LMFDB - Embedded newform 60.3.l.a.47.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(23,60)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.14
Character	$\chi$	$=$	60.47
Dual form			60.3.l.a.23.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.961083 - 1.75394i) q^{2} +(-2.86057 - 0.903948i) q^{3} +(-2.15264 - 3.37137i) q^{4} +(-4.95584 - 0.663068i) q^{5} +(-4.33472 + 4.14852i) q^{6} +(7.30016 - 7.30016i) q^{7} +(-7.98206 + 0.535443i) q^{8} +(7.36576 + 5.17162i) q^{9} +O(q^{10})$	\(q+(0.961083 - 1.75394i) q^{2} +(-2.86057 - 0.903948i) q^{3} +(-2.15264 - 3.37137i) q^{4} +(-4.95584 - 0.663068i) q^{5} +(-4.33472 + 4.14852i) q^{6} +(7.30016 - 7.30016i) q^{7} +(-7.98206 + 0.535443i) q^{8} +(7.36576 + 5.17162i) q^{9} +(-5.92596 + 8.05500i) q^{10} +4.41713 q^{11} +(3.11024 + 11.5899i) q^{12} +(7.53253 - 7.53253i) q^{13} +(-5.78801 - 19.8201i) q^{14} +(13.5772 + 6.37658i) q^{15} +(-6.73229 + 14.5147i) q^{16} +(0.350578 - 0.350578i) q^{17} +(16.1498 - 7.94877i) q^{18} -9.24359 q^{19} +(8.43269 + 18.1353i) q^{20} +(-27.4816 + 14.2837i) q^{21} +(4.24523 - 7.74740i) q^{22} +(17.9810 - 17.9810i) q^{23} +(23.3173 + 5.68370i) q^{24} +(24.1207 + 6.57212i) q^{25} +(-5.97225 - 20.4510i) q^{26} +(-16.3954 - 21.4521i) q^{27} +(-40.3261 - 8.89693i) q^{28} -5.52099 q^{29} +(24.2329 - 17.6852i) q^{30} +48.1716i q^{31} +(18.9877 + 25.7579i) q^{32} +(-12.6355 - 3.99285i) q^{33} +(-0.277960 - 0.951830i) q^{34} +(-41.0189 + 31.3379i) q^{35} +(1.57963 - 35.9653i) q^{36} +(3.39462 + 3.39462i) q^{37} +(-8.88386 + 16.2127i) q^{38} +(-28.3564 + 14.7383i) q^{39} +(39.9128 + 2.63908i) q^{40} -33.0983i q^{41} +(-1.35933 + 61.9290i) q^{42} +(-1.45103 - 1.45103i) q^{43} +(-9.50848 - 14.8918i) q^{44} +(-33.0744 - 30.5137i) q^{45} +(-14.2565 - 48.8190i) q^{46} +(-27.8943 - 27.8943i) q^{47} +(32.3787 - 35.4347i) q^{48} -57.5846i q^{49} +(34.7091 - 35.9900i) q^{50} +(-1.31976 + 0.685951i) q^{51} +(-41.6098 - 9.18014i) q^{52} +(52.6835 + 52.6835i) q^{53} +(-53.3830 + 8.13943i) q^{54} +(-21.8906 - 2.92886i) q^{55} +(-54.3615 + 62.1791i) q^{56} +(26.4420 + 8.35573i) q^{57} +(-5.30613 + 9.68351i) q^{58} +24.6578i q^{59} +(-7.72893 - 59.5001i) q^{60} +46.1739 q^{61} +(84.4904 + 46.2969i) q^{62} +(91.5248 - 16.0176i) q^{63} +(63.4266 - 8.54787i) q^{64} +(-42.3246 + 32.3354i) q^{65} +(-19.1470 + 18.3245i) q^{66} +(32.1110 - 32.1110i) q^{67} +(-1.93660 - 0.427261i) q^{68} +(-67.6900 + 35.1822i) q^{69} +(15.5424 + 102.063i) q^{70} +116.455 q^{71} +(-61.5630 - 37.3362i) q^{72} +(-72.2123 + 72.2123i) q^{73} +(9.21650 - 2.69147i) q^{74} +(-63.0581 - 40.6039i) q^{75} +(19.8981 + 31.1636i) q^{76} +(32.2457 - 32.2457i) q^{77} +(-1.40260 + 63.9003i) q^{78} +55.9466 q^{79} +(42.9884 - 67.4685i) q^{80} +(27.5087 + 76.1858i) q^{81} +(-58.0526 - 31.8102i) q^{82} +(-46.5302 + 46.5302i) q^{83} +(107.314 + 61.9031i) q^{84} +(-1.96987 + 1.50495i) q^{85} +(-3.93959 + 1.15047i) q^{86} +(15.7932 + 4.99069i) q^{87} +(-35.2578 + 2.36512i) q^{88} +33.2025 q^{89} +(-85.3065 + 28.6844i) q^{90} -109.977i q^{91} +(-99.3275 - 21.9141i) q^{92} +(43.5447 - 137.798i) q^{93} +(-75.7338 + 22.1163i) q^{94} +(45.8098 + 6.12913i) q^{95} +(-31.0319 - 90.8462i) q^{96} +(-24.6341 - 24.6341i) q^{97} +(-101.000 - 55.3436i) q^{98} +(32.5355 + 22.8437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.961083	−	1.75394i	0.480541	−	0.876972i
$2$	0.961083	−	1.75394i	0.480541	−	0.876972i
$3$	−2.86057	−	0.903948i	−0.953524	−	0.301316i
$3$	−2.86057	−	0.903948i	−0.953524	−	0.301316i
$4$	−2.15264	−	3.37137i	−0.538160	−	0.842843i
$5$	−4.95584	−	0.663068i	−0.991168	−	0.132614i
$5$	−4.95584	−	0.663068i	−0.991168	−	0.132614i
$6$	−4.33472	+	4.14852i	−0.722454	+	0.691419i
$7$	7.30016	−	7.30016i	1.04288	−	1.04288i	0.0438411	−	0.999039i	$-0.486040\pi$
$7$	7.30016	−	7.30016i	1.04288	−	1.04288i	0.999039	−	0.0438411i	$-0.0139595\pi$
$8$	−7.98206	+	0.535443i	−0.997758	+	0.0669303i
$9$	7.36576	+	5.17162i	0.818417	+	0.574624i
$10$	−5.92596	+	8.05500i	−0.592596	+	0.805500i
$11$	4.41713			0.401557			0.200779	−	0.979637i	$-0.435653\pi$
$11$	4.41713			0.401557			0.200779	+	0.979637i	$0.435653\pi$
$12$	3.11024	+	11.5899i	0.259187	+	0.965827i
$13$	7.53253	−	7.53253i	0.579426	−	0.579426i	−0.355319	−	0.934745i	$-0.615628\pi$
$13$	7.53253	−	7.53253i	0.579426	−	0.579426i	0.934745	+	0.355319i	$0.115628\pi$
$14$	−5.78801	−	19.8201i	−0.413429	−	1.41572i
$15$	13.5772	+	6.37658i	0.905144	+	0.425105i
$16$	−6.73229	+	14.5147i	−0.420768	+	0.907168i
$17$	0.350578	−	0.350578i	0.0206223	−	0.0206223i	−0.696720	−	0.717343i	$-0.745358\pi$
$17$	0.350578	−	0.350578i	0.0206223	−	0.0206223i	0.717343	+	0.696720i	$0.245358\pi$
$18$	16.1498	−	7.94877i	0.897213	−	0.441598i
$19$	−9.24359			−0.486505			−0.243252	−	0.969963i	$-0.578214\pi$
$19$	−9.24359			−0.486505			−0.243252	+	0.969963i	$0.578214\pi$
$20$	8.43269	+	18.1353i	0.421634	+	0.906766i
$21$	−27.4816	+	14.2837i	−1.30865	+	0.680175i
$22$	4.24523	−	7.74740i	0.192965	−	0.352154i
$23$	17.9810	−	17.9810i	0.781785	−	0.781785i	−0.198347	−	0.980132i	$-0.563557\pi$
$23$	17.9810	−	17.9810i	0.781785	−	0.781785i	0.980132	+	0.198347i	$0.0635573\pi$
$24$	23.3173	+	5.68370i	0.971553	+	0.236821i
$25$	24.1207	+	6.57212i	0.964827	+	0.262885i
$26$	−5.97225	−	20.4510i	−0.229702	−	0.786578i
$27$	−16.3954	−	21.4521i	−0.607237	−	0.794520i
$28$	−40.3261	−	8.89693i	−1.44022	−	0.317748i
$29$	−5.52099			−0.190379			−0.0951895	−	0.995459i	$-0.530346\pi$
$29$	−5.52099			−0.190379			−0.0951895	+	0.995459i	$0.530346\pi$
$30$	24.2329	−	17.6852i	0.807764	−	0.589505i
$31$			48.1716i			1.55392i	0.629548	+	0.776962i	$0.283240\pi$
$31$			48.1716i			1.55392i	−0.629548	+	0.776962i	$0.716760\pi$
$32$	18.9877	+	25.7579i	0.593365	+	0.804934i
$33$	−12.6355	−	3.99285i	−0.382894	−	0.120996i
$34$	−0.277960	−	0.951830i	−0.00817530	−	0.0279950i
$35$	−41.0189	+	31.3379i	−1.17197	+	0.895369i
$36$	1.57963	−	35.9653i	0.0438785	−	0.999037i
$37$	3.39462	+	3.39462i	0.0917466	+	0.0917466i	0.751491	−	0.659744i	$-0.229335\pi$
$37$	3.39462	+	3.39462i	0.0917466	+	0.0917466i	−0.659744	+	0.751491i	$0.729335\pi$
$38$	−8.88386	+	16.2127i	−0.233786	+	0.426651i
$39$	−28.3564	+	14.7383i	−0.727087	+	0.377906i
$40$	39.9128	+	2.63908i	0.997821	+	0.0659771i
$41$		−	33.0983i		−	0.807276i	−0.914919	−	0.403638i	$-0.867746\pi$
$41$		−	33.0983i		−	0.807276i	0.914919	−	0.403638i	$-0.132254\pi$
$42$	−1.35933	+	61.9290i	−0.0323650	+	1.47450i
$43$	−1.45103	−	1.45103i	−0.0337449	−	0.0337449i	0.690033	−	0.723778i	$-0.257596\pi$
$43$	−1.45103	−	1.45103i	−0.0337449	−	0.0337449i	−0.723778	+	0.690033i	$0.757596\pi$
$44$	−9.50848	−	14.8918i	−0.216102	−	0.338449i
$45$	−33.0744	−	30.5137i	−0.734986	−	0.678082i
$46$	−14.2565	−	48.8190i	−0.309923	−	1.06128i
$47$	−27.8943	−	27.8943i	−0.593496	−	0.593496i	0.345078	−	0.938574i	$-0.387853\pi$
$47$	−27.8943	−	27.8943i	−0.593496	−	0.593496i	−0.938574	+	0.345078i	$0.887853\pi$
$48$	32.3787	−	35.4347i	0.674557	−	0.738223i
$49$		−	57.5846i		−	1.17520i
$50$	34.7091	−	35.9900i	0.694182	−	0.719800i
$51$	−1.31976	+	0.685951i	−0.0258776	+	0.0134500i
$52$	−41.6098	−	9.18014i	−0.800188	−	0.176541i
$53$	52.6835	+	52.6835i	0.994028	+	0.994028i	0.999982	−	0.00595455i	$-0.00189540\pi$
$53$	52.6835	+	52.6835i	0.994028	+	0.994028i	−0.00595455	+	0.999982i	$0.501895\pi$
$54$	−53.3830	+	8.13943i	−0.988575	+	0.150730i
$55$	−21.8906	−	2.92886i	−0.398010	−	0.0532519i
$56$	−54.3615	+	62.1791i	−0.970741	+	1.11034i
$57$	26.4420	+	8.35573i	0.463894	+	0.146592i
$58$	−5.30613	+	9.68351i	−0.0914850	+	0.166957i
$59$			24.6578i			0.417929i	0.977923	+	0.208964i	$0.0670093\pi$
$59$			24.6578i			0.417929i	−0.977923	+	0.208964i	$0.932991\pi$
$60$	−7.72893	−	59.5001i	−0.128816	−	0.991669i
$61$	46.1739			0.756950			0.378475	−	0.925612i	$-0.376449\pi$
$61$	46.1739			0.756950			0.378475	+	0.925612i	$0.376449\pi$
$62$	84.4904	+	46.2969i	1.36275	+	0.746725i
$63$	91.5248	−	16.0176i	1.45277	−	0.254247i
$64$	63.4266	−	8.54787i	0.991041	−	0.133560i
$65$	−42.3246	+	32.3354i	−0.651148	+	0.497468i
$66$	−19.1470	+	18.3245i	−0.290106	+	0.277644i
$67$	32.1110	−	32.1110i	0.479269	−	0.479269i	−0.425629	−	0.904898i	$-0.639947\pi$
$67$	32.1110	−	32.1110i	0.479269	−	0.479269i	0.904898	+	0.425629i	$0.139947\pi$
$68$	−1.93660	−	0.427261i	−0.0284794	−	0.00628325i
$69$	−67.6900	+	35.1822i	−0.981015	+	0.509887i
$70$	15.5424	+	102.063i	0.222034	+	1.45805i
$71$	116.455			1.64021			0.820103	−	0.572216i	$-0.193916\pi$
$71$	116.455			1.64021			0.820103	+	0.572216i	$0.193916\pi$
$72$	−61.5630	−	37.3362i	−0.855042	−	0.518559i
$73$	−72.2123	+	72.2123i	−0.989210	+	0.989210i	−0.999942	−	0.0107324i	$-0.996584\pi$
$73$	−72.2123	+	72.2123i	−0.989210	+	0.989210i	0.0107324	+	0.999942i	$0.496584\pi$
$74$	9.21650	−	2.69147i	0.124547	−	0.0363712i
$75$	−63.0581	−	40.6039i	−0.840775	−	0.541385i
$76$	19.8981	+	31.1636i	0.261817	+	0.410047i
$77$	32.2457	−	32.2457i	0.418776	−	0.418776i
$78$	−1.40260	+	63.9003i	−0.0179821	+	0.819234i
$79$	55.9466			0.708185			0.354092	−	0.935210i	$-0.384790\pi$
$79$	55.9466			0.708185			0.354092	+	0.935210i	$0.384790\pi$
$80$	42.9884	−	67.4685i	0.537354	−	0.843357i
$81$	27.5087	+	76.1858i	0.339614	+	0.940565i
$82$	−58.0526	−	31.8102i	−0.707958	−	0.387929i
$83$	−46.5302	+	46.5302i	−0.560605	+	0.560605i	−0.929479	−	0.368874i	$-0.879743\pi$
$83$	−46.5302	+	46.5302i	−0.560605	+	0.560605i	0.368874	+	0.929479i	$0.379743\pi$
$84$	107.314	+	61.9031i	1.27754	+	0.736941i
$85$	−1.96987	+	1.50495i	−0.0231749	+	0.0177053i
$86$	−3.93959	+	1.15047i	−0.0458092	+	0.0133775i
$87$	15.7932	+	4.99069i	0.181531	+	0.0573642i
$88$	−35.2578	+	2.36512i	−0.400657	+	0.0268763i
$89$	33.2025			0.373062			0.186531	−	0.982449i	$-0.440276\pi$
$89$	33.2025			0.373062			0.186531	+	0.982449i	$0.440276\pi$
$90$	−85.3065	+	28.6844i	−0.947850	+	0.318715i
$91$		−	109.977i		−	1.20854i
$92$	−99.3275	−	21.9141i	−1.07965	−	0.238196i
$93$	43.5447	−	137.798i	0.468222	−	1.48170i
$94$	−75.7338	+	22.1163i	−0.805679	+	0.235280i
$95$	45.8098	+	6.12913i	0.482208	+	0.0645172i
$96$	−31.0319	−	90.8462i	−0.323248	−	0.946314i
$97$	−24.6341	−	24.6341i	−0.253959	−	0.253959i	0.568632	−	0.822592i	$-0.307473\pi$
$97$	−24.6341	−	24.6341i	−0.253959	−	0.253959i	−0.822592	+	0.568632i	$0.807473\pi$
$98$	−101.000	−	55.3436i	−1.03061	−	0.564730i
$99$	32.5355	+	22.8437i	0.328641	+	0.230744i
$100$	−29.7661	−	95.4672i	−0.297661	−	0.954672i
$101$		−	12.2683i		−	0.121468i	−0.998154	−	0.0607342i	$-0.980656\pi$
$101$		−	12.2683i		−	0.121468i	0.998154	−	0.0607342i	$-0.0193442\pi$
$102$	−0.0652797	+	2.97404i	−0.000639997	+	0.0291573i
$103$	−21.2333	−	21.2333i	−0.206149	−	0.206149i	0.596479	−	0.802628i	$-0.296566\pi$
$103$	−21.2333	−	21.2333i	−0.206149	−	0.206149i	−0.802628	+	0.596479i	$0.796566\pi$
$104$	−56.0919	+	64.1584i	−0.539345	+	0.616907i
$105$	145.665	−	52.5654i	1.38729	−	0.500623i
$106$	143.037	−	41.7707i	1.34941	−	0.394063i
$107$	−77.4288	−	77.4288i	−0.723634	−	0.723634i	0.245710	−	0.969343i	$-0.420979\pi$
$107$	−77.4288	−	77.4288i	−0.723634	−	0.723634i	−0.969343	+	0.245710i	$0.920979\pi$
$108$	−37.0294	+	101.454i	−0.342865	+	0.939385i
$109$			62.5243i			0.573618i	0.957988	+	0.286809i	$0.0925945\pi$
$109$			62.5243i			0.573618i	−0.957988	+	0.286809i	$0.907406\pi$
$110$	−26.1757	+	35.5800i	−0.237961	+	0.323454i
$111$	−6.64201	−	12.7791i	−0.0598379	−	0.115127i
$112$	56.8128	+	155.106i	0.507257	+	1.38488i
$113$	−64.0685	−	64.0685i	−0.566977	−	0.566977i	0.364303	−	0.931280i	$-0.381307\pi$
$113$	−64.0685	−	64.0685i	−0.566977	−	0.566977i	−0.931280	+	0.364303i	$0.881307\pi$
$114$	40.0684	−	38.3472i	0.351477	−	0.336379i
$115$	−101.034	+	77.1885i	−0.878555	+	0.671205i
$116$	11.8847	+	18.6133i	0.102454	+	0.160460i
$117$	94.4382	−	16.5274i	0.807164	−	0.141260i
$118$	43.2484	+	23.6982i	0.366512	+	0.200832i
$119$		−	5.11856i		−	0.0430131i
$120$	−111.788	−	43.6284i	−0.931567	−	0.363570i
$121$	−101.489			−0.838752
$122$	44.3770	−	80.9865i	0.363746	−	0.663824i
$123$	−29.9191	+	94.6801i	−0.243245	+	0.769757i
$124$	162.404	−	103.696i	1.30971	−	0.836259i
$125$	−115.180	−	48.5640i	−0.921444	−	0.388512i
$126$	59.8690	−	175.924i	0.475151	−	1.39622i
$127$	−36.2102	+	36.2102i	−0.285120	+	0.285120i	−0.835147	−	0.550027i	$-0.814617\pi$
$127$	−36.2102	+	36.2102i	−0.285120	+	0.285120i	0.550027	+	0.835147i	$0.314617\pi$
$128$	45.9657	−	119.462i	0.359107	−	0.933296i
$129$	2.83912	+	5.46244i	0.0220087	+	0.0423445i
$130$	16.0371	+	105.312i	0.123362	+	0.810092i
$131$	−78.8270			−0.601733			−0.300866	−	0.953666i	$-0.597276\pi$
$131$	−78.8270			−0.601733			−0.300866	+	0.953666i	$0.597276\pi$
$132$	13.7383	+	51.1942i	0.104078	+	0.387835i
$133$	−67.4797	+	67.4797i	−0.507366	+	0.507366i
$134$	−25.4596	−	87.1822i	−0.189997	−	0.650614i
$135$	67.0288	+	117.184i	0.496510	+	0.868031i
$136$	−2.61062	+	2.98605i	−0.0191958	+	0.0219563i
$137$	−178.746	+	178.746i	−1.30472	+	1.30472i	−0.379544	+	0.925174i	$0.623919\pi$
$137$	−178.746	+	178.746i	−1.30472	+	1.30472i	−0.925174	+	0.379544i	$0.876081\pi$
$138$	−3.34817	+	152.538i	−0.0242621	+	1.10534i
$139$	−15.4896			−0.111436			−0.0557180	−	0.998447i	$-0.517745\pi$
$139$	−15.4896			−0.111436			−0.0557180	+	0.998447i	$0.517745\pi$
$140$	193.951	+	70.8307i	1.38536	+	0.505934i
$141$	54.5787	+	105.009i	0.387083	+	0.744743i
$142$	111.922	−	204.255i	0.788187	−	1.43841i
$143$	33.2722	−	33.2722i	0.232672	−	0.232672i
$144$	−124.653	+	72.0949i	−0.865645	+	0.500659i
$145$	27.3611	+	3.66079i	0.188698	+	0.0252468i
$146$	57.2544	+	196.058i	0.392153	+	1.34287i
$147$	−52.0535	+	164.725i	−0.354105	+	1.12058i
$148$	4.13714	−	18.7519i	0.0279536	−	0.126702i
$149$	209.818			1.40817			0.704086	−	0.710115i	$-0.251357\pi$
$149$	209.818			1.40817			0.704086	+	0.710115i	$0.251357\pi$
$150$	−131.821	+	71.5767i	−0.878807	+	0.477178i
$151$			144.169i			0.954759i	0.878697	+	0.477380i	$0.158413\pi$
$151$			144.169i			0.954759i	−0.878697	+	0.477380i	$0.841587\pi$
$152$	73.7829	−	4.94941i	0.485414	−	0.0325619i
$153$	4.39533	−	0.769217i	0.0287277	−	0.00502756i
$154$	−25.5664	−	87.5480i	−0.166016	−	0.568494i
$155$	31.9411	−	238.731i	0.206071	−	1.54020i
$156$	110.729	+	63.8735i	0.709804	+	0.409446i
$157$	−161.893	−	161.893i	−1.03117	−	1.03117i	−0.999498	−	0.0316669i	$-0.989918\pi$
$157$	−161.893	−	161.893i	−1.03117	−	1.03117i	−0.0316669	−	0.999498i	$-0.510082\pi$
$158$	53.7693	−	98.1272i	0.340312	−	0.621058i
$159$	−103.082	−	198.328i	−0.648313	−	1.24735i
$160$	−77.0206	−	140.242i	−0.481379	−	0.876513i
$161$		−	262.529i		−	1.63061i
$162$	160.064	+	24.9721i	0.988048	+	0.154149i
$163$	19.4060	+	19.4060i	0.119055	+	0.119055i	0.764124	−	0.645069i	$-0.223171\pi$
$163$	19.4060	+	19.4060i	0.119055	+	0.119055i	−0.645069	+	0.764124i	$0.723171\pi$
$164$	−111.587	+	71.2487i	−0.680406	+	0.434443i
$165$	59.9721	+	28.1661i	0.363467	+	0.170704i
$166$	36.8920	+	126.331i	0.222241	+	0.761029i
$167$	183.816	+	183.816i	1.10069	+	1.10069i	0.994327	+	0.106366i	$0.0339216\pi$
$167$	183.816	+	183.816i	1.10069	+	1.10069i	0.106366	+	0.994327i	$0.466078\pi$
$168$	211.712	−	128.728i	1.26019	−	0.766238i
$169$			55.5219i			0.328532i
$170$	0.746397	+	4.90142i	0.00439057	+	0.0288319i
$171$	−68.0861	−	47.8043i	−0.398164	−	0.279558i
$172$	−1.76842	+	8.01551i	−0.0102815	+	0.0466018i
$173$	198.939	+	198.939i	1.14993	+	1.14993i	0.986565	+	0.163370i	$0.0522364\pi$
$173$	198.939	+	198.939i	1.14993	+	1.14993i	0.163370	+	0.986565i	$0.447764\pi$
$174$	23.9320	−	22.9039i	0.137540	−	0.131632i
$175$	224.062	−	128.107i	1.28036	−	0.732042i
$176$	−29.7374	+	64.1133i	−0.168962	+	0.364280i
$177$	22.2894	−	70.5354i	0.125929	−	0.398505i
$178$	31.9103	−	58.2353i	0.179272	−	0.327165i
$179$			167.155i			0.933828i	0.884303	+	0.466914i	$0.154634\pi$
$179$			167.155i			0.933828i	−0.884303	+	0.466914i	$0.845366\pi$
$180$	−31.6758	+	177.191i	−0.175977	+	0.984394i
$181$	46.3698			0.256187			0.128093	−	0.991762i	$-0.459114\pi$
$181$	46.3698			0.256187			0.128093	+	0.991762i	$0.459114\pi$
$182$	−192.894	−	105.697i	−1.05986	−	0.580755i
$183$	−132.084	−	41.7388i	−0.721770	−	0.228081i
$184$	−133.898	+	153.154i	−0.727707	+	0.832357i
$185$	−14.5723	−	19.0741i	−0.0787694	−	0.103103i
$186$	−199.841	−	208.811i	−1.07441	−	1.12264i
$187$	1.54855	−	1.54855i	0.00828102	−	0.00828102i
$188$	−33.9957	+	154.089i	−0.180828	+	0.819620i
$189$	−276.292	−	36.9143i	−1.46186	−	0.195314i
$190$	54.7771	−	74.4572i	0.288301	−	0.391880i
$191$	−299.293			−1.56698			−0.783490	−	0.621405i	$-0.786562\pi$
$191$	−299.293			−1.56698			−0.783490	+	0.621405i	$0.786562\pi$
$192$	−189.163	−	32.8825i	−0.985225	−	0.171263i
$193$	207.042	−	207.042i	1.07276	−	1.07276i	0.0756225	−	0.997137i	$-0.475906\pi$
$193$	207.042	−	207.042i	1.07276	−	1.07276i	0.997137	−	0.0756225i	$-0.0240944\pi$
$194$	−66.8821	+	19.5314i	−0.344753	+	0.100677i
$195$	150.302	−	54.2386i	0.770780	−	0.278147i
$196$	−194.139	+	123.959i	−0.990505	+	0.632443i
$197$	5.31992	−	5.31992i	0.0270047	−	0.0270047i	−0.693476	−	0.720480i	$-0.743921\pi$
$197$	5.31992	−	5.31992i	0.0270047	−	0.0270047i	0.720480	+	0.693476i	$0.243921\pi$
$198$	71.3359	−	35.1107i	0.360282	−	0.177327i
$199$	−61.5955			−0.309525			−0.154762	−	0.987952i	$-0.549461\pi$
$199$	−61.5955			−0.309525			−0.154762	+	0.987952i	$0.549461\pi$
$200$	−196.052	−	39.5438i	−0.980259	−	0.197719i
$201$	−120.883	+	62.8292i	−0.601406	+	0.312583i
$202$	−21.5179	−	11.7909i	−0.106524	−	0.0583706i
$203$	−40.3041	+	40.3041i	−0.198542	+	0.198542i
$204$	5.15356	+	2.97280i	0.0252626	+	0.0145725i
$205$	−21.9464	+	164.030i	−0.107056	+	0.800146i
$206$	−57.6491	+	16.8351i	−0.279850	+	0.0817237i
$207$	225.435	−	39.4529i	1.08906	−	0.190594i
$208$	58.6212	+	160.044i	0.281833	+	0.769440i
$209$	−40.8301			−0.195360
$210$	47.7997	−	306.009i	0.227618	−	1.45718i
$211$		−	184.930i		−	0.876444i	−0.898867	−	0.438222i	$-0.855608\pi$
$211$		−	184.930i		−	0.876444i	0.898867	−	0.438222i	$-0.144392\pi$
$212$	64.2070	−	291.024i	0.302863	−	1.37275i
$213$	−333.127	−	105.269i	−1.56398	−	0.494220i
$214$	−210.221	+	61.3903i	−0.982343	+	0.286871i
$215$	6.22894	+	8.15321i	0.0289718	+	0.0379219i
$216$	142.356	+	162.453i	0.659053	+	0.752096i
$217$	351.661	+	351.661i	1.62056	+	1.62056i
$218$	109.664	+	60.0911i	0.503047	+	0.275647i
$219$	271.845	−	141.292i	1.24130	−	0.645171i
$220$	37.2483	+	80.1060i	0.169310	+	0.364118i
$221$		−	5.28149i		−	0.0238981i
$222$	−28.7974	−	0.632098i	−0.129718	−	0.00284729i
$223$	−206.560	−	206.560i	−0.926280	−	0.926280i	0.0711833	−	0.997463i	$-0.477322\pi$
$223$	−206.560	−	206.560i	−0.926280	−	0.926280i	−0.997463	+	0.0711833i	$0.977322\pi$
$224$	326.650	+	49.4235i	1.45826	+	0.220641i
$225$	143.679	+	173.152i	0.638571	+	0.769563i
$226$	−173.948	+	50.7974i	−0.769680	+	0.224767i
$227$	174.751	+	174.751i	0.769827	+	0.769827i	0.978076	−	0.208249i	$-0.0667763\pi$
$227$	174.751	+	174.751i	0.769827	+	0.769827i	−0.208249	+	0.978076i	$0.566776\pi$
$228$	−28.7498	−	107.133i	−0.126096	−	0.469880i
$229$		−	287.354i		−	1.25482i	−0.778689	−	0.627410i	$-0.784115\pi$
$229$		−	287.354i		−	1.25482i	0.778689	−	0.627410i	$-0.215885\pi$
$230$	38.2825	+	251.392i	0.166446	+	1.09301i
$231$	−121.390	+	63.0928i	−0.525497	+	0.273129i
$232$	44.0689	−	2.95617i	0.189952	−	0.0127421i
$233$	1.51498	+	1.51498i	0.00650206	+	0.00650206i	0.710350	−	0.703848i	$-0.248537\pi$
$233$	1.51498	+	1.51498i	0.00650206	+	0.00650206i	−0.703848	+	0.710350i	$0.748537\pi$
$234$	61.7748	−	181.524i	0.263995	−	0.775742i
$235$	119.744	+	156.736i	0.509549	+	0.666960i
$236$	83.1306	−	53.0794i	0.352248	−	0.224913i
$237$	−160.039	−	50.5728i	−0.675271	−	0.213387i
$238$	−8.97766	−	4.91936i	−0.0377213	−	0.0206696i
$239$		−	271.429i		−	1.13569i	−0.823137	−	0.567843i	$-0.807778\pi$
$239$		−	271.429i		−	1.13569i	0.823137	−	0.567843i	$-0.192222\pi$
$240$	−183.959	+	154.139i	−0.766497	+	0.642247i
$241$	122.522			0.508390			0.254195	−	0.967153i	$-0.418190\pi$
$241$	122.522			0.508390			0.254195	+	0.967153i	$0.418190\pi$
$242$	−97.5393	+	178.006i	−0.403055	+	0.735562i
$243$	−9.82275	−	242.801i	−0.0404229	−	0.999183i
$244$	−99.3959	−	155.669i	−0.407360	−	0.637990i
$245$	−38.1825	+	285.380i	−0.155847	+	1.16482i
$246$	137.309	+	143.472i	0.558166	+	0.583219i
$247$	−69.6277	+	69.6277i	−0.281893	+	0.281893i
$248$	−25.7931	−	384.509i	−0.104005	−	1.55044i
$249$	175.164	−	91.0422i	0.703470	−	0.365631i
$250$	−195.877	+	155.346i	−0.783506	+	0.621384i
$251$	335.099			1.33506			0.667529	−	0.744584i	$-0.267352\pi$
$251$	335.099			1.33506			0.667529	+	0.744584i	$0.267352\pi$
$252$	−251.021	−	274.084i	−0.996115	−	1.08764i
$253$	79.4246	−	79.4246i	0.313931	−	0.313931i
$254$	28.7097	+	98.3118i	0.113030	+	0.387054i
$255$	6.99535	−	2.52437i	0.0274327	−	0.00989949i
$256$	−165.353	−	195.434i	−0.645909	−	0.763415i
$257$	−11.3695	+	11.3695i	−0.0442393	+	0.0442393i	−0.728880	−	0.684641i	$-0.759959\pi$
$257$	−11.3695	+	11.3695i	−0.0442393	+	0.0442393i	0.684641	+	0.728880i	$0.259959\pi$
$258$	12.3094	+	0.270190i	0.0477110	+	0.00104725i
$259$	49.5626			0.191361
$260$	200.124	+	73.0854i	0.769709	+	0.281098i
$261$	−40.6663	−	28.5525i	−0.155809	−	0.109396i
$262$	−75.7593	+	138.258i	−0.289158	+	0.527703i
$263$	−211.355	+	211.355i	−0.803631	+	0.803631i	−0.983661	−	0.180030i	$-0.942380\pi$
$263$	−211.355	+	211.355i	−0.803631	+	0.803631i	0.180030	+	0.983661i	$0.442380\pi$
$264$	102.995	+	25.1056i	0.390134	+	0.0950970i
$265$	−226.158	−	296.024i	−0.853427	−	1.11707i
$266$	53.5020	+	183.209i	0.201135	+	0.688756i
$267$	−94.9781	−	30.0133i	−0.355723	−	0.112409i
$268$	−177.382	−	39.1347i	−0.661871	−	0.146025i
$269$	174.453			0.648523			0.324261	−	0.945968i	$-0.394884\pi$
$269$	174.453			0.648523			0.324261	+	0.945968i	$0.394884\pi$
$270$	269.955	−	4.94112i	0.999833	−	0.0183004i
$271$			189.665i			0.699869i	0.936774	+	0.349935i	$0.113796\pi$
$271$			189.665i			0.699869i	−0.936774	+	0.349935i	$0.886204\pi$
$272$	2.72834	+	7.44873i	0.0100307	+	0.0273850i
$273$	−99.4138	+	314.598i	−0.364153	+	1.15237i
$274$	141.721	+	485.301i	0.517230	+	1.77117i
$275$	106.544	+	29.0299i	0.387433	+	0.105563i
$276$	264.324	+	152.474i	0.957697	+	0.552441i
$277$	46.8665	+	46.8665i	0.169193	+	0.169193i	0.786625	−	0.617431i	$-0.211827\pi$
$277$	46.8665	+	46.8665i	0.169193	+	0.169193i	−0.617431	+	0.786625i	$0.711827\pi$
$278$	−14.8868	+	27.1679i	−0.0535496	+	0.0977263i
$279$	−249.125	+	354.821i	−0.892922	+	1.27176i
$280$	310.636	−	272.104i	1.10941	−	0.971801i
$281$		−	266.157i		−	0.947179i	−0.880746	−	0.473590i	$-0.842958\pi$
$281$		−	266.157i		−	0.947179i	0.880746	−	0.473590i	$-0.157042\pi$
$282$	236.634	+	5.19408i	0.839128	+	0.0184187i
$283$	370.389	+	370.389i	1.30880	+	1.30880i	0.922285	+	0.386512i	$0.126320\pi$
$283$	370.389	+	370.389i	1.30880	+	1.30880i	0.386512	+	0.922285i	$0.373680\pi$
$284$	−250.685	−	392.612i	−0.882693	−	1.38244i
$285$	−125.502	−	58.9425i	−0.440357	−	0.206816i
$286$	−26.3802	−	90.3348i	−0.0922385	−	0.315856i
$287$	−241.623	−	241.623i	−0.841891	−	0.841891i
$288$	6.64869	+	287.923i	0.0230857	+	0.999733i
$289$			288.754i			0.999149i
$290$	32.7171	−	44.4716i	0.112818	−	0.153350i
$291$	48.1996	+	92.7354i	0.165634	+	0.318678i
$292$	398.902	+	88.0074i	1.36610	+	0.301395i
$293$	−50.2973	−	50.2973i	−0.171663	−	0.171663i	0.616047	−	0.787710i	$-0.288733\pi$
$293$	−50.2973	−	50.2973i	−0.171663	−	0.171663i	−0.787710	+	0.616047i	$0.788733\pi$
$294$	238.891	+	249.613i	0.812553	+	0.849025i
$295$	16.3498	−	122.200i	0.0554230	−	0.414238i
$296$	−28.9137	−	25.2785i	−0.0976815	−	0.0854003i
$297$	−72.4206	−	94.7565i	−0.243840	−	0.319045i
$298$	201.652	−	368.008i	0.676685	−	1.23493i
$299$		−	270.886i		−	0.905972i
$300$	−1.14928	+	299.998i	−0.00383092	+	0.999993i
$301$	−21.1855			−0.0703838
$302$	252.864	+	138.558i	0.837297	+	0.458801i
$303$	−11.0899	+	35.0944i	−0.0366004	+	0.115823i
$304$	62.2305	−	134.168i	0.204706	−	0.441342i
$305$	−228.831	−	30.6165i	−0.750264	−	0.100382i
$306$	2.87512	−	8.44845i	0.00939580	−	0.0276093i
$307$	−295.562	+	295.562i	−0.962741	+	0.962741i	−0.999330	−	0.0365891i	$-0.988351\pi$
$307$	−295.562	+	295.562i	−0.962741	+	0.962741i	0.0365891	+	0.999330i	$0.488351\pi$
$308$	−178.126	−	39.2989i	−0.578330	−	0.127594i
$309$	41.5457	+	79.9333i	0.134452	+	0.258684i
$310$	−388.023	−	285.463i	−1.25169	−	0.920848i
$311$	−168.540			−0.541930			−0.270965	−	0.962589i	$-0.587343\pi$
$311$	−168.540			−0.541930			−0.270965	+	0.962589i	$0.587343\pi$
$312$	218.451	−	132.826i	0.700163	−	0.425723i
$313$	139.822	−	139.822i	0.446717	−	0.446717i	−0.447545	−	0.894262i	$-0.647701\pi$
$313$	139.822	−	139.822i	0.446717	−	0.446717i	0.894262	+	0.447545i	$0.147701\pi$
$314$	−439.544	+	128.359i	−1.39982	+	0.408786i
$315$	−464.203	+	18.6932i	−1.47366	+	0.0593436i
$316$	−120.433	−	188.617i	−0.381117	−	0.596888i
$317$	168.037	−	168.037i	0.530086	−	0.530086i	−0.390512	−	0.920598i	$-0.627702\pi$
$317$	168.037	−	168.037i	0.530086	−	0.530086i	0.920598	+	0.390512i	$0.127702\pi$
$318$	−446.926	−	9.80996i	−1.40543	−	0.0308489i
$319$	−24.3869			−0.0764480
$320$	−320.000	+	0.305719i	−1.00000	+	0.000955372i
$321$	151.499	+	291.482i	0.471960	+	0.908045i
$322$	−460.461	−	252.312i	−1.43000	−	0.783578i
$323$	−3.24061	+	3.24061i	−0.0100328	+	0.0100328i
$324$	197.634	−	256.743i	0.609982	−	0.792415i
$325$	231.195	−	132.185i	0.711368	−	0.406724i
$326$	52.6878	−	15.3863i	0.161619	−	0.0471971i
$327$	56.5187	−	178.855i	0.172840	−	0.546958i
$328$	17.7222	+	264.193i	0.0540312	+	0.805465i
$329$	−407.266			−1.23789
$330$	107.040	−	78.1176i	0.324364	−	0.236720i
$331$		−	278.549i		−	0.841538i	−0.907168	−	0.420769i	$-0.861760\pi$
$331$		−	278.549i		−	0.841538i	0.907168	−	0.420769i	$-0.138240\pi$
$332$	257.034	+	56.7079i	0.774197	+	0.170807i
$333$	7.44827	+	42.5597i	0.0223672	+	0.127807i
$334$	499.065	−	145.740i	1.49421	−	0.436349i
$335$	−180.429	+	137.845i	−0.538593	+	0.411478i
$336$	−22.3091	−	495.049i	−0.0663963	−	1.47336i
$337$	−371.125	−	371.125i	−1.10126	−	1.10126i	−0.994259	−	0.107001i	$-0.965875\pi$
$337$	−371.125	−	371.125i	−1.10126	−	1.10126i	−0.107001	−	0.994259i	$-0.534125\pi$
$338$	97.3823	+	53.3611i	0.288113	+	0.157873i
$339$	125.358	+	241.187i	0.369787	+	0.711466i
$340$	9.31417	+	3.40153i	0.0273946	+	0.0100045i
$341$			212.780i			0.623989i
$342$	−149.282	+	73.4752i	−0.436498	+	0.214840i
$343$	−62.6689	−	62.6689i	−0.182708	−	0.182708i
$344$	12.3592	+	10.8053i	0.0359278	+	0.0314107i
$345$	358.789	−	129.474i	1.03997	−	0.375287i
$346$	540.124	−	157.731i	1.56105	−	0.455869i
$347$	−160.180	−	160.180i	−0.461613	−	0.461613i	0.437571	−	0.899184i	$-0.355839\pi$
$347$	−160.180	−	160.180i	−0.461613	−	0.461613i	−0.899184	+	0.437571i	$0.855839\pi$
$348$	−17.1716	−	63.9879i	−0.0493437	−	0.183873i
$349$			395.209i			1.13240i	0.824266	+	0.566202i	$0.191588\pi$
$349$			395.209i			1.13240i	−0.824266	+	0.566202i	$0.808412\pi$
$350$	−9.35063	−	516.114i	−0.0267161	−	1.47461i
$351$	−285.087	−	38.0893i	−0.812214	−	0.108517i
$352$	83.8710	+	113.776i	0.238270	+	0.323227i
$353$	−143.113	−	143.113i	−0.405418	−	0.405418i	0.474719	−	0.880137i	$-0.342550\pi$
$353$	−143.113	−	143.113i	−0.405418	−	0.405418i	−0.880137	+	0.474719i	$0.842550\pi$
$354$	−102.293	−	106.885i	−0.288964	−	0.301934i
$355$	−577.130	−	77.2173i	−1.62572	−	0.217514i
$356$	−71.4730	−	111.938i	−0.200767	−	0.314432i
$357$	−4.62691	+	14.6420i	−0.0129605	+	0.0410140i
$358$	293.181	+	160.650i	0.818941	+	0.448743i
$359$			388.897i			1.08328i	0.840611	+	0.541639i	$0.182196\pi$
$359$			388.897i			1.08328i	−0.840611	+	0.541639i	$0.817804\pi$
$360$	280.340	+	225.853i	0.778722	+	0.627369i
$361$	−275.556			−0.763313
$362$	44.5652	−	81.3301i	0.123108	−	0.224669i
$363$	290.317	+	91.7408i	0.799770	+	0.252729i
$364$	−370.774	+	236.742i	−1.01861	+	0.650389i
$365$	405.754	−	309.991i	1.11166	−	0.849290i
$366$	−200.151	+	191.553i	−0.546861	+	0.523370i
$367$	361.520	−	361.520i	0.985069	−	0.985069i	−0.0148215	−	0.999890i	$-0.504718\pi$
$367$	361.520	−	361.520i	0.985069	−	0.985069i	0.999890	+	0.0148215i	$0.00471801\pi$
$368$	139.936	+	382.043i	0.380260	+	1.03816i
$369$	171.172	−	243.794i	0.463880	−	0.660688i
$370$	−47.4601	+	7.22731i	−0.128271	+	0.0195333i
$371$	769.195			2.07330
$372$	−558.306	+	149.825i	−1.50082	+	0.402756i
$373$	−104.714	+	104.714i	−0.280735	+	0.280735i	−0.833402	−	0.552667i	$-0.813610\pi$
$373$	−104.714	+	104.714i	−0.280735	+	0.280735i	0.552667	+	0.833402i	$0.313610\pi$
$374$	−1.22779	−	4.20435i	−0.00328285	−	0.0112416i
$375$	285.583	+	243.038i	0.761554	+	0.648101i
$376$	237.590	+	207.718i	0.631888	+	0.552442i
$377$	−41.5870	+	41.5870i	−0.110310	+	0.110310i
$378$	−330.286	+	449.124i	−0.873771	+	1.18816i
$379$	40.1346			0.105896			0.0529480	−	0.998597i	$-0.483138\pi$
$379$	40.1346			0.105896			0.0529480	+	0.998597i	$0.483138\pi$
$380$	−77.9483	−	167.636i	−0.205127	−	0.441146i
$381$	136.314	−	70.8499i	0.357780	−	0.185958i
$382$	−287.645	+	524.943i	−0.752998	+	1.37420i
$383$	340.574	−	340.574i	0.889226	−	0.889226i	−0.105223	−	0.994449i	$-0.533556\pi$
$383$	340.574	−	340.574i	0.889226	−	0.889226i	0.994449	+	0.105223i	$0.0335556\pi$
$384$	−239.476	+	300.179i	−0.623635	+	0.781716i
$385$	−181.186	+	138.424i	−0.470612	+	0.359542i
$386$	−164.156	−	562.126i	−0.425275	−	1.45628i
$387$	−3.18376	−	18.1921i	−0.00822678	−	0.0470081i
$388$	−30.0223	+	136.079i	−0.0773771	+	0.350719i
$389$	−98.4019			−0.252961			−0.126481	−	0.991969i	$-0.540368\pi$
$389$	−98.4019			−0.252961			−0.126481	+	0.991969i	$0.540368\pi$
$390$	49.3213	−	315.749i	0.126465	−	0.809614i
$391$		−	12.6075i		−	0.0322443i
$392$	30.8332	+	459.644i	0.0786562	+	1.17256i
$393$	225.490	+	71.2555i	0.573767	+	0.181312i
$394$	−4.21796	−	14.4437i	−0.0107055	−	0.0366592i
$395$	−277.262	−	37.0964i	−0.701930	−	0.0939149i
$396$	6.97741	−	158.863i	0.0176197	−	0.401170i
$397$	323.459	+	323.459i	0.814758	+	0.814758i	0.985343	−	0.170585i	$-0.0545658\pi$
$397$	323.459	+	323.459i	0.814758	+	0.814758i	−0.170585	+	0.985343i	$0.554566\pi$
$398$	−59.1983	+	108.035i	−0.148740	+	0.271445i
$399$	254.029	−	132.032i	0.636663	−	0.330908i
$400$	−257.780	+	305.859i	−0.644449	+	0.764647i
$401$			648.291i			1.61669i	0.588712	+	0.808343i	$0.299635\pi$
$401$			648.291i			1.61669i	−0.588712	+	0.808343i	$0.700365\pi$
$402$	−5.97925	+	272.405i	−0.0148738	+	0.677625i
$403$	362.854	+	362.854i	0.900383	+	0.900383i
$404$	−41.3610	+	26.4092i	−0.102379	+	0.0653694i
$405$	−85.8125	−	395.805i	−0.211883	−	0.977295i
$406$	31.9556	+	109.427i	0.0787083	+	0.269524i
$407$	14.9945	+	14.9945i	0.0368415	+	0.0368415i
$408$	10.1671	−	6.18196i	0.0249194	−	0.0151519i
$409$		−	13.9598i		−	0.0341315i	−0.999854	−	0.0170658i	$-0.994568\pi$
$409$		−	13.9598i		−	0.0341315i	0.999854	−	0.0170658i	$-0.00543247\pi$
$410$	266.607	+	196.139i	0.650261	+	0.478388i
$411$	672.894	−	349.740i	1.63721	−	0.850948i
$412$	−25.8777	+	117.293i	−0.0628100	+	0.284692i
$413$	180.006	+	180.006i	0.435849	+	0.435849i
$414$	147.464	−	433.318i	0.356192	−	1.04666i
$415$	261.449	−	199.744i	0.629998	−	0.481310i
$416$	337.047	+	50.9968i	0.810210	+	0.122588i
$417$	44.3092	+	14.0018i	0.106257	+	0.0335775i
$418$	−39.2411	+	71.6138i	−0.0938783	+	0.171325i
$419$			317.783i			0.758433i	0.925308	+	0.379216i	$0.123806\pi$
$419$			317.783i			0.758433i	−0.925308	+	0.379216i	$0.876194\pi$
$420$	−490.783	−	377.938i	−1.16853	−	0.899852i
$421$	−56.9987			−0.135389			−0.0676944	−	0.997706i	$-0.521564\pi$
$421$	−56.9987			−0.135389			−0.0676944	+	0.997706i	$0.521564\pi$
$422$	−324.356	−	177.733i	−0.768617	−	0.421168i
$423$	−61.2040	−	349.722i	−0.144690	−	0.826765i
$424$	−448.732	−	392.314i	−1.05833	−	0.925268i
$425$	10.7602	−	6.15215i	0.0253182	−	0.0144756i
$426$	−504.798	+	483.114i	−1.18497	+	1.13407i
$427$	337.077	−	337.077i	0.789408	−	0.789408i
$428$	−94.3649	+	427.718i	−0.220479	+	0.999340i
$429$	−125.254	+	65.1011i	−0.291967	+	0.151751i
$430$	20.2868	−	3.08931i	0.0471786	−	0.00718444i
$431$	−146.371			−0.339607			−0.169803	−	0.985478i	$-0.554313\pi$
$431$	−146.371			−0.339607			−0.169803	+	0.985478i	$0.554313\pi$
$432$	421.749	−	93.5530i	0.976270	−	0.216558i
$433$	−425.454	+	425.454i	−0.982572	+	0.982572i	−0.999851	−	0.0172788i	$-0.994500\pi$
$433$	−425.454	+	425.454i	−0.982572	+	0.982572i	0.0172788	+	0.999851i	$0.494500\pi$
$434$	954.768	−	278.818i	2.19993	−	0.642438i
$435$	−74.9594	−	35.2050i	−0.172320	−	0.0809311i
$436$	210.793	−	134.592i	0.483470	−	0.308698i
$437$	−166.210	+	166.210i	−0.380342	+	0.380342i
$438$	13.4463	−	612.594i	0.0306994	−	1.39862i
$439$	−679.724			−1.54835			−0.774173	−	0.632974i	$-0.781834\pi$
$439$	−679.724			−1.54835			−0.774173	+	0.632974i	$0.781834\pi$
$440$	176.300	+	11.6572i	0.400682	+	0.0264936i
$441$	297.806	−	424.154i	0.675296	−	0.961801i
$442$	−9.26343	−	5.07595i	−0.0209580	−	0.0114840i
$443$	192.731	−	192.731i	0.435059	−	0.435059i	−0.455286	−	0.890345i	$-0.650463\pi$
$443$	192.731	−	192.731i	0.435059	−	0.435059i	0.890345	+	0.455286i	$0.150463\pi$
$444$	−28.7854	+	49.9015i	−0.0648319	+	0.112391i
$445$	−164.546	−	22.0155i	−0.369767	−	0.0494730i
$446$	−560.817	+	163.774i	−1.25744	+	0.367206i
$447$	−600.199	−	189.664i	−1.34273	−	0.424305i
$448$	400.623	−	525.425i	0.894249	−	1.17282i
$449$	167.799			0.373717			0.186859	−	0.982387i	$-0.440169\pi$
$449$	167.799			0.373717			0.186859	+	0.982387i	$0.440169\pi$
$450$	441.785	−	85.5912i	0.981745	−	0.190203i
$451$		−	146.199i		−	0.324167i
$452$	−78.0822	+	353.915i	−0.172748	+	0.782997i
$453$	130.321	−	412.405i	0.287684	−	0.910386i
$454$	474.453	−	138.553i	1.04505	−	0.305183i
$455$	−72.9225	+	545.030i	−0.160269	+	1.19787i
$456$	−215.535	−	52.5378i	−0.472666	−	0.115214i
$457$	−124.480	−	124.480i	−0.272385	−	0.272385i	0.557674	−	0.830060i	$-0.311694\pi$
$457$	−124.480	−	124.480i	−0.272385	−	0.272385i	−0.830060	+	0.557674i	$0.811694\pi$
$458$	−504.002	−	276.171i	−1.10044	−	0.602993i
$459$	−13.2685	−	1.77275i	−0.0289074	−	0.00386220i
$460$	477.721	+	174.463i	1.03852	+	0.379268i
$461$		−	355.022i		−	0.770114i	−0.922893	−	0.385057i	$-0.874182\pi$
$461$		−	355.022i		−	0.770114i	0.922893	−	0.385057i	$-0.125818\pi$
$462$	−6.00434	+	273.548i	−0.0129964	+	0.592096i
$463$	−244.127	−	244.127i	−0.527272	−	0.527272i	0.392486	−	0.919758i	$-0.371615\pi$
$463$	−244.127	−	244.127i	−0.527272	−	0.527272i	−0.919758	+	0.392486i	$0.871615\pi$
$464$	37.1689	−	80.1355i	0.0801054	−	0.172706i
$465$	−307.170	+	654.034i	−0.660581	+	1.40652i
$466$	4.11321	−	1.20117i	0.00882663	−	0.00257762i
$467$	−184.217	−	184.217i	−0.394468	−	0.394468i	0.481808	−	0.876277i	$-0.339980\pi$
$467$	−184.217	−	184.217i	−0.394468	−	0.394468i	−0.876277	+	0.481808i	$0.839980\pi$
$468$	−259.011	−	282.809i	−0.553443	−	0.604292i
$469$		−	468.831i		−	0.999639i
$470$	389.989	−	59.3883i	0.829764	−	0.126358i
$471$	316.764	+	609.449i	0.672535	+	1.29395i
$472$	−13.2028	−	196.820i	−0.0279721	−	0.416992i
$473$	−6.40939	−	6.40939i	−0.0135505	−	0.0135505i
$474$	−242.513	+	232.095i	−0.511631	+	0.489653i
$475$	−222.962	−	60.7500i	−0.469393	−	0.127895i
$476$	−17.2566	+	11.0184i	−0.0362533	+	0.0231479i
$477$	115.595	+	660.512i	0.242337	+	1.38472i
$478$	−476.071	−	260.866i	−0.995965	−	0.545744i
$479$			178.759i			0.373192i	0.982437	+	0.186596i	$0.0597455\pi$
$479$			178.759i			0.373192i	−0.982437	+	0.186596i	$0.940254\pi$
$480$	93.5517	+	470.795i	0.194899	+	0.980823i
$481$	51.1402			0.106321
$482$	117.754	−	214.897i	0.244302	−	0.445844i
$483$	−237.313	+	750.983i	−0.491330	+	1.55483i
$484$	218.469	+	342.157i	0.451383	+	0.706936i
$485$	105.748	+	138.416i	0.218038	+	0.285395i
$486$	−435.301	−	216.124i	−0.895680	−	0.444699i
$487$	11.7814	−	11.7814i	0.0241918	−	0.0241918i	−0.694907	−	0.719099i	$-0.744555\pi$
$487$	11.7814	−	11.7814i	0.0241918	−	0.0241918i	0.719099	+	0.694907i	$0.244555\pi$
$488$	−368.563	+	24.7235i	−0.755253	+	0.0506629i
$489$	−37.9703	−	73.0543i	−0.0776488	−	0.149395i
$490$	463.844	+	341.244i	0.946620	+	0.696416i
$491$	−741.254			−1.50968			−0.754842	−	0.655907i	$-0.772286\pi$
$491$	−741.254			−1.50968			−0.754842	+	0.655907i	$0.772286\pi$
$492$	383.607	−	102.944i	0.779689	−	0.209235i
$493$	−1.93554	+	1.93554i	−0.00392605	+	0.00392605i
$494$	55.2051	+	189.041i	0.111751	+	0.382674i
$495$	−146.094	−	134.783i	−0.295139	−	0.272289i
$496$	−699.197	−	324.305i	−1.40967	−	0.653841i
$497$	850.137	−	850.137i	1.71054	−	1.71054i
$498$	8.66419	−	394.727i	0.0173980	−	0.792625i
$499$	659.372			1.32139			0.660693	−	0.750656i	$-0.270262\pi$
$499$	659.372			1.32139			0.660693	+	0.750656i	$0.270262\pi$
$500$	84.2147	+	492.857i	0.168429	+	0.985714i
$501$	−359.659	−	691.978i	−0.717881	−	1.38119i
$502$	322.058	−	587.746i	0.641550	−	1.17081i
$503$	138.296	−	138.296i	0.274942	−	0.274942i	−0.556144	−	0.831086i	$-0.687720\pi$
$503$	138.296	−	138.296i	0.274942	−	0.274942i	0.831086	+	0.556144i	$0.187720\pi$
$504$	−721.980	+	176.859i	−1.43250	+	0.350911i
$505$	−8.13472	+	60.7998i	−0.0161084	+	0.120396i
$506$	−62.9727	−	215.640i	−0.124452	−	0.426166i
$507$	50.1889	−	158.824i	0.0989919	−	0.313263i
$508$	200.026	+	44.1306i	0.393751	+	0.0868712i
$509$	−0.354751			−0.000696957			−0.000348478	−	1.00000i	$-0.500111\pi$
$509$	−0.354751			−0.000696957			−0.000348478		1.00000i	$0.500111\pi$
$510$	2.29551	−	14.6956i	0.00450099	−	0.0288149i
$511$			1054.32i			2.06325i
$512$	−501.698	+	102.191i	−0.979879	+	0.199592i
$513$	151.553	+	198.294i	0.295424	+	0.386538i
$514$	9.01444	+	30.8685i	0.0175378	+	0.0600555i
$515$	91.1499	+	119.308i	0.176990	+	0.231666i
$516$	12.3043	−	21.3304i	0.0238455	−	0.0413380i
$517$	−123.213	−	123.213i	−0.238323	−	0.238323i
$518$	47.6338	−	86.9300i	0.0919571	−	0.167819i
$519$	−389.249	−	748.909i	−0.749997	−	1.44298i
$520$	320.524	−	280.766i	0.616392	−	0.539934i
$521$			594.299i			1.14069i	0.821406	+	0.570345i	$0.193190\pi$
$521$			594.299i			1.14069i	−0.821406	+	0.570345i	$0.806810\pi$
$522$	−89.1631	+	43.8851i	−0.170810	+	0.0840711i
$523$	−543.498	−	543.498i	−1.03919	−	1.03919i	−0.999200	−	0.0399922i	$-0.987267\pi$
$523$	−543.498	−	543.498i	−1.03919	−	1.03919i	−0.0399922	−	0.999200i	$-0.512733\pi$
$524$	169.686	+	265.755i	0.323829	+	0.507166i
$525$	−756.749	+	163.920i	−1.44143	+	0.312228i
$526$	167.575	+	573.834i	0.318584	+	1.09094i
$527$	16.8879	+	16.8879i	0.0320454	+	0.0320454i
$528$	143.021	−	156.520i	0.270873	−	0.296439i
$529$		−	117.636i		−	0.222375i
$530$	−736.565	+	112.165i	−1.38975	+	0.211633i
$531$	−127.521	+	181.623i	−0.240152	+	0.342040i
$532$	372.759	+	82.2396i	0.700674	+	0.154586i
$533$	−249.314	−	249.314i	−0.467756	−	0.467756i
$534$	−143.924	+	137.741i	−0.269520	+	0.257942i
$535$	332.384	+	435.065i	0.621279	+	0.813206i
$536$	−239.118	+	273.506i	−0.446116	+	0.510272i
$537$	151.100	−	478.160i	0.281377	−	0.890428i
$538$	167.663	−	305.980i	0.311642	−	0.568736i
$539$		−	254.359i		−	0.471908i
$540$	250.782	−	478.234i	0.464412	−	0.885619i
$541$	−446.978			−0.826206			−0.413103	−	0.910684i	$-0.635555\pi$
$541$	−446.978			−0.826206			−0.413103	+	0.910684i	$0.635555\pi$
$542$	332.661	+	182.283i	0.613766	+	0.336316i
$543$	−132.644	−	41.9159i	−0.244280	−	0.0771932i
$544$	15.6868	+	2.37349i	0.0288361	+	0.00436303i
$545$	41.4579	−	309.861i	0.0760695	−	0.568551i
$546$	456.243	+	476.721i	0.835610	+	0.873116i
$547$	−492.299	+	492.299i	−0.899998	+	0.899998i	−0.995435	−	0.0954376i	$-0.969575\pi$
$547$	−492.299	+	492.299i	−0.899998	+	0.899998i	0.0954376	+	0.995435i	$0.469575\pi$
$548$	987.397	+	217.844i	1.80182	+	0.397525i
$549$	340.106	+	238.794i	0.619501	+	0.434962i
$550$	153.315	−	158.972i	0.278754	−	0.289041i
$551$	51.0338			0.0926203
$552$	521.468	−	317.070i	0.944688	−	0.574403i
$553$	408.419	−	408.419i	0.738552	−	0.738552i
$554$	127.244	−	37.1587i	0.229682	−	0.0670734i
$555$	24.4433	+	67.7354i	0.0440420	+	0.122046i
$556$	33.3436	+	52.2212i	0.0599704	+	0.0939231i
$557$	−367.436	+	367.436i	−0.659670	+	0.659670i	−0.955302	−	0.295632i	$-0.904470\pi$
$557$	−367.436	+	367.436i	−0.659670	+	0.659670i	0.295632	+	0.955302i	$0.404470\pi$
$558$	382.905	+	777.964i	0.686210	+	1.39420i
$559$	−21.8599			−0.0391053
$560$	−178.709	−	806.353i	−0.319123	−	1.43992i
$561$	−5.82955	+	3.02993i	−0.0103914	+	0.00540095i
$562$	−466.825	−	255.799i	−0.830650	−	0.455159i
$563$	−129.412	+	129.412i	−0.229861	+	0.229861i	−0.812635	−	0.582773i	$-0.801968\pi$
$563$	−129.412	+	129.412i	−0.229861	+	0.229861i	0.582773	+	0.812635i	$0.301968\pi$
$564$	236.535	−	410.051i	0.419389	−	0.727041i
$565$	275.031	+	359.995i	0.486781	+	0.637159i
$566$	1005.62	−	293.667i	1.77671	−	0.518847i
$567$	756.986	+	355.350i	1.33507	+	0.626720i
$568$	−929.548	+	62.3547i	−1.63653	+	0.109779i
$569$	−658.832			−1.15788			−0.578939	−	0.815371i	$-0.696533\pi$
$569$	−658.832			−1.15788			−0.578939	+	0.815371i	$0.696533\pi$
$570$	−223.999	+	163.474i	−0.392981	+	0.286797i
$571$			153.311i			0.268496i	0.990948	+	0.134248i	$0.0428618\pi$
$571$			153.311i			0.268496i	−0.990948	+	0.134248i	$0.957138\pi$
$572$	−183.796	−	40.5498i	−0.321321	−	0.0708913i
$573$	856.149	+	270.545i	1.49415	+	0.472156i
$574$	−656.012	+	191.573i	−1.14288	+	0.333751i
$575$	551.889	−	315.542i	0.959806	−	0.548768i
$576$	511.391	+	265.057i	0.887832	+	0.460168i
$577$	379.812	+	379.812i	0.658252	+	0.658252i	0.954966	−	0.296714i	$-0.0958909\pi$
$577$	379.812	+	379.812i	0.658252	+	0.658252i	−0.296714	+	0.954966i	$0.595891\pi$
$578$	506.459	+	277.517i	0.876226	+	0.480133i
$579$	−779.416	+	405.105i	−1.34614	+	0.699662i
$580$	−46.5568	−	100.125i	−0.0802703	−	0.172629i
$581$			679.356i			1.16929i
$582$	208.977	+	4.58700i	0.359066	+	0.00788144i
$583$	232.710	+	232.710i	0.399159	+	0.399159i
$584$	537.738	−	615.069i	0.920784	−	1.05320i
$585$	−478.979	+	19.2883i	−0.818768	+	0.0329714i
$586$	−136.559	+	39.8788i	−0.233035	+	0.0680525i
$587$	−80.3753	−	80.3753i	−0.136925	−	0.136925i	0.635322	−	0.772247i	$-0.280867\pi$
$587$	−80.3753	−	80.3753i	−0.136925	−	0.136925i	−0.772247	+	0.635322i	$0.780867\pi$
$588$	667.401	−	179.102i	1.13504	−	0.304595i
$589$		−	445.279i		−	0.755992i
$590$	−198.619	−	146.121i	−0.336642	−	0.247663i
$591$	−20.0270	+	10.4091i	−0.0338866	+	0.0176127i
$592$	−72.1255	+	26.4184i	−0.121834	+	0.0446256i
$593$	−417.804	−	417.804i	−0.704559	−	0.704559i	0.260826	−	0.965386i	$-0.416005\pi$
$593$	−417.804	−	417.804i	−0.704559	−	0.704559i	−0.965386	+	0.260826i	$0.916005\pi$
$594$	−235.800	+	35.9529i	−0.396969	+	0.0605268i
$595$	−3.39395	+	25.3667i	−0.00570412	+	0.0426332i
$596$	−451.662	−	707.373i	−0.757822	−	1.18687i
$597$	176.198	+	55.6791i	0.295140	+	0.0932648i
$598$	−475.118	−	260.344i	−0.794512	−	0.435357i
$599$		−	806.349i		−	1.34616i	−0.739570	−	0.673080i	$-0.764971\pi$
$599$		−	806.349i		−	1.34616i	0.739570	−	0.673080i	$-0.235029\pi$
$600$	525.075	+	290.338i	0.875125	+	0.483897i
$601$	687.797			1.14442			0.572211	−	0.820107i	$-0.306086\pi$
$601$	687.797			1.14442			0.572211	+	0.820107i	$0.306086\pi$
$602$	−20.3610	+	37.1582i	−0.0338223	+	0.0617246i
$603$	402.588	−	70.4560i	0.667641	−	0.116842i
$604$	486.046	−	310.343i	0.804712	−	0.513813i
$605$	502.963	+	67.2941i	0.831344	+	0.111230i
$606$	50.8953	+	53.1797i	0.0839856	+	0.0877553i
$607$	232.895	−	232.895i	0.383682	−	0.383682i	−0.488745	−	0.872427i	$-0.662545\pi$
$607$	232.895	−	232.895i	0.383682	−	0.383682i	0.872427	+	0.488745i	$0.162545\pi$
$608$	−175.514	−	238.095i	−0.288675	−	0.391604i
$609$	151.726	−	78.8600i	0.249139	−	0.129491i
$610$	−273.625	+	371.931i	−0.448565	+	0.609723i
$611$	−420.230			−0.687774
$612$	−12.0549	−	13.1625i	−0.0196975	−	0.0215073i
$613$	−575.631	+	575.631i	−0.939038	+	0.939038i	−0.998246	−	0.0592074i	$-0.981143\pi$
$613$	−575.631	+	575.631i	−0.939038	+	0.939038i	0.0592074	+	0.998246i	$0.481143\pi$
$614$	234.339	+	802.458i	0.381660	+	1.30693i
$615$	211.054	−	449.381i	0.343177	−	0.730701i
$616$	−240.122	+	274.653i	−0.389808	+	0.445865i
$617$	−475.711	+	475.711i	−0.771007	+	0.771007i	−0.978283	−	0.207275i	$-0.933540\pi$
$617$	−475.711	+	475.711i	−0.771007	+	0.771007i	0.207275	+	0.978283i	$0.433540\pi$
$618$	180.127	+	3.95377i	0.291468	+	0.00639768i
$619$	215.170			0.347610			0.173805	−	0.984780i	$-0.444394\pi$
$619$	215.170			0.347610			0.173805	+	0.984780i	$0.444394\pi$
$620$	−873.608	+	406.216i	−1.40905	+	0.655188i
$621$	−680.537	−	90.9238i	−1.09587	−	0.146415i
$622$	−161.981	+	295.610i	−0.260420	+	0.475258i
$623$	242.383	−	242.383i	0.389058	−	0.389058i
$624$	−23.0193	−	510.807i	−0.0368899	−	0.818601i
$625$	538.615	+	317.048i	0.861783	+	0.507277i
$626$	−110.860	−	379.622i	−0.177092	−	0.606424i
$627$	116.798	+	36.9083i	0.186280	+	0.0588649i
$628$	−197.304	+	894.298i	−0.314178	+	1.42404i
$629$	2.38016			0.00378405
$630$	−413.351	+	832.152i	−0.656112	+	1.32088i
$631$		−	710.672i		−	1.12626i	−0.826367	−	0.563132i	$-0.809596\pi$
$631$		−	710.672i		−	1.12626i	0.826367	−	0.563132i	$-0.190404\pi$
$632$	−446.569	+	29.9562i	−0.706597	+	0.0473990i
$633$	−167.167	+	529.005i	−0.264087	+	0.835711i
$634$	−133.230	−	456.225i	−0.210142	−	0.719598i
$635$	203.462	−	155.442i	0.320413	−	0.244791i
$636$	−446.739	+	774.456i	−0.702420	+	1.21770i
$637$	−433.758	−	433.758i	−0.680939	−	0.680939i
$638$	−23.4379	+	42.7733i	−0.0367364	+	0.0670428i
$639$	857.776	+	602.259i	1.34237	+	0.942502i
$640$	−307.010	+	561.556i	−0.479703	+	0.877431i
$641$		−	445.381i		−	0.694822i	−0.937713	−	0.347411i	$-0.887061\pi$
$641$		−	445.381i		−	0.694822i	0.937713	−	0.347411i	$-0.112939\pi$
$642$	656.847	+	14.4177i	1.02313	+	0.0224574i
$643$	−310.249	−	310.249i	−0.482502	−	0.482502i	0.423428	−	0.905930i	$-0.360827\pi$
$643$	−310.249	−	310.249i	−0.482502	−	0.482502i	−0.905930	+	0.423428i	$0.860827\pi$
$644$	−885.083	+	565.130i	−1.37435	+	0.877531i
$645$	−10.4483	−	28.9535i	−0.0161989	−	0.0448891i
$646$	2.56935	+	8.79833i	0.00397732	+	0.0136197i
$647$	797.318	+	797.318i	1.23233	+	1.23233i	0.963066	+	0.269265i	$0.0867806\pi$
$647$	797.318	+	797.318i	1.23233	+	1.23233i	0.269265	+	0.963066i	$0.413219\pi$
$648$	−260.369	−	593.390i	−0.401805	−	0.915725i
$649$			108.917i			0.167822i
$650$	−9.64828	−	532.543i	−0.0148435	−	0.819297i
$651$	−688.068	−	1323.83i	−1.05694	−	2.03354i
$652$	23.6507	−	107.199i	0.0362741	−	0.164416i
$653$	−686.842	−	686.842i	−1.05183	−	1.05183i	−0.998582	−	0.0532438i	$-0.983044\pi$
$653$	−686.842	−	686.842i	−1.05183	−	1.05183i	−0.0532438	−	0.998582i	$-0.516956\pi$
$654$	−259.383	−	271.026i	−0.396610	−	0.414412i
$655$	390.654	+	52.2677i	0.596418	+	0.0797980i
$656$	480.412	+	222.827i	0.732335	+	0.339676i
$657$	−905.353	+	158.444i	−1.37801	+	0.241163i
$658$	−391.416	+	714.322i	−0.594858	+	1.08560i
$659$			633.604i			0.961463i	0.876868	+	0.480732i	$0.159629\pi$
$659$			633.604i			0.961463i	−0.876868	+	0.480732i	$0.840371\pi$
$660$	−34.1397	−	262.820i	−0.0517268	−	0.398212i
$661$	893.706			1.35205			0.676026	−	0.736878i	$-0.263701\pi$
$661$	893.706			1.35205			0.676026	+	0.736878i	$0.263701\pi$
$662$	−488.560	−	267.709i	−0.738006	−	0.404394i
$663$	−4.77419	+	15.1081i	−0.00720089	+	0.0227875i
$664$	346.493	−	396.322i	0.521827	−	0.596870i
$665$	379.162	−	289.675i	0.570169	−	0.435601i
$666$	81.8057	+	27.8395i	0.122831	+	0.0418011i
$667$	−99.2732	+	99.2732i	−0.148835	+	0.148835i
$668$	224.022	−	1015.40i	0.335362	−	1.52006i
$669$	404.161	+	777.601i	0.604128	+	1.16233i
$670$	68.3658	+	448.943i	0.102038	+	0.670064i
$671$	203.956			0.303959
$672$	−889.729	−	436.654i	−1.32400	−	0.649782i
$673$	656.768	−	656.768i	0.975881	−	0.975881i	−0.0238351	−	0.999716i	$-0.507588\pi$
$673$	656.768	−	656.768i	0.975881	−	0.975881i	0.999716	+	0.0238351i	$0.00758766\pi$
$674$	−1007.61	+	294.250i	−1.49498	+	0.436573i
$675$	−254.483	−	625.191i	−0.377012	−	0.926208i
$676$	187.185	−	119.519i	0.276901	−	0.176803i
$677$	119.083	−	119.083i	0.175898	−	0.175898i	−0.613667	−	0.789565i	$-0.710306\pi$
$677$	119.083	−	119.083i	0.175898	−	0.175898i	0.789565	+	0.613667i	$0.210306\pi$
$678$	543.508	+	11.9299i	0.801634	+	0.0175957i
$679$	−359.665			−0.529698
$680$	14.9178	−	13.0674i	0.0219379	−	0.0192167i
$681$	−341.922	−	657.853i	−0.502088	−	0.966010i
$682$	373.205	+	204.499i	0.547221	+	0.299853i
$683$	−894.185	+	894.185i	−1.30920	+	1.30920i	−0.387211	+	0.921991i	$0.626561\pi$
$683$	−894.185	+	894.185i	−1.30920	+	1.30920i	−0.921991	+	0.387211i	$0.873439\pi$
$684$	−14.6014	+	332.449i	−0.0213471	+	0.486036i
$685$	1004.36	−	767.317i	1.46622	−	1.12017i
$686$	−170.148	+	49.6878i	−0.248029	+	0.0724312i
$687$	−259.753	+	821.996i	−0.378097	+	1.19650i
$688$	30.8300	−	11.2925i	0.0448111	−	0.0164135i
$689$	793.680			1.15193
$690$	117.736	−	753.731i	0.170632	−	1.09236i
$691$		−	957.776i		−	1.38607i	−0.720903	−	0.693036i	$-0.756272\pi$
$691$		−	957.776i		−	1.38607i	0.720903	−	0.693036i	$-0.243728\pi$
$692$	242.453	−	1098.94i	0.350365	−	1.58806i
$693$	404.277	−	70.7516i	0.583372	−	0.102095i
$694$	−434.892	+	127.000i	−0.626646	+	0.182998i
$695$	76.7640	+	10.2707i	0.110452	+	0.0147779i
$696$	−128.734	−	31.3796i	−0.184963	−	0.0450857i
$697$	−11.6036	−	11.6036i	−0.0166478	−	0.0166478i
$698$	693.175	+	379.829i	0.993087	+	0.544167i
$699$	−2.96425	−	5.70317i	−0.00424070	−	0.00815905i
$700$	−914.223	−	479.628i	−1.30603	−	0.685183i
$701$		−	236.408i		−	0.337244i	−0.985681	−	0.168622i	$-0.946068\pi$
$701$		−	236.408i		−	0.337244i	0.985681	−	0.168622i	$-0.0539317\pi$
$702$	−340.799	+	463.420i	−0.485469	+	0.660143i
$703$	−31.3785	−	31.3785i	−0.0446352	−	0.0446352i
$704$	280.163	−	37.7570i	0.397959	−	0.0536322i
$705$	−200.855	−	556.596i	−0.284901	−	0.789498i
$706$	−388.555	+	113.469i	−0.550361	+	0.160720i
$707$	−89.5606	−	89.5606i	−0.126677	−	0.126677i
$708$	−285.782	+	76.6916i	−0.403647	+	0.108322i
$709$			3.07348i			0.00433495i	0.999998	+	0.00216747i	$0.000689929\pi$
$709$			3.07348i			0.00433495i	−0.999998	+	0.00216747i	$0.999310\pi$
$710$	−690.105	+	938.042i	−0.971978	+	1.32119i
$711$	412.089	+	289.334i	0.579591	+	0.406940i
$712$	−265.024	+	17.7780i	−0.372225	+	0.0249691i
$713$	866.177	+	866.177i	1.21483	+	1.21483i
$714$	21.2344	+	22.1875i	0.0297401	+	0.0310750i
$715$	−186.953	+	142.830i	−0.261473	+	0.199762i
$716$	563.542	−	359.825i	0.787070	−	0.502549i
$717$	−245.358	+	776.442i	−0.342200	+	1.08290i
$718$	682.103	+	373.762i	0.950004	+	0.520560i
$719$		−	893.990i		−	1.24338i	−0.783264	−	0.621690i	$-0.786447\pi$
$719$		−	893.990i		−	1.24338i	0.783264	−	0.621690i	$-0.213553\pi$
$720$	665.563	−	274.637i	0.924393	−	0.381441i
$721$	−310.013			−0.429977
$722$	−264.832	+	483.310i	−0.366803	+	0.669404i
$723$	−350.483	−	110.753i	−0.484762	−	0.153186i
$724$	−99.8175	−	156.330i	−0.137869	−	0.215925i
$725$	−133.170	−	36.2846i	−0.183683	−	0.0500477i
$726$	439.926	−	421.029i	0.605959	−	0.579929i
$727$	319.871	−	319.871i	0.439988	−	0.439988i	−0.452020	−	0.892008i	$-0.649296\pi$
$727$	319.871	−	319.871i	0.439988	−	0.439988i	0.892008	+	0.452020i	$0.149296\pi$
$728$	58.8866	+	877.846i	0.0808881	+	1.20583i
$729$	−191.381	+	703.430i	−0.262526	+	0.964925i
$730$	−153.743	−	1009.60i	−0.210607	−	1.38301i
$731$	−1.01740			−0.00139179
$732$	143.612	+	535.153i	0.196191	+	0.731083i
$733$	−577.382	+	577.382i	−0.787698	+	0.787698i	−0.981116	−	0.193419i	$-0.938042\pi$
$733$	−577.382	+	577.382i	−0.787698	+	0.787698i	0.193419	+	0.981116i	$0.438042\pi$
$734$	−286.635	−	981.537i	−0.390511	−	1.33724i
$735$	367.193	−	781.835i	0.499582	−	1.06372i
$736$	804.572	+	121.735i	1.09317	+	0.165401i
$737$	141.838	−	141.838i	0.192454	−	0.192454i
$738$	−263.091	−	534.532i	−0.356492	−	0.724298i
$739$	1125.12			1.52248			0.761242	−	0.648468i	$-0.224590\pi$
$739$	1125.12			1.52248			0.761242	+	0.648468i	$0.224590\pi$
$740$	−32.9368	+	90.1884i	−0.0445092	+	0.121876i
$741$	262.115	−	136.235i	0.353731	−	0.183853i
$742$	739.260	−	1349.13i	0.996308	−	1.81823i
$743$	63.1774	−	63.1774i	0.0850302	−	0.0850302i	−0.663312	−	0.748343i	$-0.730850\pi$
$743$	63.1774	−	63.1774i	0.0850302	−	0.0850302i	0.748343	+	0.663312i	$0.230850\pi$
$744$	−273.793	+	1123.23i	−0.368001	+	1.50972i
$745$	−1039.82	−	139.123i	−1.39573	−	0.186743i
$746$	83.0237	+	284.302i	0.111292	+	0.381101i
$747$	−583.367	+	102.094i	−0.780947	+	0.136672i
$748$	−8.55421	−	1.88727i	−0.0114361	−	0.00252308i
$749$	−1130.49			−1.50933
$750$	700.744	−	267.317i	0.934325	−	0.356422i
$751$			705.259i			0.939093i	0.882908	+	0.469547i	$0.155583\pi$
$751$			705.259i			0.939093i	−0.882908	+	0.469547i	$0.844417\pi$
$752$	592.670	−	217.085i	0.788125	−	0.288677i
$753$	−958.576	−	302.912i	−1.27301	−	0.402274i
$754$	32.9728	+	112.910i	0.0437304	+	0.149748i
$755$	95.5936	−	714.477i	0.126614	−	0.946327i
$756$	470.306	+	1010.95i	0.622098	+	1.33723i
$757$	−555.302	−	555.302i	−0.733556	−	0.733556i	0.237766	−	0.971322i	$-0.423585\pi$
$757$	−555.302	−	555.302i	−0.733556	−	0.733556i	−0.971322	+	0.237766i	$0.923585\pi$
$758$	38.5727	−	70.3938i	0.0508874	−	0.0928679i
$759$	−298.996	+	155.404i	−0.393934	+	0.204749i
$760$	−368.938	−	24.3946i	−0.485445	−	0.0320982i
$761$			1189.64i			1.56326i	0.623745	+	0.781628i	$0.285610\pi$
$761$			1189.64i			1.56326i	−0.623745	+	0.781628i	$0.714390\pi$
$762$	6.74255	−	307.180i	0.00884849	−	0.403123i
$763$	456.438	+	456.438i	0.598214	+	0.598214i
$764$	644.270	+	1009.03i	0.843285	+	1.32072i
$765$	−22.2926	+	0.897713i	−0.0291407	+	0.00117348i
$766$	−270.028	−	924.666i	−0.352516	−	1.20714i
$767$	185.736	+	185.736i	0.242159	+	0.242159i
$768$	296.341	+	708.524i	0.385861	+	0.922557i
$769$			900.882i			1.17150i	0.810492	+	0.585749i	$0.199200\pi$
$769$			900.882i			1.17150i	−0.810492	+	0.585749i	$0.800800\pi$
$770$	68.6526	+	450.826i	0.0891592	+	0.585489i
$771$	42.8007	−	22.2459i	0.0555133	−	0.0288533i
$772$	−1143.70	−	252.329i	−1.48148	−	0.326851i
$773$	−464.010	−	464.010i	−0.600272	−	0.600272i	0.340113	−	0.940385i	$-0.389535\pi$
$773$	−464.010	−	464.010i	−0.600272	−	0.600272i	−0.940385	+	0.340113i	$0.889535\pi$
$774$	−34.9678	−	11.9000i	−0.0451781	−	0.0153747i
$775$	−316.590	+	1161.93i	−0.408503	+	1.49927i
$776$	209.821	+	183.440i	0.270387	+	0.236392i
$777$	−141.777	−	44.8020i	−0.182468	−	0.0576602i
$778$	−94.5724	+	172.591i	−0.121558	+	0.221840i
$779$			305.947i			0.392744i
$780$	−506.405	−	389.968i	−0.649237	−	0.499959i
$781$	514.395			0.658636
$782$	−22.1129	−	12.1169i	−0.0282774	−	0.0154947i
$783$	90.5189	+	118.437i	0.115605	+	0.151260i
$784$	835.823	+	387.676i	1.06610	+	0.494485i
$785$	694.969	+	909.662i	0.885311	+	1.15880i
$786$	341.693	−	327.015i	0.434724	−	0.416050i
$787$	−511.685	+	511.685i	−0.650172	+	0.650172i	−0.953034	−	0.302862i	$-0.902058\pi$
$787$	−511.685	+	511.685i	−0.650172	+	0.650172i	0.302862	+	0.953034i	$0.402058\pi$
$788$	−29.3873	−	6.48355i	−0.0372935	−	0.00822786i
$789$	795.650	−	413.542i	1.00843	−	0.524135i
$790$	−331.537	+	450.650i	−0.419667	+	0.570443i
$791$	−935.420			−1.18258
$792$	−271.932	−	164.919i	−0.343348	−	0.208231i
$793$	347.807	−	347.807i	0.438596	−	0.438596i
$794$	878.200	−	256.458i	1.10604	−	0.322995i
$795$	379.352	+	1051.23i	0.477172	+	1.32230i
$796$	132.593	+	207.661i	0.166574	+	0.260881i
$797$	606.760	−	606.760i	0.761305	−	0.761305i	−0.215253	−	0.976558i	$-0.569058\pi$
$797$	606.760	−	606.760i	0.761305	−	0.761305i	0.976558	+	0.215253i	$0.0690576\pi$
$798$	12.5651	−	572.446i	0.0157457	−	0.717351i
$799$	−19.5583			−0.0244785
$800$	288.712	+	746.087i	0.360890	+	0.932608i
$801$	244.561	+	171.711i	0.305320	+	0.214370i
$802$	1137.07	+	623.062i	1.41779	+	0.776885i
$803$	−318.971	+	318.971i	−0.397224	+	0.397224i
$804$	472.037	+	272.291i	0.587111	+	0.338671i
$805$	−174.075	+	1301.05i	−0.216242	+	1.61621i
$806$	985.160	−	287.693i	1.22228	−	0.356939i
$807$	−499.034	−	157.696i	−0.618382	−	0.195410i
$808$	6.56897	+	97.9264i	0.00812992	+	0.121196i
$809$	9.70812			0.0120001			0.00600007	−	0.999982i	$-0.498090\pi$
$809$	9.70812			0.0120001			0.00600007	+	0.999982i	$0.498090\pi$
$810$	−776.692	−	229.891i	−0.958879	−	0.283816i
$811$			109.279i			0.134747i	0.997728	+	0.0673733i	$0.0214618\pi$
$811$			109.279i			0.134747i	−0.997728	+	0.0673733i	$0.978538\pi$
$812$	222.640	+	49.1199i	0.274188	+	0.0604925i
$813$	171.447	−	542.549i	0.210882	−	0.667342i
$814$	40.7104	−	11.8886i	0.0500128	−	0.0146051i
$815$	−83.3055	−	109.040i	−0.102215	−	0.133792i
$816$	−1.07136	−	23.7739i	−0.00131294	−	0.0291347i
$817$	13.4127	+	13.4127i	0.0164171	+	0.0164171i
$818$	−24.4847	−	13.4165i	−0.0299324	−	0.0164016i
$819$	568.761	−	810.066i	0.694458	−	0.989092i
$820$	600.248	−	279.108i	0.732010	−	0.340375i
$821$			219.704i			0.267606i	0.991008	+	0.133803i	$0.0427189\pi$
$821$			219.704i			0.267606i	−0.991008	+	0.133803i	$0.957281\pi$
$822$	33.2836	−	1516.35i	0.0404910	−	1.84471i
$823$	1.99663	+	1.99663i	0.00242604	+	0.00242604i	0.708319	−	0.705893i	$-0.249454\pi$
$823$	1.99663	+	1.99663i	0.00242604	+	0.00242604i	−0.705893	+	0.708319i	$0.749454\pi$
$824$	180.855	+	158.117i	0.219484	+	0.191889i
$825$	−278.536	−	179.352i	−0.337619	−	0.217397i
$826$	488.721	−	142.720i	0.591672	−	0.172784i
$827$	917.802	+	917.802i	1.10980	+	1.10980i	0.993177	+	0.116620i	$0.0372061\pi$
$827$	917.802	+	917.802i	1.10980	+	1.10980i	0.116620	+	0.993177i	$0.462794\pi$
$828$	−618.291	−	675.098i	−0.746728	−	0.815335i
$829$		−	1134.07i		−	1.36800i	−0.729482	−	0.684000i	$-0.760239\pi$
$829$		−	1134.07i		−	1.36800i	0.729482	−	0.684000i	$-0.239761\pi$
$830$	−99.0650	−	650.537i	−0.119355	−	0.783780i
$831$	−91.7003	−	176.430i	−0.110349	−	0.212311i
$832$	413.376	−	542.150i	0.496846	−	0.651623i
$833$	−20.1879	−	20.1879i	−0.0242352	−	0.0242352i
$834$	67.1432	−	64.2589i	0.0805074	−	0.0770491i
$835$	−789.079	−	1032.84i	−0.945005	−	1.23694i
$836$	87.8926	+	137.654i	0.105135	+	0.164657i
$837$	1033.38	−	789.794i	1.23462	−	0.943601i
$838$	557.374	+	305.416i	0.665124	+	0.364458i
$839$		−	624.895i		−	0.744809i	−0.928070	−	0.372405i	$-0.878533\pi$
$839$		−	624.895i		−	0.744809i	0.928070	−	0.372405i	$-0.121467\pi$
$840$	−1134.56	+	497.576i	−1.35067	+	0.592352i
$841$	−810.519			−0.963756
$842$	−54.7805	+	99.9726i	−0.0650600	+	0.118732i
$843$	−240.592	+	761.362i	−0.285400	+	0.903158i
$844$	−623.467	+	398.087i	−0.738705	+	0.471667i
$845$	36.8148	−	275.158i	0.0435678	−	0.325630i
$846$	−672.214	−	228.763i	−0.794579	−	0.270405i
$847$	−740.886	+	740.886i	−0.874717	+	0.874717i
$848$	−1119.36	+	410.004i	−1.32001	+	0.483496i
$849$	−724.713	−	1394.34i	−0.853608	−	1.64233i
$850$	−0.449049	−	24.7856i	−0.000528293	−	0.0291595i
$851$	122.078			0.143452
$852$	362.202	+	1349.70i	0.425119	+	1.58415i
$853$	−462.091	+	462.091i	−0.541724	+	0.541724i	−0.924034	−	0.382310i	$-0.875129\pi$
$853$	−462.091	+	462.091i	−0.541724	+	0.541724i	0.382310	+	0.924034i	$0.375129\pi$
$854$	−267.255	−	915.173i	−0.312945	−	1.07163i
$855$	305.726	+	282.056i	0.357574	+	0.329890i
$856$	659.500	+	576.583i	0.770444	+	0.673578i
$857$	343.527	−	343.527i	0.400848	−	0.400848i	−0.477684	−	0.878532i	$-0.658524\pi$
$857$	343.527	−	343.527i	0.400848	−	0.400848i	0.878532	+	0.477684i	$0.158524\pi$
$858$	−6.19546	+	282.256i	−0.00722082	+	0.328969i
$859$	−1108.16			−1.29006			−0.645028	−	0.764159i	$-0.723154\pi$
$859$	−1108.16			−1.29006			−0.645028	+	0.764159i	$0.723154\pi$
$860$	14.0788	−	38.5510i	0.0163707	−	0.0448268i
$861$	472.765	+	909.594i	0.549089	+	1.05644i
$862$	−140.674	+	256.726i	−0.163195	+	0.297826i
$863$	−247.757	+	247.757i	−0.287089	+	0.287089i	−0.835928	−	0.548839i	$-0.815070\pi$
$863$	−247.757	+	247.757i	−0.287089	+	0.287089i	0.548839	+	0.835928i	$0.315070\pi$
$864$	241.249	−	829.636i	0.279223	−	0.960226i
$865$	−853.998	−	1117.82i	−0.987281	−	1.29228i
$866$	337.326	+	1155.12i	0.389522	+	1.33385i
$867$	261.019	−	826.002i	0.301060	−	0.952713i
$868$	428.580	−	1942.58i	0.493756	−	2.23799i
$869$	247.123			0.284377
$870$	−133.790	+	97.6396i	−0.153781	+	0.112229i
$871$		−	483.754i		−	0.555401i
$872$	−33.4782	−	499.073i	−0.0383924	−	0.572332i
$873$	−54.0505	−	308.846i	−0.0619135	−	0.353776i
$874$	131.781	+	451.263i	0.150779	+	0.516320i
$875$	−1195.36	+	486.311i	−1.36613	+	0.555784i
$876$	−1061.53	−	612.338i	−1.21180	−	0.699016i
$877$	477.322	+	477.322i	0.544266	+	0.544266i	0.924777	−	0.380510i	$-0.124252\pi$
$877$	477.322	+	477.322i	0.544266	+	0.544266i	−0.380510	+	0.924777i	$0.624252\pi$
$878$	−653.271	+	1192.20i	−0.744044	+	1.35786i
$879$	98.4130	+	189.345i	0.111960	+	0.215410i
$880$	189.885	−	298.017i	0.215778	−	0.338656i
$881$		−	907.230i		−	1.02977i	−0.857259	−	0.514886i	$-0.827834\pi$
$881$		−	907.230i		−	1.02977i	0.857259	−	0.514886i	$-0.172166\pi$
$882$	−457.727	−	929.982i	−0.518965	−	1.05440i
$883$	−55.2196	−	55.2196i	−0.0625364	−	0.0625364i	0.675147	−	0.737683i	$-0.264080\pi$
$883$	−55.2196	−	55.2196i	−0.0625364	−	0.0625364i	−0.737683	+	0.675147i	$0.764080\pi$
$884$	−17.8059	+	11.3691i	−0.0201424	+	0.0128610i
$885$	−157.232	+	334.783i	−0.177664	+	0.378286i
$886$	−152.809	−	523.270i	−0.172471	−	0.590599i
$887$	−587.061	−	587.061i	−0.661850	−	0.661850i	0.293966	−	0.955816i	$-0.405025\pi$
$887$	−587.061	−	587.061i	−0.661850	−	0.661850i	−0.955816	+	0.293966i	$0.905025\pi$
$888$	59.8594	+	98.4474i	0.0674092	+	0.110864i
$889$			528.681i			0.594692i
$890$	−196.756	+	267.446i	−0.221075	+	0.300501i
$891$	121.510	+	336.522i	0.136374	+	0.377691i
$892$	−251.742	+	1141.04i	−0.282222	+	1.27920i
$893$	257.844	+	257.844i	0.288739	+	0.288739i
$894$	−909.501	+	870.432i	−1.01734	+	0.973637i
$895$	110.835	−	828.394i	0.123838	−	0.925580i
$896$	−536.534	−	1207.65i	−0.598810	−	1.34782i
$897$	−244.867	+	774.888i	−0.272984	+	0.863867i
$898$	161.269	−	294.310i	0.179587	−	0.327740i
$899$		−	265.955i		−	0.295834i
$900$	274.470	−	857.127i	0.304967	−	0.952363i
$901$	36.9394			0.0409982
$902$	−256.426	−	140.510i	−0.284286	−	0.155776i
$903$	60.6027	+	19.1506i	0.0671126	+	0.0212078i
$904$	545.703	+	477.093i	0.603654	+	0.527758i
$905$	−229.801	−	30.7463i	−0.253924	−	0.0339739i
$906$	−598.086	−	624.931i	−0.660139	−	0.689769i
$907$	570.349	−	570.349i	0.628831	−	0.628831i	−0.318943	−	0.947774i	$-0.603328\pi$
$907$	570.349	−	570.349i	0.628831	−	0.628831i	0.947774	+	0.318943i	$0.103328\pi$
$908$	212.974	−	965.325i	0.234553	−	1.06313i
$909$	63.4470	−	90.3654i	0.0697987	−	0.0994118i
$910$	885.868	+	651.721i	0.973481	+	0.716177i
$911$	809.153			0.888203			0.444102	−	0.895976i	$-0.353523\pi$
$911$	809.153			0.888203			0.444102	+	0.895976i	$0.353523\pi$
$912$	−299.296	+	327.544i	−0.328175	+	0.359149i
$913$	−205.530	+	205.530i	−0.225115	+	0.225115i
$914$	−337.967	+	98.6954i	−0.369767	+	0.107982i
$915$	626.911	+	294.432i	0.685149	+	0.321783i
$916$	−968.776	+	618.569i	−1.05762	+	0.675293i
$917$	−575.450	+	575.450i	−0.627535	+	0.627535i
$918$	−15.8614	+	21.5685i	−0.0172783	+	0.0234951i
$919$	683.390			0.743623			0.371812	−	0.928308i	$-0.378737\pi$
$919$	683.390			0.743623			0.371812	+	0.928308i	$0.378737\pi$
$920$	765.128	−	670.221i	0.831661	−	0.728501i
$921$	1112.65	−	578.303i	1.20809	−	0.627908i
$922$	−622.689	−	341.206i	−0.675368	−	0.370071i
$923$	877.198	−	877.198i	0.950377	−	0.950377i
$924$	474.018	+	273.434i	0.513006	+	0.295924i
$925$	59.5708	+	104.191i	0.0644009	+	0.112638i
$926$	−662.811	+	193.559i	−0.715778	+	0.209027i
$927$	−46.5889	−	266.210i	−0.0502577	−	0.287174i
$928$	−104.831	−	142.209i	−0.112964	−	0.153242i
$929$	−533.625			−0.574408			−0.287204	−	0.957869i	$-0.592726\pi$
$929$	−533.625			−0.574408			−0.287204	+	0.957869i	$0.592726\pi$
$930$	851.923	+	1167.34i	0.916047	+	1.25520i
$931$			532.289i			0.571739i
$932$	1.84635	−	8.36876i	0.00198107	−	0.00897936i
$933$	482.122	+	152.352i	0.516744	+	0.163292i
$934$	−500.153	+	146.058i	−0.535496	+	0.156379i
$935$	−8.70116	+	6.64757i	−0.00930605	+	0.00710970i
$936$	−744.962	+	182.489i	−0.795899	+	0.194967i
$937$	757.665	+	757.665i	0.808607	+	0.808607i	0.984423	−	0.175816i	$-0.0562564\pi$
$937$	757.665	+	757.665i	0.808607	+	0.808607i	−0.175816	+	0.984423i	$0.556256\pi$
$938$	−822.303	−	450.585i	−0.876656	−	0.480368i
$939$	−526.364	+	273.580i	−0.560558	+	0.291352i
$940$	270.648	−	741.096i	0.287924	−	0.788401i
$941$		−	1555.04i		−	1.65254i	−0.563277	−	0.826268i	$-0.690460\pi$
$941$		−	1555.04i		−	1.65254i	0.563277	−	0.826268i	$-0.309540\pi$
$942$	1373.38	+	30.1454i	1.45794	+	0.0320015i
$943$	−595.142	−	595.142i	−0.631116	−	0.631116i
$944$	−357.900	−	166.003i	−0.379132	−	0.175851i
$945$	1344.78	+	366.142i	1.42305	+	0.387452i
$946$	−17.4017	+	5.08176i	−0.0183950	+	0.00537184i
$947$	−385.141	−	385.141i	−0.406696	−	0.406696i	0.473889	−	0.880585i	$-0.342850\pi$
$947$	−385.141	−	385.141i	−0.406696	−	0.406696i	−0.880585	+	0.473889i	$0.842850\pi$
$948$	174.007	+	648.417i	0.183552	+	0.683984i
$949$			1087.88i			1.14635i
$950$	−320.837	+	332.677i	−0.337723	+	0.350186i
$951$	−632.579	+	328.786i	−0.665173	+	0.345726i
$952$	2.74069	+	40.8566i	0.00287888	+	0.0429166i
$953$	450.513	+	450.513i	0.472731	+	0.472731i	0.902797	−	0.430066i	$-0.141510\pi$
$953$	450.513	+	450.513i	0.472731	+	0.472731i	−0.430066	+	0.902797i	$0.641510\pi$
$954$	1269.60	+	432.060i	1.33082	+	0.452893i
$955$	1483.25	+	198.452i	1.55314	+	0.207803i
$956$	−915.088	+	584.289i	−0.957205	+	0.611181i
$957$	69.7606	+	22.0445i	0.0728951	+	0.0230350i
$958$	313.533	+	171.802i	0.327279	+	0.179334i
$959$			2609.75i			2.72133i
$960$	915.659	+	288.389i	0.953812	+	0.300405i
$961$	−1359.51			−1.41468
$962$	49.1500	−	89.6971i	0.0510915	−	0.0932403i
$963$	−169.889	−	970.754i	−0.176417	−	1.00805i
$964$	−263.746	−	413.067i	−0.273595	−	0.428493i
$965$	−1163.35	+	888.786i	−1.20555	+	0.921022i
$966$	1089.11	+	1137.99i	1.12744	+	1.17804i
$967$	577.404	−	577.404i	0.597108	−	0.597108i	−0.342434	−	0.939542i	$-0.611251\pi$
$967$	577.404	−	577.404i	0.597108	−	0.597108i	0.939542	+	0.342434i	$0.111251\pi$
$968$	810.091	−	54.3415i	0.836871	−	0.0561379i
$969$	12.1993	−	6.34065i	0.0125896	−	0.00654350i
$970$	344.408	−	52.4470i	0.355059	−	0.0540691i
$971$	983.651			1.01303			0.506514	−	0.862231i	$-0.330934\pi$
$971$	983.651			1.01303			0.506514	+	0.862231i	$0.330934\pi$
$972$	−797.429	+	555.780i	−0.820400	+	0.571790i
$973$	−113.077	+	113.077i	−0.116214	+	0.116214i
$974$	−9.34100	−	31.9868i	−0.00959035	−	0.0328406i
$975$	−780.837	+	169.137i	−0.800859	+	0.173474i
$976$	−310.856	+	670.201i	−0.318500	+	0.686681i
$977$	−734.412	+	734.412i	−0.751702	+	0.751702i	−0.974797	−	0.223095i	$-0.928384\pi$
$977$	−734.412	+	734.412i	−0.751702	+	0.751702i	0.223095	+	0.974797i	$0.428384\pi$
$978$	−164.626	−	3.61351i	−0.168329	−	0.00369479i
$979$	146.660			0.149806
$980$	1044.32	−	485.593i	1.06563	−	0.495503i
$981$	−323.352	+	460.539i	−0.329615	+	0.469459i
$982$	−712.407	+	1300.12i	−0.725465	+	1.32395i
$983$	421.808	−	421.808i	0.429103	−	0.429103i	−0.459220	−	0.888323i	$-0.651871\pi$
$983$	421.808	−	421.808i	0.429103	−	0.429103i	0.888323	+	0.459220i	$0.151871\pi$
$984$	188.121	−	771.762i	0.191180	−	0.784311i
$985$	−29.8921	+	22.8372i	−0.0303473	+	0.0231850i
$986$	1.53462	+	5.25504i	0.00155640	+	0.00532966i
$987$	1165.01	+	368.147i	1.18036	+	0.372996i
$988$	384.624	+	84.8574i	0.389296	+	0.0858881i
$989$	−52.1821			−0.0527625
$990$	−376.810	+	126.703i	−0.380616	+	0.127982i
$991$		−	1077.21i		−	1.08699i	−0.839411	−	0.543496i	$-0.817100\pi$
$991$		−	1077.21i		−	1.08699i	0.839411	−	0.543496i	$-0.182900\pi$
$992$	−1240.80	+	914.667i	−1.25081	+	0.922044i
$993$	−251.794	+	796.810i	−0.253569	+	0.802427i
$994$	−674.040	−	2308.14i	−0.678109	−	2.32208i
$995$	305.257	+	40.8420i	0.306791	+	0.0410472i
$996$	−684.002	−	394.562i	−0.686749	−	0.396147i
$997$	−999.351	−	999.351i	−1.00236	−	1.00236i	−0.999997	−	0.00236078i	$-0.999249\pi$
$997$	−999.351	−	999.351i	−1.00236	−	1.00236i	−0.00236078	−	0.999997i	$-0.500751\pi$
$998$	633.711	−	1156.50i	0.634981	−	1.15882i
$999$	17.1654	−	128.478i	0.0171826	−	0.128607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.l.a.47.14	yes	40
3.2	odd	2	inner	60.3.l.a.47.7	yes	40
4.3	odd	2	inner	60.3.l.a.47.17	yes	40
5.2	odd	4		300.3.l.g.143.17		40
5.3	odd	4	inner	60.3.l.a.23.4	✓	40
5.4	even	2		300.3.l.g.107.7		40
12.11	even	2	inner	60.3.l.a.47.4	yes	40
15.2	even	4		300.3.l.g.143.4		40
15.8	even	4	inner	60.3.l.a.23.17	yes	40
15.14	odd	2		300.3.l.g.107.14		40
20.3	even	4	inner	60.3.l.a.23.7	yes	40
20.7	even	4		300.3.l.g.143.14		40
20.19	odd	2		300.3.l.g.107.4		40
60.23	odd	4	inner	60.3.l.a.23.14	yes	40
60.47	odd	4		300.3.l.g.143.7		40
60.59	even	2		300.3.l.g.107.17		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.4	✓	40	5.3	odd	4	inner
60.3.l.a.23.7	yes	40	20.3	even	4	inner
60.3.l.a.23.14	yes	40	60.23	odd	4	inner
60.3.l.a.23.17	yes	40	15.8	even	4	inner
60.3.l.a.47.4	yes	40	12.11	even	2	inner
60.3.l.a.47.7	yes	40	3.2	odd	2	inner
60.3.l.a.47.14	yes	40	1.1	even	1	trivial
60.3.l.a.47.17	yes	40	4.3	odd	2	inner
300.3.l.g.107.4		40	20.19	odd	2
300.3.l.g.107.7		40	5.4	even	2
300.3.l.g.107.14		40	15.14	odd	2
300.3.l.g.107.17		40	60.59	even	2
300.3.l.g.143.4		40	15.2	even	4
300.3.l.g.143.7		40	60.47	odd	4
300.3.l.g.143.14		40	20.7	even	4
300.3.l.g.143.17		40	5.2	odd	4

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.961083 - 1.75394i) q^{2} +(-2.86057 - 0.903948i) q^{3} +(-2.15264 - 3.37137i) q^{4} +(-4.95584 - 0.663068i) q^{5} +(-4.33472 + 4.14852i) q^{6} +(7.30016 - 7.30016i) q^{7} +(-7.98206 + 0.535443i) q^{8} +(7.36576 + 5.17162i) q^{9} +O(q^{10})\)	\(q+(0.961083 - 1.75394i) q^{2} +(-2.86057 - 0.903948i) q^{3} +(-2.15264 - 3.37137i) q^{4} +(-4.95584 - 0.663068i) q^{5} +(-4.33472 + 4.14852i) q^{6} +(7.30016 - 7.30016i) q^{7} +(-7.98206 + 0.535443i) q^{8} +(7.36576 + 5.17162i) q^{9} +(-5.92596 + 8.05500i) q^{10} +4.41713 q^{11} +(3.11024 + 11.5899i) q^{12} +(7.53253 - 7.53253i) q^{13} +(-5.78801 - 19.8201i) q^{14} +(13.5772 + 6.37658i) q^{15} +(-6.73229 + 14.5147i) q^{16} +(0.350578 - 0.350578i) q^{17} +(16.1498 - 7.94877i) q^{18} -9.24359 q^{19} +(8.43269 + 18.1353i) q^{20} +(-27.4816 + 14.2837i) q^{21} +(4.24523 - 7.74740i) q^{22} +(17.9810 - 17.9810i) q^{23} +(23.3173 + 5.68370i) q^{24} +(24.1207 + 6.57212i) q^{25} +(-5.97225 - 20.4510i) q^{26} +(-16.3954 - 21.4521i) q^{27} +(-40.3261 - 8.89693i) q^{28} -5.52099 q^{29} +(24.2329 - 17.6852i) q^{30} +48.1716i q^{31} +(18.9877 + 25.7579i) q^{32} +(-12.6355 - 3.99285i) q^{33} +(-0.277960 - 0.951830i) q^{34} +(-41.0189 + 31.3379i) q^{35} +(1.57963 - 35.9653i) q^{36} +(3.39462 + 3.39462i) q^{37} +(-8.88386 + 16.2127i) q^{38} +(-28.3564 + 14.7383i) q^{39} +(39.9128 + 2.63908i) q^{40} -33.0983i q^{41} +(-1.35933 + 61.9290i) q^{42} +(-1.45103 - 1.45103i) q^{43} +(-9.50848 - 14.8918i) q^{44} +(-33.0744 - 30.5137i) q^{45} +(-14.2565 - 48.8190i) q^{46} +(-27.8943 - 27.8943i) q^{47} +(32.3787 - 35.4347i) q^{48} -57.5846i q^{49} +(34.7091 - 35.9900i) q^{50} +(-1.31976 + 0.685951i) q^{51} +(-41.6098 - 9.18014i) q^{52} +(52.6835 + 52.6835i) q^{53} +(-53.3830 + 8.13943i) q^{54} +(-21.8906 - 2.92886i) q^{55} +(-54.3615 + 62.1791i) q^{56} +(26.4420 + 8.35573i) q^{57} +(-5.30613 + 9.68351i) q^{58} +24.6578i q^{59} +(-7.72893 - 59.5001i) q^{60} +46.1739 q^{61} +(84.4904 + 46.2969i) q^{62} +(91.5248 - 16.0176i) q^{63} +(63.4266 - 8.54787i) q^{64} +(-42.3246 + 32.3354i) q^{65} +(-19.1470 + 18.3245i) q^{66} +(32.1110 - 32.1110i) q^{67} +(-1.93660 - 0.427261i) q^{68} +(-67.6900 + 35.1822i) q^{69} +(15.5424 + 102.063i) q^{70} +116.455 q^{71} +(-61.5630 - 37.3362i) q^{72} +(-72.2123 + 72.2123i) q^{73} +(9.21650 - 2.69147i) q^{74} +(-63.0581 - 40.6039i) q^{75} +(19.8981 + 31.1636i) q^{76} +(32.2457 - 32.2457i) q^{77} +(-1.40260 + 63.9003i) q^{78} +55.9466 q^{79} +(42.9884 - 67.4685i) q^{80} +(27.5087 + 76.1858i) q^{81} +(-58.0526 - 31.8102i) q^{82} +(-46.5302 + 46.5302i) q^{83} +(107.314 + 61.9031i) q^{84} +(-1.96987 + 1.50495i) q^{85} +(-3.93959 + 1.15047i) q^{86} +(15.7932 + 4.99069i) q^{87} +(-35.2578 + 2.36512i) q^{88} +33.2025 q^{89} +(-85.3065 + 28.6844i) q^{90} -109.977i q^{91} +(-99.3275 - 21.9141i) q^{92} +(43.5447 - 137.798i) q^{93} +(-75.7338 + 22.1163i) q^{94} +(45.8098 + 6.12913i) q^{95} +(-31.0319 - 90.8462i) q^{96} +(-24.6341 - 24.6341i) q^{97} +(-101.000 - 55.3436i) q^{98} +(32.5355 + 22.8437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Introduction

L-functions

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