LMFDB - Embedded newform 39.4.e.a.16.1

Newspace parameters

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.e (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	39.16
Dual form			39.4.e.a.22.1

$q$-expansion

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(-4.50000 + 7.79423i) q^{6} +(-1.00000 + 1.73205i) q^{7} -21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(-4.50000 + 7.79423i) q^{6} +(-1.00000 + 1.73205i) q^{7} -21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(13.5000 + 23.3827i) q^{10} +(-15.0000 - 25.9808i) q^{11} +3.00000 q^{12} +(32.5000 - 33.7750i) q^{13} +6.00000 q^{14} +(13.5000 + 23.3827i) q^{15} +(35.5000 + 61.4878i) q^{16} +(55.5000 - 96.1288i) q^{17} +27.0000 q^{18} +(23.0000 - 39.8372i) q^{19} +(4.50000 - 7.79423i) q^{20} +6.00000 q^{21} +(-45.0000 + 77.9423i) q^{22} +(3.00000 + 5.19615i) q^{23} +(31.5000 + 54.5596i) q^{24} -44.0000 q^{25} +(-136.500 - 33.7750i) q^{26} +27.0000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(52.5000 + 90.9327i) q^{29} +(40.5000 - 70.1481i) q^{30} -100.000 q^{31} +(22.5000 - 38.9711i) q^{32} +(-45.0000 + 77.9423i) q^{33} -333.000 q^{34} +(9.00000 - 15.5885i) q^{35} +(-4.50000 - 7.79423i) q^{36} +(-8.50000 - 14.7224i) q^{37} -138.000 q^{38} +(-136.500 - 33.7750i) q^{39} +189.000 q^{40} +(115.500 + 200.052i) q^{41} +(-9.00000 - 15.5885i) q^{42} +(257.000 - 445.137i) q^{43} +30.0000 q^{44} +(40.5000 - 70.1481i) q^{45} +(9.00000 - 15.5885i) q^{46} -162.000 q^{47} +(106.500 - 184.463i) q^{48} +(169.500 + 293.583i) q^{49} +(66.0000 + 114.315i) q^{50} -333.000 q^{51} +(13.0000 + 45.0333i) q^{52} +639.000 q^{53} +(-40.5000 - 70.1481i) q^{54} +(135.000 + 233.827i) q^{55} +(21.0000 - 36.3731i) q^{56} -138.000 q^{57} +(157.500 - 272.798i) q^{58} +(-300.000 + 519.615i) q^{59} -27.0000 q^{60} +(-116.500 + 201.784i) q^{61} +(150.000 + 259.808i) q^{62} +(-9.00000 - 15.5885i) q^{63} +433.000 q^{64} +(-292.500 + 303.975i) q^{65} +270.000 q^{66} +(-463.000 - 801.940i) q^{67} +(55.5000 + 96.1288i) q^{68} +(9.00000 - 15.5885i) q^{69} -54.0000 q^{70} +(465.000 - 805.404i) q^{71} +(94.5000 - 163.679i) q^{72} -253.000 q^{73} +(-25.5000 + 44.1673i) q^{74} +(66.0000 + 114.315i) q^{75} +(23.0000 + 39.8372i) q^{76} +60.0000 q^{77} +(117.000 + 405.300i) q^{78} -1324.00 q^{79} +(-319.500 - 553.390i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(346.500 - 600.156i) q^{82} +810.000 q^{83} +(-3.00000 + 5.19615i) q^{84} +(-499.500 + 865.159i) q^{85} -1542.00 q^{86} +(157.500 - 272.798i) q^{87} +(315.000 + 545.596i) q^{88} +(-249.000 - 431.281i) q^{89} -243.000 q^{90} +(26.0000 + 90.0666i) q^{91} -6.00000 q^{92} +(150.000 + 259.808i) q^{93} +(243.000 + 420.888i) q^{94} +(-207.000 + 358.535i) q^{95} -135.000 q^{96} +(-679.000 + 1176.06i) q^{97} +(508.500 - 880.748i) q^{98} +270.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 3 q^{3} - q^{4} - 18 q^{5} - 9 q^{6} - 2 q^{7} - 42 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 3 * q^3 - q^4 - 18 * q^5 - 9 * q^6 - 2 * q^7 - 42 * q^8 - 9 * q^9	\( 2 q - 3 q^{2} - 3 q^{3} - q^{4} - 18 q^{5} - 9 q^{6} - 2 q^{7} - 42 q^{8} - 9 q^{9} + 27 q^{10} - 30 q^{11} + 6 q^{12} + 65 q^{13} + 12 q^{14} + 27 q^{15} + 71 q^{16} + 111 q^{17} + 54 q^{18} + 46 q^{19} + 9 q^{20} + 12 q^{21} - 90 q^{22} + 6 q^{23} + 63 q^{24} - 88 q^{25} - 273 q^{26} + 54 q^{27} - 2 q^{28} + 105 q^{29} + 81 q^{30} - 200 q^{31} + 45 q^{32} - 90 q^{33} - 666 q^{34} + 18 q^{35} - 9 q^{36} - 17 q^{37} - 276 q^{38} - 273 q^{39} + 378 q^{40} + 231 q^{41} - 18 q^{42} + 514 q^{43} + 60 q^{44} + 81 q^{45} + 18 q^{46} - 324 q^{47} + 213 q^{48} + 339 q^{49} + 132 q^{50} - 666 q^{51} + 26 q^{52} + 1278 q^{53} - 81 q^{54} + 270 q^{55} + 42 q^{56} - 276 q^{57} + 315 q^{58} - 600 q^{59} - 54 q^{60} - 233 q^{61} + 300 q^{62} - 18 q^{63} + 866 q^{64} - 585 q^{65} + 540 q^{66} - 926 q^{67} + 111 q^{68} + 18 q^{69} - 108 q^{70} + 930 q^{71} + 189 q^{72} - 506 q^{73} - 51 q^{74} + 132 q^{75} + 46 q^{76} + 120 q^{77} + 234 q^{78} - 2648 q^{79} - 639 q^{80} - 81 q^{81} + 693 q^{82} + 1620 q^{83} - 6 q^{84} - 999 q^{85} - 3084 q^{86} + 315 q^{87} + 630 q^{88} - 498 q^{89} - 486 q^{90} + 52 q^{91} - 12 q^{92} + 300 q^{93} + 486 q^{94} - 414 q^{95} - 270 q^{96} - 1358 q^{97} + 1017 q^{98} + 540 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 3 * q^3 - q^4 - 18 * q^5 - 9 * q^6 - 2 * q^7 - 42 * q^8 - 9 * q^9 + 27 * q^10 - 30 * q^11 + 6 * q^12 + 65 * q^13 + 12 * q^14 + 27 * q^15 + 71 * q^16 + 111 * q^17 + 54 * q^18 + 46 * q^19 + 9 * q^20 + 12 * q^21 - 90 * q^22 + 6 * q^23 + 63 * q^24 - 88 * q^25 - 273 * q^26 + 54 * q^27 - 2 * q^28 + 105 * q^29 + 81 * q^30 - 200 * q^31 + 45 * q^32 - 90 * q^33 - 666 * q^34 + 18 * q^35 - 9 * q^36 - 17 * q^37 - 276 * q^38 - 273 * q^39 + 378 * q^40 + 231 * q^41 - 18 * q^42 + 514 * q^43 + 60 * q^44 + 81 * q^45 + 18 * q^46 - 324 * q^47 + 213 * q^48 + 339 * q^49 + 132 * q^50 - 666 * q^51 + 26 * q^52 + 1278 * q^53 - 81 * q^54 + 270 * q^55 + 42 * q^56 - 276 * q^57 + 315 * q^58 - 600 * q^59 - 54 * q^60 - 233 * q^61 + 300 * q^62 - 18 * q^63 + 866 * q^64 - 585 * q^65 + 540 * q^66 - 926 * q^67 + 111 * q^68 + 18 * q^69 - 108 * q^70 + 930 * q^71 + 189 * q^72 - 506 * q^73 - 51 * q^74 + 132 * q^75 + 46 * q^76 + 120 * q^77 + 234 * q^78 - 2648 * q^79 - 639 * q^80 - 81 * q^81 + 693 * q^82 + 1620 * q^83 - 6 * q^84 - 999 * q^85 - 3084 * q^86 + 315 * q^87 + 630 * q^88 - 498 * q^89 - 486 * q^90 + 52 * q^91 - 12 * q^92 + 300 * q^93 + 486 * q^94 - 414 * q^95 - 270 * q^96 - 1358 * q^97 + 1017 * q^98 + 540 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.50000	−	2.59808i	−0.530330	−	0.918559i	−0.999374	−	0.0353837i	$-0.988735\pi$
$2$	−1.50000	−	2.59808i	−0.530330	−	0.918559i	0.469044	−	0.883175i	$-0.344599\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$5$	−9.00000			−0.804984			−0.402492	−	0.915423i	$-0.631856\pi$
$5$	−9.00000			−0.804984			−0.402492	+	0.915423i	$0.631856\pi$
$6$	−4.50000	+	7.79423i	−0.306186	+	0.530330i
$7$	−1.00000	+	1.73205i	−0.0539949	+	0.0935220i	−0.891760	−	0.452510i	$-0.850529\pi$
$7$	−1.00000	+	1.73205i	−0.0539949	+	0.0935220i	0.837765	+	0.546032i	$0.183862\pi$
$8$	−21.0000			−0.928078
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	13.5000	+	23.3827i	0.426907	+	0.739425i
$11$	−15.0000	−	25.9808i	−0.411152	−	0.712136i	0.583864	−	0.811851i	$-0.301540\pi$
$11$	−15.0000	−	25.9808i	−0.411152	−	0.712136i	−0.995016	+	0.0997155i	$0.968207\pi$
$12$	3.00000			0.0721688
$13$	32.5000	−	33.7750i	0.693375	−	0.720577i
$13$	32.5000	−	33.7750i	0.693375	−	0.720577i
$14$	6.00000			0.114541
$15$	13.5000	+	23.3827i	0.232379	+	0.402492i
$16$	35.5000	+	61.4878i	0.554688	+	0.960747i
$17$	55.5000	−	96.1288i	0.791807	−	1.37145i	−0.133039	−	0.991111i	$-0.542474\pi$
$17$	55.5000	−	96.1288i	0.791807	−	1.37145i	0.924847	−	0.380340i	$-0.124193\pi$
$18$	27.0000			0.353553
$19$	23.0000	−	39.8372i	0.277714	−	0.481014i	−0.693102	−	0.720839i	$-0.743757\pi$
$19$	23.0000	−	39.8372i	0.277714	−	0.481014i	0.970816	+	0.239825i	$0.0770900\pi$
$20$	4.50000	−	7.79423i	0.0503115	−	0.0871421i
$21$	6.00000			0.0623480
$22$	−45.0000	+	77.9423i	−0.436092	+	0.755334i
$23$	3.00000	+	5.19615i	0.0271975	+	0.0471075i	0.879304	−	0.476261i	$-0.158008\pi$
$23$	3.00000	+	5.19615i	0.0271975	+	0.0471075i	−0.852106	+	0.523369i	$0.824675\pi$
$24$	31.5000	+	54.5596i	0.267913	+	0.464039i
$25$	−44.0000			−0.352000
$26$	−136.500	−	33.7750i	−1.02961	−	0.254762i
$27$	27.0000			0.192450
$28$	−1.00000	−	1.73205i	−0.00674937	−	0.0116902i
$29$	52.5000	+	90.9327i	0.336173	+	0.582268i	0.983709	−	0.179766i	$-0.0575341\pi$
$29$	52.5000	+	90.9327i	0.336173	+	0.582268i	−0.647537	+	0.762034i	$0.724201\pi$
$30$	40.5000	−	70.1481i	0.246475	−	0.426907i
$31$	−100.000			−0.579372			−0.289686	−	0.957122i	$-0.593551\pi$
$31$	−100.000			−0.579372			−0.289686	+	0.957122i	$0.593551\pi$
$32$	22.5000	−	38.9711i	0.124296	−	0.215287i
$33$	−45.0000	+	77.9423i	−0.237379	+	0.411152i
$34$	−333.000			−1.67968
$35$	9.00000	−	15.5885i	0.0434651	−	0.0752837i
$36$	−4.50000	−	7.79423i	−0.0208333	−	0.0360844i
$37$	−8.50000	−	14.7224i	−0.0377673	−	0.0654149i	0.846524	−	0.532351i	$-0.178691\pi$
$37$	−8.50000	−	14.7224i	−0.0377673	−	0.0654149i	−0.884291	+	0.466936i	$0.845358\pi$
$38$	−138.000			−0.589120
$39$	−136.500	−	33.7750i	−0.560449	−	0.138675i
$40$	189.000			0.747088
$41$	115.500	+	200.052i	0.439953	+	0.762021i	0.997685	−	0.0680000i	$-0.0216618\pi$
$41$	115.500	+	200.052i	0.439953	+	0.762021i	−0.557732	+	0.830021i	$0.688328\pi$
$42$	−9.00000	−	15.5885i	−0.0330650	−	0.0572703i
$43$	257.000	−	445.137i	0.911445	−	1.57867i	0.0994205	−	0.995046i	$-0.468301\pi$
$43$	257.000	−	445.137i	0.911445	−	1.57867i	0.812024	−	0.583623i	$-0.198366\pi$
$44$	30.0000			0.102788
$45$	40.5000	−	70.1481i	0.134164	−	0.232379i
$46$	9.00000	−	15.5885i	0.0288473	−	0.0499651i
$47$	−162.000			−0.502769			−0.251384	−	0.967887i	$-0.580886\pi$
$47$	−162.000			−0.502769			−0.251384	+	0.967887i	$0.580886\pi$
$48$	106.500	−	184.463i	0.320249	−	0.554688i
$49$	169.500	+	293.583i	0.494169	+	0.855926i
$50$	66.0000	+	114.315i	0.186676	+	0.323333i
$51$	−333.000			−0.914301
$52$	13.0000	+	45.0333i	0.0346688	+	0.120096i
$53$	639.000			1.65610			0.828051	−	0.560653i	$-0.189450\pi$
$53$	639.000			1.65610			0.828051	+	0.560653i	$0.189450\pi$
$54$	−40.5000	−	70.1481i	−0.102062	−	0.176777i
$55$	135.000	+	233.827i	0.330971	+	0.573258i
$56$	21.0000	−	36.3731i	0.0501115	−	0.0867956i
$57$	−138.000			−0.320676
$58$	157.500	−	272.798i	0.356565	−	0.617588i
$59$	−300.000	+	519.615i	−0.661978	+	1.14658i	0.318118	+	0.948051i	$0.396949\pi$
$59$	−300.000	+	519.615i	−0.661978	+	1.14658i	−0.980095	+	0.198527i	$0.936384\pi$
$60$	−27.0000			−0.0580948
$61$	−116.500	+	201.784i	−0.244529	+	0.423537i	−0.961999	−	0.273052i	$-0.911967\pi$
$61$	−116.500	+	201.784i	−0.244529	+	0.423537i	0.717470	+	0.696590i	$0.245300\pi$
$62$	150.000	+	259.808i	0.307258	+	0.532187i
$63$	−9.00000	−	15.5885i	−0.0179983	−	0.0311740i
$64$	433.000			0.845703
$65$	−292.500	+	303.975i	−0.558156	+	0.580053i
$66$	270.000			0.503556
$67$	−463.000	−	801.940i	−0.844246	−	1.46228i	−0.886275	−	0.463160i	$-0.846716\pi$
$67$	−463.000	−	801.940i	−0.844246	−	1.46228i	0.0420292	−	0.999116i	$-0.486618\pi$
$68$	55.5000	+	96.1288i	0.0989759	+	0.171431i
$69$	9.00000	−	15.5885i	0.0157025	−	0.0271975i
$70$	−54.0000			−0.0922033
$71$	465.000	−	805.404i	0.777258	−	1.34625i	−0.156258	−	0.987716i	$-0.549943\pi$
$71$	465.000	−	805.404i	0.777258	−	1.34625i	0.933516	−	0.358535i	$-0.116724\pi$
$72$	94.5000	−	163.679i	0.154680	−	0.267913i
$73$	−253.000			−0.405636			−0.202818	−	0.979216i	$-0.565010\pi$
$73$	−253.000			−0.405636			−0.202818	+	0.979216i	$0.565010\pi$
$74$	−25.5000	+	44.1673i	−0.0400583	+	0.0693830i
$75$	66.0000	+	114.315i	0.101614	+	0.176000i
$76$	23.0000	+	39.8372i	0.0347142	+	0.0601268i
$77$	60.0000			0.0888004
$78$	117.000	+	405.300i	0.169842	+	0.588348i
$79$	−1324.00			−1.88559			−0.942795	−	0.333373i	$-0.891813\pi$
$79$	−1324.00			−1.88559			−0.942795	+	0.333373i	$0.891813\pi$
$80$	−319.500	−	553.390i	−0.446515	−	0.773386i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	346.500	−	600.156i	0.466641	−	0.808245i
$83$	810.000			1.07119			0.535597	−	0.844474i	$-0.320087\pi$
$83$	810.000			1.07119			0.535597	+	0.844474i	$0.320087\pi$
$84$	−3.00000	+	5.19615i	−0.00389675	+	0.00674937i
$85$	−499.500	+	865.159i	−0.637393	+	1.10400i
$86$	−1542.00			−1.93347
$87$	157.500	−	272.798i	0.194089	−	0.336173i
$88$	315.000	+	545.596i	0.381581	+	0.660917i
$89$	−249.000	−	431.281i	−0.296561	−	0.513659i	0.678786	−	0.734336i	$-0.262507\pi$
$89$	−249.000	−	431.281i	−0.296561	−	0.513659i	−0.975347	+	0.220677i	$0.929173\pi$
$90$	−243.000			−0.284605
$91$	26.0000	+	90.0666i	0.0299510	+	0.103753i
$92$	−6.00000			−0.00679938
$93$	150.000	+	259.808i	0.167250	+	0.289686i
$94$	243.000	+	420.888i	0.266633	+	0.461823i
$95$	−207.000	+	358.535i	−0.223555	+	0.387209i
$96$	−135.000			−0.143525
$97$	−679.000	+	1176.06i	−0.710742	+	1.23104i	0.253837	+	0.967247i	$0.418307\pi$
$97$	−679.000	+	1176.06i	−0.710742	+	1.23104i	−0.964579	+	0.263795i	$0.915026\pi$
$98$	508.500	−	880.748i	0.524145	−	0.907847i
$99$	270.000			0.274101
$100$	22.0000	−	38.1051i	0.0220000	−	0.0381051i
$101$	178.500	+	309.171i	0.175856	+	0.304591i	0.940457	−	0.339913i	$-0.110397\pi$
$101$	178.500	+	309.171i	0.175856	+	0.304591i	−0.764601	+	0.644503i	$0.777064\pi$
$102$	499.500	+	865.159i	0.484881	+	0.839839i
$103$	1118.00			1.06951			0.534756	−	0.845006i	$-0.320403\pi$
$103$	1118.00			1.06951			0.534756	+	0.845006i	$0.320403\pi$
$104$	−682.500	+	709.275i	−0.643506	+	0.668751i
$105$	−54.0000			−0.0501891
$106$	−958.500	−	1660.17i	−0.878281	−	1.52123i
$107$	−357.000	−	618.342i	−0.322547	−	0.558667i	0.658466	−	0.752610i	$-0.271206\pi$
$107$	−357.000	−	618.342i	−0.322547	−	0.558667i	−0.981013	+	0.193943i	$0.937872\pi$
$108$	−13.5000	+	23.3827i	−0.0120281	+	0.0208333i
$109$	2006.00			1.76275			0.881376	−	0.472416i	$-0.156618\pi$
$109$	2006.00			1.76275			0.881376	+	0.472416i	$0.156618\pi$
$110$	405.000	−	701.481i	0.351048	−	0.608032i
$111$	−25.5000	+	44.1673i	−0.0218050	+	0.0377673i
$112$	−142.000			−0.119801
$113$	559.500	−	969.082i	0.465782	−	0.806758i	−0.533455	−	0.845829i	$-0.679107\pi$
$113$	559.500	−	969.082i	0.465782	−	0.806758i	0.999236	+	0.0390710i	$0.0124399\pi$
$114$	207.000	+	358.535i	0.170064	+	0.294560i
$115$	−27.0000	−	46.7654i	−0.0218936	−	0.0379208i
$116$	−105.000			−0.0840431
$117$	117.000	+	405.300i	0.0924500	+	0.320256i
$118$	1800.00			1.40427
$119$	111.000	+	192.258i	0.0855072	+	0.148103i
$120$	−283.500	−	491.036i	−0.215666	−	0.373544i
$121$	215.500	−	373.257i	0.161908	−	0.280433i
$122$	699.000			0.518725
$123$	346.500	−	600.156i	0.254007	−	0.439953i
$124$	50.0000	−	86.6025i	0.0362107	−	0.0627189i
$125$	1521.00			1.08834
$126$	−27.0000	+	46.7654i	−0.0190901	+	0.0330650i
$127$	302.000	+	523.079i	0.211009	+	0.365479i	0.952031	−	0.306003i	$-0.0989917\pi$
$127$	302.000	+	523.079i	0.211009	+	0.365479i	−0.741021	+	0.671481i	$0.765658\pi$
$128$	−829.500	−	1436.74i	−0.572798	−	0.992115i
$129$	−1542.00			−1.05245
$130$	1228.50	+	303.975i	0.828820	+	0.205080i
$131$	−1584.00			−1.05645			−0.528224	−	0.849105i	$-0.677142\pi$
$131$	−1584.00			−1.05645			−0.528224	+	0.849105i	$0.677142\pi$
$132$	−45.0000	−	77.9423i	−0.0296723	−	0.0513940i
$133$	46.0000	+	79.6743i	0.0299903	+	0.0519447i
$134$	−1389.00	+	2405.82i	−0.895458	+	1.55098i
$135$	−243.000			−0.154919
$136$	−1165.50	+	2018.71i	−0.734859	+	1.27281i
$137$	−358.500	+	620.940i	−0.223567	+	0.387230i	−0.955889	−	0.293729i	$-0.905104\pi$
$137$	−358.500	+	620.940i	−0.223567	+	0.387230i	0.732321	+	0.680959i	$0.238437\pi$
$138$	−54.0000			−0.0333100
$139$	410.000	−	710.141i	0.250185	−	0.433334i	−0.713391	−	0.700766i	$-0.752842\pi$
$139$	410.000	−	710.141i	0.250185	−	0.433334i	0.963577	+	0.267432i	$0.0861751\pi$
$140$	9.00000	+	15.5885i	0.00543313	+	0.00941046i
$141$	243.000	+	420.888i	0.145137	+	0.251384i
$142$	−2790.00			−1.64881
$143$	−1365.00	−	337.750i	−0.798231	−	0.197511i
$144$	−639.000			−0.369792
$145$	−472.500	−	818.394i	−0.270614	−	0.468717i
$146$	379.500	+	657.313i	0.215121	+	0.372600i
$147$	508.500	−	880.748i	0.285309	−	0.494169i
$148$	17.0000			0.00944183
$149$	874.500	−	1514.68i	0.480818	−	0.832801i	−0.518940	−	0.854811i	$-0.673673\pi$
$149$	874.500	−	1514.68i	0.480818	−	0.832801i	0.999758	+	0.0220100i	$0.00700656\pi$
$150$	198.000	−	342.946i	0.107778	−	0.186676i
$151$	−370.000			−0.199405			−0.0997026	−	0.995017i	$-0.531789\pi$
$151$	−370.000			−0.199405			−0.0997026	+	0.995017i	$0.531789\pi$
$152$	−483.000	+	836.581i	−0.257740	+	0.446419i
$153$	499.500	+	865.159i	0.263936	+	0.457150i
$154$	−90.0000	−	155.885i	−0.0470935	−	0.0815684i
$155$	900.000			0.466385
$156$	97.5000	−	101.325i	0.0500400	−	0.0520031i
$157$	−2611.00			−1.32726			−0.663632	−	0.748059i	$-0.730986\pi$
$157$	−2611.00			−1.32726			−0.663632	+	0.748059i	$0.730986\pi$
$158$	1986.00	+	3439.85i	0.999985	+	1.73203i
$159$	−958.500	−	1660.17i	−0.478075	−	0.828051i
$160$	−202.500	+	350.740i	−0.100056	+	0.173303i
$161$	−12.0000			−0.00587411
$162$	−121.500	+	210.444i	−0.0589256	+	0.102062i
$163$	818.000	−	1416.82i	0.393072	−	0.680820i	−0.599781	−	0.800164i	$-0.704746\pi$
$163$	818.000	−	1416.82i	0.393072	−	0.680820i	0.992853	+	0.119344i	$0.0380790\pi$
$164$	−231.000			−0.109988
$165$	405.000	−	701.481i	0.191086	−	0.330971i
$166$	−1215.00	−	2104.44i	−0.568086	−	0.983954i
$167$	−132.000	−	228.631i	−0.0611645	−	0.105940i	0.833822	−	0.552034i	$-0.186148\pi$
$167$	−132.000	−	228.631i	−0.0611645	−	0.105940i	−0.894986	+	0.446094i	$0.852815\pi$
$168$	−126.000			−0.0578638
$169$	−84.5000	−	2195.37i	−0.0384615	−	0.999260i
$170$	2997.00			1.35211
$171$	207.000	+	358.535i	0.0925713	+	0.160338i
$172$	257.000	+	445.137i	0.113931	+	0.197334i
$173$	−705.000	+	1221.10i	−0.309827	+	0.536637i	−0.978324	−	0.207078i	$-0.933605\pi$
$173$	−705.000	+	1221.10i	−0.309827	+	0.536637i	0.668497	+	0.743715i	$0.266938\pi$
$174$	−945.000			−0.411726
$175$	44.0000	−	76.2102i	0.0190062	−	0.0329197i
$176$	1065.00	−	1844.63i	0.456122	−	0.790026i
$177$	1800.00			0.764386
$178$	−747.000	+	1293.84i	−0.314551	+	0.544818i
$179$	237.000	+	410.496i	0.0989621	+	0.171407i	0.911255	−	0.411842i	$-0.135114\pi$
$179$	237.000	+	410.496i	0.0989621	+	0.171407i	−0.812293	+	0.583249i	$0.801781\pi$
$180$	40.5000	+	70.1481i	0.0167705	+	0.0290474i
$181$	2249.00			0.923574			0.461787	−	0.886991i	$-0.347208\pi$
$181$	2249.00			0.923574			0.461787	+	0.886991i	$0.347208\pi$
$182$	195.000	−	202.650i	0.0794196	−	0.0825352i
$183$	699.000			0.282358
$184$	−63.0000	−	109.119i	−0.0252414	−	0.0437194i
$185$	76.5000	+	132.502i	0.0304021	+	0.0526580i
$186$	450.000	−	779.423i	0.177396	−	0.307258i
$187$	−3330.00			−1.30221
$188$	81.0000	−	140.296i	0.0314230	−	0.0544263i
$189$	−27.0000	+	46.7654i	−0.0103913	+	0.0179983i
$190$	1242.00			0.474232
$191$	−1722.00	+	2982.59i	−0.652354	+	1.12991i	0.330197	+	0.943912i	$0.392885\pi$
$191$	−1722.00	+	2982.59i	−0.652354	+	1.12991i	−0.982550	+	0.185997i	$0.940448\pi$
$192$	−649.500	−	1124.97i	−0.244133	−	0.422852i
$193$	2136.50	+	3700.53i	0.796832	+	1.38015i	0.921669	+	0.387977i	$0.126826\pi$
$193$	2136.50	+	3700.53i	0.796832	+	1.38015i	−0.124837	+	0.992177i	$0.539841\pi$
$194$	4074.00			1.50771
$195$	1228.50	+	303.975i	0.451152	+	0.111631i
$196$	−339.000			−0.123542
$197$	993.000	+	1719.93i	0.359129	+	0.622029i	0.987815	−	0.155630i	$-0.0497406\pi$
$197$	993.000	+	1719.93i	0.359129	+	0.622029i	−0.628687	+	0.777658i	$0.716407\pi$
$198$	−405.000	−	701.481i	−0.145364	−	0.251778i
$199$	1193.00	−	2066.34i	0.424973	−	0.736074i	−0.571445	−	0.820640i	$-0.693617\pi$
$199$	1193.00	−	2066.34i	0.424973	−	0.736074i	0.996418	+	0.0845661i	$0.0269504\pi$
$200$	924.000			0.326683
$201$	−1389.00	+	2405.82i	−0.487425	+	0.844246i
$202$	535.500	−	927.513i	0.186523	−	0.323067i
$203$	−210.000			−0.0726065
$204$	166.500	−	288.386i	0.0571438	−	0.0989759i
$205$	−1039.50	−	1800.47i	−0.354155	−	0.613415i
$206$	−1677.00	−	2904.65i	−0.567195	−	0.982410i
$207$	−54.0000			−0.0181317
$208$	3230.50	+	799.341i	1.07690	+	0.266463i
$209$	−1380.00			−0.456730
$210$	81.0000	+	140.296i	0.0266168	+	0.0461017i
$211$	800.000	+	1385.64i	0.261016	+	0.452092i	0.966512	−	0.256621i	$-0.0826093\pi$
$211$	800.000	+	1385.64i	0.261016	+	0.452092i	−0.705497	+	0.708713i	$0.749276\pi$
$212$	−319.500	+	553.390i	−0.103506	+	0.179278i
$213$	−2790.00			−0.897501
$214$	−1071.00	+	1855.03i	−0.342112	+	0.592556i
$215$	−2313.00	+	4006.23i	−0.733699	+	1.27080i
$216$	−567.000			−0.178609
$217$	100.000	−	173.205i	0.0312831	−	0.0541840i
$218$	−3009.00	−	5211.74i	−0.934840	−	1.61919i
$219$	379.500	+	657.313i	0.117097	+	0.202818i
$220$	−270.000			−0.0827427
$221$	−1443.00	−	4998.70i	−0.439216	−	1.52149i
$222$	153.000			0.0462553
$223$	1916.00	+	3318.61i	0.575358	+	0.996549i	0.996003	+	0.0893239i	$0.0284706\pi$
$223$	1916.00	+	3318.61i	0.575358	+	0.996549i	−0.420645	+	0.907226i	$0.638196\pi$
$224$	45.0000	+	77.9423i	0.0134227	+	0.0232488i
$225$	198.000	−	342.946i	0.0586667	−	0.101614i
$226$	−3357.00			−0.988072
$227$	699.000	−	1210.70i	0.204380	−	0.353997i	−0.745555	−	0.666444i	$-0.767816\pi$
$227$	699.000	−	1210.70i	0.204380	−	0.353997i	0.949935	+	0.312448i	$0.101149\pi$
$228$	69.0000	−	119.512i	0.0200423	−	0.0347142i
$229$	4466.00			1.28874			0.644370	−	0.764714i	$-0.277120\pi$
$229$	4466.00			1.28874			0.644370	+	0.764714i	$0.277120\pi$
$230$	−81.0000	+	140.296i	−0.0232217	+	0.0402211i
$231$	−90.0000	−	155.885i	−0.0256345	−	0.0444002i
$232$	−1102.50	−	1909.59i	−0.311994	−	0.540390i
$233$	−1638.00			−0.460553			−0.230277	−	0.973125i	$-0.573963\pi$
$233$	−1638.00			−0.460553			−0.230277	+	0.973125i	$0.573963\pi$
$234$	877.500	−	911.925i	0.245145	−	0.254762i
$235$	1458.00			0.404721
$236$	−300.000	−	519.615i	−0.0827472	−	0.143322i
$237$	1986.00	+	3439.85i	0.544323	+	0.942795i
$238$	333.000	−	576.773i	0.0906941	−	0.157087i
$239$	−594.000			−0.160764			−0.0803821	−	0.996764i	$-0.525614\pi$
$239$	−594.000			−0.160764			−0.0803821	+	0.996764i	$0.525614\pi$
$240$	−958.500	+	1660.17i	−0.257795	+	0.446515i
$241$	−1151.50	+	1994.46i	−0.307779	+	0.533088i	−0.977876	−	0.209185i	$-0.932919\pi$
$241$	−1151.50	+	1994.46i	−0.307779	+	0.533088i	0.670098	+	0.742273i	$0.266252\pi$
$242$	−1293.00			−0.343459
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−116.500	−	201.784i	−0.0305662	−	0.0529422i
$245$	−1525.50	−	2642.24i	−0.397798	−	0.689007i
$246$	−2079.00			−0.538830
$247$	−598.000	−	2071.53i	−0.154048	−	0.533638i
$248$	2100.00			0.537702
$249$	−1215.00	−	2104.44i	−0.309227	−	0.535597i
$250$	−2281.50	−	3951.67i	−0.577179	−	0.999703i
$251$	−3162.00	+	5476.74i	−0.795154	+	1.37725i	0.127587	+	0.991827i	$0.459277\pi$
$251$	−3162.00	+	5476.74i	−0.795154	+	1.37725i	−0.922741	+	0.385420i	$0.874057\pi$
$252$	18.0000			0.00449958
$253$	90.0000	−	155.885i	0.0223646	−	0.0387367i
$254$	906.000	−	1569.24i	0.223809	−	0.387649i
$255$	2997.00			0.735998
$256$	−756.500	+	1310.30i	−0.184692	+	0.319897i
$257$	−3916.50	−	6783.58i	−0.950601	−	1.64649i	−0.744127	−	0.668038i	$-0.767134\pi$
$257$	−3916.50	−	6783.58i	−0.950601	−	1.64649i	−0.206474	−	0.978452i	$-0.566199\pi$
$258$	2313.00	+	4006.23i	0.558144	+	0.966733i
$259$	34.0000			0.00815698
$260$	−117.000	−	405.300i	−0.0279078	−	0.0966755i
$261$	−945.000			−0.224115
$262$	2376.00	+	4115.35i	0.560266	+	0.970410i
$263$	1515.00	+	2624.06i	0.355205	+	0.615233i	0.987153	−	0.159778i	$-0.0510777\pi$
$263$	1515.00	+	2624.06i	0.355205	+	0.615233i	−0.631948	+	0.775011i	$0.717744\pi$
$264$	945.000	−	1636.79i	0.220306	−	0.381581i
$265$	−5751.00			−1.33314
$266$	138.000	−	239.023i	0.0318095	−	0.0550956i
$267$	−747.000	+	1293.84i	−0.171220	+	0.296561i
$268$	926.000			0.211061
$269$	267.000	−	462.458i	0.0605178	−	0.104820i	−0.834179	−	0.551493i	$-0.814058\pi$
$269$	267.000	−	462.458i	0.0605178	−	0.104820i	0.894697	+	0.446674i	$0.147391\pi$
$270$	364.500	+	631.333i	0.0821584	+	0.142302i
$271$	1844.00	+	3193.90i	0.413340	+	0.715925i	0.995253	−	0.0973259i	$-0.0310289\pi$
$271$	1844.00	+	3193.90i	0.413340	+	0.715925i	−0.581913	+	0.813251i	$0.697696\pi$
$272$	7881.00			1.75682
$273$	195.000	−	202.650i	0.0432305	−	0.0449265i
$274$	2151.00			0.474258
$275$	660.000	+	1143.15i	0.144725	+	0.250672i
$276$	9.00000	+	15.5885i	0.00196281	+	0.00339969i
$277$	−932.500	+	1615.14i	−0.202269	+	0.350340i	−0.949259	−	0.314495i	$-0.898165\pi$
$277$	−932.500	+	1615.14i	−0.202269	+	0.350340i	0.746990	+	0.664835i	$0.231498\pi$
$278$	−2460.00			−0.530723
$279$	450.000	−	779.423i	0.0965620	−	0.167250i
$280$	−189.000	+	327.358i	−0.0403390	+	0.0698691i
$281$	2997.00			0.636249			0.318125	−	0.948049i	$-0.396947\pi$
$281$	2997.00			0.636249			0.318125	+	0.948049i	$0.396947\pi$
$282$	729.000	−	1262.67i	0.153941	−	0.266633i
$283$	2057.00	+	3562.83i	0.432071	+	0.748368i	0.997051	−	0.0767359i	$-0.0244498\pi$
$283$	2057.00	+	3562.83i	0.432071	+	0.748368i	−0.564981	+	0.825104i	$0.691116\pi$
$284$	465.000	+	805.404i	0.0971573	+	0.168281i
$285$	1242.00			0.258139
$286$	1170.00	+	4053.00i	0.241901	+	0.837968i
$287$	−462.000			−0.0950209
$288$	202.500	+	350.740i	0.0414320	+	0.0717624i
$289$	−3704.00	−	6415.52i	−0.753918	−	1.30582i
$290$	−1417.50	+	2455.18i	−0.287029	+	0.497149i
$291$	4074.00			0.820695
$292$	126.500	−	219.104i	0.0253522	−	0.0439114i
$293$	2332.50	−	4040.01i	0.465072	−	0.805528i	−0.534133	−	0.845401i	$-0.679362\pi$
$293$	2332.50	−	4040.01i	0.465072	−	0.805528i	0.999205	+	0.0398722i	$0.0126951\pi$
$294$	−3051.00			−0.605231
$295$	2700.00	−	4676.54i	0.532882	−	0.922978i
$296$	178.500	+	309.171i	0.0350510	+	0.0607101i
$297$	−405.000	−	701.481i	−0.0791262	−	0.137051i
$298$	−5247.00			−1.01997
$299$	273.000	+	67.5500i	0.0528027	+	0.0130653i
$300$	−132.000			−0.0254034
$301$	514.000	+	890.274i	0.0984268	+	0.170480i
$302$	555.000	+	961.288i	0.105751	+	0.183165i
$303$	535.500	−	927.513i	0.101530	−	0.175856i
$304$	3266.00			0.616177
$305$	1048.50	−	1816.06i	0.196842	−	0.340941i
$306$	1498.50	−	2595.48i	0.279946	−	0.484881i
$307$	1502.00			0.279230			0.139615	−	0.990206i	$-0.455413\pi$
$307$	1502.00			0.279230			0.139615	+	0.990206i	$0.455413\pi$
$308$	−30.0000	+	51.9615i	−0.00555003	+	0.00961293i
$309$	−1677.00	−	2904.65i	−0.308742	−	0.534756i
$310$	−1350.00	−	2338.27i	−0.247338	−	0.428402i
$311$	2106.00			0.383988			0.191994	−	0.981396i	$-0.438505\pi$
$311$	2106.00			0.383988			0.191994	+	0.981396i	$0.438505\pi$
$312$	2866.50	+	709.275i	0.520140	+	0.128701i
$313$	−3898.00			−0.703923			−0.351962	−	0.936014i	$-0.614485\pi$
$313$	−3898.00			−0.703923			−0.351962	+	0.936014i	$0.614485\pi$
$314$	3916.50	+	6783.58i	0.703888	+	1.21917i
$315$	81.0000	+	140.296i	0.0144884	+	0.0250946i
$316$	662.000	−	1146.62i	0.117849	−	0.204121i
$317$	9351.00			1.65680			0.828398	−	0.560140i	$-0.189253\pi$
$317$	9351.00			1.65680			0.828398	+	0.560140i	$0.189253\pi$
$318$	−2875.50	+	4980.51i	−0.507076	+	0.878281i
$319$	1575.00	−	2727.98i	0.276436	−	0.478801i
$320$	−3897.00			−0.680778
$321$	−1071.00	+	1855.03i	−0.186222	+	0.322547i
$322$	18.0000	+	31.1769i	0.00311522	+	0.00539572i
$323$	−2553.00	−	4421.93i	−0.439792	−	0.761742i
$324$	81.0000			0.0138889
$325$	−1430.00	+	1486.10i	−0.244068	+	0.253643i
$326$	−4908.00			−0.833831
$327$	−3009.00	−	5211.74i	−0.508863	−	0.881376i
$328$	−2425.50	−	4201.09i	−0.408310	−	0.707214i
$329$	162.000	−	280.592i	0.0271470	−	0.0470199i
$330$	−2430.00			−0.405355
$331$	4586.00	−	7943.19i	0.761539	−	1.31902i	−0.180518	−	0.983572i	$-0.557778\pi$
$331$	4586.00	−	7943.19i	0.761539	−	1.31902i	0.942057	−	0.335452i	$-0.108889\pi$
$332$	−405.000	+	701.481i	−0.0669496	+	0.115960i
$333$	153.000			0.0251782
$334$	−396.000	+	685.892i	−0.0648747	+	0.112366i
$335$	4167.00	+	7217.46i	0.679605	+	1.17711i
$336$	213.000	+	368.927i	0.0345836	+	0.0599006i
$337$	−11089.0			−1.79245			−0.896226	−	0.443598i	$-0.853702\pi$
$337$	−11089.0			−1.79245			−0.896226	+	0.443598i	$0.853702\pi$
$338$	−5577.00	+	3512.60i	−0.897482	+	0.565267i
$339$	−3357.00			−0.537838
$340$	−499.500	−	865.159i	−0.0796741	−	0.138000i
$341$	1500.00	+	2598.08i	0.238210	+	0.412592i
$342$	621.000	−	1075.60i	0.0981866	−	0.170064i
$343$	−1364.00			−0.214720
$344$	−5397.00	+	9347.88i	−0.845892	+	1.46513i
$345$	−81.0000	+	140.296i	−0.0126403	+	0.0218936i
$346$	4230.00			0.657243
$347$	−4881.00	+	8454.14i	−0.755118	+	1.30790i	0.190198	+	0.981746i	$0.439087\pi$
$347$	−4881.00	+	8454.14i	−0.755118	+	1.30790i	−0.945316	+	0.326156i	$0.894246\pi$
$348$	157.500	+	272.798i	0.0242612	+	0.0420216i
$349$	4145.00	+	7179.35i	0.635750	+	1.10115i	0.986356	+	0.164628i	$0.0526424\pi$
$349$	4145.00	+	7179.35i	0.635750	+	1.10115i	−0.350606	+	0.936523i	$0.614024\pi$
$350$	−264.000			−0.0403183
$351$	877.500	−	911.925i	0.133440	−	0.138675i
$352$	−1350.00			−0.204418
$353$	−6202.50	−	10743.0i	−0.935200	−	1.61981i	−0.774276	−	0.632848i	$-0.781886\pi$
$353$	−6202.50	−	10743.0i	−0.935200	−	1.61981i	−0.160924	−	0.986967i	$-0.551448\pi$
$354$	−2700.00	−	4676.54i	−0.405377	−	0.702133i
$355$	−4185.00	+	7248.63i	−0.625681	+	1.08371i
$356$	498.000			0.0741403
$357$	333.000	−	576.773i	0.0493676	−	0.0855072i
$358$	711.000	−	1231.49i	0.104965	−	0.181805i
$359$	−1098.00			−0.161421			−0.0807106	−	0.996738i	$-0.525719\pi$
$359$	−1098.00			−0.161421			−0.0807106	+	0.996738i	$0.525719\pi$
$360$	−850.500	+	1473.11i	−0.124515	+	0.215666i
$361$	2371.50	+	4107.56i	0.345750	+	0.598857i
$362$	−3373.50	−	5843.07i	−0.489799	−	0.848357i
$363$	−1293.00			−0.186956
$364$	−91.0000	−	22.5167i	−0.0131036	−	0.00324229i
$365$	2277.00			0.326530
$366$	−1048.50	−	1816.06i	−0.149743	−	0.259363i
$367$	2867.00	+	4965.79i	0.407783	+	0.706300i	0.994641	−	0.103390i	$-0.0329688\pi$
$367$	2867.00	+	4965.79i	0.407783	+	0.706300i	−0.586858	+	0.809690i	$0.699635\pi$
$368$	−213.000	+	368.927i	−0.0301723	+	0.0522599i
$369$	−2079.00			−0.293302
$370$	229.500	−	397.506i	0.0322463	−	0.0558523i
$371$	−639.000	+	1106.78i	−0.0894211	+	0.154882i
$372$	−300.000			−0.0418126
$373$	4485.50	−	7769.11i	0.622655	−	1.07847i	−0.366334	−	0.930483i	$-0.619387\pi$
$373$	4485.50	−	7769.11i	0.622655	−	1.07847i	0.988989	−	0.147987i	$-0.0472794\pi$
$374$	4995.00	+	8651.59i	0.690602	+	1.19616i
$375$	−2281.50	−	3951.67i	−0.314176	−	0.544170i
$376$	3402.00			0.466608
$377$	4777.50	+	1182.12i	0.652663	+	0.161492i
$378$	162.000			0.0220433
$379$	−3622.00	−	6273.49i	−0.490896	−	0.850257i	0.509049	−	0.860738i	$-0.329997\pi$
$379$	−3622.00	−	6273.49i	−0.490896	−	0.850257i	−0.999945	+	0.0104805i	$0.996664\pi$
$380$	−207.000	−	358.535i	−0.0279444	−	0.0484011i
$381$	906.000	−	1569.24i	0.121826	−	0.211009i
$382$	10332.0			1.38385
$383$	3156.00	−	5466.35i	0.421055	−	0.729289i	−0.574988	−	0.818162i	$-0.694993\pi$
$383$	3156.00	−	5466.35i	0.421055	−	0.729289i	0.996043	+	0.0888732i	$0.0283266\pi$
$384$	−2488.50	+	4310.21i	−0.330705	+	0.572798i
$385$	−540.000			−0.0714830
$386$	6409.50	−	11101.6i	0.845168	−	1.46387i
$387$	2313.00	+	4006.23i	0.303815	+	0.526223i
$388$	−679.000	−	1176.06i	−0.0888428	−	0.153880i
$389$	3627.00			0.472741			0.236370	−	0.971663i	$-0.424042\pi$
$389$	3627.00			0.472741			0.236370	+	0.971663i	$0.424042\pi$
$390$	−1053.00	−	3647.70i	−0.136720	−	0.473611i
$391$	666.000			0.0861408
$392$	−3559.50	−	6165.23i	−0.458627	−	0.794366i
$393$	2376.00	+	4115.35i	0.304970	+	0.528224i
$394$	2979.00	−	5159.78i	0.380913	−	0.659761i
$395$	11916.0			1.51787
$396$	−135.000	+	233.827i	−0.0171313	+	0.0296723i
$397$	1949.00	−	3375.77i	0.246392	−	0.426763i	−0.716130	−	0.697967i	$-0.754088\pi$
$397$	1949.00	−	3375.77i	0.246392	−	0.426763i	0.962522	+	0.271204i	$0.0874217\pi$
$398$	−7158.00			−0.901503
$399$	138.000	−	239.023i	0.0173149	−	0.0299903i
$400$	−1562.00	−	2705.46i	−0.195250	−	0.338183i
$401$	2851.50	+	4938.94i	0.355105	+	0.615060i	0.987136	−	0.159883i	$-0.0511118\pi$
$401$	2851.50	+	4938.94i	0.355105	+	0.615060i	−0.632031	+	0.774943i	$0.717778\pi$
$402$	8334.00			1.03399
$403$	−3250.00	+	3377.50i	−0.401722	+	0.417482i
$404$	−357.000			−0.0439639
$405$	364.500	+	631.333i	0.0447214	+	0.0774597i
$406$	315.000	+	545.596i	0.0385054	+	0.0666933i
$407$	−255.000	+	441.673i	−0.0310562	+	0.0537909i
$408$	6993.00			0.848542
$409$	−3155.50	+	5465.49i	−0.381490	+	0.660760i	−0.991275	−	0.131806i	$-0.957922\pi$
$409$	−3155.50	+	5465.49i	−0.381490	+	0.660760i	0.609785	+	0.792567i	$0.291256\pi$
$410$	−3118.50	+	5401.40i	−0.375638	+	0.650625i
$411$	2151.00			0.258153
$412$	−559.000	+	968.216i	−0.0668445	+	0.115778i
$413$	−600.000	−	1039.23i	−0.0714869	−	0.123819i
$414$	81.0000	+	140.296i	0.00961578	+	0.0166550i
$415$	−7290.00			−0.862294
$416$	−585.000	−	2026.50i	−0.0689471	−	0.238840i
$417$	−2460.00			−0.288889
$418$	2070.00	+	3585.35i	0.242218	+	0.419533i
$419$	1164.00	+	2016.11i	0.135716	+	0.235067i	0.925871	−	0.377840i	$-0.123333\pi$
$419$	1164.00	+	2016.11i	0.135716	+	0.235067i	−0.790155	+	0.612908i	$0.790000\pi$
$420$	27.0000	−	46.7654i	0.00313682	−	0.00543313i
$421$	2045.00			0.236739			0.118370	−	0.992970i	$-0.462233\pi$
$421$	2045.00			0.236739			0.118370	+	0.992970i	$0.462233\pi$
$422$	2400.00	−	4156.92i	0.276849	−	0.479516i
$423$	729.000	−	1262.67i	0.0837948	−	0.145137i
$424$	−13419.0			−1.53699
$425$	−2442.00	+	4229.67i	−0.278716	+	0.482751i
$426$	4185.00	+	7248.63i	0.475972	+	0.824407i
$427$	−233.000	−	403.568i	−0.0264067	−	0.0457377i
$428$	714.000			0.0806367
$429$	1170.00	+	4053.00i	0.131674	+	0.456132i
$430$	13878.0			1.55641
$431$	−2517.00	−	4359.57i	−0.281298	−	0.487223i	0.690406	−	0.723422i	$-0.257432\pi$
$431$	−2517.00	−	4359.57i	−0.281298	−	0.487223i	−0.971705	+	0.236199i	$0.924098\pi$
$432$	958.500	+	1660.17i	0.106750	+	0.184896i
$433$	−2141.50	+	3709.19i	−0.237676	+	0.411668i	−0.960047	−	0.279838i	$-0.909719\pi$
$433$	−2141.50	+	3709.19i	−0.237676	+	0.411668i	0.722371	+	0.691506i	$0.243052\pi$
$434$	−600.000			−0.0663616
$435$	−1417.50	+	2455.18i	−0.156239	+	0.270614i
$436$	−1003.00	+	1737.25i	−0.110172	+	0.190823i
$437$	276.000			0.0302125
$438$	1138.50	−	1971.94i	0.124200	−	0.215121i
$439$	653.000	+	1131.03i	0.0709931	+	0.122964i	0.899337	−	0.437257i	$-0.144050\pi$
$439$	653.000	+	1131.03i	0.0709931	+	0.122964i	−0.828344	+	0.560220i	$0.810716\pi$
$440$	−2835.00	−	4910.36i	−0.307167	−	0.532028i
$441$	−3051.00			−0.329446
$442$	−10822.5	+	11247.1i	−1.16465	+	1.21034i
$443$	−5796.00			−0.621617			−0.310808	−	0.950473i	$-0.600600\pi$
$443$	−5796.00			−0.621617			−0.310808	+	0.950473i	$0.600600\pi$
$444$	−25.5000	−	44.1673i	−0.00272562	−	0.00472092i
$445$	2241.00	+	3881.53i	0.238727	+	0.413488i
$446$	5748.00	−	9955.83i	0.610259	−	1.05700i
$447$	−5247.00			−0.555200
$448$	−433.000	+	749.978i	−0.0456637	+	0.0790918i
$449$	−1353.00	+	2343.46i	−0.142209	+	0.246314i	−0.928328	−	0.371761i	$-0.878754\pi$
$449$	−1353.00	+	2343.46i	−0.142209	+	0.246314i	0.786119	+	0.618075i	$0.212087\pi$
$450$	−1188.00			−0.124451
$451$	3465.00	−	6001.56i	0.361775	−	0.626612i
$452$	559.500	+	969.082i	0.0582227	+	0.100845i
$453$	555.000	+	961.288i	0.0575633	+	0.0997026i
$454$	−4194.00			−0.433555
$455$	−234.000	−	810.600i	−0.0241101	−	0.0835198i
$456$	2898.00			0.297612
$457$	414.500	+	717.935i	0.0424278	+	0.0734871i	0.886459	−	0.462806i	$-0.153157\pi$
$457$	414.500	+	717.935i	0.0424278	+	0.0734871i	−0.844032	+	0.536293i	$0.819824\pi$
$458$	−6699.00	−	11603.0i	−0.683458	−	1.18378i
$459$	1498.50	−	2595.48i	0.152383	−	0.263936i
$460$	54.0000			0.00547340
$461$	2746.50	−	4757.08i	0.277478	−	0.480606i	−0.693279	−	0.720669i	$-0.743835\pi$
$461$	2746.50	−	4757.08i	0.277478	−	0.480606i	0.970757	+	0.240063i	$0.0771682\pi$
$462$	−270.000	+	467.654i	−0.0271895	+	0.0470935i
$463$	−15346.0			−1.54037			−0.770183	−	0.637823i	$-0.779835\pi$
$463$	−15346.0			−1.54037			−0.770183	+	0.637823i	$0.779835\pi$
$464$	−3727.50	+	6456.22i	−0.372941	+	0.645954i
$465$	−1350.00	−	2338.27i	−0.134634	−	0.233193i
$466$	2457.00	+	4255.65i	0.244245	+	0.423045i
$467$	−9594.00			−0.950658			−0.475329	−	0.879808i	$-0.657671\pi$
$467$	−9594.00			−0.950658			−0.475329	+	0.879808i	$0.657671\pi$
$468$	−409.500	−	101.325i	−0.0404469	−	0.0100080i
$469$	1852.00			0.182340
$470$	−2187.00	−	3788.00i	−0.214636	−	0.371760i
$471$	3916.50	+	6783.58i	0.383148	+	0.663632i
$472$	6300.00	−	10911.9i	0.614367	−	1.06411i
$473$	−15420.0			−1.49897
$474$	5958.00	−	10319.6i	0.577342	−	0.999985i
$475$	−1012.00	+	1752.84i	−0.0977553	+	0.169317i
$476$	−222.000			−0.0213768
$477$	−2875.50	+	4980.51i	−0.276017	+	0.478075i
$478$	891.000	+	1543.26i	0.0852581	+	0.147671i
$479$	6420.00	+	11119.8i	0.612395	+	1.06070i	0.990836	+	0.135074i	$0.0431272\pi$
$479$	6420.00	+	11119.8i	0.612395	+	1.06070i	−0.378440	+	0.925626i	$0.623539\pi$
$480$	1215.00			0.115535
$481$	−773.500	−	191.392i	−0.0733234	−	0.0181428i
$482$	6909.00			0.652897
$483$	18.0000	+	31.1769i	0.00169571	+	0.00293706i
$484$	215.500	+	373.257i	0.0202385	+	0.0350542i
$485$	6111.00	−	10584.6i	0.572137	−	0.990970i
$486$	729.000			0.0680414
$487$	7043.00	−	12198.8i	0.655336	−	1.13508i	−0.326473	−	0.945207i	$-0.605860\pi$
$487$	7043.00	−	12198.8i	0.655336	−	1.13508i	0.981809	−	0.189869i	$-0.0608064\pi$
$488$	2446.50	−	4237.46i	0.226942	−	0.393076i
$489$	−4908.00			−0.453880
$490$	−4576.50	+	7926.73i	−0.421929	+	0.730802i
$491$	−5847.00	−	10127.3i	−0.537416	−	0.930832i	−0.999042	−	0.0437577i	$-0.986067\pi$
$491$	−5847.00	−	10127.3i	−0.537416	−	0.930832i	0.461626	−	0.887075i	$-0.347266\pi$
$492$	346.500	+	600.156i	0.0317509	+	0.0549941i
$493$	11655.0			1.06474
$494$	−4485.00	+	4660.95i	−0.408481	+	0.424506i
$495$	−2430.00			−0.220647
$496$	−3550.00	−	6148.78i	−0.321370	−	0.556630i
$497$	930.000	+	1610.81i	0.0839360	+	0.145381i
$498$	−3645.00	+	6313.33i	−0.327985	+	0.568086i
$499$	−3688.00			−0.330857			−0.165428	−	0.986222i	$-0.552901\pi$
$499$	−3688.00			−0.330857			−0.165428	+	0.986222i	$0.552901\pi$
$500$	−760.500	+	1317.22i	−0.0680212	+	0.117816i
$501$	−396.000	+	685.892i	−0.0353133	+	0.0611645i
$502$	18972.0			1.68678
$503$	2373.00	−	4110.16i	0.210352	−	0.364340i	−0.741473	−	0.670983i	$-0.765872\pi$
$503$	2373.00	−	4110.16i	0.210352	−	0.364340i	0.951825	+	0.306643i	$0.0992058\pi$
$504$	189.000	+	327.358i	0.0167038	+	0.0289319i
$505$	−1606.50	−	2782.54i	−0.141561	−	0.245191i
$506$	−540.000			−0.0474425
$507$	−5577.00	+	3512.60i	−0.488527	+	0.307692i
$508$	−604.000			−0.0527523
$509$	7252.50	+	12561.7i	0.631555	+	1.09389i	0.987234	+	0.159277i	$0.0509163\pi$
$509$	7252.50	+	12561.7i	0.631555	+	1.09389i	−0.355679	+	0.934608i	$0.615750\pi$
$510$	−4495.50	−	7786.43i	−0.390322	−	0.676057i
$511$	253.000	−	438.209i	0.0219023	−	0.0379358i
$512$	−8733.00			−0.753804
$513$	621.000	−	1075.60i	0.0534460	−	0.0925713i
$514$	−11749.5	+	20350.7i	−1.00827	+	1.74637i
$515$	−10062.0			−0.860941
$516$	771.000	−	1335.41i	0.0657779	−	0.113931i
$517$	2430.00	+	4208.88i	0.206714	+	0.358040i
$518$	−51.0000	−	88.3346i	−0.00432589	−	0.00749266i
$519$	4230.00			0.357758
$520$	6142.50	−	6383.47i	0.518012	−	0.538334i
$521$	5085.00			0.427597			0.213798	−	0.976878i	$-0.431416\pi$
$521$	5085.00			0.427597			0.213798	+	0.976878i	$0.431416\pi$
$522$	1417.50	+	2455.18i	0.118855	+	0.205863i
$523$	5441.00	+	9424.09i	0.454911	+	0.787929i	0.998683	−	0.0513043i	$-0.0163378\pi$
$523$	5441.00	+	9424.09i	0.454911	+	0.787929i	−0.543772	+	0.839233i	$0.683004\pi$
$524$	792.000	−	1371.78i	0.0660280	−	0.114364i
$525$	−264.000			−0.0219465
$526$	4545.00	−	7872.17i	0.376752	−	0.652553i
$527$	−5550.00	+	9612.88i	−0.458751	+	0.794580i
$528$	−6390.00			−0.526684
$529$	6065.50	−	10505.8i	0.498521	−	0.863463i
$530$	8626.50	+	14941.5i	0.707002	+	1.22456i
$531$	−2700.00	−	4676.54i	−0.220659	−	0.382193i
$532$	−92.0000			−0.00749757
$533$	10510.5	+	2600.67i	0.854147	+	0.211347i
$534$	4482.00			0.363212
$535$	3213.00	+	5565.08i	0.259645	+	0.449718i
$536$	9723.00	+	16840.7i	0.783525	+	1.35711i
$537$	711.000	−	1231.49i	0.0571358	−	0.0989621i
$538$	−1602.00			−0.128378
$539$	5085.00	−	8807.48i	0.406357	−	0.703831i
$540$	121.500	−	210.444i	0.00968246	−	0.0167705i
$541$	−4699.00			−0.373430			−0.186715	−	0.982414i	$-0.559784\pi$
$541$	−4699.00			−0.373430			−0.186715	+	0.982414i	$0.559784\pi$
$542$	5532.00	−	9581.71i	0.438413	−	0.759353i
$543$	−3373.50	−	5843.07i	−0.266613	−	0.461787i
$544$	−2497.50	−	4325.80i	−0.196837	−	0.340932i
$545$	−18054.0			−1.41899
$546$	−819.000	−	202.650i	−0.0641941	−	0.0158839i
$547$	8270.00			0.646434			0.323217	−	0.946325i	$-0.395236\pi$
$547$	8270.00			0.646434			0.323217	+	0.946325i	$0.395236\pi$
$548$	−358.500	−	620.940i	−0.0279459	−	0.0484037i
$549$	−1048.50	−	1816.06i	−0.0815098	−	0.141179i
$550$	1980.00	−	3429.46i	0.153505	−	0.265878i
$551$	4830.00			0.373439
$552$	−189.000	+	327.358i	−0.0145731	+	0.0252414i
$553$	1324.00	−	2293.24i	0.101812	−	0.176344i
$554$	5595.00			0.429077
$555$	229.500	−	397.506i	0.0175527	−	0.0304021i
$556$	410.000	+	710.141i	0.0312732	+	0.0541667i
$557$	11392.5	+	19732.4i	0.866635	+	1.50106i	0.865414	+	0.501057i	$0.167055\pi$
$557$	11392.5	+	19732.4i	0.866635	+	1.50106i	0.00122056	+	0.999999i	$0.499611\pi$
$558$	−2700.00			−0.204839
$559$	−6682.00	−	23147.1i	−0.505579	−	1.75138i
$560$	1278.00			0.0964381
$561$	4995.00	+	8651.59i	0.375916	+	0.651106i
$562$	−4495.50	−	7786.43i	−0.337422	−	0.584432i
$563$	5964.00	−	10330.0i	0.446452	−	0.773278i	−0.551700	−	0.834043i	$-0.686021\pi$
$563$	5964.00	−	10330.0i	0.446452	−	0.773278i	0.998152	+	0.0607647i	$0.0193539\pi$
$564$	−486.000			−0.0362842
$565$	−5035.50	+	8721.74i	−0.374947	+	0.649427i
$566$	6171.00	−	10688.5i	0.458280	−	0.793764i
$567$	162.000			0.0119989
$568$	−9765.00	+	16913.5i	−0.721356	+	1.24943i
$569$	3981.00	+	6895.29i	0.293308	+	0.508024i	0.974590	−	0.223997i	$-0.0719106\pi$
$569$	3981.00	+	6895.29i	0.293308	+	0.508024i	−0.681282	+	0.732021i	$0.738577\pi$
$570$	−1863.00	−	3226.81i	−0.136899	−	0.237116i
$571$	20618.0			1.51110			0.755549	−	0.655093i	$-0.227370\pi$
$571$	20618.0			1.51110			0.755549	+	0.655093i	$0.227370\pi$
$572$	975.000	−	1013.25i	0.0712706	−	0.0740666i
$573$	10332.0			0.753273
$574$	693.000	+	1200.31i	0.0503924	+	0.0872823i
$575$	−132.000	−	228.631i	−0.00957353	−	0.0165818i
$576$	−1948.50	+	3374.90i	−0.140951	+	0.244133i
$577$	−3493.00			−0.252020			−0.126010	−	0.992029i	$-0.540217\pi$
$577$	−3493.00			−0.252020			−0.126010	+	0.992029i	$0.540217\pi$
$578$	−11112.0	+	19246.5i	−0.799651	+	1.38504i
$579$	6409.50	−	11101.6i	0.460051	−	0.796832i
$580$	945.000			0.0676534
$581$	−810.000	+	1402.96i	−0.0578390	+	0.100180i
$582$	−6111.00	−	10584.6i	−0.435239	−	0.753856i
$583$	−9585.00	−	16601.7i	−0.680909	−	1.17937i
$584$	5313.00			0.376461
$585$	−1053.00	−	3647.70i	−0.0744208	−	0.257801i
$586$	−13995.0			−0.986567
$587$	−5208.00	−	9020.52i	−0.366196	−	0.634270i	0.622771	−	0.782404i	$-0.286007\pi$
$587$	−5208.00	−	9020.52i	−0.366196	−	0.634270i	−0.988967	+	0.148134i	$0.952673\pi$
$588$	508.500	+	880.748i	0.0356636	+	0.0617711i
$589$	−2300.00	+	3983.72i	−0.160900	+	0.278686i
$590$	−16200.0			−1.13041
$591$	2979.00	−	5159.78i	0.207343	−	0.359129i
$592$	603.500	−	1045.29i	0.0418981	−	0.0725697i
$593$	2061.00			0.142724			0.0713618	−	0.997450i	$-0.477266\pi$
$593$	2061.00			0.142724			0.0713618	+	0.997450i	$0.477266\pi$
$594$	−1215.00	+	2104.44i	−0.0839260	+	0.145364i
$595$	−999.000	−	1730.32i	−0.0688319	−	0.119220i
$596$	874.500	+	1514.68i	0.0601022	+	0.104100i
$597$	−7158.00			−0.490716
$598$	−234.000	−	810.600i	−0.0160016	−	0.0554313i
$599$	12456.0			0.849647			0.424823	−	0.905276i	$-0.360336\pi$
$599$	12456.0			0.849647			0.424823	+	0.905276i	$0.360336\pi$
$600$	−1386.00	−	2400.62i	−0.0943054	−	0.163342i
$601$	390.500	+	676.366i	0.0265039	+	0.0459061i	0.878973	−	0.476871i	$-0.158229\pi$
$601$	390.500	+	676.366i	0.0265039	+	0.0459061i	−0.852469	+	0.522777i	$0.824896\pi$
$602$	1542.00	−	2670.82i	0.104397	−	0.180822i
$603$	8334.00			0.562830
$604$	185.000	−	320.429i	0.0124628	−	0.0215862i
$605$	−1939.50	+	3359.31i	−0.130334	+	0.225745i
$606$	−3213.00			−0.215378
$607$	−9652.00	+	16717.8i	−0.645408	+	1.11788i	0.338799	+	0.940859i	$0.389979\pi$
$607$	−9652.00	+	16717.8i	−0.645408	+	1.11788i	−0.984207	+	0.177021i	$0.943354\pi$
$608$	−1035.00	−	1792.67i	−0.0690375	−	0.119576i
$609$	315.000	+	545.596i	0.0209597	+	0.0363032i
$610$	−6291.00			−0.417566
$611$	−5265.00	+	5471.55i	−0.348607	+	0.362283i
$612$	−999.000			−0.0659840
$613$	−6020.50	−	10427.8i	−0.396681	−	0.687072i	0.596633	−	0.802514i	$-0.296505\pi$
$613$	−6020.50	−	10427.8i	−0.396681	−	0.687072i	−0.993314	+	0.115442i	$0.963172\pi$
$614$	−2253.00	−	3902.31i	−0.148084	−	0.256489i
$615$	−3118.50	+	5401.40i	−0.204472	+	0.354155i
$616$	−1260.00			−0.0824137
$617$	−4858.50	+	8415.17i	−0.317011	+	0.549079i	−0.979863	−	0.199671i	$-0.936013\pi$
$617$	−4858.50	+	8415.17i	−0.317011	+	0.549079i	0.662852	+	0.748751i	$0.269346\pi$
$618$	−5031.00	+	8713.95i	−0.327470	+	0.567195i
$619$	−21040.0			−1.36619			−0.683093	−	0.730332i	$-0.739366\pi$
$619$	−21040.0			−1.36619			−0.683093	+	0.730332i	$0.739366\pi$
$620$	−450.000	+	779.423i	−0.0291491	+	0.0504877i
$621$	81.0000	+	140.296i	0.00523417	+	0.00906584i
$622$	−3159.00	−	5471.55i	−0.203640	−	0.352716i
$623$	996.000			0.0640512
$624$	−2769.00	−	9592.10i	−0.177642	−	0.615371i
$625$	−8189.00			−0.524096
$626$	5847.00	+	10127.3i	0.373312	+	0.646595i
$627$	2070.00	+	3585.35i	0.131847	+	0.228365i
$628$	1305.50	−	2261.19i	0.0829540	−	0.143681i
$629$	−1887.00			−0.119618
$630$	243.000	−	420.888i	0.0153672	−	0.0266168i
$631$	2534.00	−	4389.02i	0.159868	−	0.276900i	−0.774953	−	0.632019i	$-0.782226\pi$
$631$	2534.00	−	4389.02i	0.159868	−	0.276900i	0.934821	+	0.355119i	$0.115560\pi$
$632$	27804.0			1.74997
$633$	2400.00	−	4156.92i	0.150697	−	0.261016i
$634$	−14026.5	−	24294.6i	−0.878649	−	1.52186i
$635$	−2718.00	−	4707.71i	−0.169859	−	0.294205i
$636$	1917.00			0.119519
$637$	15424.5	+	3816.57i	0.959405	+	0.237391i
$638$	−9450.00			−0.586409
$639$	4185.00	+	7248.63i	0.259086	+	0.448750i
$640$	7465.50	+	12930.6i	0.461093	+	0.798637i
$641$	−5092.50	+	8820.47i	−0.313794	+	0.543506i	−0.979180	−	0.202992i	$-0.934933\pi$
$641$	−5092.50	+	8820.47i	−0.313794	+	0.543506i	0.665387	+	0.746499i	$0.268267\pi$
$642$	6426.00			0.395037
$643$	−12964.0	+	22454.3i	−0.795101	+	1.37716i	0.127673	+	0.991816i	$0.459249\pi$
$643$	−12964.0	+	22454.3i	−0.795101	+	1.37716i	−0.922775	+	0.385340i	$0.874084\pi$
$644$	6.00000	−	10.3923i	0.000367132	−	0.000635892i
$645$	13878.0			0.847203
$646$	−7659.00	+	13265.8i	−0.466470	+	0.807949i
$647$	−11580.0	−	20057.1i	−0.703643	−	1.21874i	−0.967179	−	0.254095i	$-0.918222\pi$
$647$	−11580.0	−	20057.1i	−0.703643	−	1.21874i	0.263537	−	0.964649i	$-0.415111\pi$
$648$	850.500	+	1473.11i	0.0515599	+	0.0893043i
$649$	18000.0			1.08869
$650$	6006.00	+	1486.10i	0.362423	+	0.0896763i
$651$	−600.000			−0.0361227
$652$	818.000	+	1416.82i	0.0491340	+	0.0851025i
$653$	−8313.00	−	14398.5i	−0.498182	−	0.862876i	0.501816	−	0.864974i	$-0.332666\pi$
$653$	−8313.00	−	14398.5i	−0.498182	−	0.862876i	−0.999998	+	0.00209801i	$0.999332\pi$
$654$	−9027.00	+	15635.2i	−0.539730	+	0.934840i
$655$	14256.0			0.850424
$656$	−8200.50	+	14203.7i	−0.488073	+	0.845367i
$657$	1138.50	−	1971.94i	0.0676060	−	0.117097i
$658$	−972.000			−0.0575874
$659$	7404.00	−	12824.1i	0.437661	−	0.758052i	−0.559847	−	0.828596i	$-0.689140\pi$
$659$	7404.00	−	12824.1i	0.437661	−	0.758052i	0.997509	+	0.0705440i	$0.0224735\pi$
$660$	405.000	+	701.481i	0.0238858	+	0.0413714i
$661$	−2426.50	−	4202.82i	−0.142784	−	0.247308i	0.785760	−	0.618531i	$-0.212272\pi$
$661$	−2426.50	−	4202.82i	−0.142784	−	0.247308i	−0.928544	+	0.371223i	$0.878939\pi$
$662$	−27516.0			−1.61547
$663$	−10822.5	+	11247.1i	−0.633953	+	0.658824i
$664$	−17010.0			−0.994151
$665$	−414.000	−	717.069i	−0.0241417	−	0.0418147i
$666$	−229.500	−	397.506i	−0.0133528	−	0.0231277i
$667$	−315.000	+	545.596i	−0.0182861	+	0.0316725i
$668$	264.000			0.0152911
$669$	5748.00	−	9955.83i	0.332183	−	0.575358i
$670$	12501.0	−	21652.4i	0.720829	−	1.24851i
$671$	6990.00			0.402155
$672$	135.000	−	233.827i	0.00774961	−	0.0134227i
$673$	8082.50	+	13999.3i	0.462938	+	0.801833i	0.999106	−	0.0422789i	$-0.0134618\pi$
$673$	8082.50	+	13999.3i	0.462938	+	0.801833i	−0.536168	+	0.844112i	$0.680128\pi$
$674$	16633.5	+	28810.1i	0.950591	+	1.64647i
$675$	−1188.00			−0.0677424
$676$	1943.50	+	1024.51i	0.110577	+	0.0582902i
$677$	−25686.0			−1.45819			−0.729094	−	0.684414i	$-0.760058\pi$
$677$	−25686.0			−1.45819			−0.729094	+	0.684414i	$0.760058\pi$
$678$	5035.50	+	8721.74i	0.285232	+	0.494036i
$679$	−1358.00	−	2352.12i	−0.0767530	−	0.132940i
$680$	10489.5	−	18168.3i	0.591550	−	1.02459i
$681$	−4194.00			−0.235998
$682$	4500.00	−	7794.23i	0.252660	−	0.437619i
$683$	9528.00	−	16503.0i	0.533790	−	0.924552i	−0.465431	−	0.885084i	$-0.654100\pi$
$683$	9528.00	−	16503.0i	0.533790	−	0.924552i	0.999221	−	0.0394675i	$-0.0125662\pi$
$684$	−414.000			−0.0231428
$685$	3226.50	−	5588.46i	0.179968	−	0.311714i
$686$	2046.00	+	3543.78i	0.113873	+	0.197233i
$687$	−6699.00	−	11603.0i	−0.372027	−	0.644370i
$688$	36494.0			2.02227
$689$	20767.5	−	21582.2i	1.14830	−	1.19335i
$690$	486.000			0.0268141
$691$	8195.00	+	14194.2i	0.451161	+	0.781434i	0.998458	−	0.0555040i	$-0.0176766\pi$
$691$	8195.00	+	14194.2i	0.451161	+	0.781434i	−0.547297	+	0.836938i	$0.684343\pi$
$692$	−705.000	−	1221.10i	−0.0387284	−	0.0670796i
$693$	−270.000	+	467.654i	−0.0148001	+	0.0256345i
$694$	29286.0			1.60185
$695$	−3690.00	+	6391.27i	−0.201395	+	0.348827i
$696$	−3307.50	+	5728.76i	−0.180130	+	0.311994i
$697$	25641.0			1.39343
$698$	12435.0	−	21538.1i	0.674315	−	1.16795i
$699$	2457.00	+	4255.65i	0.132950	+	0.230277i
$700$	44.0000	+	76.2102i	0.00237578	+	0.00411497i
$701$	−27846.0			−1.50033			−0.750163	−	0.661253i	$-0.770025\pi$
$701$	−27846.0			−1.50033			−0.750163	+	0.661253i	$0.770025\pi$
$702$	−3685.50	−	911.925i	−0.198148	−	0.0490290i
$703$	−782.000			−0.0419540
$704$	−6495.00	−	11249.7i	−0.347712	−	0.602256i
$705$	−2187.00	−	3788.00i	−0.116833	−	0.202360i
$706$	−18607.5	+	32229.1i	−0.991930	+	1.71807i
$707$	−714.000			−0.0379812
$708$	−900.000	+	1558.85i	−0.0477741	+	0.0827472i
$709$	6141.50	−	10637.4i	0.325316	−	0.563463i	−0.656260	−	0.754534i	$-0.727863\pi$
$709$	6141.50	−	10637.4i	0.325316	−	0.563463i	0.981576	+	0.191071i	$0.0611961\pi$
$710$	25110.0			1.32727
$711$	5958.00	−	10319.6i	0.314265	−	0.544323i
$712$	5229.00	+	9056.89i	0.275232	+	0.476716i
$713$	−300.000	−	519.615i	−0.0157575	−	0.0272928i
$714$	−1998.00			−0.104724
$715$	12285.0	+	3039.75i	0.642564	+	0.158993i
$716$	−474.000			−0.0247405
$717$	891.000	+	1543.26i	0.0464087	+	0.0803821i
$718$	1647.00	+	2852.69i	0.0856065	+	0.148275i
$719$	−12756.0	+	22094.0i	−0.661639	+	1.14599i	0.318546	+	0.947908i	$0.396806\pi$
$719$	−12756.0	+	22094.0i	−0.661639	+	1.14599i	−0.980185	+	0.198085i	$0.936528\pi$
$720$	5751.00			0.297677
$721$	−1118.00	+	1936.43i	−0.0577483	+	0.100023i
$722$	7114.50	−	12322.7i	0.366723	−	0.635184i
$723$	6909.00			0.355392
$724$	−1124.50	+	1947.69i	−0.0577234	+	0.0999798i
$725$	−2310.00	−	4001.04i	−0.118333	−	0.204958i
$726$	1939.50	+	3359.31i	0.0991482	+	0.171730i
$727$	6110.00			0.311702			0.155851	−	0.987781i	$-0.450188\pi$
$727$	6110.00			0.311702			0.155851	+	0.987781i	$0.450188\pi$
$728$	−546.000	−	1891.40i	−0.0277968	−	0.0962911i
$729$	729.000			0.0370370
$730$	−3415.50	−	5915.82i	−0.173169	−	0.299937i
$731$	−28527.0	−	49410.2i	−1.44338	−	2.50000i
$732$	−349.500	+	605.352i	−0.0176474	+	0.0305662i
$733$	−27127.0			−1.36693			−0.683464	−	0.729984i	$-0.739527\pi$
$733$	−27127.0			−1.36693			−0.683464	+	0.729984i	$0.739527\pi$
$734$	8601.00	−	14897.4i	0.432519	−	0.749144i
$735$	−4576.50	+	7926.73i	−0.229669	+	0.397798i
$736$	270.000			0.0135222
$737$	−13890.0	+	24058.2i	−0.694226	+	1.20244i
$738$	3118.50	+	5401.40i	0.155547	+	0.269415i
$739$	440.000	+	762.102i	0.0219021	+	0.0379356i	0.876769	−	0.480912i	$-0.159694\pi$
$739$	440.000	+	762.102i	0.0219021	+	0.0379356i	−0.854867	+	0.518848i	$0.826361\pi$
$740$	−153.000			−0.00760053
$741$	−4485.00	+	4660.95i	−0.222349	+	0.231072i
$742$	3834.00			0.189691
$743$	10938.0	+	18945.2i	0.540076	+	0.935439i	0.998899	+	0.0469111i	$0.0149378\pi$
$743$	10938.0	+	18945.2i	0.540076	+	0.935439i	−0.458823	+	0.888528i	$0.651729\pi$
$744$	−3150.00	−	5455.96i	−0.155221	−	0.268851i
$745$	−7870.50	+	13632.1i	−0.387051	+	0.670392i
$746$	−26913.0			−1.32085
$747$	−3645.00	+	6313.33i	−0.178532	+	0.309227i
$748$	1665.00	−	2883.86i	0.0813883	−	0.140969i
$749$	1428.00			0.0696635
$750$	−6844.50	+	11855.0i	−0.333234	+	0.577179i
$751$	−5899.00	−	10217.4i	−0.286628	−	0.496454i	0.686375	−	0.727248i	$-0.259201\pi$
$751$	−5899.00	−	10217.4i	−0.286628	−	0.496454i	−0.973003	+	0.230794i	$0.925868\pi$
$752$	−5751.00	−	9961.02i	−0.278880	−	0.483033i
$753$	18972.0			0.918165
$754$	−4095.00	−	14185.5i	−0.197787	−	0.685153i
$755$	3330.00			0.160518
$756$	−27.0000	−	46.7654i	−0.00129892	−	0.00224979i
$757$	4037.00	+	6992.29i	0.193827	+	0.335719i	0.946515	−	0.322658i	$-0.104577\pi$
$757$	4037.00	+	6992.29i	0.193827	+	0.335719i	−0.752688	+	0.658377i	$0.771243\pi$
$758$	−10866.0	+	18820.5i	−0.520674	+	0.901834i
$759$	−540.000			−0.0258245
$760$	4347.00	−	7529.22i	0.207477	−	0.359360i
$761$	−9777.00	+	16934.3i	−0.465724	+	0.806658i	−0.999234	−	0.0391362i	$-0.987539\pi$
$761$	−9777.00	+	16934.3i	−0.465724	+	0.806658i	0.533510	+	0.845794i	$0.320873\pi$
$762$	−5436.00			−0.258432
$763$	−2006.00	+	3474.49i	−0.0951797	+	0.164856i
$764$	−1722.00	−	2982.59i	−0.0815442	−	0.141239i
$765$	−4495.50	−	7786.43i	−0.212464	−	0.367999i
$766$	−18936.0			−0.893193
$767$	7800.00	+	27020.0i	0.367199	+	1.27201i
$768$	4539.00			0.213264
$769$	−7015.00	−	12150.3i	−0.328956	−	0.569769i	0.653349	−	0.757057i	$-0.273364\pi$
$769$	−7015.00	−	12150.3i	−0.328956	−	0.569769i	−0.982305	+	0.187288i	$0.940030\pi$
$770$	810.000	+	1402.96i	0.0379096	+	0.0656613i
$771$	−11749.5	+	20350.7i	−0.548830	+

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(-4.50000 + 7.79423i) q^{6} +(-1.00000 + 1.73205i) q^{7} -21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(-4.50000 + 7.79423i) q^{6} +(-1.00000 + 1.73205i) q^{7} -21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(13.5000 + 23.3827i) q^{10} +(-15.0000 - 25.9808i) q^{11} +3.00000 q^{12} +(32.5000 - 33.7750i) q^{13} +6.00000 q^{14} +(13.5000 + 23.3827i) q^{15} +(35.5000 + 61.4878i) q^{16} +(55.5000 - 96.1288i) q^{17} +27.0000 q^{18} +(23.0000 - 39.8372i) q^{19} +(4.50000 - 7.79423i) q^{20} +6.00000 q^{21} +(-45.0000 + 77.9423i) q^{22} +(3.00000 + 5.19615i) q^{23} +(31.5000 + 54.5596i) q^{24} -44.0000 q^{25} +(-136.500 - 33.7750i) q^{26} +27.0000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(52.5000 + 90.9327i) q^{29} +(40.5000 - 70.1481i) q^{30} -100.000 q^{31} +(22.5000 - 38.9711i) q^{32} +(-45.0000 + 77.9423i) q^{33} -333.000 q^{34} +(9.00000 - 15.5885i) q^{35} +(-4.50000 - 7.79423i) q^{36} +(-8.50000 - 14.7224i) q^{37} -138.000 q^{38} +(-136.500 - 33.7750i) q^{39} +189.000 q^{40} +(115.500 + 200.052i) q^{41} +(-9.00000 - 15.5885i) q^{42} +(257.000 - 445.137i) q^{43} +30.0000 q^{44} +(40.5000 - 70.1481i) q^{45} +(9.00000 - 15.5885i) q^{46} -162.000 q^{47} +(106.500 - 184.463i) q^{48} +(169.500 + 293.583i) q^{49} +(66.0000 + 114.315i) q^{50} -333.000 q^{51} +(13.0000 + 45.0333i) q^{52} +639.000 q^{53} +(-40.5000 - 70.1481i) q^{54} +(135.000 + 233.827i) q^{55} +(21.0000 - 36.3731i) q^{56} -138.000 q^{57} +(157.500 - 272.798i) q^{58} +(-300.000 + 519.615i) q^{59} -27.0000 q^{60} +(-116.500 + 201.784i) q^{61} +(150.000 + 259.808i) q^{62} +(-9.00000 - 15.5885i) q^{63} +433.000 q^{64} +(-292.500 + 303.975i) q^{65} +270.000 q^{66} +(-463.000 - 801.940i) q^{67} +(55.5000 + 96.1288i) q^{68} +(9.00000 - 15.5885i) q^{69} -54.0000 q^{70} +(465.000 - 805.404i) q^{71} +(94.5000 - 163.679i) q^{72} -253.000 q^{73} +(-25.5000 + 44.1673i) q^{74} +(66.0000 + 114.315i) q^{75} +(23.0000 + 39.8372i) q^{76} +60.0000 q^{77} +(117.000 + 405.300i) q^{78} -1324.00 q^{79} +(-319.500 - 553.390i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(346.500 - 600.156i) q^{82} +810.000 q^{83} +(-3.00000 + 5.19615i) q^{84} +(-499.500 + 865.159i) q^{85} -1542.00 q^{86} +(157.500 - 272.798i) q^{87} +(315.000 + 545.596i) q^{88} +(-249.000 - 431.281i) q^{89} -243.000 q^{90} +(26.0000 + 90.0666i) q^{91} -6.00000 q^{92} +(150.000 + 259.808i) q^{93} +(243.000 + 420.888i) q^{94} +(-207.000 + 358.535i) q^{95} -135.000 q^{96} +(-679.000 + 1176.06i) q^{97} +(508.500 - 880.748i) q^{98} +270.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 3 q^{3} - q^{4} - 18 q^{5} - 9 q^{6} - 2 q^{7} - 42 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 3 * q^3 - q^4 - 18 * q^5 - 9 * q^6 - 2 * q^7 - 42 * q^8 - 9 * q^9	\( 2 q - 3 q^{2} - 3 q^{3} - q^{4} - 18 q^{5} - 9 q^{6} - 2 q^{7} - 42 q^{8} - 9 q^{9} + 27 q^{10} - 30 q^{11} + 6 q^{12} + 65 q^{13} + 12 q^{14} + 27 q^{15} + 71 q^{16} + 111 q^{17} + 54 q^{18} + 46 q^{19} + 9 q^{20} + 12 q^{21} - 90 q^{22} + 6 q^{23} + 63 q^{24} - 88 q^{25} - 273 q^{26} + 54 q^{27} - 2 q^{28} + 105 q^{29} + 81 q^{30} - 200 q^{31} + 45 q^{32} - 90 q^{33} - 666 q^{34} + 18 q^{35} - 9 q^{36} - 17 q^{37} - 276 q^{38} - 273 q^{39} + 378 q^{40} + 231 q^{41} - 18 q^{42} + 514 q^{43} + 60 q^{44} + 81 q^{45} + 18 q^{46} - 324 q^{47} + 213 q^{48} + 339 q^{49} + 132 q^{50} - 666 q^{51} + 26 q^{52} + 1278 q^{53} - 81 q^{54} + 270 q^{55} + 42 q^{56} - 276 q^{57} + 315 q^{58} - 600 q^{59} - 54 q^{60} - 233 q^{61} + 300 q^{62} - 18 q^{63} + 866 q^{64} - 585 q^{65} + 540 q^{66} - 926 q^{67} + 111 q^{68} + 18 q^{69} - 108 q^{70} + 930 q^{71} + 189 q^{72} - 506 q^{73} - 51 q^{74} + 132 q^{75} + 46 q^{76} + 120 q^{77} + 234 q^{78} - 2648 q^{79} - 639 q^{80} - 81 q^{81} + 693 q^{82} + 1620 q^{83} - 6 q^{84} - 999 q^{85} - 3084 q^{86} + 315 q^{87} + 630 q^{88} - 498 q^{89} - 486 q^{90} + 52 q^{91} - 12 q^{92} + 300 q^{93} + 486 q^{94} - 414 q^{95} - 270 q^{96} - 1358 q^{97} + 1017 q^{98} + 540 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 3 * q^3 - q^4 - 18 * q^5 - 9 * q^6 - 2 * q^7 - 42 * q^8 - 9 * q^9 + 27 * q^10 - 30 * q^11 + 6 * q^12 + 65 * q^13 + 12 * q^14 + 27 * q^15 + 71 * q^16 + 111 * q^17 + 54 * q^18 + 46 * q^19 + 9 * q^20 + 12 * q^21 - 90 * q^22 + 6 * q^23 + 63 * q^24 - 88 * q^25 - 273 * q^26 + 54 * q^27 - 2 * q^28 + 105 * q^29 + 81 * q^30 - 200 * q^31 + 45 * q^32 - 90 * q^33 - 666 * q^34 + 18 * q^35 - 9 * q^36 - 17 * q^37 - 276 * q^38 - 273 * q^39 + 378 * q^40 + 231 * q^41 - 18 * q^42 + 514 * q^43 + 60 * q^44 + 81 * q^45 + 18 * q^46 - 324 * q^47 + 213 * q^48 + 339 * q^49 + 132 * q^50 - 666 * q^51 + 26 * q^52 + 1278 * q^53 - 81 * q^54 + 270 * q^55 + 42 * q^56 - 276 * q^57 + 315 * q^58 - 600 * q^59 - 54 * q^60 - 233 * q^61 + 300 * q^62 - 18 * q^63 + 866 * q^64 - 585 * q^65 + 540 * q^66 - 926 * q^67 + 111 * q^68 + 18 * q^69 - 108 * q^70 + 930 * q^71 + 189 * q^72 - 506 * q^73 - 51 * q^74 + 132 * q^75 + 46 * q^76 + 120 * q^77 + 234 * q^78 - 2648 * q^79 - 639 * q^80 - 81 * q^81 + 693 * q^82 + 1620 * q^83 - 6 * q^84 - 999 * q^85 - 3084 * q^86 + 315 * q^87 + 630 * q^88 - 498 * q^89 - 486 * q^90 + 52 * q^91 - 12 * q^92 + 300 * q^93 + 486 * q^94 - 414 * q^95 - 270 * q^96 - 1358 * q^97 + 1017 * q^98 + 540 * q^99

Introduction

L-functions

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