0.766826
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	11.0000			0.467345
$555$	5.50000	−	9.52628i	0.233462	−	0.404368i
$556$	6.00000	+	10.3923i	0.254457	+	0.440732i
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	0.945473	−	0.325701i	$-0.105600\pi$
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	−0.754802	+	0.655953i	$0.772267\pi$
$558$	4.00000			0.169334
$559$	10.0000	+	34.6410i	0.422955	+	1.46516i
$560$	2.00000			0.0845154
$561$	5.00000	+	8.66025i	0.211100	+	0.365636i
$562$	12.5000	+	21.6506i	0.527281	+	0.913277i
$563$	−20.0000	+	34.6410i	−0.842900	+	1.45994i	0.0445334	+	0.999008i	$0.485820\pi$
$563$	−20.0000	+	34.6410i	−0.842900	+	1.45994i	−0.887433	+	0.460937i	$0.847513\pi$
$564$	−2.00000			−0.0842152
$565$	−1.50000	+	2.59808i	−0.0631055	+	0.109302i
$566$	13.0000	−	22.5167i	0.546431	−	0.946446i
$567$	−2.00000			−0.0839921
$568$	−7.00000	+	12.1244i	−0.293713	+	0.508727i
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	−2.00000			−0.0836974			−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000			−0.0836974			−0.0418487	+	0.999124i	$0.513325\pi$
$572$	5.00000	−	5.19615i	0.209061	−	0.217262i
$573$	−4.00000			−0.167102
$574$	−5.00000	−	8.66025i	−0.208696	−	0.361472i
$575$	12.0000	+	20.7846i	0.500435	+	0.866778i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	27.0000			1.12402			0.562012	−	0.827129i	$-0.310027\pi$
$577$	27.0000			1.12402			0.562012	+	0.827129i	$0.310027\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−8.50000	+	14.7224i	−0.353248	+	0.611843i
$580$	9.00000			0.373705
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	1.00000	+	1.73205i	0.0414513	+	0.0717958i
$583$	1.00000	+	1.73205i	0.0414158	+	0.0717342i
$584$	13.0000			0.537944
$585$	−1.00000	−	3.46410i	−0.0413449	−	0.143223i
$586$	1.00000			0.0413096
$587$	16.0000	+	27.7128i	0.660391	+	1.14383i	0.980513	+	0.196454i	$0.0629426\pi$
$587$	16.0000	+	27.7128i	0.660391	+	1.14383i	−0.320122	+	0.947376i	$0.603724\pi$
$588$	−1.50000	−	2.59808i	−0.0618590	−	0.107143i
$589$	−4.00000	+	6.92820i	−0.164817	+	0.285472i
$590$	−8.00000			−0.329355
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	5.50000	−	9.52628i	0.226049	−	0.391528i
$593$	−39.0000			−1.60154			−0.800769	−	0.598973i	$-0.795576\pi$
$593$	−39.0000			−1.60154			−0.800769	+	0.598973i	$0.795576\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	−5.00000	−	8.66025i	−0.204980	−	0.355036i
$596$	−1.50000	−	2.59808i	−0.0614424	−	0.106421i
$597$	−10.0000			−0.409273
$598$	−6.00000	−	20.7846i	−0.245358	−	0.849946i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	−5.50000	−	9.52628i	−0.224350	−	0.388585i	0.731774	−	0.681547i	$-0.238692\pi$
$601$	−5.50000	−	9.52628i	−0.224350	−	0.388585i	−0.956124	+	0.292962i	$0.905359\pi$
$602$	−10.0000	+	17.3205i	−0.407570	+	0.705931i
$603$	2.00000			0.0814463
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$	−5.00000			−0.203111
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$	9.00000	+	15.5885i	0.364698	+	0.631676i
$610$	−11.0000			−0.445377
$611$	5.00000	−	5.19615i	0.202278	−	0.210214i
$612$	5.00000			0.202113
$613$	−6.50000	−	11.2583i	−0.262533	−	0.454720i	0.704382	−	0.709821i	$-0.251224\pi$
$613$	−6.50000	−	11.2583i	−0.262533	−	0.454720i	−0.966914	+	0.255102i	$0.917891\pi$
$614$	−7.00000	−	12.1244i	−0.282497	−	0.489299i
$615$	−2.50000	+	4.33013i	−0.100810	+	0.174608i
$616$	4.00000			0.161165
$617$	7.50000	−	12.9904i	0.301939	−	0.522973i	−0.674636	−	0.738150i	$-0.735700\pi$
$617$	7.50000	−	12.9904i	0.301939	−	0.522973i	0.976575	+	0.215177i	$0.0690329\pi$
$618$	−5.00000	+	8.66025i	−0.201129	+	0.348367i
$619$	32.0000			1.28619			0.643094	−	0.765787i	$-0.277650\pi$
$619$	32.0000			1.28619			0.643094	+	0.765787i	$0.277650\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$	3.00000	+	5.19615i	0.120289	+	0.208347i
$623$	−4.00000			−0.160257
$624$	−1.00000	−	3.46410i	−0.0400320	−	0.138675i
$625$	11.0000			0.440000
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$	−2.00000	−	3.46410i	−0.0798723	−	0.138343i
$628$	3.50000	−	6.06218i	0.139665	−	0.241907i
$629$	−55.0000			−2.19299
$630$	1.00000	−	1.73205i	0.0398410	−	0.0690066i
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	−0.960386	−	0.278672i	$-0.910106\pi$
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	0.721530	+	0.692383i	$0.243439\pi$
$632$	4.00000			0.159111
$633$	12.0000	−	20.7846i	0.476957	−	0.826114i
$634$	−16.5000	−	28.5788i	−0.655299	−	1.13501i
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$	1.00000			0.0396526
$637$	10.5000	+	2.59808i	0.416025	+	0.102940i
$638$	18.0000			0.712627
$639$	7.00000	+	12.1244i	0.276916	+	0.479632i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	−0.911165	−	0.412042i	$-0.864816\pi$
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	0.812421	+	0.583071i	$0.198149\pi$
$642$	−18.0000			−0.710403
$643$	−4.00000	+	6.92820i	−0.157745	+	0.273222i	−0.934055	−	0.357129i	$-0.883756\pi$
$643$	−4.00000	+	6.92820i	−0.157745	+	0.273222i	0.776310	+	0.630351i	$0.217089\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$	10.0000			0.393750
$646$	−5.00000	+	8.66025i	−0.196722	+	0.340733i
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−16.0000			−0.628055
$650$	−14.0000	−	3.46410i	−0.549125	−	0.135873i
$651$	−8.00000			−0.313545
$652$	−10.0000	−	17.3205i	−0.391630	−	0.678323i
$653$	11.0000	+	19.0526i	0.430463	+	0.745584i	0.996913	−	0.0785119i	$-0.0250169\pi$
$653$	11.0000	+	19.0526i	0.430463	+	0.745584i	−0.566450	+	0.824096i	$0.691684\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$	8.00000			0.312586
$656$	−2.50000	+	4.33013i	−0.0976086	+	0.169063i
$657$	6.50000	−	11.2583i	0.253589	−	0.439229i
$658$	4.00000			0.155936
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	−0.999309	−	0.0371821i	$-0.988162\pi$
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	0.531855	+	0.846836i	$0.321495\pi$
$660$	−1.00000	−	1.73205i	−0.0389249	−	0.0674200i
$661$	−12.5000	−	21.6506i	−0.486194	−	0.842112i	0.513680	−	0.857982i	$-0.328282\pi$
$661$	−12.5000	−	21.6506i	−0.486194	−	0.842112i	−0.999874	+	0.0158695i	$0.994948\pi$
$662$	28.0000			1.08825
$663$	−12.5000	+	12.9904i	−0.485460	+	0.504505i
$664$	−6.00000			−0.232845
$665$	2.00000	+	3.46410i	0.0775567	+	0.134332i
$666$	−5.50000	−	9.52628i	−0.213121	−	0.369136i
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	24.0000			0.928588
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$	−1.00000	+	1.73205i	−0.0386334	+	0.0669150i
$671$	−22.0000			−0.849301
$672$	1.00000	−	1.73205i	0.0385758	−	0.0668153i
$673$	−21.5000	−	37.2391i	−0.828764	−	1.43546i	−0.899008	−	0.437932i	$-0.855711\pi$
$673$	−21.5000	−	37.2391i	−0.828764	−	1.43546i	0.0702442	−	0.997530i	$-0.477622\pi$
$674$	−4.50000	−	7.79423i	−0.173334	−	0.300222i
$675$	4.00000			0.153960
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	−46.0000			−1.76792			−0.883962	−	0.467559i	$-0.845134\pi$
$677$	−46.0000			−1.76792			−0.883962	+	0.467559i	$0.845134\pi$
$678$	1.50000	+	2.59808i	0.0576072	+	0.0997785i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	−2.50000	+	4.33013i	−0.0958706	+	0.166053i
$681$	−14.0000			−0.536481
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	20.0000	−	34.6410i	0.765279	−	1.32550i	−0.174820	−	0.984600i	$-0.555934\pi$
$683$	20.0000	−	34.6410i	0.765279	−	1.32550i	0.940099	−	0.340901i	$-0.110732\pi$
$684$	−2.00000			−0.0764719
$685$	8.50000	−	14.7224i	0.324768	−	0.562515i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	5.00000	+	8.66025i	0.190762	+	0.330409i
$688$	10.0000			0.381246
$689$	−2.50000	+	2.59808i	−0.0952424	+	0.0989788i
$690$	−6.00000			−0.228416
$691$	1.00000	+	1.73205i	0.0380418	+	0.0658903i	0.884419	−	0.466693i	$-0.154555\pi$
$691$	1.00000	+	1.73205i	0.0380418	+	0.0658903i	−0.846378	+	0.532583i	$0.821221\pi$
$692$	11.0000	+	19.0526i	0.418157	+	0.724270i
$693$	2.00000	−	3.46410i	0.0759737	−	0.131590i
$694$	−6.00000			−0.227757
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$	25.0000			0.946943
$698$	3.00000	−	5.19615i	0.113552	−	0.196677i
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$	−4.00000	−	6.92820i	−0.151186	−	0.261861i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$	−3.50000	−	0.866025i	−0.132099	−	0.0326860i
$703$	22.0000			0.829746
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$	−1.00000	−	1.73205i	−0.0376622	−	0.0652328i
$706$	8.50000	−	14.7224i	0.319902	−	0.554086i
$707$	10.0000			0.376089
$708$	−4.00000	+	6.92820i	−0.150329	+	0.260378i
$709$	7.50000	−	12.9904i	0.281668	−	0.487864i	−0.690127	−	0.723688i	$-0.742446\pi$
$709$	7.50000	−	12.9904i	0.281668	−	0.487864i	0.971796	+	0.235824i	$0.0757789\pi$
$710$	−14.0000			−0.525411
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	1.00000	+	1.73205i	0.0374766	+	0.0649113i
$713$	12.0000	+	20.7846i	0.449404	+	0.778390i
$714$	−10.0000			−0.374241
$715$	7.00000	+	1.73205i	0.261785	+	0.0647750i
$716$	−6.00000			−0.224231
$717$	−3.00000	−	5.19615i	−0.112037	−	0.194054i
$718$	−15.0000	−	25.9808i	−0.559795	−	0.969593i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$	−1.00000			−0.0372678
$721$	10.0000	−	17.3205i	0.372419	−	0.645049i
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$	−7.00000			−0.260333
$724$	−2.50000	+	4.33013i	−0.0929118	+	0.160928i
$725$	−18.0000	−	31.1769i	−0.668503	−	1.15788i
$726$	3.50000	+	6.06218i	0.129897	+	0.224989i
$727$	2.00000			0.0741759			0.0370879	−	0.999312i	$-0.488192\pi$
$727$	2.00000			0.0741759			0.0370879	+	0.999312i	$0.488192\pi$
$728$	2.00000	+	6.92820i	0.0741249	+	0.256776i
$729$	1.00000			0.0370370
$730$	6.50000	+	11.2583i	0.240576	+	0.416689i
$731$	−25.0000	−	43.3013i	−0.924658	−	1.60156i
$732$	−5.50000	+	9.52628i	−0.203286	+	0.352101i
$733$	13.0000			0.480166			0.240083	−	0.970752i	$-0.422825\pi$
$733$	13.0000			0.480166			0.240083	+	0.970752i	$0.422825\pi$
$734$	−1.00000	+	1.73205i	−0.0369107	+	0.0639312i
$735$	1.50000	−	2.59808i	0.0553283	−	0.0958315i
$736$	−6.00000			−0.221163
$737$	−2.00000	+	3.46410i	−0.0736709	+	0.127602i
$738$	2.50000	+	4.33013i	0.0920263	+	0.159394i
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$	11.0000			0.404368
$741$	5.00000	−	5.19615i	0.183680	−	0.190885i
$742$	−2.00000			−0.0734223
$743$	6.00000	+	10.3923i	0.220119	+	0.381257i	0.954844	−	0.297108i	$-0.0960222\pi$
$743$	6.00000	+	10.3923i	0.220119	+	0.381257i	−0.734725	+	0.678365i	$0.762689\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	1.50000	−	2.59808i	0.0549557	−	0.0951861i
$746$	−9.00000			−0.329513
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$	−5.00000	+	8.66025i	−0.182818	+	0.316650i
$749$	36.0000			1.31541
$750$	−4.50000	+	7.79423i	−0.164317	+	0.284605i
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	0.525193	−	0.850983i	$-0.323993\pi$
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	−0.999570	+	0.0293387i	$0.990660\pi$
$752$	−1.00000	−	1.73205i	−0.0364662	−	0.0631614i
$753$	−4.00000			−0.145768
$754$	9.00000	+	31.1769i	0.327761	+	1.13540i
$755$	6.00000			0.218362
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	9.00000	+	15.5885i	0.327111	+	0.566572i	0.981937	−	0.189207i	$-0.0605917\pi$
$757$	9.00000	+	15.5885i	0.327111	+	0.566572i	−0.654827	+	0.755779i	$0.727258\pi$
$758$	6.00000	−	10.3923i	0.217930	−	0.377466i
$759$	−12.0000			−0.435572
$760$	1.00000	−	1.73205i	0.0362738	−	0.0628281i
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	0.373914	+	0.927463i	$0.378015\pi$
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	−0.990164	+	0.139912i	$0.955318\pi$
$762$	−12.0000			−0.434714
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$	2.50000	+	4.33013i	0.0903877	+	0.156556i
$766$	−24.0000			−0.867155
$767$	−8.00000	−	27.7128i	−0.288863	−	1.00065i
$768$	−1.00000			−0.0360844
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	0.990726	+	0.135877i	$0.0433852\pi$
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	−0.377690	+	0.925932i	$0.623282\pi$
$770$	2.00000	+	3.46410i	0.0720750	+	0.124838i
$771$	−1.50000	+	2.59808i	−0.0540212	+	0.0935674i
$772$	−17.0000			−0.611843
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$	5.00000	−	8.66025i	0.179721	−	0.311286i
$775$	16.0000			0.574737

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} -1.00000 q^{12} +(2.50000 - 2.59808i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} -1.00000 q^{18} +(1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.00000 q^{25} +(3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(4.50000 + 7.79423i) q^{29} +(0.500000 - 0.866025i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} -5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.50000 + 9.52628i) q^{37} +2.00000 q^{38} +(3.50000 + 0.866025i) q^{39} +1.00000 q^{40} +(-2.50000 - 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} +2.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{46} +2.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{50} -5.00000 q^{51} +(1.00000 + 3.46410i) q^{52} -1.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.00000 + 1.73205i) q^{56} +2.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(4.00000 - 6.92820i) q^{59} +1.00000 q^{60} +(5.50000 - 9.52628i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +2.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(3.00000 - 5.19615i) q^{69} -2.00000 q^{70} +(7.00000 - 12.1244i) q^{71} +(0.500000 - 0.866025i) q^{72} -13.0000 q^{73} +(-5.50000 + 9.52628i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(1.00000 + 1.73205i) q^{76} -4.00000 q^{77} +(1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(2.50000 - 4.33013i) q^{85} -10.0000 q^{86} +(-4.50000 + 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-1.00000 - 1.73205i) q^{89} +1.00000 q^{90} +(-2.00000 - 6.92820i) q^{91} +6.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-1.00000 + 1.73205i) q^{95} +1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +(-1.50000 + 2.59808i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - q^{10} - 2 q^{11} - 2 q^{12} + 5 q^{13} + 4 q^{14} - q^{15} - q^{16} - 5 q^{17} - 2 q^{18} + 2 q^{19} + q^{20} + 4 q^{21} + 2 q^{22} - 6 q^{23} - q^{24} - 8 q^{25} + 7 q^{26} - 2 q^{27} + 2 q^{28} + 9 q^{29} + q^{30} - 8 q^{31} + q^{32} + 2 q^{33} - 10 q^{34} - 2 q^{35} - q^{36} + 11 q^{37} + 4 q^{38} + 7 q^{39} + 2 q^{40} - 5 q^{41} + 2 q^{42} - 10 q^{43} + 4 q^{44} + q^{45} + 6 q^{46} + 4 q^{47} + q^{48} + 3 q^{49} - 4 q^{50} - 10 q^{51} + 2 q^{52} - 2 q^{53} - q^{54} + 2 q^{55} - 2 q^{56} + 4 q^{57} - 9 q^{58} + 8 q^{59} + 2 q^{60} + 11 q^{61} - 4 q^{62} + 2 q^{63} + 2 q^{64} - 5 q^{65} + 4 q^{66} - 2 q^{67} - 5 q^{68} + 6 q^{69} - 4 q^{70} + 14 q^{71} + q^{72} - 26 q^{73} - 11 q^{74} - 4 q^{75} + 2 q^{76} - 8 q^{77} + 2 q^{78} - 8 q^{79} + q^{80} - q^{81} + 5 q^{82} + 12 q^{83} - 2 q^{84} + 5 q^{85} - 20 q^{86} - 9 q^{87} + 2 q^{88} - 2 q^{89} + 2 q^{90} - 4 q^{91} + 12 q^{92} - 4 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} + 2 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9 - q^10 - 2 * q^11 - 2 * q^12 + 5 * q^13 + 4 * q^14 - q^15 - q^16 - 5 * q^17 - 2 * q^18 + 2 * q^19 + q^20 + 4 * q^21 + 2 * q^22 - 6 * q^23 - q^24 - 8 * q^25 + 7 * q^26 - 2 * q^27 + 2 * q^28 + 9 * q^29 + q^30 - 8 * q^31 + q^32 + 2 * q^33 - 10 * q^34 - 2 * q^35 - q^36 + 11 * q^37 + 4 * q^38 + 7 * q^39 + 2 * q^40 - 5 * q^41 + 2 * q^42 - 10 * q^43 + 4 * q^44 + q^45 + 6 * q^46 + 4 * q^47 + q^48 + 3 * q^49 - 4 * q^50 - 10 * q^51 + 2 * q^52 - 2 * q^53 - q^54 + 2 * q^55 - 2 * q^56 + 4 * q^57 - 9 * q^58 + 8 * q^59 + 2 * q^60 + 11 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 - 5 * q^65 + 4 * q^66 - 2 * q^67 - 5 * q^68 + 6 * q^69 - 4 * q^70 + 14 * q^71 + q^72 - 26 * q^73 - 11 * q^74 - 4 * q^75 + 2 * q^76 - 8 * q^77 + 2 * q^78 - 8 * q^79 + q^80 - q^81 + 5 * q^82 + 12 * q^83 - 2 * q^84 + 5 * q^85 - 20 * q^86 - 9 * q^87 + 2 * q^88 - 2 * q^89 + 2 * q^90 - 4 * q^91 + 12 * q^92 - 4 * q^93 + 2 * q^94 - 2 * q^95 + 2 * q^96 + 2 * q^97 - 3 * q^98 + 4 * q^99

Introduction

L-functions

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