LMFDB - Embedded newform 171.3.z.a.101.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,3,Mod(5,171)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("171.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([15, 16])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.z (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$38$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.34
Character	$\chi$	$=$	171.101
Dual form			171.3.z.a.149.34

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.15445 - 0.556214i) q^{2} +(0.860600 - 2.87391i) q^{3} +(5.88239 - 2.14102i) q^{4} +(-2.82950 - 3.37207i) q^{5} +(1.11621 - 9.54428i) q^{6} +(4.78818 + 8.29337i) q^{7} +(6.26894 - 3.61938i) q^{8} +(-7.51874 - 4.94657i) q^{9} +(-10.8011 - 9.06321i) q^{10} -9.47759i q^{11} +(-1.09071 - 18.7480i) q^{12} +(15.0499 + 12.6284i) q^{13} +(19.7169 + 23.4977i) q^{14} +(-12.1261 + 5.22974i) q^{15} +(-1.41958 + 1.19117i) q^{16} +(-7.28591 - 8.68301i) q^{17} +(-26.4688 - 11.4217i) q^{18} +(-11.4122 + 15.1909i) q^{19} +(-23.8639 - 13.7778i) q^{20} +(27.9551 - 6.62353i) q^{21} +(-5.27157 - 29.8966i) q^{22} +(0.814065 + 2.23663i) q^{23} +(-5.00672 - 21.1312i) q^{24} +(0.976436 - 5.53764i) q^{25} +(54.4982 + 31.4645i) q^{26} +(-20.6866 + 17.3512i) q^{27} +(45.9222 + 38.5333i) q^{28} +(15.0166 + 41.2577i) q^{29} +(-35.3423 + 23.2416i) q^{30} +28.6771 q^{31} +(-22.4274 + 26.7279i) q^{32} +(-27.2378 - 8.15641i) q^{33} +(-27.8126 - 23.3376i) q^{34} +(14.4176 - 39.6122i) q^{35} +(-54.8189 - 13.0000i) q^{36} +46.6237 q^{37} +(-27.5498 + 54.2664i) q^{38} +(49.2447 - 32.3841i) q^{39} +(-29.9428 - 10.8983i) q^{40} +(-39.9205 + 7.03907i) q^{41} +(84.4988 - 36.4426i) q^{42} +(-40.3783 - 14.6965i) q^{43} +(-20.2917 - 55.7509i) q^{44} +(4.59409 + 39.3500i) q^{45} +(3.81197 + 6.60252i) q^{46} +(-11.6887 - 32.1145i) q^{47} +(2.20163 + 5.10488i) q^{48} +(-21.3533 + 36.9850i) q^{49} -18.0113i q^{50} +(-31.2245 + 13.4665i) q^{51} +(115.567 + 42.0629i) q^{52} +(34.9566 + 6.16380i) q^{53} +(-55.6040 + 66.2395i) q^{54} +(-31.9591 + 26.8169i) q^{55} +(60.0336 + 34.6604i) q^{56} +(33.8358 + 45.8709i) q^{57} +(70.3172 + 121.793i) q^{58} +(10.4116 - 28.6058i) q^{59} +(-60.1335 + 56.7256i) q^{60} +(-79.0059 - 66.2939i) q^{61} +(90.4604 - 15.9506i) q^{62} +(5.02271 - 86.0407i) q^{63} +(-52.1733 + 90.3668i) q^{64} -86.4813i q^{65} +(-90.4568 - 10.5789i) q^{66} +(6.84057 - 38.7948i) q^{67} +(-61.4491 - 35.4776i) q^{68} +(7.12845 - 0.414712i) q^{69} +(23.4469 - 132.974i) q^{70} +(-46.0329 + 8.11684i) q^{71} +(-65.0381 - 3.79666i) q^{72} +(-87.6719 - 31.9099i) q^{73} +(147.072 - 25.9328i) q^{74} +(-15.0744 - 7.57188i) q^{75} +(-34.6071 + 113.792i) q^{76} +(78.6011 - 45.3804i) q^{77} +(137.327 - 129.545i) q^{78} +(-64.5309 + 54.1479i) q^{79} +(8.03343 + 1.41651i) q^{80} +(32.0628 + 74.3840i) q^{81} +(-122.012 + 44.4087i) q^{82} +(-20.5789 + 11.8813i) q^{83} +(150.262 - 98.8146i) q^{84} +(-8.66421 + 49.1372i) q^{85} +(-135.546 - 23.9004i) q^{86} +(131.494 - 7.64996i) q^{87} +(-34.3030 - 59.4145i) q^{88} +(-40.2654 - 110.628i) q^{89} +(36.3789 + 121.572i) q^{90} +(-32.6701 + 185.281i) q^{91} +(9.57731 + 11.4138i) q^{92} +(24.6795 - 82.4154i) q^{93} +(-54.7340 - 94.8020i) q^{94} +(83.5154 - 4.49985i) q^{95} +(57.5126 + 87.4563i) q^{96} +(4.08676 + 23.1772i) q^{97} +(-46.7862 + 128.544i) q^{98} +(-46.8816 + 71.2595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} - 12 q^{10} - 3 q^{12} + 12 q^{13} - 9 q^{14} - 48 q^{15} + 9 q^{16} - 81 q^{17} - 60 q^{18} - 33 q^{19} - 18 q^{20} + 21 q^{21}+ \cdots - 300 q^{99}+O(q^{100}) $ 228 * q - 9 * q^2 + 6 * q^3 - 3 * q^4 - 9 * q^5 - 30 * q^6 + 3 * q^7 + 30 * q^9 - 12 * q^10 - 3 * q^12 + 12 * q^13 - 9 * q^14 - 48 * q^15 + 9 * q^16 - 81 * q^17 - 60 * q^18 - 33 * q^19 - 18 * q^20 + 21 * q^21 + 81 * q^22 + 207 * q^23 - 222 * q^24 - 3 * q^25 - 216 * q^26 - 33 * q^27 - 36 * q^28 - 9 * q^29 + 171 * q^30 - 6 * q^31 - 9 * q^32 + 30 * q^33 + 33 * q^34 + 225 * q^35 - 246 * q^36 - 24 * q^37 - 9 * q^38 - 60 * q^39 - 177 * q^40 - 9 * q^41 - 15 * q^42 + 93 * q^43 + 441 * q^44 - 57 * q^45 - 6 * q^46 - 9 * q^47 - 774 * q^48 - 543 * q^49 - 81 * q^51 + 213 * q^52 + 393 * q^54 + 63 * q^55 - 459 * q^56 + 84 * q^57 - 6 * q^58 + 126 * q^59 - 333 * q^60 - 24 * q^61 - 36 * q^62 + 369 * q^63 + 372 * q^64 + 894 * q^66 + 39 * q^67 + 747 * q^68 + 231 * q^69 + 291 * q^70 + 204 * q^72 - 51 * q^73 + 333 * q^74 + 324 * q^75 - 3 * q^76 - 18 * q^77 - 1569 * q^78 - 105 * q^79 - 756 * q^80 + 1050 * q^81 + 132 * q^82 + 99 * q^83 - 69 * q^84 - 3 * q^85 - 495 * q^86 - 483 * q^87 + 387 * q^88 - 648 * q^89 - 339 * q^90 + 225 * q^91 + 27 * q^92 + 396 * q^93 - 6 * q^94 - 1305 * q^95 - 663 * q^96 - 543 * q^97 + 1125 * q^98 - 300 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	3.15445	−	0.556214i	1.57722	−	0.278107i	0.684603	−	0.728916i	$-0.259975\pi$
$2$	3.15445	−	0.556214i	1.57722	−	0.278107i	0.892621	+	0.450809i	$0.148864\pi$
$3$	0.860600	−	2.87391i	0.286867	−	0.957971i
$3$	0.860600	−	2.87391i	0.286867	−	0.957971i
$4$	5.88239	−	2.14102i	1.47060	−	0.535254i
$5$	−2.82950	−	3.37207i	−0.565900	−	0.674414i	0.404884	−	0.914368i	$-0.367312\pi$
$5$	−2.82950	−	3.37207i	−0.565900	−	0.674414i	−0.970784	+	0.239954i	$0.922868\pi$
$6$	1.11621	−	9.54428i	0.186034	−	1.59071i
$7$	4.78818	+	8.29337i	0.684025	+	1.18477i	0.973742	+	0.227654i	$0.0731055\pi$
$7$	4.78818	+	8.29337i	0.684025	+	1.18477i	−0.289717	+	0.957112i	$0.593561\pi$
$8$	6.26894	−	3.61938i	0.783618	−	0.452422i
$9$	−7.51874	−	4.94657i	−0.835415	−	0.549619i
$10$	−10.8011	−	9.06321i	−1.08011	−	0.906321i
$11$		−	9.47759i		−	0.861599i	−0.902448	−	0.430800i	$-0.858232\pi$
$11$		−	9.47759i		−	0.861599i	0.902448	−	0.430800i	$-0.141768\pi$
$12$	−1.09071	−	18.7480i	−0.0908922	−	1.56234i
$13$	15.0499	+	12.6284i	1.15768	+	0.971413i	0.999871	−	0.0160564i	$-0.00511113\pi$
$13$	15.0499	+	12.6284i	1.15768	+	0.971413i	0.157813	+	0.987469i	$0.449556\pi$
$14$	19.7169	+	23.4977i	1.40835	+	1.67841i
$15$	−12.1261	+	5.22974i	−0.808406	+	0.348649i
$16$	−1.41958	+	1.19117i	−0.0887239	+	0.0744482i
$17$	−7.28591	−	8.68301i	−0.428583	−	0.510765i	0.507930	−	0.861398i	$-0.330411\pi$
$17$	−7.28591	−	8.68301i	−0.428583	−	0.510765i	−0.936513	+	0.350633i	$0.885966\pi$
$18$	−26.4688	−	11.4217i	−1.47049	−	0.634538i
$19$	−11.4122	+	15.1909i	−0.600642	+	0.799518i
$19$	−11.4122	+	15.1909i	−0.600642	+	0.799518i
$20$	−23.8639	−	13.7778i	−1.19320	−	0.688892i
$21$	27.9551	−	6.62353i	1.33120	−	0.315406i
$22$	−5.27157	−	29.8966i	−0.239617	−	1.35893i
$23$	0.814065	+	2.23663i	0.0353941	+	0.0972446i	0.956131	−	0.292940i	$-0.0946335\pi$
$23$	0.814065	+	2.23663i	0.0353941	+	0.0972446i	−0.920737	+	0.390184i	$0.872411\pi$
$24$	−5.00672	−	21.1312i	−0.208613	−	0.880468i
$25$	0.976436	−	5.53764i	0.0390574	−	0.221506i
$26$	54.4982	+	31.4645i	2.09608	+	1.21017i
$27$	−20.6866	+	17.3512i	−0.766172	+	0.642636i
$28$	45.9222	+	38.5333i	1.64008	+	1.37619i
$29$	15.0166	+	41.2577i	0.517813	+	1.42268i	0.872924	+	0.487856i	$0.162221\pi$
$29$	15.0166	+	41.2577i	0.517813	+	1.42268i	−0.355110	+	0.934824i	$0.615557\pi$
$30$	−35.3423	+	23.2416i	−1.17808	+	0.774721i
$31$	28.6771			0.925067			0.462534	−	0.886602i	$-0.346940\pi$
$31$	28.6771			0.925067			0.462534	+	0.886602i	$0.346940\pi$
$32$	−22.4274	+	26.7279i	−0.700855	+	0.835247i
$33$	−27.2378	−	8.15641i	−0.825387	−	0.247164i
$34$	−27.8126	−	23.3376i	−0.818019	−	0.686399i
$35$	14.4176	−	39.6122i	0.411933	−	1.13178i
$36$	−54.8189	−	13.0000i	−1.52275	−	0.361110i
$37$	46.6237			1.26010			0.630050	−	0.776555i	$-0.283034\pi$
$37$	46.6237			1.26010			0.630050	+	0.776555i	$0.283034\pi$
$38$	−27.5498	+	54.2664i	−0.724994	+	1.42806i
$39$	49.2447	−	32.3841i	1.26269	−	0.830362i
$40$	−29.9428	−	10.8983i	−0.748569	−	0.272457i
$41$	−39.9205	+	7.03907i	−0.973672	+	0.171685i	−0.637782	−	0.770217i	$-0.720148\pi$
$41$	−39.9205	+	7.03907i	−0.973672	+	0.171685i	−0.335889	+	0.941901i	$0.609037\pi$
$42$	84.4988	−	36.4426i	2.01188	−	0.867681i
$43$	−40.3783	−	14.6965i	−0.939031	−	0.341779i	−0.173248	−	0.984878i	$-0.555426\pi$
$43$	−40.3783	−	14.6965i	−0.939031	−	0.341779i	−0.765783	+	0.643099i	$0.777648\pi$
$44$	−20.2917	−	55.7509i	−0.461174	−	1.26707i
$45$	4.59409	+	39.3500i	0.102091	+	0.874445i
$46$	3.81197	+	6.60252i	0.0828689	+	0.143533i
$47$	−11.6887	−	32.1145i	−0.248696	−	0.683287i	−0.999735	−	0.0230287i	$-0.992669\pi$
$47$	−11.6887	−	32.1145i	−0.248696	−	0.683287i	0.751039	−	0.660258i	$-0.229553\pi$
$48$	2.20163	+	5.10488i	0.0458673	+	0.106352i
$49$	−21.3533	+	36.9850i	−0.435781	+	0.754795i
$50$		−	18.0113i		−	0.360226i
$51$	−31.2245	+	13.4665i	−0.612244	+	0.264048i
$52$	115.567	+	42.0629i	2.22244	+	0.808903i
$53$	34.9566	+	6.16380i	0.659559	+	0.116298i	0.493402	−	0.869801i	$-0.335753\pi$
$53$	34.9566	+	6.16380i	0.659559	+	0.116298i	0.166157	+	0.986099i	$0.446864\pi$
$54$	−55.6040	+	66.2395i	−1.02970	+	1.22666i
$55$	−31.9591	+	26.8169i	−0.581074	+	0.487579i
$56$	60.0336	+	34.6604i	1.07203	+	0.618936i
$57$	33.8358	+	45.8709i	0.593611	+	0.804752i
$58$	70.3172	+	121.793i	1.21237	+	2.09988i
$59$	10.4116	−	28.6058i	0.176469	−	0.484844i	−0.819650	−	0.572865i	$-0.805832\pi$
$59$	10.4116	−	28.6058i	0.176469	−	0.484844i	0.996119	+	0.0880211i	$0.0280543\pi$
$60$	−60.1335	+	56.7256i	−1.00223	+	0.945426i
$61$	−79.0059	−	66.2939i	−1.29518	−	1.08678i	−0.990956	−	0.134184i	$-0.957159\pi$
$61$	−79.0059	−	66.2939i	−1.29518	−	1.08678i	−0.304223	−	0.952601i	$-0.598397\pi$
$62$	90.4604	−	15.9506i	1.45904	−	0.257268i
$63$	5.02271	−	86.0407i	0.0797256	−	1.36573i
$64$	−52.1733	+	90.3668i	−0.815207	+	1.41198i
$65$		−	86.4813i		−	1.33048i
$66$	−90.4568	−	10.5789i	−1.37056	−	0.160287i
$67$	6.84057	−	38.7948i	0.102098	−	0.579027i	−0.890242	−	0.455488i	$-0.849465\pi$
$67$	6.84057	−	38.7948i	0.102098	−	0.579027i	0.992340	−	0.123539i	$-0.0394243\pi$
$68$	−61.4491	−	35.4776i	−0.903663	−	0.521730i
$69$	7.12845	−	0.414712i	0.103311	−	0.00601032i
$70$	23.4469	−	132.974i	0.334955	−	1.89963i
$71$	−46.0329	+	8.11684i	−0.648351	+	0.114322i	−0.488146	−	0.872762i	$-0.662327\pi$
$71$	−46.0329	+	8.11684i	−0.648351	+	0.114322i	−0.160205	+	0.987084i	$0.551215\pi$
$72$	−65.0381	−	3.79666i	−0.903306	−	0.0527314i
$73$	−87.6719	−	31.9099i	−1.20098	−	0.437123i	−0.337417	−	0.941355i	$-0.609553\pi$
$73$	−87.6719	−	31.9099i	−1.20098	−	0.437123i	−0.863568	+	0.504233i	$0.831775\pi$
$74$	147.072	−	25.9328i	1.98746	−	0.350443i
$75$	−15.0744	−	7.57188i	−0.200992	−	0.100958i
$76$	−34.6071	+	113.792i	−0.455357	+	1.49727i
$77$	78.6011	−	45.3804i	1.02079	−	0.589356i
$78$	137.327	−	129.545i	1.76061	−	1.66083i
$79$	−64.5309	+	54.1479i	−0.816847	+	0.685416i	−0.952231	−	0.305377i	$-0.901217\pi$
$79$	−64.5309	+	54.1479i	−0.816847	+	0.685416i	0.135385	+	0.990793i	$0.456773\pi$
$80$	8.03343	+	1.41651i	0.100418	+	0.0177064i
$81$	32.0628	+	74.3840i	0.395837	+	0.918321i
$82$	−122.012	+	44.4087i	−1.48795	+	0.541570i
$83$	−20.5789	+	11.8813i	−0.247939	+	0.143148i	−0.618820	−	0.785533i	$-0.712389\pi$
$83$	−20.5789	+	11.8813i	−0.247939	+	0.143148i	0.370881	+	0.928680i	$0.379056\pi$
$84$	150.262	−	98.8146i	1.78883	−	1.17636i
$85$	−8.66421	+	49.1372i	−0.101932	+	0.578085i
$86$	−135.546	−	23.9004i	−1.57611	−	0.277911i
$87$	131.494	−	7.64996i	1.51143	−	0.0879305i
$88$	−34.3030	−	59.4145i	−0.389806	−	0.675165i
$89$	−40.2654	−	110.628i	−0.452420	−	1.24301i	−0.931016	−	0.364978i	$-0.881077\pi$
$89$	−40.2654	−	110.628i	−0.452420	−	1.24301i	0.478597	−	0.878035i	$-0.341146\pi$
$90$	36.3789	+	121.572i	0.404210	+	1.35080i
$91$	−32.6701	+	185.281i	−0.359012	+	2.03606i
$92$	9.57731	+	11.4138i	0.104101	+	0.124063i
$93$	24.6795	−	82.4154i	0.265371	−	0.886187i
$94$	−54.7340	−	94.8020i	−0.582276	−	1.00853i
$95$	83.5154	−	4.49985i	0.879110	−	0.0473668i
$96$	57.5126	+	87.4563i	0.599090	+	0.911003i
$97$	4.08676	+	23.1772i	0.0421315	+	0.238940i	0.998600	−	0.0528958i	$-0.0168451\pi$
$97$	4.08676	+	23.1772i	0.0421315	+	0.238940i	−0.956469	+	0.291836i	$0.905734\pi$
$98$	−46.7862	+	128.544i	−0.477410	+	1.31167i
$99$	−46.8816	+	71.2595i	−0.473552	+	0.719793i
$100$	−6.11240	−	34.6652i	−0.0611240	−	0.346652i
$101$	−110.345	−	19.4568i	−1.09253	−	0.192642i	−0.401777	−	0.915737i	$-0.631607\pi$
$101$	−110.345	−	19.4568i	−1.09253	−	0.192642i	−0.690748	+	0.723096i	$0.742719\pi$
$102$	−91.0057	+	59.8468i	−0.892213	+	0.586733i
$103$	8.35035	−	14.4632i	0.0810713	−	0.140420i	−0.822639	−	0.568564i	$-0.807499\pi$
$103$	8.35035	−	14.4632i	0.0810713	−	0.140420i	0.903710	+	0.428144i	$0.140833\pi$
$104$	140.054	+	24.6953i	1.34667	+	0.237454i
$105$	−101.434	−	75.5252i	−0.966038	−	0.719288i
$106$	113.697			1.07262
$107$	94.3767	+	54.4884i	0.882025	+	0.509237i	0.871326	−	0.490705i	$-0.163261\pi$
$107$	94.3767	+	54.4884i	0.882025	+	0.509237i	0.0106996	+	0.999943i	$0.496594\pi$
$108$	−84.5379	+	146.357i	−0.782758	+	1.35516i
$109$	0.701145	+	3.97639i	0.00643252	+	0.0364806i	0.987855	−	0.155378i	$-0.0496596\pi$
$109$	0.701145	+	3.97639i	0.00643252	+	0.0364806i	−0.981423	+	0.191859i	$0.938548\pi$
$110$	−85.8973	+	102.368i	−0.780885	+	0.930622i
$111$	40.1243	−	133.992i	0.361480	−	1.20714i
$112$	−16.6760	−	6.06958i	−0.148893	−	0.0541927i
$113$	143.941	−	83.1042i	1.27381	−	0.735436i	0.298109	−	0.954532i	$-0.403644\pi$
$113$	143.941	−	83.1042i	1.27381	−	0.735436i	0.975703	+	0.219096i	$0.0703109\pi$
$114$	132.247	+	125.877i	1.16006	+	1.10419i
$115$	5.23866	−	9.07362i	0.0455535	−	0.0789010i
$116$	176.667	+	210.544i	1.52299	+	1.81503i
$117$	−50.6891	−	169.395i	−0.433240	−	1.44782i
$118$	16.9321	−	96.0265i	0.143492	−	0.813784i
$119$	37.1252	−	102.001i	0.311976	−	0.857147i
$120$	−57.0894	+	76.6738i	−0.475745	+	0.638949i
$121$	31.1753			0.257647
$122$	−286.094	−	165.176i	−2.34503	−	1.35390i
$123$	−14.1259	+	120.786i	−0.114845	+	0.981999i
$124$	168.690	−	61.3981i	1.36040	−	0.495146i
$125$	−116.741	+	67.4002i	−0.933925	+	0.539202i
$126$	−32.0132	−	274.205i	−0.254073	−	2.17623i
$127$	162.762	−	59.2406i	1.28159	−	0.466462i	0.390634	−	0.920546i	$-0.372256\pi$
$127$	162.762	−	59.2406i	1.28159	−	0.466462i	0.890959	+	0.454085i	$0.150034\pi$
$128$	−66.5811	+	182.930i	−0.520165	+	1.42914i
$129$	−76.9860	+	103.396i	−0.596791	+	0.801519i
$130$	−48.1021	−	272.801i	−0.370016	−	2.09847i
$131$	22.6064	−	62.1107i	0.172568	−	0.474127i	−0.823014	−	0.568021i	$-0.807709\pi$
$131$	22.6064	−	62.1107i	0.172568	−	0.474127i	0.995582	+	0.0938939i	$0.0299314\pi$
$132$	−177.686	+	10.3373i	−1.34611	+	0.0783126i
$133$	−180.627	−	21.9090i	−1.35810	−	0.164729i
$134$		−	126.181i		−	0.941649i
$135$	117.042	+	20.6616i	0.866979	+	0.153049i
$136$	−77.1021	−	28.0629i	−0.566927	−	0.206345i
$137$	32.3828	−	38.5923i	0.236371	−	0.281696i	−0.634799	−	0.772677i	$-0.718917\pi$
$137$	32.3828	−	38.5923i	0.236371	−	0.281696i	0.871170	+	0.490981i	$0.163362\pi$
$138$	22.2556	−	5.27313i	0.161273	−	0.0382111i
$139$	130.719	+	109.686i	0.940426	+	0.789111i	0.977659	−	0.210196i	$-0.0674101\pi$
$139$	130.719	+	109.686i	0.940426	+	0.789111i	−0.0372336	+	0.999307i	$0.511855\pi$
$140$		−	263.883i		−	1.88488i
$141$	−102.353	+	5.95462i	−0.725911	+	0.0422314i
$142$	−140.694	+	51.2083i	−0.990800	+	0.360622i
$143$	119.686	−	142.637i	0.836968	−	0.997460i
$144$	16.5657	−	1.93403i	0.115040	−	0.0134308i
$145$	96.6345	−	167.376i	0.666445	−	1.15432i
$146$	−294.305	−	51.8939i	−2.01579	−	0.355438i
$147$	87.9149	+	93.1967i	0.598060	+	0.633991i
$148$	274.259	−	99.8221i	1.85310	−	0.674474i
$149$	75.1465	−	13.2504i	0.504339	−	0.0889286i	0.0843106	−	0.996440i	$-0.473131\pi$
$149$	75.1465	−	13.2504i	0.504339	−	0.0889286i	0.420028	+	0.907511i	$0.362020\pi$
$150$	−51.7629	−	15.5005i	−0.345086	−	0.103337i
$151$	−27.7148	+	48.0034i	−0.183542	+	0.317903i	−0.943084	−	0.332554i	$-0.892090\pi$
$151$	−27.7148	+	48.0034i	−0.183542	+	0.317903i	0.759542	+	0.650458i	$0.225423\pi$
$152$	−16.5610	+	136.536i	−0.108954	+	0.898260i
$153$	11.8297	+	101.326i	0.0773182	+	0.662259i
$154$	222.702	−	186.869i	1.44612	−	1.21344i
$155$	−81.1419	−	96.7011i	−0.523496	−	0.623878i
$156$	220.342	−	295.930i	1.41245	−	1.89699i
$157$	174.981	−	146.826i	1.11453	−	0.935199i	0.116212	−	0.993224i	$-0.462925\pi$
$157$	174.981	−	146.826i	1.11453	−	0.935199i	0.998315	+	0.0580249i	$0.0184803\pi$
$158$	−173.442	+	206.700i	−1.09773	+	1.30823i
$159$	47.7979	−	95.1577i	0.300616	−	0.598476i
$160$	153.587			0.959917
$161$	−14.6513	+	17.4607i	−0.0910016	+	0.108452i
$162$	142.514	+	216.807i	0.879715	+	1.33831i
$163$	−16.2165	−	28.0879i	−0.0994879	−	0.172318i	0.811985	−	0.583678i	$-0.198387\pi$
$163$	−16.2165	−	28.0879i	−0.0994879	−	0.172318i	−0.911473	+	0.411360i	$0.865054\pi$
$164$	−219.758	+	126.877i	−1.33999	+	0.773641i
$165$	49.5653	+	114.926i	0.300396	+	0.696522i
$166$	−58.3067	+	48.9251i	−0.351245	+	0.294729i
$167$	75.7072	+	208.004i	0.453337	+	1.24553i	0.930362	+	0.366643i	$0.119493\pi$
$167$	75.7072	+	208.004i	0.453337	+	1.24553i	−0.477025	+	0.878890i	$0.658285\pi$
$168$	151.276	−	142.703i	0.900452	−	0.849420i
$169$	37.6773	+	213.679i	0.222943	+	1.26437i
$170$			159.820i			0.940117i
$171$	160.948	−	57.7648i	0.941216	−	0.337806i
$172$	−268.987			−1.56388
$173$	−303.913	+	53.5881i	−1.75672	+	0.309758i	−0.956887	−	0.290460i	$-0.906192\pi$
$173$	−303.913	+	53.5881i	−1.75672	+	0.309758i	−0.799836	+	0.600218i	$0.795080\pi$
$174$	410.537	−	97.2704i	2.35941	−	0.559025i
$175$	50.6010	−	18.4173i	0.289149	−	0.105242i
$176$	11.2894	+	13.4542i	0.0641445	+	0.0764445i
$177$	−73.2502	−	54.5403i	−0.413843	−	0.308137i
$178$	−188.548	−	326.575i	−1.05926	−	1.83469i
$179$	−39.6345	+	22.8830i	−0.221422	+	0.127838i	−0.606608	−	0.795001i	$-0.707470\pi$
$179$	−39.6345	+	22.8830i	−0.221422	+	0.127838i	0.385187	+	0.922839i	$0.374137\pi$
$180$	111.273	+	221.636i	0.618185	+	1.23131i
$181$	−256.339	−	215.094i	−1.41624	−	1.18836i	−0.953320	−	0.301961i	$-0.902359\pi$
$181$	−256.339	−	215.094i	−1.41624	−	1.18836i	−0.462916	−	0.886402i	$-0.653197\pi$
$182$			602.631i			3.31116i
$183$	−258.515	+	170.004i	−1.41265	+	0.928982i
$184$	13.1985	+	11.0749i	0.0717311	+	0.0601895i
$185$	−131.922	−	157.218i	−0.713091	−	0.849829i
$186$	32.0095	−	273.702i	0.172094	−	1.47152i
$187$	−82.2940	+	69.0529i	−0.440075	+	0.369267i
$188$	−137.515	−	163.884i	−0.731464	−	0.871725i
$189$	−242.951	−	88.4814i	−1.28545	−	0.468156i
$190$	260.942	−	60.6470i	1.37338	−	0.319195i
$191$	326.163	+	188.310i	1.70766	+	0.985919i	0.937443	+	0.348138i	$0.113186\pi$
$191$	326.163	+	188.310i	1.70766	+	0.985919i	0.770218	+	0.637781i	$0.220148\pi$
$192$	214.806	+	227.711i	1.11878	+	1.18599i
$193$	−11.0948	−	62.9219i	−0.0574862	−	0.326020i	0.942480	−	0.334263i	$-0.108487\pi$
$193$	−11.0948	−	62.9219i	−0.0574862	−	0.326020i	−0.999966	+	0.00824273i	$0.997376\pi$
$194$	25.7829	+	70.8380i	0.132902	+	0.365144i
$195$	−248.540	−	74.4257i	−1.27456	−	0.381671i
$196$	−46.4230	+	263.278i	−0.236852	+	1.34325i
$197$	73.7559	+	42.5830i	0.374395	+	0.216157i	0.675377	−	0.737473i	$-0.263981\pi$
$197$	73.7559	+	42.5830i	0.374395	+	0.216157i	−0.300982	+	0.953630i	$0.597314\pi$
$198$	−108.250	+	250.861i	−0.546717	+	1.26697i
$199$	184.313	+	154.657i	0.926196	+	0.777171i	0.975131	−	0.221631i	$-0.0711380\pi$
$199$	184.313	+	154.657i	0.926196	+	0.777171i	−0.0489342	+	0.998802i	$0.515582\pi$
$200$	−13.9216	−	38.2493i	−0.0696080	−	0.191246i
$201$	−105.606	−	53.0460i	−0.525402	−	0.263910i
$202$	−358.900			−1.77673
$203$	−270.263	+	322.087i	−1.33135	+	1.58664i
$204$	−154.843	+	146.067i	−0.759033	+	0.716016i
$205$	136.691	+	114.698i	0.666788	+	0.559501i
$206$	18.2961	−	50.2681i	0.0888159	−	0.244020i
$207$	4.94289	−	20.8434i	0.0238787	−	0.100693i
$208$	−36.4071			−0.175034
$209$	143.973	+	108.160i	0.688864	+	0.517512i
$210$	−361.977	−	181.821i	−1.72370	−	0.865816i
$211$	−18.0001	−	6.55150i	−0.0853086	−	0.0310498i	0.299013	−	0.954249i	$-0.403342\pi$
$211$	−18.0001	−	6.55150i	−0.0853086	−	0.0310498i	−0.384322	+	0.923199i	$0.625565\pi$
$212$	218.826	−	38.5849i	1.03220	−	0.182004i
$213$	−16.2888	+	139.280i	−0.0764733	+	0.653896i
$214$	328.014	+	119.387i	1.53277	+	0.557884i
$215$	64.6929	+	177.742i	0.300897	+	0.826708i
$216$	−66.8830	+	183.646i	−0.309643	+	0.850214i
$217$	137.311	+	237.830i	0.632769	+	1.09599i
$218$	4.42345	+	12.1533i	0.0202911	+	0.0557492i
$219$	−167.157	+	224.499i	−0.763273	+	1.02511i
$220$	−130.581	+	226.172i	−0.593548	+	1.02806i
$221$		−	222.688i		−	1.00764i
$222$	52.0416	−	444.990i	0.234422	−	2.00446i
$223$	−92.3370	−	33.6079i	−0.414067	−	0.150708i	0.126582	−	0.991956i	$-0.459599\pi$
$223$	−92.3370	−	33.6079i	−0.414067	−	0.150708i	−0.540649	+	0.841248i	$0.681821\pi$
$224$	−329.051	−	58.0205i	−1.46898	−	0.259020i
$225$	−34.7339	+	36.8061i	−0.154373	+	0.163583i
$226$	407.830	−	342.210i	1.80456	−	1.51420i
$227$	−13.6209	−	7.86403i	−0.0600039	−	0.0346433i	0.469698	−	0.882827i	$-0.344363\pi$
$227$	−13.6209	−	7.86403i	−0.0600039	−	0.0346433i	−0.529702	+	0.848184i	$0.677696\pi$
$228$	297.246	+	197.387i	1.30371	+	0.865734i
$229$	172.008	+	297.926i	0.751125	+	1.30099i	0.947278	+	0.320413i	$0.103822\pi$
$229$	172.008	+	297.926i	0.751125	+	1.30099i	−0.196153	+	0.980573i	$0.562845\pi$
$230$	11.4782	−	31.5361i	0.0499052	−	0.137113i
$231$	−62.7751	−	264.947i	−0.271754	−	1.14696i
$232$	243.465	+	204.292i	1.04942	+	0.880568i
$233$	214.474	−	37.8176i	0.920490	−	0.162307i	0.306727	−	0.951798i	$-0.400766\pi$
$233$	214.474	−	37.8176i	0.920490	−	0.162307i	0.613763	+	0.789490i	$0.289655\pi$
$234$	−254.116	−	506.153i	−1.08596	−	2.16305i
$235$	−75.2190	+	130.283i	−0.320081	+	0.554396i
$236$		−	190.562i		−	0.807466i
$237$	100.081	+	232.056i	0.422282	+	0.979138i
$238$	60.3752	−	342.405i	0.253677	−	1.43868i
$239$	−50.4672	−	29.1373i	−0.211160	−	0.121913i	0.390690	−	0.920522i	$-0.372236\pi$
$239$	−50.4672	−	29.1373i	−0.211160	−	0.121913i	−0.601850	+	0.798609i	$0.705570\pi$
$240$	10.9845	−	21.8683i	0.0457687	−	0.0911179i
$241$	10.6685	−	60.5039i	0.0442675	−	0.251054i	−0.954641	−	0.297759i	$-0.903761\pi$
$241$	10.6685	−	60.5039i	0.0442675	−	0.251054i	0.998909	+	0.0467049i	$0.0148721\pi$
$242$	98.3408	−	17.3401i	0.406367	−	0.0716535i
$243$	241.366	−	28.1308i	0.993277	−	0.115765i
$244$	−606.680	−	220.814i	−2.48640	−	0.904974i
$245$	185.135	−	32.6443i	0.755653	−	0.133242i
$246$	22.6233	+	388.870i	0.0919647	+	1.58077i
$247$	−363.588	+	84.5035i	−1.47202	+	0.342119i
$248$	179.775	−	103.793i	0.724899	−	0.418521i
$249$	16.4355	+	69.3671i	0.0660058	+	0.278583i
$250$	−330.763	+	277.543i	−1.32305	+	1.11017i
$251$	−366.473	−	64.6191i	−1.46005	−	0.257446i	−0.613475	−	0.789714i	$-0.710229\pi$
$251$	−366.473	−	64.6191i	−1.46005	−	0.257446i	−0.846576	+	0.532267i	$0.821340\pi$
$252$	−154.669	−	516.879i	−0.613766	−	2.05111i
$253$	21.1978	−	7.71538i	0.0837858	−	0.0304956i
$254$	480.474	−	277.402i	1.89163	−	1.09213i
$255$	133.760	+	67.1876i	0.524547	+	0.263481i
$256$	−35.8000	+	203.032i	−0.139844	+	0.793094i
$257$	124.694	+	21.9870i	0.485193	+	0.0855525i	0.410893	−	0.911683i	$-0.365217\pi$
$257$	124.694	+	21.9870i	0.485193	+	0.0855525i	0.0742993	+	0.997236i	$0.476328\pi$
$258$	−185.338	+	368.978i	−0.718365	+	1.43015i
$259$	223.242	+	386.667i	0.861940	+	1.49292i
$260$	−185.158	−	508.717i	−0.712146	−	1.95660i
$261$	91.1787	−	384.487i	0.349344	−	1.47313i
$262$	36.7640	−	208.499i	0.140320	−	0.795797i
$263$	236.964	+	282.403i	0.901004	+	1.07377i	0.996923	+	0.0783852i	$0.0249764\pi$
$263$	236.964	+	282.403i	0.901004	+	1.07377i	−0.0959195	+	0.995389i	$0.530579\pi$
$264$	−200.273	+	47.4516i	−0.758610	+	0.179741i
$265$	−78.1251	−	135.317i	−0.294812	−	0.510629i
$266$	−581.964	+	31.3565i	−2.18783	+	0.117882i
$267$	−352.588	+	20.5125i	−1.32055	+	0.0768259i
$268$	−42.8214	−	242.852i	−0.159781	−	0.906165i
$269$	−22.2288	+	61.0732i	−0.0826350	+	0.227038i	−0.974128	−	0.225996i	$-0.927436\pi$
$269$	−22.2288	+	61.0732i	−0.0826350	+	0.227038i	0.891493	+	0.453034i	$0.149658\pi$
$270$	380.696	+	0.0754729i	1.40998	+	0.000279529i
$271$	85.1913	+	483.144i	0.314359	+	1.78282i	0.575791	+	0.817597i	$0.304694\pi$
$271$	85.1913	+	483.144i	0.314359	+	1.78282i	−0.261432	+	0.965222i	$0.584195\pi$
$272$	20.6859	+	3.64748i	0.0760512	+	0.0134099i
$273$	504.366	+	253.344i	1.84749	+	0.927999i
$274$	80.6842	−	139.749i	0.294468	−	0.510033i
$275$	−52.4835	−	9.25426i	−0.190849	−	0.0336518i
$276$	41.0444	−	17.7016i	0.148712	−	0.0641363i
$277$	−414.196			−1.49529			−0.747646	−	0.664098i	$-0.768816\pi$
$277$	−414.196			−1.49529			−0.747646	+	0.664098i	$0.768816\pi$
$278$	473.356	+	273.292i	1.70272	+	0.983065i
$279$	−215.615	−	141.853i	−0.772815	−	0.508435i
$280$	−52.9879	−	300.509i	−0.189242	−	1.07325i
$281$	35.4218	−	42.2140i	0.126056	−	0.150228i	−0.699325	−	0.714804i	$-0.746516\pi$
$281$	35.4218	−	42.2140i	0.126056	−	0.150228i	0.825381	+	0.564576i	$0.190960\pi$
$282$	−319.557	+	75.7140i	−1.13318	+	0.268489i
$283$	−108.754	−	39.5834i	−0.384291	−	0.139871i	0.142648	−	0.989773i	$-0.454438\pi$
$283$	−108.754	−	39.5834i	−0.384291	−	0.139871i	−0.526939	+	0.849903i	$0.676661\pi$
$284$	−253.405	+	146.304i	−0.892272	+	0.515154i
$285$	58.9412	−	243.888i	0.206811	−	0.855749i
$286$	298.208	−	516.511i	1.04269	−	1.80598i
$287$	−249.524	−	297.371i	−0.869422	−	1.03614i
$288$	300.837	−	90.0214i	1.04457	−	0.312574i
$289$	27.8741	−	158.082i	0.0964503	−	0.546997i
$290$	211.732	−	581.728i	0.730109	−	2.00596i
$291$	70.1262	+	8.20127i	0.240983	+	0.0281831i
$292$	−584.040			−2.00014
$293$	138.811	+	80.1427i	0.473759	+	0.273525i	0.717812	−	0.696237i	$-0.245144\pi$
$293$	138.811	+	80.1427i	0.473759	+	0.273525i	−0.244053	+	0.969762i	$0.578477\pi$
$294$	329.160	+	245.084i	1.11959	+	0.833621i
$295$	−125.920	+	45.8313i	−0.426849	+	0.155360i
$296$	292.281	−	168.749i	0.987437	−	0.570097i
$297$	164.447	+	196.059i	0.553694	+	0.660133i
$298$	229.676	−	83.5951i	0.770724	−	0.280521i
$299$	−15.9933	+	43.9413i	−0.0534894	+	0.146961i
$300$	−104.885	−	12.2663i	−0.349617	−	0.0408877i
$301$	−71.4550	−	405.242i	−0.237392	−	1.34632i
$302$	−60.7247	+	166.840i	−0.201075	+	0.552449i
$303$	−150.880	+	300.377i	−0.497954	+	0.991345i
$304$	−1.89436	−	35.1585i	−0.00623144	−	0.115653i
$305$			453.992i			1.48850i
$306$	93.6749	+	313.046i	0.306127	+	1.02303i
$307$	402.182	+	146.382i	1.31004	+	0.476816i	0.900254	−	0.435366i	$-0.143381\pi$
$307$	402.182	+	146.382i	1.31004	+	0.476816i	0.409787	+	0.912181i	$0.365603\pi$
$308$	365.203	−	435.232i	1.18572	−	1.41309i
$309$	−34.3797	−	36.4452i	−0.111261	−	0.117946i
$310$	−309.744	−	259.906i	−0.999175	−	0.838407i
$311$		−	387.049i		−	1.24453i	−0.782807	−	0.622265i	$-0.786213\pi$
$311$		−	387.049i		−	1.24453i	0.782807	−	0.622265i	$-0.213787\pi$
$312$	191.502	−	381.249i	0.613789	−	1.22195i
$313$	321.992	−	117.195i	1.02873	−	0.374426i	0.228132	−	0.973630i	$-0.426738\pi$
$313$	321.992	−	117.195i	1.02873	−	0.374426i	0.800597	+	0.599204i	$0.204516\pi$
$314$	470.301	−	560.483i	1.49777	−	1.78498i
$315$	−304.347	+	226.515i	−0.966181	+	0.719097i
$316$	−263.665	+	456.681i	−0.834382	+	1.44519i
$317$	−451.070	−	79.5359i	−1.42293	−	0.250902i	−0.591402	−	0.806377i	$-0.701425\pi$
$317$	−451.070	−	79.5359i	−1.42293	−	0.250902i	−0.831533	+	0.555475i	$0.812536\pi$
$318$	97.8478	−	326.756i	0.307698	−	1.02753i
$319$	391.024	−	142.321i	1.22578	−	0.446148i
$320$	452.347	−	79.7610i	1.41359	−	0.249253i
$321$	237.815	−	224.338i	0.740858	−	0.698871i
$322$	−36.5048	+	63.2281i	−0.113369	+	0.196361i
$323$	215.051	−	11.5870i	0.665791	−	0.0358731i
$324$	347.863	+	368.909i	1.07365	+	1.13861i
$325$	84.6266	−	71.0102i	0.260390	−	0.218493i
$326$	−66.7771	−	79.5818i	−0.204838	−	0.244116i
$327$	12.0312	+	1.40705i	0.0367927	+	0.00430291i
$328$	−224.783	+	188.615i	−0.685313	+	0.575046i
$329$	210.369	−	250.709i	0.639421	−	0.762032i
$330$	220.275	+	334.960i	0.667499	+	1.01503i
$331$	67.9872			0.205400			0.102700	−	0.994712i	$-0.467252\pi$
$331$	67.9872			0.205400			0.102700	+	0.994712i	$0.467252\pi$
$332$	−95.6155	+	113.950i	−0.287998	+	0.343223i
$333$	−350.551	−	230.628i	−1.05271	−	0.692575i
$334$	354.509	+	614.028i	1.06140	+	1.83841i
$335$	−150.174	+	86.7031i	−0.448281	+	0.258815i
$336$	−31.7948	+	42.7020i	−0.0946275	+	0.127089i
$337$	122.187	−	102.527i	0.362572	−	0.304234i	−0.443243	−	0.896402i	$-0.646172\pi$
$337$	122.187	−	102.527i	0.362572	−	0.304234i	0.805815	+	0.592167i	$0.201728\pi$
$338$	237.702	+	653.081i	0.703261	+	1.93219i
$339$	−114.959	−	485.192i	−0.339112	−	1.43125i
$340$	54.2372	+	307.595i	0.159521	+	0.904690i
$341$		−	271.790i		−	0.797037i
$342$	475.572	−	271.737i	1.39056	−	0.794554i
$343$	60.2683			0.175709
$344$	−306.322	+	54.0128i	−0.890470	+	0.157014i
$345$	−21.5684	−	22.8642i	−0.0625171	−	0.0662730i
$346$	−928.872	+	338.082i	−2.68460	+	0.977115i
$347$	−129.999	−	154.927i	−0.374638	−	0.446476i	0.545476	−	0.838126i	$-0.316349\pi$
$347$	−129.999	−	154.927i	−0.374638	−	0.446476i	−0.920114	+	0.391650i	$0.871904\pi$
$348$	757.123	−	326.532i	2.17564	−	0.938310i
$349$	−187.535	−	324.820i	−0.537349	−	0.930716i	−0.999046	−	0.0436779i	$-0.986092\pi$
$349$	−187.535	−	324.820i	−0.537349	−	0.930716i	0.461697	−	0.887038i	$-0.347241\pi$
$350$	149.374	−	86.2413i	0.426784	−	0.246404i
$351$	−530.449	−	0.105161i	−1.51125	−	0.000299605i
$352$	253.316	+	212.557i	0.719648	+	0.603856i
$353$		−	196.719i		−	0.557276i	−0.960396	−	0.278638i	$-0.910117\pi$
$353$		−	196.719i		−	0.557276i	0.960396	−	0.278638i	$-0.0898830\pi$
$354$	−261.400	−	131.302i	−0.738418	−	0.370909i
$355$	157.621	+	132.259i	0.444002	+	0.372562i
$356$	−473.713	−	564.550i	−1.33066	−	1.58581i
$357$	−261.191	−	194.476i	−0.731626	−	0.544751i
$358$	−112.297	+	94.2285i	−0.313679	+	0.263208i
$359$	−153.937	−	183.455i	−0.428794	−	0.511017i	0.507780	−	0.861487i	$-0.330466\pi$
$359$	−153.937	−	183.455i	−0.428794	−	0.511017i	−0.936574	+	0.350470i	$0.886022\pi$
$360$	171.223	+	230.055i	0.475619	+	0.639043i
$361$	−100.524	−	346.722i	−0.278459	−	0.960448i
$362$	−928.245	−	535.923i	−2.56421	−	1.48045i
$363$	26.8294	−	89.5950i	0.0739103	−	0.246818i
$364$	204.512	+	1159.84i	0.561846	+	3.18638i
$365$	140.465	+	385.925i	0.384836	+	1.05733i
$366$	−720.914	+	680.057i	−1.96971	+	1.85808i
$367$	35.4461	−	201.025i	0.0965834	−	0.547752i	−0.897667	−	0.440674i	$-0.854739\pi$
$367$	35.4461	−	201.025i	0.0965834	−	0.547752i	0.994251	−	0.107078i	$-0.0341494\pi$
$368$	−3.81984	−	2.20538i	−0.0103800	−	0.00599289i
$369$	334.971	+	144.545i	0.907781	+	0.391721i
$370$	−503.587	−	422.560i	−1.36105	−	1.14205i
$371$	116.260	+	319.422i	0.313369	+	0.860975i
$372$	−31.2783	−	537.639i	−0.0840814	−	1.44527i
$373$	−494.550			−1.32587			−0.662935	−	0.748677i	$-0.730690\pi$
$373$	−494.550			−1.32587			−0.662935	+	0.748677i	$0.730690\pi$
$374$	−221.184	+	263.597i	−0.591401	+	0.704804i
$375$	93.2353	+	393.507i	0.248628	+	1.04935i
$376$	−189.510	−	159.018i	−0.504017	−	0.422920i
$377$	−295.020	+	810.560i	−0.782545	+	2.15003i
$378$	−815.590	−	143.977i	−2.15765	−	0.380892i
$379$	47.5306			0.125411			0.0627053	−	0.998032i	$-0.480027\pi$
$379$	47.5306			0.125411			0.0627053	+	0.998032i	$0.480027\pi$
$380$	481.636	−	205.278i	1.26746	−	0.540205i
$381$	−30.1792	−	518.747i	−0.0792104	−	1.36154i
$382$	1133.61	+	412.599i	2.96755	+	1.08010i
$383$	69.6038	−	12.2730i	0.181733	−	0.0320444i	−0.0820409	−	0.996629i	$-0.526144\pi$
$383$	69.6038	−	12.2730i	0.181733	−	0.0320444i	0.263774	+	0.964585i	$0.415033\pi$
$384$	468.426	+	348.778i	1.21986	+	0.908276i
$385$	−375.428	−	136.645i	−0.975137	−	0.354921i
$386$	−69.9961	−	192.313i	−0.181337	−	0.498219i
$387$	230.897	+	310.233i	0.596632	+	0.801637i
$388$	73.6626	+	127.587i	0.189852	+	0.328833i
$389$	165.860	+	455.695i	0.426374	+	1.17145i	0.947998	+	0.318278i	$0.103104\pi$
$389$	165.860	+	455.695i	0.426374	+	1.17145i	−0.521623	+	0.853176i	$0.674673\pi$
$390$	−825.402	−	96.5309i	−2.11641	−	0.247515i
$391$	13.4894	−	23.3644i	0.0344998	−	0.0597555i
$392$			309.142i			0.788628i
$393$	−159.045	−	118.421i	−0.404696	−	0.301326i
$394$	256.344	+	93.3017i	0.650620	+	0.236806i
$395$	365.181	+	64.3912i	0.924508	+	0.163016i
$396$	−123.208	+	519.551i	−0.311132	+	1.31200i
$397$	−560.857	+	470.615i	−1.41274	+	1.18543i	−0.457642	+	0.889137i	$0.651306\pi$
$397$	−560.857	+	470.615i	−1.41274	+	1.18543i	−0.955097	+	0.296292i	$0.904250\pi$
$398$	667.428	+	385.340i	1.67696	+	0.968191i
$399$	−218.412	+	500.251i	−0.547398	+	1.25376i
$400$	5.21015	+	9.02425i	0.0130254	+	0.0225606i
$401$	5.31487	−	14.6025i	0.0132540	−	0.0364152i	−0.932889	−	0.360164i	$-0.882721\pi$
$401$	5.31487	−	14.6025i	0.0132540	−	0.0364152i	0.946143	+	0.323748i	$0.104943\pi$
$402$	−362.633	−	108.591i	−0.902072	−	0.270128i
$403$	431.587	+	362.145i	1.07094	+	0.898622i
$404$	−690.750	+	121.798i	−1.70978	+	0.301480i
$405$	160.106	−	318.588i	0.395324	−	0.786636i
$406$	−673.382	+	1166.33i	−1.65858	+	2.87274i
$407$		−	441.880i		−	1.08570i
$408$	−147.004	+	197.434i	−0.360304	+	0.483906i
$409$	51.4214	−	291.625i	0.125725	−	0.713020i	−0.855150	−	0.518380i	$-0.826535\pi$
$409$	51.4214	−	291.625i	0.125725	−	0.713020i	0.980875	−	0.194640i	$-0.0623538\pi$
$410$	494.983	+	285.778i	1.20727	+	0.697020i
$411$	−83.0422	−	126.278i	−0.202049	−	0.307245i
$412$	18.1540	−	102.957i	0.0440632	−	0.249895i
$413$	287.091	−	50.6219i	0.695135	−	0.122571i
$414$	3.99869	−	68.4988i	0.00965866	−	0.165456i
$415$	98.2926	+	35.7756i	0.236850	+	0.0862062i
$416$	−675.059	+	119.031i	−1.62274	+	0.286133i
$417$	427.726	−	281.279i	1.02572	−	0.674531i
$418$	514.314	+	261.106i	1.23042	+	0.624655i
$419$	387.056	−	223.467i	0.923761	−	0.533334i	0.0389280	−	0.999242i	$-0.487606\pi$
$419$	387.056	−	223.467i	0.923761	−	0.533334i	0.884833	+	0.465908i	$0.154272\pi$
$420$	−758.376	−	227.097i	−1.80566	−	0.540708i
$421$	425.650	−	357.163i	1.01105	−	0.848369i	0.0225701	−	0.999745i	$-0.492815\pi$
$421$	425.650	−	357.163i	1.01105	−	0.848369i	0.988476	+	0.151377i	$0.0483706\pi$
$422$	−60.4244	−	10.6545i	−0.143186	−	0.0252475i
$423$	−70.9723	+	299.279i	−0.167783	+	0.707516i
$424$	241.450	−	87.8807i	0.569458	−	0.207266i
$425$	−55.1976	+	31.8684i	−0.129877	+	0.0749844i
$426$	26.0872	+	448.411i	0.0612376	+	1.05261i
$427$	171.505	−	972.652i	0.401651	−	2.27787i
$428$	671.822	+	118.460i	1.56968	+	0.276776i
$429$	−306.923	−	466.721i	−0.715439	−	1.08793i
$430$	302.933	+	524.696i	0.704496	+	1.22022i
$431$	154.931	+	425.669i	0.359468	+	0.987631i	0.979214	+	0.202829i	$0.0650135\pi$
$431$	154.931	+	425.669i	0.359468	+	0.987631i	−0.619746	+	0.784803i	$0.712764\pi$
$432$	8.69819	−	49.2728i	0.0201347	−	0.114057i
$433$	131.124	−	743.643i	0.302828	−	1.71742i	−0.330731	−	0.943725i	$-0.607295\pi$
$433$	131.124	−	743.643i	0.302828	−	1.71742i	0.633558	−	0.773695i	$-0.281594\pi$
$434$	565.424	+	673.846i	1.30282	+	1.55264i
$435$	−397.860	−	421.763i	−0.914620	−	0.969569i
$436$	12.6379	+	21.8895i	0.0289861	+	0.0502054i
$437$	−43.2665	−	13.1585i	−0.0990080	−	0.0301109i
$438$	−402.417	+	801.147i	−0.918761	+	1.82910i
$439$	39.1993	+	222.310i	0.0892923	+	0.506402i	0.996348	+	0.0853903i	$0.0272137\pi$
$439$	39.1993	+	222.310i	0.0892923	+	0.506402i	−0.907055	+	0.421012i	$0.861675\pi$
$440$	−103.289	+	283.785i	−0.234749	+	0.644967i
$441$	343.498	−	172.455i	0.778908	−	0.391053i
$442$	−123.862	−	702.456i	−0.280231	−	1.58927i
$443$	−563.004	−	99.2728i	−1.27089	−	0.224092i	−0.502782	−	0.864413i	$-0.667690\pi$
$443$	−563.004	−	99.2728i	−1.27089	−	0.224092i	−0.768107	+	0.640321i	$0.778801\pi$
$444$	−50.8527	−	874.103i	−0.114533	−	1.96870i
$445$	−259.115	+	448.800i	−0.582281	+	1.00854i
$446$	−309.965	−	54.6553i	−0.694990	−	0.122545i
$447$	26.5907	−	227.368i	0.0594870	−	0.508653i
$448$	−999.259			−2.23049
$449$	−289.799	−	167.316i	−0.645433	−	0.372641i	0.141272	−	0.989971i	$-0.454881\pi$
$449$	−289.799	−	167.316i	−0.645433	−	0.372641i	−0.786704	+	0.617330i	$0.788214\pi$
$450$	−89.0943	+	135.422i	−0.197987	+	0.300938i
$451$	66.7134	+	378.350i	0.147923	+	0.838915i
$452$	668.789	−	797.031i	1.47962	−	1.76334i
$453$	114.106	+	120.962i	0.251890	+	0.267023i
$454$	−47.3405	−	17.2305i	−0.104274	−	0.0379527i
$455$	717.221	−	414.088i	1.57631	−	0.910083i
$456$	378.139	+	165.097i	0.829252	+	0.362055i
$457$	−250.877	+	434.532i	−0.548966	+	0.950837i	0.449380	+	0.893341i	$0.351645\pi$
$457$	−250.877	+	434.532i	−0.548966	+	0.950837i	−0.998346	+	0.0574960i	$0.981688\pi$
$458$	708.300	+	844.119i	1.54651	+	1.84305i
$459$	301.381	+	53.2033i	0.656604	+	0.115911i
$460$	11.3891	−	64.5907i	0.0247589	−	0.140414i
$461$	−42.4692	+	116.683i	−0.0921241	+	0.253109i	−0.977194	−	0.212350i	$-0.931888\pi$
$461$	−42.4692	+	116.683i	−0.0921241	+	0.253109i	0.885070	+	0.465459i	$0.154111\pi$
$462$	−345.388	−	800.845i	−0.747593	−	1.73343i
$463$	−202.817			−0.438050			−0.219025	−	0.975719i	$-0.570288\pi$
$463$	−202.817			−0.438050			−0.219025	+	0.975719i	$0.570288\pi$
$464$	−70.4623	−	40.6815i	−0.151859	−	0.0876755i
$465$	−347.741	+	149.974i	−0.747830	+	0.322524i
$466$	655.513	−	238.587i	1.40668	−	0.511990i
$467$	−12.8228	+	7.40326i	−0.0274579	+	0.0158528i	−0.513666	−	0.857990i	$-0.671713\pi$
$467$	−12.8228	+	7.40326i	−0.0274579	+	0.0158528i	0.486208	+	0.873843i	$0.338380\pi$
$468$	−660.850	−	887.921i	−1.41207	−	1.89727i
$469$	354.493	−	129.025i	0.755849	−	0.275107i
$470$	−164.809	+	452.809i	−0.350658	+	0.963424i
$471$	−271.377	−	629.238i	−0.576173	−	1.33596i
$472$	−38.2650	−	217.012i	−0.0810699	−	0.459770i
$473$	−139.287	+	382.689i	−0.294477	+	0.809068i
$474$	444.773	+	676.341i	0.938339	+	1.42688i
$475$	72.9782	+	78.0295i	0.153638	+	0.164273i
$476$		−	679.493i		−	1.42751i
$477$	−232.340	−	219.260i	−0.487086	−	0.459664i
$478$	−175.403	−	63.8414i	−0.366951	−	0.133559i
$479$	507.545	−	604.868i	1.05959	−	1.26277i	0.0960039	−	0.995381i	$-0.469394\pi$
$479$	507.545	−	604.868i	1.05959	−	1.26277i	0.963588	−	0.267391i	$-0.0861617\pi$
$480$	132.177	−	441.394i	0.275368	−	0.919572i
$481$	701.682	+	588.781i	1.45880	+	1.22408i
$482$		−	196.790i		−	0.408279i
$483$	37.5716	+	57.1331i	0.0777881	+	0.118288i
$484$	183.385	−	66.7468i	0.378895	−	0.137907i
$485$	66.5915	−	79.3606i	0.137302	−	0.163630i
$486$	745.730	−	222.989i	1.53442	−	0.458824i
$487$	274.763	−	475.904i	0.564196	−	0.977216i	−0.432928	−	0.901429i	$-0.642520\pi$
$487$	274.763	−	475.904i	0.564196	−	0.977216i	0.997124	−	0.0757877i	$-0.0241471\pi$
$488$	−735.226	−	129.640i	−1.50661	−	0.265656i
$489$	−94.6780	+	22.4325i	−0.193615	+	0.0458742i
$490$	565.841	−	205.949i	1.15478	−	0.420305i
$491$	25.5041	−	4.49706i	0.0519431	−	0.00915897i	−0.147616	−	0.989045i	$-0.547160\pi$
$491$	25.5041	−	4.49706i	0.0519431	−	0.00915897i	0.199559	+	0.979886i	$0.436049\pi$
$492$	175.510	+	740.754i	0.356728	+	1.50560i
$493$	248.832	−	430.989i	0.504730	−	0.874218i
$494$	−1099.92	+	468.794i	−2.22655	+	0.948977i
$495$	372.944	−	43.5409i	0.753421	−	0.0879614i
$496$	−40.7095	+	34.1593i	−0.0820756	+	0.0688696i
$497$	−287.730	−	342.903i	−0.578933	−	0.689945i
$498$	90.4277	+	209.673i	0.181582	+	0.421030i
$499$	30.7950	−	25.8400i	0.0617133	−	0.0517836i	−0.611409	−	0.791315i	$-0.709397\pi$
$499$	30.7950	−	25.8400i	0.0617133	−	0.0517836i	0.673123	+	0.739531i	$0.264953\pi$
$500$	−542.409	+	646.418i	−1.08482	+	1.29284i
$501$	662.938	−	38.5678i	1.32323	−	0.0769817i
$502$	−1191.96			−2.37443
$503$	−43.5976	+	51.9577i	−0.0866752	+	0.103296i	−0.807639	−	0.589677i	$-0.799255\pi$
$503$	−43.5976	+	51.9577i	−0.0866752	+	0.103296i	0.720964	+	0.692973i	$0.243699\pi$
$504$	−279.927	−	557.563i	−0.555410	−	1.10628i
$505$	246.612	+	427.144i	0.488340	+	0.845830i
$506$	62.5760	−	36.1283i	0.123668	−	0.0713998i
$507$	646.519	+	75.6105i	1.27518	+	0.149133i
$508$	830.597	−	696.953i	1.63503	−	1.37196i
$509$	287.232	+	789.162i	0.564306	+	1.55042i	0.813259	+	0.581902i	$0.197691\pi$
$509$	287.232	+	789.162i	0.564306	+	1.55042i	−0.248954	+	0.968515i	$0.580087\pi$
$510$	459.308	+	137.541i	0.900604	+	0.269688i
$511$	−155.148	−	879.885i	−0.303615	−	1.72189i
$512$		−	118.315i		−	0.231084i
$513$	−27.4991	−	512.262i	−0.0536044	−	0.998562i
$514$	405.572			0.789050
$515$	−72.3983	+	12.7658i	−0.140579	+	0.0247879i
$516$	−231.490	+	773.044i	−0.448624	+	1.49815i
$517$	−304.368	+	110.781i	−0.588719	+	0.214276i
$518$	919.276	+	1095.55i	1.77466	+	2.11496i
$519$	−107.540	+	919.537i	−0.207206	+	1.77175i
$520$	−313.008	−	542.146i	−0.601939	−	1.04259i
$521$	−689.254	+	397.941i	−1.32294	+	0.763802i	−0.984197	−	0.177076i	$-0.943336\pi$
$521$	−689.254	+	397.941i	−1.32294	+	0.763802i	−0.338747	+	0.940878i	$0.610003\pi$
$522$	73.7615	−	1263.56i	0.141305	−	2.42061i
$523$	25.7495	+	21.6064i	0.0492342	+	0.0413124i	0.667073	−	0.744993i	$-0.267547\pi$
$523$	25.7495	+	21.6064i	0.0492342	+	0.0413124i	−0.617839	+	0.786305i	$0.711991\pi$
$524$		−	413.760i		−	0.789619i
$525$	−9.38238	−	161.273i	−0.0178712	−	0.307186i
$526$	904.567	+	759.022i	1.71971	+	1.44301i
$527$	−208.939	−	249.003i	−0.396468	−	0.472492i
$528$	48.3819	−	20.8661i	0.0916325	−	0.0395192i
$529$	400.898	−	336.393i	0.757841	−	0.635904i
$530$	−321.707	−	383.395i	−0.606994	−	0.723387i
$531$	−219.783	+	163.577i	−0.413904	+	0.308055i
$532$	−1109.43	+	257.848i	−2.08539	+	0.484676i
$533$	−689.692	−	398.194i	−1.29398	−	0.747080i
$534$	−1100.81	+	260.820i	−2.06144	+	0.488427i
$535$	−83.3004	−	472.420i	−0.155702	−	0.883028i
$536$	−97.5299	−	267.961i	−0.181959	−	0.499927i
$537$	31.6543	+	133.599i	0.0589465	+	0.248788i
$538$	−36.1499	+	205.016i	−0.0671931	+	0.381071i
$539$	350.528	+	202.378i	0.650331	+	0.375469i
$540$	732.725	−	129.049i	1.35690	−	0.238981i
$541$	33.5300	+	28.1351i	0.0619779	+	0.0520056i	0.673250	−	0.739415i	$-0.264898\pi$
$541$	33.5300	+	28.1351i	0.0619779	+	0.0520056i	−0.611272	+	0.791420i	$0.709342\pi$
$542$	537.463	+	1476.67i	0.991629	+	2.72448i
$543$	−838.765	+	551.585i	−1.54469	+	1.01581i
$544$	395.483			0.726990
$545$	11.4248	−	13.6155i	0.0209629	−	0.0249826i
$546$	1731.91	+	518.624i	3.17199	+	0.949861i
$547$	266.934	+	223.984i	0.487996	+	0.409478i	0.853308	−	0.521408i	$-0.174593\pi$
$547$	266.934	+	223.984i	0.487996	+	0.409478i	−0.365311	+	0.930885i	$0.619037\pi$
$548$	107.862	−	296.347i	0.196828	−	0.540780i
$549$	266.097	+	889.255i	0.484695	+	1.61977i
$550$	−170.704			−0.310371
$551$	−798.112	−	242.726i	−1.44848	−	0.440520i
$552$	43.1868	−	28.4003i	0.0782370	−	0.0514499i
$553$	−758.053	−	275.909i	−1.37080	−	0.498931i
$554$	−1306.56	+	230.382i	−2.35841	+	0.415851i
$555$	−565.363	+	243.830i	−1.01867	+	0.439333i
$556$	1003.78	+	365.347i	1.80536	+	0.657099i
$557$	149.158	+	409.809i	0.267789	+	0.735743i	0.998587	+	0.0531493i	$0.0169259\pi$
$557$	149.158	+	409.809i	0.267789	+	0.735743i	−0.730798	+	0.682594i	$0.760852\pi$
$558$	−759.048	−	327.541i	−1.36030	−	0.586990i
$559$	−422.097	−	731.093i	−0.755092	−	1.30786i
$560$	26.7178	+	73.4066i	0.0477104	+	0.131083i
$561$	127.630	+	295.933i	0.227504	+	0.527509i
$562$	88.2561	−	152.864i	0.157039	−	0.272000i
$563$			251.530i			0.446767i	0.974731	+	0.223383i	$0.0717102\pi$
$563$			251.530i			0.446767i	−0.974731	+	0.223383i	$0.928290\pi$
$564$	−589.335	+	254.168i	−1.04492	+	0.450652i
$565$	−687.514	−	250.235i	−1.21684	−	0.442893i
$566$	−365.077	−	64.3730i	−0.645013	−	0.113733i
$567$	−463.371	+	622.072i	−0.817233	+	1.09713i
$568$	−259.200	+	217.494i	−0.456337	+	0.382913i
$569$	163.269	+	94.2637i	0.286941	+	0.165665i	0.636562	−	0.771226i	$-0.280356\pi$
$569$	163.269	+	94.2637i	0.286941	+	0.165665i	−0.349620	+	0.936891i	$0.613689\pi$
$570$	50.2726	−	802.117i	0.0881975	−	1.40722i
$571$	−64.2190	−	111.231i	−0.112468	−	0.194799i	0.804297	−	0.594227i	$-0.202542\pi$
$571$	−64.2190	−	111.231i	−0.112468	−	0.194799i	−0.916765	+	0.399428i	$0.869209\pi$
$572$	398.655	−	1095.30i	0.696950	−	1.91485i
$573$	821.884	−	775.305i	1.43435	−	1.35306i
$574$	−952.513	−	799.253i	−1.65943	−	1.39243i
$575$	13.1805	−	2.32408i	0.0229226	−	0.00404188i
$576$	839.283	−	421.365i	1.45709	−	0.731536i
$577$	−247.469	+	428.629i	−0.428889	+	0.742857i	−0.996775	−	0.0802501i	$-0.974428\pi$
$577$	−247.469	+	428.629i	−0.428889	+	0.742857i	0.567886	+	0.823107i	$0.307761\pi$
$578$		−	514.166i		−	0.889560i
$579$	−190.380	−	22.2650i	−0.328809	−	0.0384542i
$580$	210.088	−	1191.47i	0.362220	−	2.05425i
$581$	−197.071	−	113.779i	−0.339193	−	0.195833i
$582$	225.771	−	13.1347i	0.387923	−	0.0225682i
$583$	58.4180	−	331.305i	0.100202	−	0.568276i
$584$	−665.104	+	117.276i	−1.13888	+	0.200815i
$585$	−427.786	+	650.230i	−0.731258	+	1.11150i
$586$	482.449	+	175.597i	0.823293	+	0.299654i
$587$	−638.433	+	112.573i	−1.08762	+	0.191777i	−0.688582	−	0.725158i	$-0.741767\pi$
$587$	−638.433	+	112.573i	−1.08762	+	0.191777i	−0.399037	+	0.916935i	$0.630656\pi$
$588$	716.686	+	359.992i	1.21885	+	0.612232i
$589$	−327.268	+	435.629i	−0.555634	+	0.739608i
$590$	−371.717	+	214.611i	−0.630029	+	0.363748i
$591$	185.854	−	175.321i	0.314474	−	0.296651i
$592$	−66.1862	+	55.5368i	−0.111801	+	0.0938122i
$593$	−856.825	−	151.081i	−1.44490	−	0.254775i	−0.604440	−	0.796650i	$-0.706603\pi$
$593$	−856.825	−	151.081i	−1.44490	−	0.254775i	−0.840459	+	0.541876i	$0.817714\pi$
$594$	627.791	+	526.992i	1.05689	+	0.887191i
$595$	−448.998	+	163.422i	−0.754619	+	0.274659i
$596$	413.672	−	238.834i	0.694081	−	0.400728i
$597$	603.090	−	396.602i	1.01020	−	0.664325i
$598$	−26.0093	+	147.506i	−0.0434939	+	0.246666i
$599$	349.364	+	61.6023i	0.583246	+	0.102842i	0.457483	−	0.889218i	$-0.348751\pi$
$599$	349.364	+	61.6023i	0.583246	+	0.102842i	0.125763	+	0.992060i	$0.459862\pi$
$600$	−121.906	+	7.09213i	−0.203177	+	0.0118202i
$601$	200.654	+	347.543i	0.333867	+	0.578275i	0.983267	−	0.182173i	$-0.0583130\pi$
$601$	200.654	+	347.543i	0.333867	+	0.578275i	−0.649399	+	0.760447i	$0.724980\pi$
$602$	−450.802	−	1238.57i	−0.748841	−	2.05742i
$603$	−243.334	+	257.851i	−0.403539	+	0.427613i
$604$	−60.2532	+	341.713i	−0.0997570	+	0.565750i
$605$	−88.2105	−	105.125i	−0.145803	−	0.173761i
$606$	−308.869	+	1031.45i	−0.509685	+	1.70206i
$607$	193.306	+	334.817i	0.318462	+	0.551592i	0.980167	−	0.198172i	$-0.0635003\pi$
$607$	193.306	+	334.817i	0.318462	+	0.551592i	−0.661705	+	0.749764i	$0.730167\pi$
$608$	−150.074	−	645.715i	−0.246832	−	1.06203i
$609$	693.062	+	1053.90i	1.13803	+	1.73054i
$610$	252.517	+	1432.09i	0.413962	+	2.34770i
$611$	229.639	−	630.929i	0.375842	−	1.03262i
$612$	286.527	+	570.710i	0.468181	+	0.932532i
$613$	−36.9766	−	209.705i	−0.0603208	−	0.342096i	−1.00000		3.92334e-5i	$-0.999988\pi$
$613$	−36.9766	−	209.705i	−0.0603208	−	0.342096i	0.939679	−	0.342057i	$-0.111124\pi$
$614$	1350.08	+	238.056i	2.19883	+	0.387714i
$615$	447.268	−	294.130i	0.727265	−	0.478261i
$616$	328.497	−	568.974i	0.533275	−	0.923659i
$617$	−449.360	−	79.2342i	−0.728298	−	0.128419i	−0.202808	−	0.979219i	$-0.565007\pi$
$617$	−449.360	−	79.2342i	−0.728298	−	0.128419i	−0.525490	+	0.850800i	$0.676118\pi$
$618$	−128.720	−	95.8420i	−0.208285	−	0.155084i
$619$	−376.672			−0.608516			−0.304258	−	0.952590i	$-0.598409\pi$
$619$	−376.672			−0.608516			−0.304258	+	0.952590i	$0.598409\pi$
$620$	−684.347	−	395.108i	−1.10379	−	0.637271i
$621$	−55.6483	−	32.1433i	−0.0896108	−	0.0517605i
$622$	−215.282	−	1220.92i	−0.346112	−	1.96290i
$623$	724.682	−	863.642i	1.16321	−	1.38626i
$624$	−31.3320	+	104.631i	−0.0502115	+	0.167678i
$625$	425.497	+	154.868i	0.680795	+	0.247789i
$626$	950.521	−	548.783i	1.51840	−	0.876651i
$627$	434.745	−	320.682i	0.693374	−	0.511455i
$628$	714.949	−	1238.33i	1.13845	−	1.97186i
$629$	−339.696	−	404.834i	−0.540057	−	0.643615i
$630$	−834.055	+	883.813i	−1.32390	+	1.40288i
$631$	−134.547	+	763.053i	−0.213228	+	1.20928i	0.670727	+	0.741704i	$0.265982\pi$
$631$	−134.547	+	763.053i	−0.213228	+	1.20928i	−0.883955	+	0.467571i	$0.845129\pi$
$632$	−208.559	+	573.011i	−0.329999	+	0.906664i
$633$	−34.3193	+	46.0925i	−0.0542169	+	0.0728159i
$634$	−1467.12			−2.31406
$635$	−660.299	−	381.224i	−1.03984	−	0.600353i
$636$	77.4317	−	662.091i	0.121748	−	1.04102i
$637$	−788.424	+	286.963i	−1.23771	+	0.450491i
$638$	1154.30	−	666.437i	1.80925	−	1.04457i
$639$	386.260	+	166.677i	0.604475	+	0.260840i
$640$	805.245	−	293.085i	1.25819	−	0.457945i
$641$	43.4725	−	119.440i	0.0678197	−	0.186333i	−0.901153	−	0.433502i	$-0.857278\pi$
$641$	43.4725	−	119.440i	0.0678197	−	0.186333i	0.968973	+	0.247168i	$0.0795001\pi$
$642$	625.397	−	839.937i	0.974138	−	1.30831i
$643$	−11.9819	−	67.9529i	−0.0186344	−	0.105681i	0.974072	−	0.226239i	$-0.0726429\pi$
$643$	−11.9819	−	67.9529i	−0.0186344	−	0.105681i	−0.992706	+	0.120558i	$0.961532\pi$
$644$	−48.8009	+	134.079i	−0.0757778	+	0.208198i
$645$	566.490	−	32.9567i	0.878279	−	0.0510957i
$646$	671.921	−	156.165i	1.04013	−	0.241741i
$647$			319.967i			0.494539i	0.968947	+	0.247270i	$0.0795333\pi$
$647$			319.967i			0.494539i	−0.968947	+	0.247270i	$0.920467\pi$
$648$	470.224	+	350.262i	0.725654	+	0.540527i
$649$	−271.114	−	98.6773i	−0.417741	−	0.152045i
$650$	227.453	−	271.068i	0.349928	−	0.417028i
$651$	801.671	−	189.944i	1.23145	−	0.291772i
$652$	−155.529	−	130.504i	−0.238541	−	0.200159i
$653$			629.706i			0.964328i	0.876081	+	0.482164i	$0.160149\pi$
$653$			629.706i			0.964328i	−0.876081	+	0.482164i	$0.839851\pi$
$654$	38.7344	−	2.25345i	0.0592269	−	0.00344565i
$655$	−273.406	+	99.5118i	−0.417414	+	0.151926i
$656$	48.2858	−	57.5447i	0.0736064	−	0.0877207i
$657$	501.337	+	673.598i	0.763070	+	1.02526i
$658$	524.152	−	907.858i	0.796583	−	1.37972i
$659$	1179.87	+	208.043i	1.79040	+	0.315695i	0.967572	−	0.252597i	$-0.0812848\pi$
$659$	1179.87	+	208.043i	1.79040	+	0.315695i	0.822826	+	0.568293i	$0.192396\pi$
$660$	537.622	+	569.921i	0.814578	+	0.863517i
$661$	1006.48	−	366.328i	1.52266	−	0.554203i	0.560850	−	0.827917i	$-0.310474\pi$
$661$	1006.48	−	366.328i	1.52266	−	0.554203i	0.961811	+	0.273714i	$0.0882521\pi$
$662$	214.462	−	37.8155i	0.323961	−	0.0571231i
$663$	−639.984	−	191.645i	−0.965286	−	0.289057i
$664$	−86.0055	+	148.966i	−0.129526	+	0.224346i
$665$	437.205	+	671.078i	0.657452	+	1.00914i
$666$	−1234.07	−	532.521i	−1.85296	−	0.799581i
$667$	−80.0536	+	67.1730i	−0.120020	+	0.100709i
$668$	890.680	+	1061.47i	1.33335	+	1.58903i
$669$	−176.051	+	236.445i	−0.263156	+	0.353431i
$670$	−425.491	+	357.029i	−0.635061	+	0.532880i
$671$	−628.306	+	748.786i	−0.936373	+	1.11593i
$672$	−449.927	+	895.730i	−0.669533	+	1.33293i
$673$	−1110.14			−1.64954			−0.824769	−	0.565469i	$-0.808695\pi$
$673$	−1110.14			−1.64954			−0.824769	+	0.565469i	$0.808695\pi$
$674$	328.405	−	391.378i	0.487248	−	0.580680i
$675$	75.8854	+	131.498i	0.112423	+	0.194811i
$676$	679.122	+	1176.27i	1.00462	+	1.74005i
$677$	290.584	−	167.769i	0.429222	−	0.247812i	−0.269793	−	0.962918i	$-0.586955\pi$
$677$	290.584	−	167.769i	0.429222	−	0.247812i	0.699015	+	0.715107i	$0.253622\pi$
$678$	−632.503	−	1466.57i	−0.932895	−	2.16309i
$679$	−172.649	+	144.869i	−0.254269	+	0.213357i
$680$	123.531	+	339.397i	0.181663	+	0.499114i
$681$	−34.3226	+	32.3775i	−0.0504004	+	0.0475440i
$682$	−151.173	−	857.346i	−0.221662	−	1.25711i
$683$			1168.23i			1.71043i	0.518271	+	0.855216i	$0.326576\pi$
$683$			1168.23i			1.71043i	−0.518271	+	0.855216i	$0.673424\pi$
$684$	823.084	−	684.387i	1.20334	−	1.00057i
$685$	−221.763			−0.323742
$686$	190.113	−	33.5221i	0.277133	−	0.0488660i
$687$	1004.24	−	237.940i	1.46178	−	0.346346i
$688$	74.8264	−	27.2346i	0.108759	−	0.0395852i
$689$	448.255	+	534.210i	0.650588	+	0.775341i
$690$	−80.7538	−	60.1272i	−0.117034	−	0.0871409i
$691$	461.331	+	799.049i	0.667628	+	1.15637i	0.978566	+	0.205936i	$0.0660238\pi$
$691$	461.331	+	799.049i	0.667628	+	1.15637i	−0.310937	+	0.950430i	$0.600643\pi$
$692$	−1673.00	+	965.909i	−2.41764	+	1.39582i
$693$	−815.458	−	47.6032i	−1.17671	−	0.0686915i
$694$	−496.249	−	416.402i	−0.715056	−	0.600004i
$695$		−	751.152i		−	1.08079i
$696$	796.643	−	523.885i	1.14460	−	0.752708i
$697$	351.978	+	295.344i	0.504990	+	0.423737i
$698$	−772.238	−	920.318i	−1.10636	−	1.31851i
$699$	75.8920	−	648.926i	0.108572	−	0.928363i
$700$	258.224	−	216.675i	0.368891	−	0.309536i
$701$	−358.937	−	427.765i	−0.512036	−	0.610220i	0.446643	−	0.894712i	$-0.352620\pi$
$701$	−358.937	−	427.765i	−0.512036	−	0.610220i	−0.958678	+	0.284492i	$0.908175\pi$
$702$	−1673.33	+	294.711i	−2.38366	+	0.419817i
$703$	−532.078	+	708.253i	−0.756868	+	1.00747i
$704$	856.459	+	494.477i	1.21656	+	0.702382i
$705$	309.689	+	328.294i	0.439275	+	0.465666i
$706$	−109.418	−	620.538i	−0.154983	−	0.878950i
$707$	−366.989	−	1008.29i	−0.519079	−	1.42616i
$708$	−547.658	−	163.998i	−0.773529	−	0.231635i
$709$	145.294	−	824.004i	0.204928	−	1.16221i	−0.692625	−	0.721298i	$-0.743546\pi$
$709$	145.294	−	824.004i	0.204928	−	1.16221i	0.897553	−	0.440907i	$-0.145343\pi$
$710$	570.771	+	329.535i	0.803903	+	0.464133i
$711$	753.037	−	87.9165i	1.05912	−	0.123652i
$712$	−652.826	−	547.786i	−0.916891	−	0.769363i
$713$	23.3450	+	64.1399i	0.0327420	+	0.0899578i
$714$	−932.082	−	468.187i	−1.30544	−	0.655723i
$715$	−819.634			−1.14634
$716$	−184.153	+	219.465i	−0.257197	+	0.306515i
$717$	−127.170	+	119.963i	−0.177364	+	0.167312i
$718$	−587.627	−	493.077i	−0.818422	−	0.686737i
$719$	261.194	−	717.626i	0.363274	−	0.998088i	−0.614590	−	0.788847i	$-0.710678\pi$
$719$	261.194	−	717.626i	0.363274	−	0.998088i	0.977864	−	0.209241i	$-0.0670994\pi$
$720$	−53.3943	−	50.3883i	−0.0741588	−	0.0699838i
$721$	159.932			0.221819
$722$	−509.949	−	1037.80i	−0.706300	−	1.43740i
$723$	−164.702	−	82.7299i	−0.227803	−	0.114426i
$724$	−1968.40	−	716.441i	−2.71879	−	0.989559i
$725$	243.133	−	42.8710i	0.335356	−	0.0591324i
$726$	34.7980	−	297.546i	0.0479312	−	0.409843i
$727$	657.917	+	239.462i	0.904975	+	0.329384i	0.752244	−	0.658884i	$-0.228971\pi$
$727$	657.917	+	239.462i	0.904975	+	0.329384i	0.152730	+	0.988268i	$0.451193\pi$
$728$	465.795	+	1279.76i	0.639829	+	1.75792i
$729$	126.874	−	717.875i	0.174039	−	0.984739i
$730$	657.747	+	1139.25i	0.901023	+	1.56062i
$731$	166.583	+	457.683i	0.227884	+	0.626105i
$732$	−1156.71	+	1553.51i	−1.58020	+	2.12229i
$733$	75.1441	−	130.153i	0.102516	−	0.177563i	−0.810205	−	0.586147i	$-0.800644\pi$
$733$	75.1441	−	130.153i	0.102516	−	0.177563i	0.912721	+	0.408584i	$0.133977\pi$
$734$		−	653.838i		−	0.890788i
$735$	65.5103	−	560.155i	0.0891296	−	0.762116i
$736$	−78.0377	−	28.4034i	−0.106029	−	0.0385916i
$737$	−367.681	−	64.8321i	−0.498889	−	0.0879676i
$738$	1137.05	+	269.644i	1.54071	+	0.365371i
$739$	45.8994	−	38.5142i	0.0621101	−	0.0521166i	−0.611204	−	0.791473i	$-0.709315\pi$
$739$	45.8994	−	38.5142i	0.0621101	−	0.0521166i	0.673314	+	0.739356i	$0.264870\pi$
$740$	−1112.62	−	642.373i	−1.50354	−	0.868072i
$741$	−70.0481	+	1117.64i	−0.0945319	+	1.50829i
$742$	544.403	+	942.933i	0.733696	+	1.27080i
$743$	−35.0392	+	96.2695i	−0.0471591	+	0.129569i	−0.961036	−	0.276422i	$-0.910851\pi$
$743$	−35.0392	+	96.2695i	−0.0471591	+	0.129569i	0.913877	+	0.405991i	$0.133073\pi$
$744$	−143.578	−	605.982i	−0.192981	−	0.814492i
$745$	−257.308	−	215.907i	−0.345380	−	0.289808i
$746$	−1560.03	+	275.076i	−2.09120	+	0.368734i
$747$	213.499	+	12.4632i	0.285809	+	0.0166844i
$748$	−336.243	+	582.389i	−0.449522	+	0.778595i
$749$			1043.60i			1.39333i
$750$	512.980	+	1189.44i	0.683973	+	1.58592i
$751$	−73.0112	+	414.067i	−0.0972186	+	0.551354i	0.896826	+	0.442383i	$0.145867\pi$
$751$	−73.0112	+	414.067i	−0.0972186	+	0.551354i	−0.994045	+	0.108971i	$0.965244\pi$
$752$	54.8470	+	31.6659i	0.0729348	+	0.0421089i
$753$	−501.096	+	997.600i	−0.665466	+	1.32483i
$754$	−479.779	+	2720.96i	−0.636312	+	3.60870i
$755$	240.290	−	42.3696i	0.318265	−	0.0561187i
$756$	−1618.57	−	0.320882i	−2.14097	−	0.000424447i
$757$	−164.373	−	59.8271i	−0.217138	−	0.0790318i	0.231161	−	0.972916i	$-0.425748\pi$
$757$	−164.373	−	59.8271i	−0.217138	−	0.0790318i	−0.448299	+	0.893884i	$0.647970\pi$
$758$	149.933	−	26.4372i	0.197800	−	0.0348776i
$759$	−3.93047	−	67.5605i	−0.00517849	−	0.0890125i
$760$	507.267	−	330.483i	0.667456	−	0.434846i
$761$	527.393	−	304.490i	0.693026	−	0.400119i	−0.111719	−	0.993740i	$-0.535636\pi$
$761$	527.393	−	304.490i	0.693026	−	0.400119i	0.804745	+	0.593621i	$0.202302\pi$
$762$	−383.733	−	1619.57i	−0.503586	−	2.12542i
$763$	−29.6204	+	24.8545i	−0.0388210	+	0.0325747i
$764$	2321.80	+	409.395i	3.03900	+	0.535858i
$765$	308.205	−	326.591i	0.402882	−	0.426917i
$766$	212.735	−	77.4292i	0.277722	−	0.101082i
$767$	517.938	−	299.032i	0.675278	−	0.389872i
$768$	552.686	+	277.615i	0.719644	+	0.361478i
$769$	−94.5873	+	536.431i	−0.123000	+	0.697570i	0.859475	+	0.511178i	$0.170791\pi$
$769$	−94.5873	+	536.431i	−0.123000	+	0.697570i	−0.982475	+	0.186392i	$0.940320\pi$
$770$	−1260.27	−	222.220i	−1.63672	−	0.288597i
$771$	170.501	−	339.439i	0.221142	−	0.440258i
$772$	−199.981	−	346.377i	−0.259043	−	0.448675i
$773$	−452.051	−	1242.00i	−0.584801	−	1.60673i	−0.779873	−	0.625937i	$-0.784717\pi$
$773$	−452.051	−	1242.00i	−0.584801	−	1.60673i	0.195073	−	0.980789i	$-0.437506\pi$
$774$	900.907	+	850.187i	1.16396	+	1.09843i
$775$	28.0013	−	158.803i	0.0361307	−	0.204908i
$776$	109.507	+	130.505i	0.141117	+	0.168176i
$777$	1303.37	−	308.813i	1.67744	−	0.397443i
$778$	776.660	+	1345.21i	0.998277	+	1.72907i
$779$	348.651	−	686.758i	0.447563	−	0.881589i
$780$	−1621.35	+	94.3256i	−2.07866	+	0.120930i
$781$	76.9281	+	436.281i	0.0984995	+	0.558618i
$782$	29.5561	−	81.2048i	0.0377956	−	0.103842i
$783$	−1026.51	−	592.929i	−1.31100	−	0.757253i
$784$	−13.7427	−	77.9386i	−0.0175289	−	0.0994115i
$785$	−990.217	−	174.602i	−1.26142	−	0.222423i
$786$	−567.568	−	285.090i	−0.722097	−	0.362710i
$787$	187.733	−	325.164i	0.238543	−	0.413169i	−0.721753	−	0.692150i	$-0.756664\pi$
$787$	187.733	−	325.164i	0.238543	−	0.413169i	0.960296	+	0.278982i	$0.0899969\pi$
$788$	525.032	+	92.5773i	0.666284	+	0.117484i
$789$	1015.53	−	437.978i	1.28711	−	0.555105i
$790$	1187.76			1.50349
$791$	1378.43	+	795.835i	1.74264	+	1.00611i
$792$	−35.9832	+	616.404i	−0.0454333	+	0.778288i
$793$	−351.848	−	1995.43i	−0.443693	−	2.51631i
$794$	−1507.43	+	1796.49i	−1.89853	+	2.26258i
$795$	−456.123	+	108.071i	−0.573739	+	0.135939i
$796$	1415.33	+	515.136i	1.77805	+	0.647156i
$797$	−1298.74	+	749.827i	−1.62953	+	0.940812i	−0.645303	+	0.763927i	$0.723269\pi$
$797$	−1298.74	+	749.827i	−1.62953	+	0.940812i	−0.984232	+	0.176885i	$0.943398\pi$
$798$	−410.722	+	1699.50i	−0.514690	+	2.12970i
$799$	−193.687	+	335.477i	−0.242412	+	0.419870i
$800$	126.111	+	150.293i	0.157638	+	0.187866i
$801$	−244.486	+	1030.96i	−0.305226	+	1.28709i
$802$	8.64337	−	49.0190i	0.0107773	−	0.0611209i
$803$	−302.429	+	830.918i	−0.376624	+	1.03477i
$804$	−734.788	−	85.9336i	−0.913915	−	0.106883i
$805$	100.334			0.124639
$806$	1562.85	+	902.311i	1.93902	+	1.11949i
$807$	156.389	+	116.443i	0.193790	+	0.144292i
$808$	−762.168	+	277.407i	−0.943278	+	0.343325i
$809$	−749.875	+	432.940i	−0.926916	+	0.535155i	−0.885835	−	0.464001i	$-0.846413\pi$
$809$	−749.875	+	432.940i	−0.926916	+	0.535155i	−0.0410809	+	0.999156i	$0.513080\pi$
$810$	327.844	−	1094.02i	0.404745	−	1.35064i
$811$	−895.326	+	325.872i	−1.10398	+	0.401815i	−0.828781	−	0.559573i	$-0.810965\pi$
$811$	−895.326	+	325.872i	−1.10398	+	0.401815i	−0.275196	+	0.961388i	$0.588743\pi$
$812$	−900.202	+	2473.28i	−1.10862	+	3.04592i
$813$	1461.83	+	170.961i	1.79807	+	0.210284i
$814$	−245.780	−	1393.89i	−0.301941	−	1.71239i
$815$	−48.8295	+	134.158i	−0.0599135	+	0.164611i
$816$	28.2848	−	56.3105i	0.0346628	−	0.0690079i
$817$	684.057	−	445.662i	0.837280	−	0.545485i
$818$		−	948.518i		−	1.15956i
$819$	1162.14	−	1231.48i	1.41898	−	1.50363i
$820$	1049.64	+	382.039i	1.28005	+	0.465901i
$821$	310.042	−	369.493i	0.377639	−	0.450052i	−0.543429	−	0.839455i	$-0.682874\pi$
$821$	310.042	−	369.493i	0.377639	−	0.450052i	0.921068	+	0.389403i	$0.127319\pi$
$822$	−332.190	−	352.147i	−0.404124	−	0.428403i
$823$	162.034	+	135.962i	0.196882	+	0.165203i	0.735899	−	0.677091i	$-0.236760\pi$
$823$	162.034	+	135.962i	0.196882	+	0.165203i	−0.539017	+	0.842295i	$0.681204\pi$
$824$		−	120.892i		−	0.146714i
$825$	−71.7632	+	142.869i	−0.0869857	+	0.173174i
$826$	877.457	−	319.368i	1.06230	−	0.386644i
$827$	−135.039	+	160.934i	−0.163288	+	0.194599i	−0.841484	−	0.540282i	$-0.818318\pi$
$827$	−135.039	+	160.934i	−0.163288	+	0.194599i	0.678196	+	0.734881i	$0.262762\pi$
$828$	−15.5501	−	133.192i	−0.0187803	−	0.160860i
$829$	182.253	−	315.671i	0.219847	−	0.380785i	−0.734914	−	0.678160i	$-0.762778\pi$
$829$	182.253	−	315.671i	0.219847	−	0.380785i	0.954761	+	0.297375i	$0.0961110\pi$
$830$	329.958	+	58.1804i	0.397539	+	0.0700969i
$831$	−356.457	+	1190.36i	−0.428949	+	1.43245i
$832$	−1926.39	+	701.147i	−2.31537	+	0.842725i
$833$	476.719	−	84.0584i	0.572292	−	0.100910i
$834$	1192.79	−	1125.19i	1.43020	−	1.34915i
$835$	487.190	−	843.837i	0.583461	−	1.01058i
$836$	1078.48	+	327.992i	1.29004	+	0.392335i
$837$	−593.233	+	497.581i	−0.708760	+	0.594481i
$838$	1096.65	−	920.200i	1.30865	−	1.09809i
$839$	−951.161	−	1133.55i	−1.13368	−	1.35107i	−0.928056	−	0.372442i	$-0.878521\pi$
$839$	−951.161	−	1133.55i	−1.13368	−	1.35107i	−0.205628	−	0.978630i	$-0.565924\pi$
$840$	−909.238	−	106.336i	−1.08243	−	0.126590i
$841$	−832.460	+	698.517i	−0.989845	+	0.830579i
$842$	1144.03	−	1363.41i	1.35871	−	1.61925i
$843$	−90.8354	−	138.128i	−0.107753	−	0.163853i
$844$	−119.911			−0.142074
$845$	613.931	−	731.655i	0.726546	−	0.865863i
$846$	−57.4149	+	983.537i	−0.0678664	+	1.16257i
$847$	149.273	+	258.548i	0.176237	+	0.305252i
$848$	−56.9660	+	32.8893i	−0.0671769	+	0.0387846i
$849$	−207.353	+	278.485i	−0.244232	+	0.328016i
$850$	−156.392	+	131.229i	−0.183991	+	0.154387i
$851$	37.9547	+	104.280i	0.0446001	+	0.122538i
$852$	202.383	+	854.173i	0.237539	+	1.00255i
$853$	31.7993	+	180.343i	0.0372794	+	0.211422i	0.997757	−	0.0669339i	$-0.0213217\pi$
$853$	31.7993	+	180.343i	0.0372794	+	0.211422i	−0.960478	+	0.278356i	$0.910211\pi$
$854$		−	3163.57i		−	3.70442i
$855$	−650.189	−	379.282i	−0.760455	−	0.443605i
$856$	788.856			0.921561
$857$	−851.578	+	150.156i	−0.993674	+	0.175211i	−0.646767	−	0.762688i	$-0.723879\pi$
$857$	−851.578	+	150.156i	−0.993674	+	0.175211i	−0.346907	+	0.937900i	$0.612768\pi$
$858$	−1227.77	−	1301.53i	−1.43097	−	1.51694i
$859$	−437.893	+	159.380i	−0.509770	+	0.185541i	−0.584083	−	0.811694i	$-0.698546\pi$
$859$	−437.893	+	159.380i	−0.509770	+	0.185541i	0.0743130	+	0.997235i	$0.476324\pi$
$860$	761.098	+	907.042i	0.884998	+	1.05470i
$861$	−1069.36	+	461.193i	−1.24200	+	0.535648i
$862$	725.485	+	1256.58i	0.841630	+	1.45775i
$863$	−190.913	+	110.224i	−0.221221	+	0.127722i	−0.606515	−	0.795072i	$-0.707433\pi$
$863$	−190.913	+	110.224i	−0.221221	+	0.127722i	0.385295	+	0.922794i	$0.374100\pi$
$864$	0.186762	−	942.052i	0.000216159	−	1.09034i
$865$	1040.63	+	873.189i	1.20304	+	1.00947i
$866$		−	2418.72i		−	2.79297i
$867$	−430.326	−	216.153i	−0.496339	−	0.249312i
$868$	1316.91	+	1105.02i	1.51718	+	1.27307i
$869$	513.191	+	611.597i	0.590554	+	0.703795i
$870$	−1489.62	−	1109.13i	−1.71220	−	1.27487i
$871$	592.865	−	497.473i	0.680671	−	0.571151i
$872$	18.7875	+	22.3901i	0.0215453	+	0.0256767i
$873$	83.9203	−	194.478i	0.0961286	−	0.222770i
$874$	−143.801	−	17.4422i	−0.164532	−	0.0199568i
$875$	−1117.95	−	645.448i	−1.27766	−	0.737655i
$876$	−502.625	+	1678.48i	−0.573773	+	1.91607i
$877$	45.9127	+	260.384i	0.0523520	+	0.296903i	0.999731	−	0.0232124i	$-0.00738940\pi$
$877$	45.9127	+	260.384i	0.0523520	+	0.296903i	−0.947379	+	0.320115i	$0.896278\pi$
$878$	247.304	+	679.463i	0.281668	+	0.773876i
$879$	349.784	−	329.961i	0.397934	−	0.375382i
$880$	13.4251	−	76.1375i	0.0152558	−	0.0865199i
$881$	−2.49616	−	1.44116i	−0.00283333	−	0.00163582i	0.498583	−	0.866842i	$-0.333854\pi$
$881$	−2.49616	−	1.44116i	−0.00283333	−	0.00163582i	−0.501416	+	0.865206i	$0.667187\pi$
$882$	987.626	−	735.058i	1.11976	−	0.833399i
$883$	−215.946	−	181.201i	−0.244560	−	0.205210i	0.512266	−	0.858827i	$-0.328806\pi$
$883$	−215.946	−	181.201i	−0.244560	−	0.205210i	−0.756826	+	0.653617i	$0.773251\pi$
$884$	−476.778	−	1309.94i	−0.539341	−	1.48183i
$885$	23.3480	+	401.327i	0.0263819	+	0.453476i
$886$	−1831.18			−2.06680
$887$	−273.628	+	326.098i	−0.308487	+	0.367641i	−0.897906	−	0.440187i	$-0.854912\pi$
$887$	−273.628	+	326.098i	−0.308487	+	0.367641i	0.589419	+	0.807828i	$0.299357\pi$
$888$	−233.432	−	985.216i	−0.262873	−	1.10948i
$889$	1270.64	+	1066.19i	1.42929	+	1.19932i
$890$	−567.735	+	1559.84i	−0.637905	+	1.75263i
$891$	704.981	−	303.878i	0.791224	−	0.341053i
$892$	−615.118			−0.689594
$893$	621.240	+	188.935i	0.695678	+	0.211573i
$894$	−42.5862	−	732.010i	−0.0476355	−	0.818803i
$895$	189.309	+	68.9028i	0.211518	+	0.0769864i
$896$	−1835.91	+	323.720i	−2.04901	+	0.361295i
$897$	112.520	+	83.7793i	0.125440	+	0.0933994i
$898$	−1007.22	−	366.598i	−1.12163	−	0.408238i
$899$	430.632	+	1183.15i	0.479012	+	1.31608i
$900$	−125.516	+	290.874i	−0.139463	+	0.323193i
$901$	−201.171	−	348.438i	−0.223275	−	0.386723i
$902$	420.888	+	1156.38i	0.466616	+	1.28202i
$903$	−1226.12	−	143.395i	−1.35783	−	0.158799i
$904$	601.571	−	1041.95i	0.665455	−	1.15260i
$905$			1473.00i			1.62762i
$906$	427.223	+	318.099i	0.471548	+	0.351103i
$907$	−445.583	−	162.179i	−0.491271	−	0.178808i	0.0844927	−	0.996424i	$-0.473073\pi$
$907$	−445.583	−	162.179i	−0.491271	−	0.178808i	−0.575764	+	0.817616i	$0.695295\pi$
$908$	−96.9605	−	17.0967i	−0.106785	−	0.0188290i
$909$	733.411	+	692.121i	0.806833	+	0.761409i
$910$	2032.11	−	1705.15i	2.23309	−	1.87379i
$911$	−957.665	−	552.908i	−1.05122	−	0.606924i	−0.128232	−	0.991744i	$-0.540930\pi$
$911$	−957.665	−	552.908i	−1.05122	−	0.606924i	−0.922992	+	0.384820i	$0.874264\pi$
$912$	−102.673	−	24.8132i	−0.112580	−	0.0272075i
$913$	112.606	+	195.039i	0.123336	+	0.213624i
$914$	−549.687	+	1510.25i	−0.601408	+	1.65235i
$915$	1304.73	+	390.705i	1.42594	+	0.427000i
$916$	1649.68	+	1384.25i	1.80096	+	1.51119i
$917$	623.350	−	109.913i	0.679771	−	0.119862i
$918$	980.284	+	0.194341i	1.06785	+	0.000211701i
$919$	213.019	−	368.960i	0.231795	−	0.401480i	−0.726542	−	0.687122i	$-0.758874\pi$
$919$	213.019	−	368.960i	0.231795	−	0.401480i	0.958336	+	0.285642i	$0.0922069\pi$
$920$		−	75.8427i		−	0.0824377i
$921$	766.808	−	1029.86i	0.832582	−	1.11820i
$922$	−69.0661	+	391.693i	−0.0749090	+	0.424830i
$923$	−795.293	−	459.162i	−0.861639	−	0.497467i
$924$	−936.524	−	1424.12i	−1.01355	−	1.54126i
$925$	45.5250	−	258.185i	0.0492163	−	0.279119i
$926$	−639.777	+	112.810i	−0.690903	+	0.121825i
$927$	−134.328	+	67.4396i	−0.144906	+	0.0727504i
$928$	−1439.52	−	523.941i	−1.55120	−	0.564591i
$929$	−99.2689	+	17.5038i	−0.106856	+	0.0188415i	−0.226820	−	0.973937i	$-0.572833\pi$
$929$	−99.2689	+	17.5038i	−0.106856	+	0.0188415i	0.119965	+	0.992778i	$0.461722\pi$
$930$	−1013.51	+	666.502i	−1.08980	+	0.716669i
$931$	−318.145	−	746.454i	−0.341724	−	0.801776i
$932$	1180.65	−	681.651i	1.26680	−	0.731385i
$933$	−1112.34	−	333.094i	−1.19222	−	0.357014i
$934$	−36.3311	+	30.4854i	−0.0388984	+	0.0326396i
$935$	465.702	+	82.1159i	0.498077	+	0.0878244i
$936$	−930.870	−	878.463i	−0.994520	−	0.938529i
$937$	268.848	−	97.8525i	0.286924	−	0.104432i	−0.194549	−	0.980893i	$-0.562324\pi$
$937$	268.848	−	97.8525i	0.286924	−	0.104432i	0.481473	+	0.876461i	$0.340102\pi$
$938$	1046.47	−	604.177i	1.11563	−	0.644112i
$939$	−59.7033	−	1026.23i	−0.0635818	−	1.09290i
$940$	−163.530	+	927.422i	−0.173968	+	0.986619i
$941$	−856.314	−	150.991i	−0.910004	−	0.160458i	−0.300999	−	0.953624i	$-0.597320\pi$
$941$	−856.314	−	150.991i	−0.910004	−	0.160458i	−0.609005	+	0.793166i	$0.708431\pi$
$942$	−1206.04	−	1833.95i	−1.28029	−	1.94687i
$943$	−48.2417	−	83.5570i	−0.0511577	−	0.0886077i
$944$	19.2942	+	53.0103i	0.0204387	+	0.0561550i
$945$	389.064	+	1069.61i	0.411708	+	1.13186i
$946$	−226.518	+	1284.65i	−0.239448	+	1.35798i
$947$	−26.5347	−	31.6228i	−0.0280197	−	0.0333926i	0.751853	−	0.659331i	$-0.229160\pi$
$947$	−26.5347	−	31.6228i	−0.0280197	−	0.0333926i	−0.779872	+	0.625939i	$0.784716\pi$
$948$	1085.55	+	1150.77i	1.14510	+	1.21389i
$949$	−916.482	−	1587.39i	−0.965735	−	1.67270i
$950$	273.607	+	205.548i	0.288007	+	0.216367i
$951$	−616.770	+	1227.89i	−0.648549	+	1.29115i
$952$	−136.443	−	773.805i	−0.143322	−	0.812821i
$953$	395.027	−	1085.33i	0.414509	−	1.13885i	−0.540258	−	0.841499i	$-0.681673\pi$
$953$	395.027	−	1085.33i	0.414509	−	1.13885i	0.954767	−	0.297355i	$-0.0961045\pi$
$954$	−854.860	−	562.412i	−0.896080	−	0.589531i
$955$	−287.884	−	1632.67i	−0.301449	−	1.70960i
$956$	−359.251	−	63.3457i	−0.375786	−	0.0662612i
$957$	−72.5031	−	1246.25i	−0.0757609	−	1.30225i
$958$	1264.59	−	2190.33i	1.32003	−	2.28635i
$959$	475.114	+	83.7755i	0.495427	+	0.0873571i
$960$	160.064	−	1368.65i	0.166733	−	1.42568i
$961$	−138.625			−0.144251
$962$	2540.91	+	1466.99i	2.64127	+	1.52494i
$963$	−440.063	−	876.525i	−0.456970	−	0.910203i
$964$	−66.7837	−	378.749i	−0.0692777	−	0.392894i
$965$	−180.784	+	215.450i	−0.187341	+	0.223264i
$966$	150.296	+	159.326i	0.155586	+	0.164933i
$967$	1386.68	+	504.712i	1.43401	+	0.521936i	0.938077	−	0.346427i	$-0.112605\pi$
$967$	1386.68	+	504.712i	1.43401	+	0.521936i	0.495930	+	0.868363i	$0.334827\pi$
$968$	195.436	−	112.835i	0.201897	−	0.116565i
$969$	151.772	−	628.008i	0.156628	−	0.648099i
$970$	165.918	−	287.378i	0.171049	−	0.296266i
$971$	130.446	+	155.460i	0.134342	+	0.160103i	0.829021	−	0.559217i	$-0.188898\pi$
$971$	130.446	+	155.460i	0.134342	+	0.160103i	−0.694679	+	0.719320i	$0.744454\pi$
$972$	1359.58	−	682.246i	1.39875	−	0.701899i
$973$	−283.763	+	1609.30i	−0.291637	+	1.65396i
$974$	602.022	−	1654.04i	0.618093	−	1.69820i
$975$	−131.247	−	304.321i	−0.134613	−	0.312124i
$976$	191.123			0.195823
$977$	1341.85	+	774.717i	1.37344	+	0.792955i	0.991359	−	0.131175i	$-0.0418750\pi$
$977$	1341.85	+	774.717i	1.37344	+	0.792955i	0.382079	+	0.924130i	$0.375208\pi$
$978$	−286.179	+	123.423i	−0.292617	+	0.126200i
$979$	−1048.49	+	381.618i	−1.07098	+	0.389804i
$980$	1019.14	−	588.404i	1.03994	−	0.600412i
$981$	14.3978	−	33.3657i	0.0146766	−	0.0340119i
$982$	77.9499	−	28.3714i	0.0793787	−	0.0288915i
$983$	62.6379	−	172.096i	0.0637211	−	0.175072i	−0.903746	−	0.428069i	$-0.859194\pi$
$983$	62.6379	−	172.096i	0.0637211	−	0.175072i	0.967467	+	0.252997i	$0.0814162\pi$
$984$	348.615	+	808.327i	0.354283	+	0.821471i
$985$	−65.0997	−	369.199i	−0.0660910	−	0.374821i
$986$	545.205	−	1497.94i	0.552946	−	1.51921i
$987$	−539.470	−	820.343i	−0.546576	−	0.831148i
$988$	−1957.84	+	1275.53i	−1.98162	+	1.29102i
$989$		−	102.275i		−	0.103413i
$990$	1152.21	−	344.784i	1.16385	−	0.348267i
$991$	690.955	+	251.487i	0.697230	+	0.253771i	0.666228	−	0.745748i	$-0.267908\pi$
$991$	690.955	+	251.487i	0.697230	+	0.253771i	0.0310021	+	0.999519i	$0.490130\pi$
$992$	−643.152	+	766.478i	−0.648338	+	0.772660i
$993$	58.5098	−	195.389i	0.0589223	−	0.196767i
$994$	−1098.36	−	921.629i	−1.10498	−	0.927192i
$995$		−	1059.12i		−	1.06444i
$996$	245.196	+	372.856i	0.246181	+	0.374353i
$997$	213.995	−	77.8877i	0.214639	−	0.0781220i	−0.232463	−	0.972605i	$-0.574678\pi$
$997$	213.995	−	77.8877i	0.214639	−	0.0781220i	0.447102	+	0.894483i	$0.352456\pi$
$998$	82.7685	−	98.6396i	0.0829343	−	0.0988373i
$999$	−964.487	+	808.975i	−0.965453	+	0.809785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.z.a.101.34	✓	228
9.5	odd	6		171.3.bf.a.158.34	yes	228
19.16	even	9		171.3.bf.a.92.34	yes	228
171.149	odd	18	inner	171.3.z.a.149.34	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.3.z.a.101.34	✓	228	1.1	even	1	trivial
171.3.z.a.149.34	yes	228	171.149	odd	18	inner
171.3.bf.a.92.34	yes	228	19.16	even	9
171.3.bf.a.158.34	yes	228	9.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(3.15445 - 0.556214i) q^{2} +(0.860600 - 2.87391i) q^{3} +(5.88239 - 2.14102i) q^{4} +(-2.82950 - 3.37207i) q^{5} +(1.11621 - 9.54428i) q^{6} +(4.78818 + 8.29337i) q^{7} +(6.26894 - 3.61938i) q^{8} +(-7.51874 - 4.94657i) q^{9} +(-10.8011 - 9.06321i) q^{10} -9.47759i q^{11} +(-1.09071 - 18.7480i) q^{12} +(15.0499 + 12.6284i) q^{13} +(19.7169 + 23.4977i) q^{14} +(-12.1261 + 5.22974i) q^{15} +(-1.41958 + 1.19117i) q^{16} +(-7.28591 - 8.68301i) q^{17} +(-26.4688 - 11.4217i) q^{18} +(-11.4122 + 15.1909i) q^{19} +(-23.8639 - 13.7778i) q^{20} +(27.9551 - 6.62353i) q^{21} +(-5.27157 - 29.8966i) q^{22} +(0.814065 + 2.23663i) q^{23} +(-5.00672 - 21.1312i) q^{24} +(0.976436 - 5.53764i) q^{25} +(54.4982 + 31.4645i) q^{26} +(-20.6866 + 17.3512i) q^{27} +(45.9222 + 38.5333i) q^{28} +(15.0166 + 41.2577i) q^{29} +(-35.3423 + 23.2416i) q^{30} +28.6771 q^{31} +(-22.4274 + 26.7279i) q^{32} +(-27.2378 - 8.15641i) q^{33} +(-27.8126 - 23.3376i) q^{34} +(14.4176 - 39.6122i) q^{35} +(-54.8189 - 13.0000i) q^{36} +46.6237 q^{37} +(-27.5498 + 54.2664i) q^{38} +(49.2447 - 32.3841i) q^{39} +(-29.9428 - 10.8983i) q^{40} +(-39.9205 + 7.03907i) q^{41} +(84.4988 - 36.4426i) q^{42} +(-40.3783 - 14.6965i) q^{43} +(-20.2917 - 55.7509i) q^{44} +(4.59409 + 39.3500i) q^{45} +(3.81197 + 6.60252i) q^{46} +(-11.6887 - 32.1145i) q^{47} +(2.20163 + 5.10488i) q^{48} +(-21.3533 + 36.9850i) q^{49} -18.0113i q^{50} +(-31.2245 + 13.4665i) q^{51} +(115.567 + 42.0629i) q^{52} +(34.9566 + 6.16380i) q^{53} +(-55.6040 + 66.2395i) q^{54} +(-31.9591 + 26.8169i) q^{55} +(60.0336 + 34.6604i) q^{56} +(33.8358 + 45.8709i) q^{57} +(70.3172 + 121.793i) q^{58} +(10.4116 - 28.6058i) q^{59} +(-60.1335 + 56.7256i) q^{60} +(-79.0059 - 66.2939i) q^{61} +(90.4604 - 15.9506i) q^{62} +(5.02271 - 86.0407i) q^{63} +(-52.1733 + 90.3668i) q^{64} -86.4813i q^{65} +(-90.4568 - 10.5789i) q^{66} +(6.84057 - 38.7948i) q^{67} +(-61.4491 - 35.4776i) q^{68} +(7.12845 - 0.414712i) q^{69} +(23.4469 - 132.974i) q^{70} +(-46.0329 + 8.11684i) q^{71} +(-65.0381 - 3.79666i) q^{72} +(-87.6719 - 31.9099i) q^{73} +(147.072 - 25.9328i) q^{74} +(-15.0744 - 7.57188i) q^{75} +(-34.6071 + 113.792i) q^{76} +(78.6011 - 45.3804i) q^{77} +(137.327 - 129.545i) q^{78} +(-64.5309 + 54.1479i) q^{79} +(8.03343 + 1.41651i) q^{80} +(32.0628 + 74.3840i) q^{81} +(-122.012 + 44.4087i) q^{82} +(-20.5789 + 11.8813i) q^{83} +(150.262 - 98.8146i) q^{84} +(-8.66421 + 49.1372i) q^{85} +(-135.546 - 23.9004i) q^{86} +(131.494 - 7.64996i) q^{87} +(-34.3030 - 59.4145i) q^{88} +(-40.2654 - 110.628i) q^{89} +(36.3789 + 121.572i) q^{90} +(-32.6701 + 185.281i) q^{91} +(9.57731 + 11.4138i) q^{92} +(24.6795 - 82.4154i) q^{93} +(-54.7340 - 94.8020i) q^{94} +(83.5154 - 4.49985i) q^{95} +(57.5126 + 87.4563i) q^{96} +(4.08676 + 23.1772i) q^{97} +(-46.7862 + 128.544i) q^{98} +(-46.8816 + 71.2595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} - 12 q^{10} - 3 q^{12} + 12 q^{13} - 9 q^{14} - 48 q^{15} + 9 q^{16} - 81 q^{17} - 60 q^{18} - 33 q^{19} - 18 q^{20} + 21 q^{21}+ \cdots - 300 q^{99}+O(q^{100}) \) 228 * q - 9 * q^2 + 6 * q^3 - 3 * q^4 - 9 * q^5 - 30 * q^6 + 3 * q^7 + 30 * q^9 - 12 * q^10 - 3 * q^12 + 12 * q^13 - 9 * q^14 - 48 * q^15 + 9 * q^16 - 81 * q^17 - 60 * q^18 - 33 * q^19 - 18 * q^20 + 21 * q^21 + 81 * q^22 + 207 * q^23 - 222 * q^24 - 3 * q^25 - 216 * q^26 - 33 * q^27 - 36 * q^28 - 9 * q^29 + 171 * q^30 - 6 * q^31 - 9 * q^32 + 30 * q^33 + 33 * q^34 + 225 * q^35 - 246 * q^36 - 24 * q^37 - 9 * q^38 - 60 * q^39 - 177 * q^40 - 9 * q^41 - 15 * q^42 + 93 * q^43 + 441 * q^44 - 57 * q^45 - 6 * q^46 - 9 * q^47 - 774 * q^48 - 543 * q^49 - 81 * q^51 + 213 * q^52 + 393 * q^54 + 63 * q^55 - 459 * q^56 + 84 * q^57 - 6 * q^58 + 126 * q^59 - 333 * q^60 - 24 * q^61 - 36 * q^62 + 369 * q^63 + 372 * q^64 + 894 * q^66 + 39 * q^67 + 747 * q^68 + 231 * q^69 + 291 * q^70 + 204 * q^72 - 51 * q^73 + 333 * q^74 + 324 * q^75 - 3 * q^76 - 18 * q^77 - 1569 * q^78 - 105 * q^79 - 756 * q^80 + 1050 * q^81 + 132 * q^82 + 99 * q^83 - 69 * q^84 - 3 * q^85 - 495 * q^86 - 483 * q^87 + 387 * q^88 - 648 * q^89 - 339 * q^90 + 225 * q^91 + 27 * q^92 + 396 * q^93 - 6 * q^94 - 1305 * q^95 - 663 * q^96 - 543 * q^97 + 1125 * q^98 - 300 * q^99

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