LMFDB - Embedded newform 60.3.l.a.23.14

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			23.14
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.14

$q$-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 $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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	0.999039	+	0.0438411i	$0.0139595\pi$
$7$	7.30016	+	7.30016i	1.04288	+	1.04288i	0.0438411	+	0.999039i	$0.486040\pi$
$8$	−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	0.934745	−	0.355319i	$-0.115628\pi$
$13$	7.53253	+	7.53253i	0.579426	+	0.579426i	−0.355319	+	0.934745i	$0.615628\pi$
$14$	−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	0.717343	−	0.696720i	$-0.245358\pi$
$17$	0.350578	+	0.350578i	0.0206223	+	0.0206223i	−0.696720	+	0.717343i	$0.745358\pi$
$18$	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	0.980132	−	0.198347i	$-0.0635573\pi$
$23$	17.9810	+	17.9810i	0.781785	+	0.781785i	−0.198347	+	0.980132i	$0.563557\pi$
$24$	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	$-0.716760\pi$
$31$		−	48.1716i		−	1.55392i	0.629548	−	0.776962i	$-0.283240\pi$
$32$	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	−0.659744	−	0.751491i	$-0.729335\pi$
$37$	3.39462	−	3.39462i	0.0917466	−	0.0917466i	0.751491	+	0.659744i	$0.229335\pi$
$38$	−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	$0.132254\pi$
$41$			33.0983i			0.807276i	−0.914919	+	0.403638i	$0.867746\pi$
$42$	−1.35933	−	61.9290i	−0.0323650	−	1.47450i
$43$	−1.45103	+	1.45103i	−0.0337449	+	0.0337449i	−0.723778	−	0.690033i	$-0.757596\pi$
$43$	−1.45103	+	1.45103i	−0.0337449	+	0.0337449i	0.690033	+	0.723778i	$0.257596\pi$
$44$	−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	−0.938574	−	0.345078i	$-0.887853\pi$
$47$	−27.8943	+	27.8943i	−0.593496	+	0.593496i	0.345078	+	0.938574i	$0.387853\pi$
$48$	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	−0.00595455	−	0.999982i	$-0.501895\pi$
$53$	52.6835	−	52.6835i	0.994028	−	0.994028i	0.999982	+	0.00595455i	$0.00189540\pi$
$54$	−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	$-0.932991\pi$
$59$		−	24.6578i		−	0.417929i	0.977923	−	0.208964i	$-0.0670093\pi$
$60$	−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	0.904898	−	0.425629i	$-0.139947\pi$
$67$	32.1110	+	32.1110i	0.479269	+	0.479269i	−0.425629	+	0.904898i	$0.639947\pi$
$68$	−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	0.0107324	−	0.999942i	$-0.496584\pi$
$73$	−72.2123	−	72.2123i	−0.989210	−	0.989210i	−0.999942	+	0.0107324i	$0.996584\pi$
$74$	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	0.368874	−	0.929479i	$-0.379743\pi$
$83$	−46.5302	−	46.5302i	−0.560605	−	0.560605i	−0.929479	+	0.368874i	$0.879743\pi$
$84$	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	−0.822592	−	0.568632i	$-0.807473\pi$
$97$	−24.6341	+	24.6341i	−0.253959	+	0.253959i	0.568632	+	0.822592i	$0.307473\pi$
$98$	−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	$0.0193442\pi$
$101$			12.2683i			0.121468i	−0.998154	+	0.0607342i	$0.980656\pi$
$102$	−0.0652797	−	2.97404i	−0.000639997	−	0.0291573i
$103$	−21.2333	+	21.2333i	−0.206149	+	0.206149i	−0.802628	−	0.596479i	$-0.796566\pi$
$103$	−21.2333	+	21.2333i	−0.206149	+	0.206149i	0.596479	+	0.802628i	$0.296566\pi$
$104$	−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	−0.969343	−	0.245710i	$-0.920979\pi$
$107$	−77.4288	+	77.4288i	−0.723634	+	0.723634i	0.245710	+	0.969343i	$0.420979\pi$
$108$	−37.0294	−	101.454i	−0.342865	−	0.939385i
$109$		−	62.5243i		−	0.573618i	−0.957988	−	0.286809i	$-0.907406\pi$
$109$		−	62.5243i		−	0.573618i	0.957988	−	0.286809i	$-0.0925945\pi$
$110$	−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	−0.931280	−	0.364303i	$-0.881307\pi$
$113$	−64.0685	+	64.0685i	−0.566977	+	0.566977i	0.364303	+	0.931280i	$0.381307\pi$
$114$	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	0.550027	−	0.835147i	$-0.314617\pi$
$127$	−36.2102	−	36.2102i	−0.285120	−	0.285120i	−0.835147	+	0.550027i	$0.814617\pi$
$128$	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	−0.925174	−	0.379544i	$-0.876081\pi$
$137$	−178.746	−	178.746i	−1.30472	−	1.30472i	−0.379544	−	0.925174i	$-0.623919\pi$
$138$	−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	$-0.841587\pi$
$151$		−	144.169i		−	0.954759i	0.878697	−	0.477380i	$-0.158413\pi$
$152$	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	−0.0316669	+	0.999498i	$0.510082\pi$
$157$	−161.893	+	161.893i	−1.03117	+	1.03117i	−0.999498	+	0.0316669i	$0.989918\pi$
$158$	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	−0.645069	−	0.764124i	$-0.723171\pi$
$163$	19.4060	−	19.4060i	0.119055	−	0.119055i	0.764124	+	0.645069i	$0.223171\pi$
$164$	−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	0.106366	−	0.994327i	$-0.466078\pi$
$167$	183.816	−	183.816i	1.10069	−	1.10069i	0.994327	−	0.106366i	$-0.0339216\pi$
$168$	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	0.163370	−	0.986565i	$-0.447764\pi$
$173$	198.939	−	198.939i	1.14993	−	1.14993i	0.986565	−	0.163370i	$-0.0522364\pi$
$174$	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	$-0.845366\pi$
$179$		−	167.155i		−	0.933828i	0.884303	−	0.466914i	$-0.154634\pi$
$180$	−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	0.997137	+	0.0756225i	$0.0240944\pi$
$193$	207.042	+	207.042i	1.07276	+	1.07276i	0.0756225	+	0.997137i	$0.475906\pi$
$194$	−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	0.720480	−	0.693476i	$-0.243921\pi$
$197$	5.31992	+	5.31992i	0.0270047	+	0.0270047i	−0.693476	+	0.720480i	$0.743921\pi$
$198$	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	$0.144392\pi$
$211$			184.930i			0.876444i	−0.898867	+	0.438222i	$0.855608\pi$
$212$	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	−0.997463	−	0.0711833i	$-0.977322\pi$
$223$	−206.560	+	206.560i	−0.926280	+	0.926280i	0.0711833	+	0.997463i	$0.477322\pi$
$224$	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	−0.208249	−	0.978076i	$-0.566776\pi$
$227$	174.751	−	174.751i	0.769827	−	0.769827i	0.978076	+	0.208249i	$0.0667763\pi$
$228$	−28.7498	+	107.133i	−0.126096	+	0.469880i
$229$			287.354i			1.25482i	0.778689	+	0.627410i	$0.215885\pi$
$229$			287.354i			1.25482i	−0.778689	+	0.627410i	$0.784115\pi$
$230$	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	−0.703848	−	0.710350i	$-0.748537\pi$
$233$	1.51498	−	1.51498i	0.00650206	−	0.00650206i	0.710350	+	0.703848i	$0.248537\pi$
$234$	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	$0.192222\pi$
$239$			271.429i			1.13569i	−0.823137	+	0.567843i	$0.807778\pi$
$240$	−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	0.684641	−	0.728880i	$-0.259959\pi$
$257$	−11.3695	−	11.3695i	−0.0442393	−	0.0442393i	−0.728880	+	0.684641i	$0.759959\pi$
$258$	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	0.180030	−	0.983661i	$-0.442380\pi$
$263$	−211.355	−	211.355i	−0.803631	−	0.803631i	−0.983661	+	0.180030i	$0.942380\pi$
$264$	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	$-0.886204\pi$
$271$		−	189.665i		−	0.699869i	0.936774	−	0.349935i	$-0.113796\pi$
$272$	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	−0.617431	−	0.786625i	$-0.711827\pi$
$277$	46.8665	−	46.8665i	0.169193	−	0.169193i	0.786625	+	0.617431i	$0.211827\pi$
$278$	−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	$0.157042\pi$
$281$			266.157i			0.947179i	−0.880746	+	0.473590i	$0.842958\pi$
$282$	236.634	−	5.19408i	0.839128	−	0.0184187i
$283$	370.389	−	370.389i	1.30880	−	1.30880i	0.386512	−	0.922285i	$-0.373680\pi$
$283$	370.389	−	370.389i	1.30880	−	1.30880i	0.922285	−	0.386512i	$-0.126320\pi$
$284$	−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	−0.787710	−	0.616047i	$-0.788733\pi$
$293$	−50.2973	+	50.2973i	−0.171663	+	0.171663i	0.616047	+	0.787710i	$0.288733\pi$
$294$	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	0.0365891	−	0.999330i	$-0.488351\pi$
$307$	−295.562	−	295.562i	−0.962741	−	0.962741i	−0.999330	+	0.0365891i	$0.988351\pi$
$308$	−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	0.894262	−	0.447545i	$-0.147701\pi$
$313$	139.822	+	139.822i	0.446717	+	0.446717i	−0.447545	+	0.894262i	$0.647701\pi$
$314$	−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	0.920598	−	0.390512i	$-0.127702\pi$
$317$	168.037	+	168.037i	0.530086	+	0.530086i	−0.390512	+	0.920598i	$0.627702\pi$
$318$	−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	$0.138240\pi$
$331$			278.549i			0.841538i	−0.907168	+	0.420769i	$0.861760\pi$
$332$	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	−0.107001	+	0.994259i	$0.534125\pi$
$337$	−371.125	+	371.125i	−1.10126	+	1.10126i	−0.994259	+	0.107001i	$0.965875\pi$
$338$	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	−0.899184	−	0.437571i	$-0.855839\pi$
$347$	−160.180	+	160.180i	−0.461613	+	0.461613i	0.437571	+	0.899184i	$0.355839\pi$
$348$	−17.1716	+	63.9879i	−0.0493437	+	0.183873i
$349$		−	395.209i		−	1.13240i	−0.824266	−	0.566202i	$-0.808412\pi$
$349$		−	395.209i		−	1.13240i	0.824266	−	0.566202i	$-0.191588\pi$
$350$	−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	−0.880137	−	0.474719i	$-0.842550\pi$
$353$	−143.113	+	143.113i	−0.405418	+	0.405418i	0.474719	+	0.880137i	$0.342550\pi$
$354$	−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	$-0.817804\pi$
$359$		−	388.897i		−	1.08328i	0.840611	−	0.541639i	$-0.182196\pi$
$360$	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	0.999890	−	0.0148215i	$-0.00471801\pi$
$367$	361.520	+	361.520i	0.985069	+	0.985069i	−0.0148215	+	0.999890i	$0.504718\pi$
$368$	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	0.552667	−	0.833402i	$-0.313610\pi$
$373$	−104.714	−	104.714i	−0.280735	−	0.280735i	−0.833402	+	0.552667i	$0.813610\pi$
$374$	−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	0.994449	−	0.105223i	$-0.0335556\pi$
$383$	340.574	+	340.574i	0.889226	+	0.889226i	−0.105223	+	0.994449i	$0.533556\pi$
$384$	−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	−0.170585	−	0.985343i	$-0.554566\pi$
$397$	323.459	−	323.459i	0.814758	−	0.814758i	0.985343	+	0.170585i	$0.0545658\pi$
$398$	−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	$-0.700365\pi$
$401$		−	648.291i		−	1.61669i	0.588712	−	0.808343i	$-0.299635\pi$
$402$	−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	$0.00543247\pi$
$409$			13.9598i			0.0341315i	−0.999854	+	0.0170658i	$0.994568\pi$
$410$	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	$-0.876194\pi$
$419$		−	317.783i		−	0.758433i	0.925308	−	0.379216i	$-0.123806\pi$
$420$	−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	0.0172788	−	0.999851i	$-0.494500\pi$
$433$	−425.454	−	425.454i	−0.982572	−	0.982572i	−0.999851	+	0.0172788i	$0.994500\pi$
$434$	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	0.890345	−	0.455286i	$-0.150463\pi$
$443$	192.731	+	192.731i	0.435059	+	0.435059i	−0.455286	+	0.890345i	$0.650463\pi$
$444$	−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	−0.830060	−	0.557674i	$-0.811694\pi$
$457$	−124.480	+	124.480i	−0.272385	+	0.272385i	0.557674	+	0.830060i	$0.311694\pi$
$458$	−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	$0.125818\pi$
$461$			355.022i			0.770114i	−0.922893	+	0.385057i	$0.874182\pi$
$462$	−6.00434	−	273.548i	−0.0129964	−	0.592096i
$463$	−244.127	+	244.127i	−0.527272	+	0.527272i	−0.919758	−	0.392486i	$-0.871615\pi$
$463$	−244.127	+	244.127i	−0.527272	+	0.527272i	0.392486	+	0.919758i	$0.371615\pi$
$464$	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	−0.876277	−	0.481808i	$-0.839980\pi$
$467$	−184.217	+	184.217i	−0.394468	+	0.394468i	0.481808	+	0.876277i	$0.339980\pi$
$468$	−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	$-0.940254\pi$
$479$		−	178.759i		−	0.373192i	0.982437	−	0.186596i	$-0.0597455\pi$
$480$	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	0.719099	−	0.694907i	$-0.244555\pi$
$487$	11.7814	+	11.7814i	0.0241918	+	0.0241918i	−0.694907	+	0.719099i	$0.744555\pi$
$488$	−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	0.831086	−	0.556144i	$-0.187720\pi$
$503$	138.296	+	138.296i	0.274942	+	0.274942i	−0.556144	+	0.831086i	$0.687720\pi$
$504$	−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	$-0.806810\pi$
$521$		−	594.299i		−	1.14069i	0.821406	−	0.570345i	$-0.193190\pi$
$522$	−89.1631	−	43.8851i	−0.170810	−	0.0840711i
$523$	−543.498	+	543.498i	−1.03919	+	1.03919i	−0.0399922	+	0.999200i	$0.512733\pi$
$523$	−543.498	+	543.498i	−1.03919	+	1.03919i	−0.999200	+	0.0399922i	$0.987267\pi$
$524$	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	0.0954376	−	0.995435i	$-0.469575\pi$
$547$	−492.299	−	492.299i	−0.899998	−	0.899998i	−0.995435	+	0.0954376i	$0.969575\pi$
$548$	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	0.295632	−	0.955302i	$-0.404470\pi$
$557$	−367.436	−	367.436i	−0.659670	−	0.659670i	−0.955302	+	0.295632i	$0.904470\pi$
$558$	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	0.582773	−	0.812635i	$-0.301968\pi$
$563$	−129.412	−	129.412i	−0.229861	−	0.229861i	−0.812635	+	0.582773i	$0.801968\pi$
$564$	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	$-0.957138\pi$
$571$		−	153.311i		−	0.268496i	0.990948	−	0.134248i	$-0.0428618\pi$
$572$	−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	−0.296714	−	0.954966i	$-0.595891\pi$
$577$	379.812	−	379.812i	0.658252	−	0.658252i	0.954966	+	0.296714i	$0.0958909\pi$
$578$	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	−0.772247	−	0.635322i	$-0.780867\pi$
$587$	−80.3753	+	80.3753i	−0.136925	+	0.136925i	0.635322	+	0.772247i	$0.280867\pi$
$588$	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	−0.965386	−	0.260826i	$-0.916005\pi$
$593$	−417.804	+	417.804i	−0.704559	+	0.704559i	0.260826	+	0.965386i	$0.416005\pi$
$594$	−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	$0.235029\pi$
$599$			806.349i			1.34616i	−0.739570	+	0.673080i	$0.764971\pi$
$600$	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	0.872427	−	0.488745i	$-0.162545\pi$
$607$	232.895	+	232.895i	0.383682	+	0.383682i	−0.488745	+	0.872427i	$0.662545\pi$
$608$	−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	0.0592074	−	0.998246i	$-0.481143\pi$
$613$	−575.631	−	575.631i	−0.939038	−	0.939038i	−0.998246	+	0.0592074i	$0.981143\pi$
$614$	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	0.207275	−	0.978283i	$-0.433540\pi$
$617$	−475.711	−	475.711i	−0.771007	−	0.771007i	−0.978283	+	0.207275i	$0.933540\pi$
$618$	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	$0.190404\pi$
$631$			710.672i			1.12626i	−0.826367	+	0.563132i	$0.809596\pi$
$632$	−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	$0.112939\pi$
$641$			445.381i			0.694822i	−0.937713	+	0.347411i	$0.887061\pi$
$642$	656.847	−	14.4177i	1.02313	−	0.0224574i
$643$	−310.249	+	310.249i	−0.482502	+	0.482502i	−0.905930	−	0.423428i	$-0.860827\pi$
$643$	−310.249	+	310.249i	−0.482502	+	0.482502i	0.423428	+	0.905930i	$0.360827\pi$
$644$	−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	0.269265	−	0.963066i	$-0.413219\pi$
$647$	797.318	−	797.318i	1.23233	−	1.23233i	0.963066	−	0.269265i	$-0.0867806\pi$
$648$	−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	−0.0532438	+	0.998582i	$0.516956\pi$
$653$	−686.842	+	686.842i	−1.05183	+	1.05183i	−0.998582	+	0.0532438i	$0.983044\pi$
$654$	−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	$-0.840371\pi$
$659$		−	633.604i		−	0.961463i	0.876868	−	0.480732i	$-0.159629\pi$
$660$	−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	0.999716	−	0.0238351i	$-0.00758766\pi$
$673$	656.768	+	656.768i	0.975881	+	0.975881i	−0.0238351	+	0.999716i	$0.507588\pi$
$674$	−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	0.789565	−	0.613667i	$-0.210306\pi$
$677$	119.083	+	119.083i	0.175898	+	0.175898i	−0.613667	+	0.789565i	$0.710306\pi$
$678$	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	−0.921991	−	0.387211i	$-0.873439\pi$
$683$	−894.185	−	894.185i	−1.30920	−	1.30920i	−0.387211	−	0.921991i	$-0.626561\pi$
$684$	−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	$0.243728\pi$
$691$			957.776i			1.38607i	−0.720903	+	0.693036i	$0.756272\pi$
$692$	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	$0.0539317\pi$
$701$			236.408i			0.337244i	−0.985681	+	0.168622i	$0.946068\pi$
$702$	−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	$-0.999310\pi$
$709$		−	3.07348i		−	0.00433495i	0.999998	−	0.00216747i	$-0.000689929\pi$
$710$	−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	$0.213553\pi$
$719$			893.990i			1.24338i	−0.783264	+	0.621690i	$0.786447\pi$
$720$	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	0.892008	−	0.452020i	$-0.149296\pi$
$727$	319.871	+	319.871i	0.439988	+	0.439988i	−0.452020	+	0.892008i	$0.649296\pi$
$728$	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	0.193419	−	0.981116i	$-0.438042\pi$
$733$	−577.382	−	577.382i	−0.787698	−	0.787698i	−0.981116	+	0.193419i	$0.938042\pi$
$734$	−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	0.748343	−	0.663312i	$-0.230850\pi$
$743$	63.1774	+	63.1774i	0.0850302	+	0.0850302i	−0.663312	+	0.748343i	$0.730850\pi$
$744$	−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	$-0.844417\pi$
$751$		−	705.259i		−	0.939093i	0.882908	−	0.469547i	$-0.155583\pi$
$752$	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	−0.971322	−	0.237766i	$-0.923585\pi$
$757$	−555.302	+	555.302i	−0.733556	+	0.733556i	0.237766	+	0.971322i	$0.423585\pi$
$758$	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	$-0.714390\pi$
$761$		−	1189.64i		−	1.56326i	0.623745	−	0.781628i	$-0.285610\pi$
$762$	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	$-0.800800\pi$
$769$		−	900.882i		−	1.17150i	0.810492	−	0.585749i	$-0.199200\pi$
$770$	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	−0.940385	−	0.340113i	$-0.889535\pi$
$773$	−464.010	+	464.010i	−0.600272	+	0.600272i	0.340113	+	0.940385i	$0.389535\pi$
$774$	−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	0.302862	−	0.953034i	$-0.402058\pi$
$787$	−511.685	−	511.685i	−0.650172	−	0.650172i	−0.953034	+	0.302862i	$0.902058\pi$
$788$	−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	0.976558	−	0.215253i	$-0.0690576\pi$
$797$	606.760	+	606.760i	0.761305	+	0.761305i	−0.215253	+	0.976558i	$0.569058\pi$
$798$	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	$-0.978538\pi$
$811$		−	109.279i		−	0.134747i	0.997728	−	0.0673733i	$-0.0214618\pi$
$812$	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	$-0.957281\pi$
$821$		−	219.704i		−	0.267606i	0.991008	−	0.133803i	$-0.0427189\pi$
$822$	33.2836	+	1516.35i	0.0404910	+	1.84471i
$823$	1.99663	−	1.99663i	0.00242604	−	0.00242604i	−0.705893	−	0.708319i	$-0.749454\pi$
$823$	1.99663	−	1.99663i	0.00242604	−	0.00242604i	0.708319	+	0.705893i	$0.249454\pi$
$824$	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	0.116620	−	0.993177i	$-0.462794\pi$
$827$	917.802	−	917.802i	1.10980	−	1.10980i	0.993177	−	0.116620i	$-0.0372061\pi$
$828$	−618.291	+	675.098i	−0.746728	+	0.815335i
$829$			1134.07i			1.36800i	0.729482	+	0.684000i	$0.239761\pi$
$829$			1134.07i			1.36800i	−0.729482	+	0.684000i	$0.760239\pi$
$830$	−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	$0.121467\pi$
$839$			624.895i			0.744809i	−0.928070	+	0.372405i	$0.878533\pi$
$840$	−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	0.382310	−	0.924034i	$-0.375129\pi$
$853$	−462.091	−	462.091i	−0.541724	−	0.541724i	−0.924034	+	0.382310i	$0.875129\pi$
$854$	−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	0.878532	−	0.477684i	$-0.158524\pi$
$857$	343.527	+	343.527i	0.400848	+	0.400848i	−0.477684	+	0.878532i	$0.658524\pi$
$858$	−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	0.548839	−	0.835928i	$-0.315070\pi$
$863$	−247.757	−	247.757i	−0.287089	−	0.287089i	−0.835928	+	0.548839i	$0.815070\pi$
$864$	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	−0.380510	−	0.924777i	$-0.624252\pi$
$877$	477.322	−	477.322i	0.544266	−	0.544266i	0.924777	+	0.380510i	$0.124252\pi$
$878$	−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	$0.172166\pi$
$881$			907.230i			1.02977i	−0.857259	+	0.514886i	$0.827834\pi$
$882$	−457.727	+	929.982i	−0.518965	+	1.05440i
$883$	−55.2196	+	55.2196i	−0.0625364	+	0.0625364i	−0.737683	−	0.675147i	$-0.764080\pi$
$883$	−55.2196	+	55.2196i	−0.0625364	+	0.0625364i	0.675147	+	0.737683i	$0.264080\pi$
$884$	−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	−0.955816	−	0.293966i	$-0.905025\pi$
$887$	−587.061	+	587.061i	−0.661850	+	0.661850i	0.293966	+	0.955816i	$0.405025\pi$
$888$	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	0.947774	−	0.318943i	$-0.103328\pi$
$907$	570.349	+	570.349i	0.628831	+	0.628831i	−0.318943	+	0.947774i	$0.603328\pi$
$908$	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	−0.175816	−	0.984423i	$-0.556256\pi$
$937$	757.665	−	757.665i	0.808607	−	0.808607i	0.984423	+	0.175816i	$0.0562564\pi$
$938$	−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	$0.309540\pi$
$941$			1555.04i			1.65254i	−0.563277	+	0.826268i	$0.690460\pi$
$942$	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	−0.880585	−	0.473889i	$-0.842850\pi$
$947$	−385.141	+	385.141i	−0.406696	+	0.406696i	0.473889	+	0.880585i	$0.342850\pi$
$948$	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	−0.430066	−	0.902797i	$-0.641510\pi$
$953$	450.513	−	450.513i	0.472731	−	0.472731i	0.902797	+	0.430066i	$0.141510\pi$
$954$	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	0.939542	−	0.342434i	$-0.111251\pi$
$967$	577.404	+	577.404i	0.597108	+	0.597108i	−0.342434	+	0.939542i	$0.611251\pi$
$968$	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	0.223095	−	0.974797i	$-0.428384\pi$
$977$	−734.412	−	734.412i	−0.751702	−	0.751702i	−0.974797	+	0.223095i	$0.928384\pi$
$978$	−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	0.888323	−	0.459220i	$-0.151871\pi$
$983$	421.808	+	421.808i	0.429103	+	0.429103i	−0.459220	+	0.888323i	$0.651871\pi$
$984$	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	$0.182900\pi$
$991$			1077.21i			1.08699i	−0.839411	+	0.543496i	$0.817100\pi$
$992$	−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	−0.00236078	+	0.999997i	$0.500751\pi$
$997$	−999.351	+	999.351i	−1.00236	+	1.00236i	−0.999997	+	0.00236078i	$0.999249\pi$
$998$	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.23.14	yes	40
3.2	odd	2	inner	60.3.l.a.23.7	yes	40
4.3	odd	2	inner	60.3.l.a.23.17	yes	40
5.2	odd	4	inner	60.3.l.a.47.4	yes	40
5.3	odd	4		300.3.l.g.107.17		40
5.4	even	2		300.3.l.g.143.7		40
12.11	even	2	inner	60.3.l.a.23.4	✓	40
15.2	even	4	inner	60.3.l.a.47.17	yes	40
15.8	even	4		300.3.l.g.107.4		40
15.14	odd	2		300.3.l.g.143.14		40
20.3	even	4		300.3.l.g.107.14		40
20.7	even	4	inner	60.3.l.a.47.7	yes	40
20.19	odd	2		300.3.l.g.143.4		40
60.23	odd	4		300.3.l.g.107.7		40
60.47	odd	4	inner	60.3.l.a.47.14	yes	40
60.59	even	2		300.3.l.g.143.17		40

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

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

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