LMFDB - Embedded newform 126.3.i.a.65.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(65,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.65"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.5
Character	$\chi$	$=$	126.65
Dual form			126.3.i.a.95.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 0.707107i) q^{2} +(0.810726 + 2.88838i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.39465i q^{5} +(-3.03532 - 2.96426i) q^{6} +(6.52929 + 2.52357i) q^{7} +2.82843i q^{8} +(-7.68545 + 4.68336i) q^{9} +(-1.69327 - 2.93283i) q^{10} +5.83940i q^{11} +(5.81354 + 1.48416i) q^{12} +(-2.87005 - 4.97107i) q^{13} +(-9.78115 + 1.52617i) q^{14} +(-6.91665 + 1.94140i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-21.4241 + 12.3692i) q^{17} +(6.10108 - 11.1704i) q^{18} +(-1.06883 + 1.85127i) q^{19} +(4.14765 + 2.39465i) q^{20} +(-1.99557 + 20.9050i) q^{21} +(-4.12908 - 7.15177i) q^{22} +0.142721i q^{23} +(-8.16956 + 2.29308i) q^{24} +19.2657 q^{25} +(7.03015 + 4.05886i) q^{26} +(-19.7581 - 18.4016i) q^{27} +(10.9002 - 8.78548i) q^{28} +(31.4557 + 18.1610i) q^{29} +(7.09835 - 7.26853i) q^{30} +(-6.52325 + 11.2986i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-16.8664 + 4.73415i) q^{33} +(17.4927 - 30.2982i) q^{34} +(-6.04307 + 15.6353i) q^{35} +(0.426375 + 17.9949i) q^{36} +(16.0604 - 27.8173i) q^{37} -3.02311i q^{38} +(12.0315 - 12.3200i) q^{39} -6.77309 q^{40} +(27.3943 - 15.8161i) q^{41} +(-12.3380 - 27.0143i) q^{42} +(40.1194 - 69.4888i) q^{43} +(10.1141 + 5.83940i) q^{44} +(-11.2150 - 18.4040i) q^{45} +(-0.100919 - 0.174796i) q^{46} +(52.9798 - 30.5879i) q^{47} +(8.38418 - 8.58519i) q^{48} +(36.2631 + 32.9543i) q^{49} +(-23.5955 + 13.6229i) q^{50} +(-53.0959 - 51.8528i) q^{51} -11.4802 q^{52} +(-22.5819 + 13.0377i) q^{53} +(37.2105 + 8.56611i) q^{54} -13.9833 q^{55} +(-7.13774 + 18.4676i) q^{56} +(-6.21370 - 1.58632i) q^{57} -51.3669 q^{58} +(-19.7078 - 11.3783i) q^{59} +(-3.55404 + 13.9214i) q^{60} +(51.3320 + 88.9096i) q^{61} -18.4505i q^{62} +(-61.9993 + 11.1842i) q^{63} -8.00000 q^{64} +(11.9040 - 6.87276i) q^{65} +(17.3095 - 17.7245i) q^{66} +(-35.1190 + 60.8279i) q^{67} +49.4768i q^{68} +(-0.412231 + 0.115707i) q^{69} +(-3.65464 - 23.4224i) q^{70} -100.792i q^{71} +(-13.2466 - 21.7377i) q^{72} +(-4.36953 - 7.56824i) q^{73} +45.4255i q^{74} +(15.6192 + 55.6465i) q^{75} +(2.13766 + 3.70254i) q^{76} +(-14.7362 + 38.1271i) q^{77} +(-6.02400 + 23.5964i) q^{78} +(31.1461 + 53.9466i) q^{79} +(8.29531 - 4.78930i) q^{80} +(37.1322 - 71.9875i) q^{81} +(-22.3674 + 38.7414i) q^{82} +(-51.5381 - 29.7555i) q^{83} +(34.2129 + 24.3614i) q^{84} +(-29.6199 - 51.3031i) q^{85} +113.475i q^{86} +(-26.9537 + 105.579i) q^{87} -16.5163 q^{88} +(94.6860 + 54.6670i) q^{89} +(26.7491 + 14.6099i) q^{90} +(-6.19450 - 39.7003i) q^{91} +(0.247199 + 0.142721i) q^{92} +(-37.9232 - 9.68155i) q^{93} +(-43.2578 + 74.9248i) q^{94} +(-4.43315 - 2.55948i) q^{95} +(-4.19784 + 16.4432i) q^{96} +(-79.8603 + 138.322i) q^{97} +(-67.7153 - 14.7187i) q^{98} +(-27.3480 - 44.8784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 8 q^{6} + 2 q^{7} + 4 q^{9} + 10 q^{13} + 36 q^{14} + 10 q^{15} - 64 q^{16} + 54 q^{17} + 24 q^{18} + 28 q^{19} + 16 q^{21} + 8 q^{24} - 160 q^{25} + 72 q^{26} - 126 q^{27} - 4 q^{28}+ \cdots + 394 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 + 8 * q^6 + 2 * q^7 + 4 * q^9 + 10 * q^13 + 36 * q^14 + 10 * q^15 - 64 * q^16 + 54 * q^17 + 24 * q^18 + 28 * q^19 + 16 * q^21 + 8 * q^24 - 160 * q^25 + 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 - 80 * q^30 - 8 * q^31 - 106 * q^33 + 90 * q^35 + 40 * q^36 + 22 * q^37 - 170 * q^39 + 72 * q^41 + 72 * q^42 + 16 * q^43 - 72 * q^44 - 250 * q^45 - 12 * q^46 - 108 * q^47 + 74 * q^49 - 288 * q^50 + 122 * q^51 + 40 * q^52 + 72 * q^53 + 8 * q^54 - 24 * q^55 - 282 * q^57 + 48 * q^58 - 90 * q^59 + 52 * q^60 - 62 * q^61 - 438 * q^63 - 256 * q^64 + 378 * q^65 + 224 * q^66 + 70 * q^67 + 218 * q^69 - 108 * q^70 + 48 * q^72 + 196 * q^73 + 166 * q^75 - 56 * q^76 + 630 * q^77 + 32 * q^78 - 38 * q^79 + 400 * q^81 + 184 * q^84 + 60 * q^85 - 98 * q^87 + 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 - 182 * q^93 + 168 * q^94 - 72 * q^95 - 16 * q^96 - 38 * q^97 - 288 * q^98 + 394 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	0.810726	+	2.88838i	0.270242	+	0.962792i
$3$	0.810726	+	2.88838i	0.270242	+	0.962792i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$			2.39465i			0.478930i	0.970905	+	0.239465i	$0.0769720\pi$
$5$			2.39465i			0.478930i	−0.970905	+	0.239465i	$0.923028\pi$
$6$	−3.03532	−	2.96426i	−0.505887	−	0.494043i
$7$	6.52929	+	2.52357i	0.932755	+	0.360511i
$7$	6.52929	+	2.52357i	0.932755	+	0.360511i
$8$			2.82843i			0.353553i
$9$	−7.68545	+	4.68336i	−0.853939	+	0.520374i
$10$	−1.69327	−	2.93283i	−0.169327	−	0.293283i
$11$			5.83940i			0.530854i	0.964131	+	0.265427i	$0.0855130\pi$
$11$			5.83940i			0.530854i	−0.964131	+	0.265427i	$0.914487\pi$
$12$	5.81354	+	1.48416i	0.484462	+	0.123680i
$13$	−2.87005	−	4.97107i	−0.220773	−	0.382390i	0.734270	−	0.678858i	$-0.237525\pi$
$13$	−2.87005	−	4.97107i	−0.220773	−	0.382390i	−0.955043	+	0.296468i	$0.904191\pi$
$14$	−9.78115	+	1.52617i	−0.698653	+	0.109012i
$15$	−6.91665	+	1.94140i	−0.461110	+	0.129427i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−21.4241	+	12.3692i	−1.26024	+	0.727600i	−0.973121	−	0.230296i	$-0.926031\pi$
$17$	−21.4241	+	12.3692i	−1.26024	+	0.727600i	−0.287119	+	0.957895i	$0.592697\pi$
$18$	6.10108	−	11.1704i	0.338949	−	0.620575i
$19$	−1.06883	+	1.85127i	−0.0562543	+	0.0974353i	−0.892781	−	0.450491i	$-0.851249\pi$
$19$	−1.06883	+	1.85127i	−0.0562543	+	0.0974353i	0.836527	+	0.547926i	$0.184582\pi$
$20$	4.14765	+	2.39465i	0.207383	+	0.119732i
$21$	−1.99557	+	20.9050i	−0.0950274	+	0.995475i
$22$	−4.12908	−	7.15177i	−0.187685	−	0.325081i
$23$			0.142721i			0.00620524i	0.999995	+	0.00310262i	$0.000987596\pi$
$23$			0.142721i			0.00620524i	−0.999995	+	0.00310262i	$0.999012\pi$
$24$	−8.16956	+	2.29308i	−0.340399	+	0.0955449i
$25$	19.2657			0.770626
$26$	7.03015	+	4.05886i	0.270391	+	0.156110i
$27$	−19.7581	−	18.4016i	−0.731782	−	0.681539i
$28$	10.9002	−	8.78548i	0.389294	−	0.313767i
$29$	31.4557	+	18.1610i	1.08468	+	0.626240i	0.932155	−	0.362060i	$-0.117926\pi$
$29$	31.4557	+	18.1610i	1.08468	+	0.626240i	0.152524	+	0.988300i	$0.451260\pi$
$30$	7.09835	−	7.26853i	0.236612	−	0.242284i
$31$	−6.52325	+	11.2986i	−0.210427	+	0.364471i	−0.951848	−	0.306569i	$-0.900819\pi$
$31$	−6.52325	+	11.2986i	−0.210427	+	0.364471i	0.741421	+	0.671040i	$0.234152\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	−16.8664	+	4.73415i	−0.511103	+	0.143459i
$34$	17.4927	−	30.2982i	0.514491	−	0.891124i
$35$	−6.04307	+	15.6353i	−0.172659	+	0.446724i
$36$	0.426375	+	17.9949i	0.0118437	+	0.499860i
$37$	16.0604	−	27.8173i	0.434064	−	0.751820i	−0.563155	−	0.826351i	$-0.690413\pi$
$37$	16.0604	−	27.8173i	0.434064	−	0.751820i	0.997219	+	0.0745311i	$0.0237460\pi$
$38$		−	3.02311i		−	0.0795556i
$39$	12.0315	−	12.3200i	0.308500	−	0.315896i
$40$	−6.77309			−0.169327
$41$	27.3943	−	15.8161i	0.668155	−	0.385759i	−0.127222	−	0.991874i	$-0.540606\pi$
$41$	27.3943	−	15.8161i	0.668155	−	0.385759i	0.795377	+	0.606115i	$0.207273\pi$
$42$	−12.3380	−	27.0143i	−0.293761	−	0.643198i
$43$	40.1194	−	69.4888i	0.933009	−	1.61602i	0.154863	−	0.987936i	$-0.450506\pi$
$43$	40.1194	−	69.4888i	0.933009	−	1.61602i	0.778146	−	0.628083i	$-0.216160\pi$
$44$	10.1141	+	5.83940i	0.229867	+	0.132714i
$45$	−11.2150	−	18.4040i	−0.249222	−	0.408977i
$46$	−0.100919	−	0.174796i	−0.00219388	−	0.00379992i
$47$	52.9798	−	30.5879i	1.12723	−	0.650807i	0.183993	−	0.982927i	$-0.441098\pi$
$47$	52.9798	−	30.5879i	1.12723	−	0.650807i	0.943237	+	0.332121i	$0.107764\pi$
$48$	8.38418	−	8.58519i	0.174670	−	0.178858i
$49$	36.2631	+	32.9543i	0.740064	+	0.672536i
$50$	−23.5955	+	13.6229i	−0.471910	+	0.272458i
$51$	−53.0959	−	51.8528i	−1.04110	−	1.01672i
$52$	−11.4802			−0.220773
$53$	−22.5819	+	13.0377i	−0.426074	+	0.245994i	−0.697673	−	0.716417i	$-0.745781\pi$
$53$	−22.5819	+	13.0377i	−0.426074	+	0.245994i	0.271599	+	0.962411i	$0.412448\pi$
$54$	37.2105	+	8.56611i	0.689083	+	0.158632i
$55$	−13.9833			−0.254242
$56$	−7.13774	+	18.4676i	−0.127460	+	0.329779i
$57$	−6.21370	−	1.58632i	−0.109012	−	0.0278301i
$58$	−51.3669			−0.885637
$59$	−19.7078	−	11.3783i	−0.334031	−	0.192853i	0.323598	−	0.946195i	$-0.395107\pi$
$59$	−19.7078	−	11.3783i	−0.334031	−	0.192853i	−0.657629	+	0.753342i	$0.728441\pi$
$60$	−3.55404	+	13.9214i	−0.0592340	+	0.232023i
$61$	51.3320	+	88.9096i	0.841508	+	1.45754i	0.888619	+	0.458645i	$0.151665\pi$
$61$	51.3320	+	88.9096i	0.841508	+	1.45754i	−0.0471111	+	0.998890i	$0.515001\pi$
$62$		−	18.4505i		−	0.297589i
$63$	−61.9993	+	11.1842i	−0.984116	+	0.177527i
$64$	−8.00000			−0.125000
$65$	11.9040	−	6.87276i	0.183138	−	0.105735i
$66$	17.3095	−	17.7245i	0.262265	−	0.268552i
$67$	−35.1190	+	60.8279i	−0.524164	+	0.907879i	0.475440	+	0.879748i	$0.342289\pi$
$67$	−35.1190	+	60.8279i	−0.524164	+	0.907879i	−0.999604	+	0.0281308i	$0.991044\pi$
$68$			49.4768i			0.727600i
$69$	−0.412231	+	0.115707i	−0.00597436	+	0.00167692i
$70$	−3.65464	−	23.4224i	−0.0522091	−	0.334606i
$71$		−	100.792i		−	1.41961i	−0.704399	−	0.709804i	$-0.748784\pi$
$71$		−	100.792i		−	1.41961i	0.704399	−	0.709804i	$-0.251216\pi$
$72$	−13.2466	−	21.7377i	−0.183980	−	0.301913i
$73$	−4.36953	−	7.56824i	−0.0598565	−	0.103675i	0.834544	−	0.550941i	$-0.185731\pi$
$73$	−4.36953	−	7.56824i	−0.0598565	−	0.103675i	−0.894401	+	0.447266i	$0.852398\pi$
$74$			45.4255i			0.613859i
$75$	15.6192	+	55.6465i	0.208255	+	0.741953i
$76$	2.13766	+	3.70254i	0.0281272	+	0.0487177i
$77$	−14.7362	+	38.1271i	−0.191379	+	0.495157i
$78$	−6.02400	+	23.5964i	−0.0772307	+	0.302517i
$79$	31.1461	+	53.9466i	0.394254	+	0.682868i	0.993006	−	0.118067i	$-0.0376696\pi$
$79$	31.1461	+	53.9466i	0.394254	+	0.682868i	−0.598751	+	0.800935i	$0.704336\pi$
$80$	8.29531	−	4.78930i	0.103691	−	0.0598662i
$81$	37.1322	−	71.9875i	0.458422	−	0.888734i
$82$	−22.3674	+	38.7414i	−0.272773	+	0.472457i
$83$	−51.5381	−	29.7555i	−0.620941	−	0.358501i	0.156294	−	0.987711i	$-0.450045\pi$
$83$	−51.5381	−	29.7555i	−0.620941	−	0.358501i	−0.777235	+	0.629210i	$0.783379\pi$
$84$	34.2129	+	24.3614i	0.407296	+	0.290017i
$85$	−29.6199	−	51.3031i	−0.348469	−	0.603566i
$86$			113.475i			1.31947i
$87$	−26.9537	+	105.579i	−0.309813	+	1.21356i
$88$	−16.5163			−0.187685
$89$	94.6860	+	54.6670i	1.06389	+	0.614236i	0.926505	−	0.376282i	$-0.122798\pi$
$89$	94.6860	+	54.6670i	1.06389	+	0.614236i	0.137382	+	0.990518i	$0.456131\pi$
$90$	26.7491	+	14.6099i	0.297212	+	0.162333i
$91$	−6.19450	−	39.7003i	−0.0680715	−	0.436267i
$92$	0.247199	+	0.142721i	0.00268695	+	0.00155131i
$93$	−37.9232	−	9.68155i	−0.407776	−	0.104103i
$94$	−43.2578	+	74.9248i	−0.460190	+	0.797072i
$95$	−4.43315	−	2.55948i	−0.0466647	−	0.0269419i
$96$	−4.19784	+	16.4432i	−0.0437275	+	0.171283i
$97$	−79.8603	+	138.322i	−0.823302	+	1.42600i	0.0799082	+	0.996802i	$0.474537\pi$
$97$	−79.8603	+	138.322i	−0.823302	+	1.42600i	−0.903210	+	0.429199i	$0.858796\pi$
$98$	−67.7153	−	14.7187i	−0.690972	−	0.150190i
$99$	−27.3480	−	44.8784i	−0.276243	−	0.453317i
$100$	19.2657	−	33.3691i	0.192657	−	0.333691i
$101$		−	127.320i		−	1.26060i	−0.776353	−	0.630298i	$-0.782933\pi$
$101$		−	127.320i		−	1.26060i	0.776353	−	0.630298i	$-0.217067\pi$
$102$	101.694	+	25.9619i	0.997004	+	0.254529i
$103$	−48.9784			−0.475518			−0.237759	−	0.971324i	$-0.576413\pi$
$103$	−48.9784			−0.475518			−0.237759	+	0.971324i	$0.576413\pi$
$104$	14.0603	−	8.11772i	0.135195	−	0.0780550i
$105$	−50.0601	−	4.77870i	−0.476762	−	0.0455114i
$106$	18.4380	−	31.9356i	0.173944	−	0.301280i
$107$	−116.454	−	67.2350i	−1.08836	−	0.628364i	−0.155220	−	0.987880i	$-0.549608\pi$
$107$	−116.454	−	67.2350i	−1.08836	−	0.628364i	−0.933139	+	0.359516i	$0.882942\pi$
$108$	−51.6305	+	15.8205i	−0.478060	+	0.146486i
$109$	−83.0714	−	143.884i	−0.762123	−	1.32004i	−0.941754	−	0.336302i	$-0.890824\pi$
$109$	−83.0714	−	143.884i	−0.762123	−	1.32004i	0.179631	−	0.983734i	$-0.442510\pi$
$110$	17.1260	−	9.88769i	0.155691	−	0.0898881i
$111$	93.3675	+	23.8361i	0.841149	+	0.214740i
$112$	−4.31666	−	27.6653i	−0.0385416	−	0.247011i
$113$	174.655	−	100.837i	1.54562	−	0.892363i	0.547149	−	0.837035i	$-0.315713\pi$
$113$	174.655	−	100.837i	1.54562	−	0.892363i	0.998468	−	0.0553276i	$-0.0176203\pi$
$114$	8.73189	−	2.45092i	0.0765956	−	0.0214993i
$115$	−0.341766			−0.00297187
$116$	62.9114	−	36.3219i	0.542340	−	0.313120i
$117$	45.3389	+	24.7634i	0.387512	+	0.211653i
$118$	32.1827			0.272735
$119$	−171.098	+	26.6968i	−1.43780	+	0.224343i
$120$	−5.49112	−	19.5632i	−0.0457593	−	0.163027i
$121$	86.9014			0.718194
$122$	−125.737	−	72.5944i	−1.03063	−	0.595036i
$123$	67.8922	+	66.3026i	0.551969	+	0.539046i
$124$	13.0465	+	22.5972i	0.105214	+	0.182236i
$125$			106.001i			0.848006i
$126$	68.0249	−	57.5379i	0.539880	−	0.456650i
$127$	−32.4486			−0.255501			−0.127750	−	0.991806i	$-0.540776\pi$
$127$	−32.4486			−0.255501			−0.127750	+	0.991806i	$0.540776\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	233.236	+	59.5436i	1.80803	+	0.461578i
$130$	−9.71955	+	16.8348i	−0.0747658	+	0.129498i
$131$		−	183.000i		−	1.39695i	−0.715636	−	0.698473i	$-0.753863\pi$
$131$		−	183.000i		−	1.39695i	0.715636	−	0.698473i	$-0.246137\pi$
$132$	−8.66660	+	33.9476i	−0.0656560	+	0.257179i
$133$	−11.6505	+	9.39020i	−0.0875980	+	0.0706030i
$134$		−	99.3315i		−	0.741280i
$135$	44.0653	−	47.3137i	0.326409	−	0.350472i
$136$	−34.9854	−	60.5964i	−0.257245	−	0.445562i
$137$			30.8245i			0.224997i	0.993652	+	0.112498i	$0.0358853\pi$
$137$			30.8245i			0.224997i	−0.993652	+	0.112498i	$0.964115\pi$
$138$	0.423060	−	0.433203i	0.00306565	−	0.00313915i
$139$	27.7854	+	48.1257i	0.199895	+	0.346228i	0.948494	−	0.316795i	$-0.102607\pi$
$139$	27.7854	+	48.1257i	0.199895	+	0.346228i	−0.748599	+	0.663023i	$0.769273\pi$
$140$	21.0381	+	26.1023i	0.150272	+	0.186445i
$141$	131.302	+	128.227i	0.931217	+	0.909413i
$142$	71.2708	+	123.445i	0.501907	+	0.869329i
$143$	29.0281	−	16.7594i	0.202993	−	0.117198i
$144$	31.5945	+	17.2564i	0.219407	+	0.119836i
$145$	−43.4891	+	75.3253i	−0.299925	+	0.519485i
$146$	10.7031	+	6.17945i	0.0733090	+	0.0423250i
$147$	−65.7849	+	131.459i	−0.447516	+	0.894276i
$148$	−32.1207	−	55.6347i	−0.217032	−	0.375910i
$149$		−	7.38142i		−	0.0495397i	−0.999693	−	0.0247699i	$-0.992115\pi$
$149$		−	7.38142i		−	0.0495397i	0.999693	−	0.0247699i	$-0.00788530\pi$
$150$	−58.4775	−	57.1083i	−0.389850	−	0.380722i
$151$	34.5368			0.228720			0.114360	−	0.993439i	$-0.463518\pi$
$151$	34.5368			0.228720			0.114360	+	0.993439i	$0.463518\pi$
$152$	−5.23619	−	3.02311i	−0.0344486	−	0.0198889i
$153$	106.724	−	195.399i	0.697543	−	1.27712i
$154$	−8.91190	−	57.1160i	−0.0578695	−	0.370883i
$155$	−27.0562	−	15.6209i	−0.174556	−	0.100780i
$156$	−9.30729	−	33.1591i	−0.0596621	−	0.212559i
$157$	−96.3161	+	166.824i	−0.613478	+	1.06258i	0.377171	+	0.926144i	$0.376897\pi$
$157$	−96.3161	+	166.824i	−0.613478	+	1.06258i	−0.990649	+	0.136432i	$0.956436\pi$
$158$	−76.2920	−	44.0472i	−0.482861	−	0.278780i
$159$	−55.9654	−	54.6551i	−0.351984	−	0.343743i
$160$	−6.77309	+	11.7313i	−0.0423318	+	0.0733209i
$161$	−0.360166	+	0.931863i	−0.00223705	+	0.00578797i
$162$	5.42534	+	114.423i	0.0334898	+	0.706313i
$163$	113.038	−	195.787i	0.693484	−	1.20115i	−0.277205	−	0.960811i	$-0.589408\pi$
$163$	113.038	−	195.787i	0.693484	−	1.20115i	0.970689	−	0.240339i	$-0.0772586\pi$
$164$		−	63.2645i		−	0.385759i
$165$	−11.3366	−	40.3891i	−0.0687068	−	0.244782i
$166$	84.1614			0.506996
$167$	−113.351	+	65.4431i	−0.678747	+	0.391875i	−0.799383	−	0.600822i	$-0.794840\pi$
$167$	−113.351	+	65.4431i	−0.678747	+	0.391875i	0.120636	+	0.992697i	$0.461507\pi$
$168$	−59.1282	−	5.64434i	−0.351953	−	0.0335972i
$169$	68.0256	−	117.824i	0.402519	−	0.697183i
$170$	72.5536	+	41.8888i	0.426786	+	0.246405i
$171$	−0.455723	−	19.2336i	−0.00266505	−	0.112477i
$172$	−80.2388	−	138.978i	−0.466505	−	0.808010i
$173$	−69.4338	+	40.0876i	−0.401351	+	0.231720i	−0.687067	−	0.726594i	$-0.741102\pi$
$173$	−69.4338	+	40.0876i	−0.401351	+	0.231720i	0.285716	+	0.958314i	$0.407769\pi$
$174$	−41.6445	−	148.367i	−0.239336	−	0.852684i
$175$	125.791	+	48.6183i	0.718806	+	0.277819i
$176$	20.2283	−	11.6788i	0.114933	−	0.0663568i
$177$	16.8872	−	66.1483i	0.0954081	−	0.373719i
$178$	−154.622			−0.868660
$179$	90.6710	−	52.3489i	0.506542	−	0.292452i	−0.224869	−	0.974389i	$-0.572195\pi$
$179$	90.6710	−	52.3489i	0.506542	−	0.292452i	0.731411	+	0.681937i	$0.238862\pi$
$180$	−43.0916	+	1.02102i	−0.239398	+	0.00567232i
$181$	−177.386			−0.980033			−0.490016	−	0.871713i	$-0.663009\pi$
$181$	−177.386			−0.980033			−0.490016	+	0.871713i	$0.663009\pi$
$182$	35.6590	+	44.2426i	0.195929	+	0.243091i
$183$	−215.188	+	220.348i	−1.17589	+	1.20408i
$184$	−0.403675			−0.00219388
$185$	66.6128	+	38.4589i	0.360069	+	0.207886i
$186$	53.2921	−	14.9583i	0.286517	−	0.0804211i
$187$	−72.2286	−	125.104i	−0.386249	−	0.669004i
$188$		−	122.352i		−	0.650807i
$189$	−82.5687	−	170.010i	−0.436871	−	0.899524i
$190$	7.23930			0.0381016
$191$	−152.173	+	87.8573i	−0.796719	+	0.459986i	−0.842322	−	0.538974i	$-0.818812\pi$
$191$	−152.173	+	87.8573i	−0.796719	+	0.459986i	0.0456039	+	0.998960i	$0.485479\pi$
$192$	−6.48580	−	23.1070i	−0.0337802	−	0.120349i
$193$	−40.8408	+	70.7383i	−0.211610	+	0.366520i	−0.952219	−	0.305417i	$-0.901204\pi$
$193$	−40.8408	+	70.7383i	−0.211610	+	0.366520i	0.740608	+	0.671937i	$0.234537\pi$
$194$		−	225.879i		−	1.16432i
$195$	29.5020	+	28.8112i	0.151292	+	0.147750i
$196$	93.3416	−	29.8553i	0.476233	−	0.152323i
$197$			318.861i			1.61858i	0.587407	+	0.809292i	$0.300149\pi$
$197$			318.861i			1.61858i	−0.587407	+	0.809292i	$0.699851\pi$
$198$	65.2282	+	35.6266i	0.329435	+	0.179932i
$199$	187.878	+	325.414i	0.944109	+	1.63524i	0.757525	+	0.652806i	$0.226408\pi$
$199$	187.878	+	325.414i	0.944109	+	1.63524i	0.186583	+	0.982439i	$0.440259\pi$
$200$			54.4915i			0.272458i
$201$	−204.166	−	52.1222i	−1.01575	−	0.259314i
$202$	90.0290	+	155.935i	0.445688	+	0.771955i
$203$	159.553	+	197.959i	0.785974	+	0.975167i
$204$	−142.908	+	40.1121i	−0.700527	+	0.196628i
$205$	37.8741	+	65.5998i	0.184752	+	0.319999i
$206$	59.9860	−	34.6329i	0.291194	−	0.168121i
$207$	−0.668412	−	1.09687i	−0.00322904	−	0.00529889i
$208$	−11.4802	+	19.8843i	−0.0551932	+	0.0955975i
$209$	−10.8103	−	6.24134i	−0.0517240	−	0.0298629i
$210$	64.6899	−	29.5451i	0.308047	−	0.140691i
$211$	−130.248	−	225.596i	−0.617289	−	1.06918i	−0.989978	−	0.141220i	$-0.954898\pi$
$211$	−130.248	−	225.596i	−0.617289	−	1.06918i	0.372689	−	0.927956i	$-0.378436\pi$
$212$			52.1507i			0.245994i
$213$	291.126	−	81.7148i	1.36679	−	0.383638i
$214$	190.169			0.888641
$215$	166.401	+	96.0719i	0.773960	+	0.446846i
$216$	52.0474	−	55.8844i	0.240960	−	0.258724i
$217$	−71.1050	+	57.3099i	−0.327673	+	0.264101i
$218$	203.483	+	117.481i	0.933406	+	0.538902i
$219$	18.3175	−	18.7566i	0.0836414	−	0.0856466i
$220$	−13.9833	+	24.2198i	−0.0635605	+	0.110090i
$221$	122.976	+	71.0004i	0.556453	+	0.321269i
$222$	−131.206	+	36.8276i	−0.591018	+	0.165890i
$223$	118.795	−	205.760i	0.532715	−	0.922690i	−0.466555	−	0.884492i	$-0.654505\pi$
$223$	118.795	−	205.760i	0.532715	−	0.922690i	0.999270	−	0.0381976i	$-0.0121616\pi$
$224$	24.8491	+	30.8305i	0.110933	+	0.137636i
$225$	−148.065	+	90.2281i	−0.658068	+	0.401014i
$226$	−142.605	+	246.999i	−0.630996	+	1.09292i
$227$		−	236.026i		−	1.03976i	−0.854238	−	0.519882i	$-0.825976\pi$
$227$		−	236.026i		−	1.03976i	0.854238	−	0.519882i	$-0.174024\pi$
$228$	−8.96128	+	9.17613i	−0.0393039	+	0.0402462i
$229$	−398.258			−1.73912			−0.869559	−	0.493830i	$-0.835597\pi$
$229$	−398.258			−1.73912			−0.869559	+	0.493830i	$0.835597\pi$
$230$	0.418576	−	0.241665i	0.00181989	−	0.00105072i
$231$	−122.072	−	11.6530i	−0.528452	−	0.0504457i
$232$	−51.3669	+	88.9701i	−0.221409	+	0.383492i
$233$	−131.868	−	76.1339i	−0.565956	−	0.326755i	0.189577	−	0.981866i	$-0.439288\pi$
$233$	−131.868	−	76.1339i	−0.565956	−	0.326755i	−0.755532	+	0.655111i	$0.772622\pi$
$234$	−73.0390	+	1.73060i	−0.312132	+	0.00739571i
$235$	73.2473	+	126.868i	0.311691	+	0.539864i
$236$	−39.4156	+	22.7566i	−0.167015	+	0.0964264i
$237$	−130.567	+	133.698i	−0.550917	+	0.564125i
$238$	190.674	−	153.682i	0.801153	−	0.645721i
$239$	−60.0571	+	34.6740i	−0.251285	+	0.145079i	−0.620353	−	0.784323i	$-0.713010\pi$
$239$	−60.0571	+	34.6740i	−0.251285	+	0.145079i	0.369067	+	0.929403i	$0.379677\pi$
$240$	20.5585	+	20.0772i	0.0856605	+	0.0836549i
$241$	−30.7525			−0.127604			−0.0638018	−	0.997963i	$-0.520323\pi$
$241$	−30.7525			−0.127604			−0.0638018	+	0.997963i	$0.520323\pi$
$242$	−106.432	+	61.4486i	−0.439802	+	0.253920i
$243$	238.031	+	48.8898i	0.979552	+	0.201192i
$244$	205.328			0.841508
$245$	−78.9139	+	86.8375i	−0.322098	+	0.354439i
$246$	−130.034	−	33.1968i	−0.528592	−	0.134946i
$247$	12.2704			0.0496777
$248$	−31.9573	−	18.4505i	−0.128860	−	0.0743973i
$249$	44.1620	−	172.985i	0.177357	−	0.694719i
$250$	−74.9538	−	129.824i	−0.299815	−	0.519295i
$251$			297.840i			1.18661i	0.804976	+	0.593307i	$0.202178\pi$
$251$			297.840i			1.18661i	−0.804976	+	0.593307i	$0.797822\pi$
$252$	−42.6277	+	118.570i	−0.169157	+	0.470517i
$253$	−0.833402			−0.00329408
$254$	39.7413	−	22.9446i	0.156462	−	0.0903332i
$255$	124.169	−	127.146i	0.486938	−	0.498612i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$		−	105.571i		−	0.410780i	−0.978680	−	0.205390i	$-0.934154\pi$
$257$		−	105.571i		−	0.410780i	0.978680	−	0.205390i	$-0.0658464\pi$
$258$	−327.758	+	91.9969i	−1.27038	+	0.356577i
$259$	175.062	−	141.098i	0.675914	−	0.544780i
$260$		−	27.4910i		−	0.105735i
$261$	−326.805	+	7.74337i	−1.25213	+	0.0296681i
$262$	129.400	+	224.128i	0.493895	+	0.855451i
$263$		−	106.110i		−	0.403459i	−0.979441	−	0.201730i	$-0.935344\pi$
$263$		−	106.110i		−	0.403459i	0.979441	−	0.201730i	$-0.0646563\pi$
$264$	−13.3902	−	47.7053i	−0.0507204	−	0.180702i
$265$	−31.2206	−	54.0757i	−0.117814	−	0.204059i
$266$	7.62905	−	19.7388i	0.0286806	−	0.0742059i
$267$	−81.1345	+	317.809i	−0.303875	+	1.19029i
$268$	70.2380	+	121.656i	0.262082	+	0.453939i
$269$	−195.184	+	112.689i	−0.725591	+	0.418920i	−0.816807	−	0.576911i	$-0.804258\pi$
$269$	−195.184	+	112.689i	−0.725591	+	0.418920i	0.0912161	+	0.995831i	$0.470925\pi$
$270$	−20.5128	+	89.1061i	−0.0759735	+	0.330023i
$271$	84.0102	−	145.510i	0.310001	−	0.536937i	−0.668362	−	0.743837i	$-0.733004\pi$
$271$	84.0102	−	145.510i	0.310001	−	0.536937i	0.978362	+	0.206900i	$0.0663374\pi$
$272$	85.6963	+	49.4768i	0.315060	+	0.181900i
$273$	109.647	−	50.0781i	0.401639	−	0.183436i
$274$	−21.7962	−	37.7522i	−0.0795483	−	0.137782i
$275$			112.500i			0.409090i
$276$	−0.211820	+	0.829712i	−0.000767464	+	0.00300620i
$277$	−335.538			−1.21133			−0.605663	−	0.795721i	$-0.707092\pi$
$277$	−335.538			−1.21133			−0.605663	+	0.795721i	$0.707092\pi$
$278$	−68.0600	−	39.2944i	−0.244820	−	0.141347i
$279$	−2.78135	−	117.386i	−0.00996899	−	0.420737i
$280$	−44.2234	−	17.0924i	−0.157941	−	0.0610443i
$281$	468.870	+	270.702i	1.66858	+	0.963353i	0.968406	+	0.249377i	$0.0802259\pi$
$281$	468.870	+	270.702i	1.66858	+	0.963353i	0.700170	+	0.713976i	$0.253107\pi$
$282$	−251.481	−	64.2015i	−0.891778	−	0.227665i
$283$	158.255	−	274.105i	0.559204	−	0.968570i	−0.438359	−	0.898800i	$-0.644440\pi$
$283$	158.255	−	274.105i	0.559204	−	0.968570i	0.997563	−	0.0697700i	$-0.0222265\pi$
$284$	−174.577	−	100.792i	−0.614708	−	0.354902i
$285$	3.79867	−	14.8796i	0.0133287	−	0.0522092i
$286$	−23.7013	+	41.0519i	−0.0828717	+	0.143538i
$287$	218.779	−	34.1364i	0.762295	−	0.118942i
$288$	−50.8974	+	1.20597i	−0.176727	+	0.00418739i
$289$	161.494	−	279.715i	0.558802	−	0.967874i
$290$		−	123.006i		−	0.424158i
$291$	−464.271	−	118.525i	−1.59543	−	0.407304i
$292$	−17.4781			−0.0598565
$293$	−224.604	+	129.675i	−0.766568	+	0.442578i	−0.831649	−	0.555302i	$-0.812603\pi$
$293$	−224.604	+	129.675i	−0.766568	+	0.442578i	0.0650812	+	0.997880i	$0.479269\pi$
$294$	−12.3855	−	207.520i	−0.0421275	−	0.705851i
$295$	27.2471	−	47.1933i	0.0923629	−	0.159977i
$296$	78.6793	+	45.4255i	0.265809	+	0.153465i
$297$	107.454	−	115.375i	0.361798	−	0.388470i
$298$	5.21945	+	9.04035i	0.0175149	+	0.0303368i
$299$	0.709473	−	0.409615i	0.00237282	−	0.00136995i
$300$	112.002	+	28.5933i	0.373339	+	0.0953110i
$301$	437.311	−	352.468i	1.45286	−	1.17099i
$302$	−42.2987	+	24.4212i	−0.140062	+	0.0808649i
$303$	367.749	−	103.222i	1.21369	−	0.340666i
$304$	8.55066			0.0281272
$305$	−212.907	+	122.922i	−0.698057	+	0.403023i
$306$	7.45844	+	314.780i	0.0243740	+	1.02869i
$307$	185.899			0.605534			0.302767	−	0.953065i	$-0.402090\pi$
$307$	185.899			0.605534			0.302767	+	0.953065i	$0.402090\pi$
$308$	51.3019	+	63.6509i	0.166565	+	0.206659i
$309$	−39.7080	−	141.468i	−0.128505	−	0.457825i
$310$	44.1826			0.142524
$311$	−6.01043	−	3.47012i	−0.0193261	−	0.0111579i	0.490306	−	0.871550i	$-0.336885\pi$
$311$	−6.01043	−	3.47012i	−0.0193261	−	0.0111579i	−0.509632	+	0.860393i	$0.670218\pi$
$312$	34.8461	+	34.0302i	0.111686	+	0.109071i
$313$	−198.056	−	343.043i	−0.632767	−	1.09598i	−0.986984	−	0.160821i	$-0.948586\pi$
$313$	−198.056	−	343.043i	−0.632767	−	1.09598i	0.354217	−	0.935163i	$-0.384748\pi$
$314$		−	272.423i		−	0.867589i
$315$	−26.7823	−	148.467i	−0.0850231	−	0.471322i
$316$	124.584			0.394254
$317$	−48.9278	+	28.2485i	−0.154346	+	0.0891120i	−0.575184	−	0.818024i	$-0.695070\pi$
$317$	−48.9278	+	28.2485i	−0.154346	+	0.0891120i	0.420838	+	0.907136i	$0.361736\pi$
$318$	107.190	+	27.3650i	0.337077	+	0.0860535i
$319$	−106.049	+	183.682i	−0.332442	+	0.575807i
$320$		−	19.1572i		−	0.0598662i
$321$	99.7874	−	390.873i	0.310864	−	1.21767i
$322$	−0.217815	−	1.39597i	−0.000676446	−	0.00433531i
$323$		−	52.8824i		−	0.163722i
$324$	−87.5538	−	136.302i	−0.270228	−	0.420686i
$325$	−55.2934	−	95.7709i	−0.170133	−	0.294680i
$326$			319.720i			0.980735i
$327$	348.243	−	356.592i	1.06496	−	1.09050i
$328$	44.7348	+	77.4829i	0.136386	+	0.236228i
$329$	423.111	−	66.0187i	1.28605	−	0.200665i
$330$	42.4439	+	41.4501i	0.128618	+	0.125606i
$331$	110.431	+	191.272i	0.333628	+	0.577861i	0.983220	−	0.182422i	$-0.0583937\pi$
$331$	110.431	+	191.272i	0.333628	+	0.577861i	−0.649592	+	0.760283i	$0.725060\pi$
$332$	−103.076	+	59.5111i	−0.310471	+	0.179250i
$333$	6.84773	+	289.005i	0.0205637	+	0.867883i
$334$	92.5505	−	160.302i	0.277097	−	0.479946i
$335$	−145.661	−	84.0977i	−0.434810	−	0.251038i
$336$	76.4081	−	34.8971i	0.227405	−	0.103860i
$337$	−171.431	−	296.928i	−0.508698	−	0.881092i	−0.999949	−	0.0100734i	$-0.996793\pi$
$337$	−171.431	−	296.928i	−0.508698	−	0.881092i	0.491251	−	0.871018i	$-0.336540\pi$
$338$			192.406i			0.569247i
$339$	432.852	+	422.718i	1.27685	+	1.24696i
$340$	−118.479			−0.348469
$341$	−65.9770	−	38.0919i	−0.193481	−	0.111706i
$342$	14.1583	+	23.2340i	0.0413987	+	0.0679356i
$343$	153.610	+	306.681i	0.447842	+	0.894113i
$344$	196.544	+	113.475i	0.571349	+	0.329869i
$345$	−0.277078	−	0.987148i	−0.000803125	−	0.00286130i
$346$	56.6924	−	98.1942i	0.163851	−	0.283798i
$347$	−316.483	−	182.721i	−0.912054	−	0.526574i	−0.0309622	−	0.999521i	$-0.509857\pi$
$347$	−316.483	−	182.721i	−0.912054	−	0.526574i	−0.881091	+	0.472946i	$0.843190\pi$
$348$	155.915	+	152.265i	0.448032	+	0.437542i
$349$	−2.62605	+	4.54846i	−0.00752451	+	0.0130328i	−0.869763	−	0.493469i	$-0.835728\pi$
$349$	−2.62605	+	4.54846i	−0.00752451	+	0.0130328i	0.862239	+	0.506502i	$0.169062\pi$
$350$	−188.440	+	29.4026i	−0.538401	+	0.0840075i
$351$	−34.7687	+	151.032i	−0.0990560	+	0.430291i
$352$	−16.5163	+	28.6071i	−0.0469213	+	0.0812701i
$353$		−	150.096i		−	0.425202i	−0.977139	−	0.212601i	$-0.931807\pi$
$353$		−	150.096i		−	0.425202i	0.977139	−	0.212601i	$-0.0681935\pi$
$354$	26.0914	+	92.9559i	0.0737044	+	0.262587i
$355$	241.362			0.679893
$356$	189.372	−	109.334i	0.531944	−	0.307118i
$357$	−215.824	−	472.553i	−0.604550	−	1.32368i
$358$	−74.0325	+	128.228i	−0.206795	+	0.358179i
$359$	−21.1053	−	12.1852i	−0.0587893	−	0.0339420i	0.470317	−	0.882497i	$-0.344139\pi$
$359$	−21.1053	−	12.1852i	−0.0587893	−	0.0339420i	−0.529107	+	0.848555i	$0.677473\pi$
$360$	52.0542	−	31.7208i	0.144595	−	0.0881134i
$361$	178.215	+	308.678i	0.493671	+	0.855063i
$362$	217.252	−	125.431i	0.600145	−	0.346494i
$363$	70.4532	+	251.004i	0.194086	+	0.691471i
$364$	−74.9575	−	28.9711i	−0.205927	−	0.0795910i
$365$	18.1233	−	10.4635i	0.0496528	−	0.0286671i
$366$	107.742	−	422.031i	0.294376	−	1.15309i
$367$	−543.780			−1.48169			−0.740845	−	0.671676i	$-0.765575\pi$
$367$	−543.780			−1.48169			−0.740845	+	0.671676i	$0.765575\pi$
$368$	0.494398	−	0.285441i	0.00134347	−	0.000775655i
$369$	−136.465	+	249.852i	−0.369824	+	0.677105i
$370$	−108.778			−0.293995
$371$	−180.345	+	28.1396i	−0.486106	+	0.0758479i
$372$	−54.6921	+	56.0034i	−0.147022	+	0.150547i
$373$	291.891			0.782551			0.391275	−	0.920274i	$-0.372034\pi$
$373$	291.891			0.782551			0.391275	+	0.920274i	$0.372034\pi$
$374$	176.923	+	102.147i	0.473057	+	0.273120i
$375$	−306.170	+	85.9375i	−0.816453	+	0.229167i
$376$	86.5157	+	149.850i	0.230095	+	0.398536i
$377$		−	208.491i		−	0.553027i
$378$	221.341	+	149.834i	0.585558	+	0.396386i
$379$	−387.585			−1.02265			−0.511325	−	0.859387i	$-0.670845\pi$
$379$	−387.585			−1.02265			−0.511325	+	0.859387i	$0.670845\pi$
$380$	−8.86629	+	5.11896i	−0.0233323	+	0.0134709i
$381$	−26.3069	−	93.7238i	−0.0690470	−	0.245994i
$382$	124.249	−	215.205i	0.325259	−	0.563365i
$383$		−	350.417i		−	0.914927i	−0.889229	−	0.457463i	$-0.848758\pi$
$383$		−	350.417i		−	0.914927i	0.889229	−	0.457463i	$-0.151242\pi$
$384$	24.2826	+	23.7140i	0.0632359	+	0.0617553i
$385$	−91.3010	−	35.2879i	−0.237146	−	0.0916569i
$386$		−	115.515i		−	0.299262i
$387$	17.1059	+	721.946i	0.0442013	+	1.86549i
$388$	159.721	+	276.644i	0.411651	+	0.713000i
$389$		−	513.942i		−	1.32119i	−0.750743	−	0.660594i	$-0.770304\pi$
$389$		−	513.942i		−	1.32119i	0.750743	−	0.660594i	$-0.229696\pi$
$390$	−56.5050	−	14.4254i	−0.144885	−	0.0369881i
$391$	−1.76534	−	3.05765i	−0.00451493	−	0.00782009i
$392$	−93.2088	+	102.568i	−0.237777	+	0.261652i
$393$	528.573	−	148.363i	1.34497	−	0.377513i
$394$	−225.469	−	390.523i	−0.572256	−	0.991176i
$395$	−129.183	+	74.5839i	−0.327046	+	0.188820i
$396$	−105.080	+	2.48977i	−0.265353	+	0.00628730i
$397$	−223.785	+	387.607i	−0.563690	+	0.976339i	0.433481	+	0.901163i	$0.357285\pi$
$397$	−223.785	+	387.607i	−0.563690	+	0.976339i	−0.997170	+	0.0751762i	$0.976048\pi$
$398$	−460.204	−	265.699i	−1.15629	−	0.667586i
$399$	−36.5678	−	26.0383i	−0.0916487	−	0.0652588i
$400$	−38.5313	−	66.7382i	−0.0963283	−	0.166845i
$401$			311.741i			0.777410i	0.921362	+	0.388705i	$0.127077\pi$
$401$			311.741i			0.777410i	−0.921362	+	0.388705i	$0.872923\pi$
$402$	286.907	−	80.5306i	0.713699	−	0.200325i
$403$	74.8882			0.185827
$404$	−220.525	−	127.320i	−0.545854	−	0.315149i
$405$	172.385	+	88.9186i	0.425641	+	0.219552i
$406$	−335.389	−	129.628i	−0.826082	−	0.319281i
$407$	162.437	+	93.7828i	0.399107	+	0.230425i
$408$	146.662	−	150.178i	0.359465	−	0.368083i
$409$	147.944	−	256.247i	0.361722	−	0.626521i	−0.626522	−	0.779403i	$-0.715522\pi$
$409$	147.944	−	256.247i	0.361722	−	0.626521i	0.988244	+	0.152883i	$0.0488557\pi$
$410$	−92.7722	−	53.5620i	−0.226274	−	0.130639i
$411$	−89.0329	+	24.9902i	−0.216625	+	0.0608035i
$412$	−48.9784	+	84.8330i	−0.118880	+	0.205905i
$413$	−99.9640	−	124.026i	−0.242043	−	0.300306i
$414$	1.59424	+	0.870749i	0.00385082	+	0.00210326i
$415$	71.2541	−	123.416i	0.171697	−	0.297387i
$416$		−	32.4709i		−	0.0780550i
$417$	−116.479	+	119.271i	−0.279326	+	0.286022i
$418$	17.6532			0.0422325
$419$	−327.219	+	188.920i	−0.780952	+	0.450883i	−0.836767	−	0.547558i	$-0.815557\pi$
$419$	−327.219	+	188.920i	−0.780952	+	0.450883i	0.0558158	+	0.998441i	$0.482224\pi$
$420$	−58.3370	+	81.9279i	−0.138898	+	0.195066i
$421$	−282.035	+	488.499i	−0.669918	+	1.16033i	0.308009	+	0.951383i	$0.400337\pi$
$421$	−282.035	+	488.499i	−0.669918	+	1.16033i	−0.977927	+	0.208948i	$0.932996\pi$
$422$	319.041	+	184.199i	0.756022	+	0.436489i
$423$	−263.919	+	483.206i	−0.623923	+	1.14233i
$424$	−36.8761	−	63.8713i	−0.0869719	−	0.150640i
$425$	−412.749	+	238.301i	−0.971173	+	0.560707i
$426$	−298.774	+	305.937i	−0.701347	+	0.718162i
$427$	110.791	+	710.057i	0.259464	+	1.66290i
$428$	−232.909	+	134.470i	−0.544179	+	0.314182i
$429$	71.9411	+	70.2567i	0.167695	+	0.163769i
$430$	−271.732			−0.631936
$431$	651.482	−	376.134i	1.51156	−	0.872700i	0.511651	−	0.859193i	$-0.329034\pi$
$431$	651.482	−	376.134i	1.51156	−	0.872700i	0.999909	−	0.0135064i	$-0.00429935\pi$
$432$	−24.2286	+	105.247i	−0.0560848	+	0.243628i
$433$	−451.261			−1.04217			−0.521087	−	0.853503i	$-0.674473\pi$
$433$	−451.261			−1.04217			−0.521087	+	0.853503i	$0.674473\pi$
$434$	46.5613	−	120.469i	0.107284	−	0.277578i
$435$	−252.826	−	64.5448i	−0.581209	−	0.148379i
$436$	−332.286			−0.762123
$437$	−0.264214	−	0.152544i	−0.000604610	−	0.000349072i
$438$	−9.17128	+	35.9245i	−0.0209390	+	0.0820193i
$439$	66.4641	+	115.119i	0.151399	+	0.262230i	0.931742	−	0.363121i	$-0.118289\pi$
$439$	66.4641	+	115.119i	0.151399	+	0.262230i	−0.780343	+	0.625352i	$0.784956\pi$
$440$		−	39.5508i		−	0.0898881i
$441$	−433.035	−	83.4348i	−0.981940	−	0.189195i
$442$	−200.819			−0.454342
$443$	−359.619	+	207.626i	−0.811781	+	0.468682i	−0.847574	−	0.530677i	$-0.821938\pi$
$443$	−359.619	+	207.626i	−0.811781	+	0.468682i	0.0357932	+	0.999359i	$0.488604\pi$
$444$	134.653	−	137.881i	0.303272	−	0.310543i
$445$	−130.908	+	226.740i	−0.294176	+	0.509527i
$446$			336.004i			0.753373i
$447$	21.3203	−	5.98430i	0.0476965	−	0.0133877i
$448$	−52.2343	−	20.1886i	−0.116594	−	0.0450638i
$449$		−	262.832i		−	0.585372i	−0.956209	−	0.292686i	$-0.905451\pi$
$449$		−	262.832i		−	0.585372i	0.956209	−	0.292686i	$-0.0945490\pi$
$450$	117.541	−	215.204i	0.261203	−	0.478232i
$451$	92.3567	+	159.966i	0.204782	+	0.354693i
$452$		−	403.348i		−	0.892363i
$453$	27.9998	+	99.7552i	0.0618098	+	0.220210i
$454$	166.896	+	289.072i	0.367612	+	0.636723i
$455$	95.0683	−	14.8337i	0.208941	−	0.0326015i
$456$	4.48678	−	17.5750i	0.00983944	−	0.0385417i
$457$	253.013	+	438.232i	0.553639	+	0.958931i	0.998008	+	0.0630874i	$0.0200947\pi$
$457$	253.013	+	438.232i	0.553639	+	0.958931i	−0.444369	+	0.895844i	$0.646572\pi$
$458$	487.764	−	281.611i	1.06499	−	0.614871i
$459$	650.911	+	149.844i	1.41811	+	0.326458i
$460$	−0.341766	+	0.591955i	−0.000742969	+	0.00128686i
$461$	660.234	+	381.186i	1.43218	+	0.826868i	0.997287	−	0.0736145i	$-0.0234534\pi$
$461$	660.234	+	381.186i	1.43218	+	0.826868i	0.434891	+	0.900483i	$0.356787\pi$
$462$	157.747	−	72.0463i	0.341445	−	0.155944i
$463$	−14.2110	−	24.6141i	−0.0306932	−	0.0531622i	0.850271	−	0.526346i	$-0.176438\pi$
$463$	−14.2110	−	24.6141i	−0.0306932	−	0.0531622i	−0.880964	+	0.473183i	$0.843105\pi$
$464$		−	145.288i		−	0.313120i
$465$	23.1839	−	90.8127i	0.0498579	−	0.195296i
$466$	215.339			0.462101
$467$	126.660	+	73.1271i	0.271220	+	0.156589i	0.629442	−	0.777047i	$-0.283283\pi$
$467$	126.660	+	73.1271i	0.271220	+	0.156589i	−0.358222	+	0.933637i	$0.616617\pi$
$468$	88.2304	−	53.7659i	0.188527	−	0.114884i
$469$	−382.806	+	308.537i	−0.816217	+	0.657862i
$470$	−179.419	−	103.587i	−0.381742	−	0.220399i
$471$	−559.938	−	142.948i	−1.18883	−	0.303500i
$472$	32.1827	−	55.7421i	0.0681838	−	0.118098i
$473$	405.773	+	234.273i	0.857871	+	0.495292i
$474$	65.3731	−	256.070i	0.137918	−	0.540233i
$475$	−20.5918	+	35.6660i	−0.0433511	+	0.0750862i
$476$	−124.858	+	323.048i	−0.262307	+	0.678672i
$477$	112.492	−	205.960i	0.235832	−	0.431781i
$478$	49.0364	−	84.9336i	0.102587	−	0.177685i
$479$		−	55.1020i		−	0.115035i	−0.998344	−	0.0575177i	$-0.981681\pi$
$479$		−	55.1020i		−	0.115035i	0.998344	−	0.0575177i	$-0.0183186\pi$
$480$	−39.3756	−	10.0523i	−0.0820326	−	0.0209424i
$481$	−184.376			−0.383318
$482$	37.6639	−	21.7453i	0.0781409	−	0.0451147i
$483$	−2.98357	−	0.284809i	−0.00617716	−	0.000589667i
$484$	86.9014	−	150.518i	0.179548	−	0.310987i
$485$	−331.233	−	191.237i	−0.682954	−	0.394304i
$486$	−326.098	+	108.436i	−0.670983	+	0.223119i
$487$	238.930	+	413.839i	0.490616	+	0.849772i	0.999942	−	0.0108019i	$-0.00343842\pi$
$487$	238.930	+	413.839i	0.490616	+	0.849772i	−0.509326	+	0.860574i	$0.670105\pi$
$488$	−251.474	+	145.189i	−0.515316	+	0.297518i
$489$	657.151	+	167.766i	1.34387	+	0.343080i
$490$	35.2460	−	162.154i	0.0719306	−	0.330927i
$491$	412.348	−	238.069i	0.839813	−	0.484866i	−0.0173875	−	0.999849i	$-0.505535\pi$
$491$	412.348	−	238.069i	0.839813	−	0.484866i	0.857201	+	0.514982i	$0.172202\pi$
$492$	182.732	−	51.2902i	0.371406	−	0.104248i
$493$	−898.545			−1.82261
$494$	−15.0281	+	8.67648i	−0.0304213	+	0.0175637i
$495$	107.468	−	65.4889i	0.217107	−	0.132301i
$496$	52.1860			0.105214
$497$	254.356	−	658.101i	0.511784	−	1.32415i
$498$	68.2318	+	243.090i	0.137012	+	0.488132i
$499$	49.9559			0.100112			0.0500560	−	0.998746i	$-0.484060\pi$
$499$	49.9559			0.100112			0.0500560	+	0.998746i	$0.484060\pi$
$500$	183.599	+	106.001i	0.367197	+	0.212001i
$501$	−280.921	−	274.343i	−0.560720	−	0.547591i
$502$	−210.605	−	364.778i	−0.419531	−	0.726650i
$503$		−	807.461i		−	1.60529i	−0.596457	−	0.802645i	$-0.703425\pi$
$503$		−	807.461i		−	1.60529i	0.596457	−	0.802645i	$-0.296575\pi$
$504$	−31.6338	−	175.361i	−0.0627654	−	0.347938i
$505$	304.887			0.603737
$506$	1.02070	−	0.589304i	0.00201720	−	0.00116463i
$507$	395.470	+	100.961i	0.780020	+	0.199134i
$508$	−32.4486	+	56.2026i	−0.0638752	+	0.110635i
$509$			247.402i			0.486056i	0.970019	+	0.243028i	$0.0781407\pi$
$509$			247.402i			0.486056i	−0.970019	+	0.243028i	$0.921859\pi$
$510$	−62.1697	+	243.522i	−0.121901	+	0.477495i
$511$	−9.43087	−	60.4421i	−0.0184557	−	0.118282i
$512$		−	22.6274i		−	0.0441942i
$513$	55.1844	−	16.9095i	0.107572	−	0.0329619i
$514$	74.6497	+	129.297i	0.145233	+	0.251551i
$515$		−	117.286i		−	0.227740i
$516$	336.368	−	344.433i	0.651877	−	0.667505i
$517$	178.615	+	309.370i	0.345484	+	0.598395i
$518$	−114.635	+	296.596i	−0.221302	+	0.572580i
$519$	−172.080	−	168.051i	−0.331560	−	0.323797i
$520$	19.4391	+	33.6695i	0.0373829	+	0.0647490i
$521$	−451.108	+	260.448i	−0.865851	+	0.499899i	−0.865967	−	0.500101i	$-0.833296\pi$
$521$	−451.108	+	260.448i	−0.865851	+	0.499899i	0.000116349		1.00000i	$0.499963\pi$
$522$	394.778	−	240.570i	0.756279	−	0.460862i
$523$	232.863	−	403.331i	0.445245	−	0.771187i	−0.552824	−	0.833298i	$-0.686450\pi$
$523$	232.863	−	403.331i	0.445245	−	0.771187i	0.998069	+	0.0621107i	$0.0197832\pi$
$524$	−316.965	−	183.000i	−0.604895	−	0.349236i
$525$	−38.4461	+	402.748i	−0.0732306	+	0.767139i
$526$	75.0310	+	129.957i	0.142644	+	0.247067i
$527$		−	322.749i		−	0.612428i
$528$	50.1323	+	48.9586i	0.0949476	+	0.0927246i
$529$	528.980			0.999961
$530$	76.4746	+	44.1526i	0.144292	+	0.0833069i
$531$	204.752	−	4.85142i	0.385597	−	0.00913639i
$532$	4.61378	+	29.5695i	0.00867252	+	0.0555818i
$533$	−157.246	−	90.7861i	−0.295021	−	0.170330i
$534$	−125.356	−	446.605i	−0.234748	−	0.836340i
$535$	161.004	−	278.867i	0.300942	−	0.521247i
$536$	−172.047	−	99.3315i	−0.320984	−	0.185320i
$537$	224.713	+	219.451i	0.418459	+	0.408662i
$538$	159.367	−	276.032i	0.296221	−	0.513070i
$539$	−192.433	+	211.755i	−0.357019	+	0.392866i
$540$	−37.8845	−	123.637i	−0.0701566	−	0.228957i
$541$	272.202	−	471.468i	0.503147	−	0.871476i	−0.496847	−	0.867838i	$-0.665509\pi$
$541$	272.202	−	471.468i	0.503147	−	0.871476i	0.999993	−	0.00363728i	$-0.00115778\pi$
$542$			237.617i			0.438407i
$543$	−143.811	−	512.357i	−0.264846	−	0.943568i
$544$	−139.941			−0.257245
$545$	344.551	−	198.927i	0.632204	−	0.365003i
$546$	−98.8796	+	138.865i	−0.181098	+	0.254332i
$547$	−166.024	+	287.563i	−0.303518	+	0.525709i	−0.976930	−	0.213558i	$-0.931495\pi$
$547$	−166.024	+	287.563i	−0.303518	+	0.525709i	0.673412	+	0.739267i	$0.264828\pi$
$548$	53.3897	+	30.8245i	0.0974264	+	0.0562492i
$549$	−810.906	−	442.904i	−1.47706	−	0.806747i
$550$	−79.5494	−	137.784i	−0.144635	−	0.250516i
$551$	−67.2417	+	38.8220i	−0.122036	+	0.0704574i
$552$	−0.327269	−	1.16596i	−0.000592879	−	0.00211225i
$553$	67.2235	+	430.832i	0.121561	+	0.779082i
$554$	410.948	−	237.261i	0.741783	−	0.428269i
$555$	−57.0791	+	223.582i	−0.102845	+	0.402851i
$556$	111.141			0.199895
$557$	384.372	−	221.918i	0.690076	−	0.398416i	−0.113564	−	0.993531i	$-0.536227\pi$
$557$	384.372	−	221.918i	0.690076	−	0.398416i	0.803641	+	0.595115i	$0.202893\pi$
$558$	86.4106	+	141.801i	0.154858	+	0.254123i
$559$	−460.578			−0.823933
$560$	66.2486	−	10.3369i	0.118301	−	0.0184587i
$561$	302.789	−	310.048i	0.539731	−	0.552671i
$562$	−765.662			−1.36239
$563$	−697.747	−	402.845i	−1.23934	−	0.715532i	−0.270379	−	0.962754i	$-0.587149\pi$
$563$	−697.747	−	402.845i	−1.23934	−	0.715532i	−0.968959	+	0.247222i	$0.920482\pi$
$564$	353.398	−	99.1936i	0.626592	−	0.175875i
$565$	241.469	+	418.237i	0.427379	+	0.740242i
$566$			447.612i			0.790834i
$567$	424.113	−	376.321i	0.747994	−	0.663705i
$568$	285.083			0.501907
$569$	660.080	−	381.097i	1.16007	−	0.669767i	0.208749	−	0.977969i	$-0.433061\pi$
$569$	660.080	−	381.097i	1.16007	−	0.669767i	0.951321	+	0.308203i	$0.0997275\pi$
$570$	5.86908	+	20.9098i	0.0102966	+	0.0366839i
$571$	447.631	−	775.319i	0.783941	−	1.35783i	−0.145688	−	0.989331i	$-0.546540\pi$
$571$	447.631	−	775.319i	0.783941	−	1.35783i	0.929629	−	0.368496i	$-0.120127\pi$
$572$		−	67.0374i		−	0.117198i
$573$	−377.136	−	368.306i	−0.658177	−	0.642767i
$574$	−243.810	+	196.508i	−0.424756	+	0.342349i
$575$			2.74960i			0.00478192i
$576$	61.4836	−	37.4669i	0.106742	−	0.0650467i
$577$	−0.145650	−	0.252273i	−0.000252426	−	0.000437215i	0.865899	−	0.500219i	$-0.166747\pi$
$577$	−0.145650	−	0.252273i	−0.000252426	−	0.000437215i	−0.866152	+	0.499781i	$0.833414\pi$
$578$			456.773i			0.790266i
$579$	−237.430	−	60.6143i	−0.410069	−	0.104688i
$580$	86.9782	+	150.651i	0.149962	+	0.259743i
$581$	−261.417	−	324.343i	−0.449943	−	0.558249i
$582$	652.424	−	183.126i	1.12100	−	0.314649i
$583$	−76.1321	−	131.865i	−0.130587	−	0.226183i
$584$	21.4062	−	12.3589i	0.0366545	−	0.0211625i
$585$	−59.2997	+	108.571i	−0.101367	+	0.185591i
$586$	183.389	−	317.638i	0.312950	−	0.542045i
$587$	316.757	+	182.880i	0.539621	+	0.311550i	0.744925	−	0.667148i	$-0.232485\pi$
$587$	316.757	+	182.880i	0.539621	+	0.311550i	−0.205304	+	0.978698i	$0.565818\pi$
$588$	161.908	+	245.401i	0.275354	+	0.417349i
$589$	−13.9445	−	24.1526i	−0.0236749	−	0.0410061i
$590$			77.0663i			0.130621i
$591$	−920.991	+	258.509i	−1.55836	+	0.437409i
$592$	−128.483			−0.217032
$593$	248.305	+	143.359i	0.418726	+	0.241752i	0.694532	−	0.719462i	$-0.255611\pi$
$593$	248.305	+	143.359i	0.418726	+	0.241752i	−0.275806	+	0.961213i	$0.588945\pi$
$594$	−50.0209	+	217.287i	−0.0842103	+	0.365803i
$595$	−63.9294	−	409.721i	−0.107444	−	0.688606i
$596$	−12.7850	−	7.38142i	−0.0214513	−	0.0123849i
$597$	−787.600	+	806.483i	−1.31926	+	1.35089i
$598$	−0.579283	+	1.00335i	−0.000968700	+	0.00167784i
$599$	31.3304	+	18.0886i	0.0523046	+	0.0301980i	0.525924	−	0.850531i	$-0.323720\pi$
$599$	31.3304	+	18.0886i	0.0523046	+	0.0301980i	−0.473620	+	0.880729i	$0.657053\pi$
$600$	−157.392	+	44.1777i	−0.262320	+	0.0736294i
$601$	450.390	−	780.099i	0.749402	−	1.29800i	−0.198708	−	0.980059i	$-0.563675\pi$
$601$	450.390	−	780.099i	0.749402	−	1.29800i	0.948110	−	0.317943i	$-0.102992\pi$
$602$	−286.362	+	740.909i	−0.475684	+	1.23075i
$603$	−14.9739	−	631.965i	−0.0248323	−	1.04803i
$604$	34.5368	−	59.8194i	0.0571801	−	0.0990388i
$605$			208.098i			0.343964i
$606$	−377.410	+	386.458i	−0.622789	+	0.637720i
$607$	15.7658			0.0259734			0.0129867	−	0.999916i	$-0.495866\pi$
$607$	15.7658			0.0259734			0.0129867	+	0.999916i	$0.495866\pi$
$608$	−10.4724	+	6.04623i	−0.0172243	+	0.00994445i
$609$	−442.426	+	621.339i	−0.726480	+	1.02026i
$610$	173.838	−	301.097i	0.284981	−	0.493601i
$611$	−304.109	−	175.578i	−0.497724	−	0.287361i
$612$	−231.718	−	380.251i	−0.378624	−	0.621325i
$613$	44.9747	+	77.8984i	0.0733681	+	0.127077i	0.900375	−	0.435114i	$-0.143292\pi$
$613$	44.9747	+	77.8984i	0.0733681	+	0.127077i	−0.827007	+	0.562191i	$0.809959\pi$
$614$	−227.679	+	131.451i	−0.370813	+	0.214089i
$615$	−158.772	+	162.578i	−0.258165	+	0.264355i
$616$	−107.840	−	41.6801i	−0.175064	−	0.0676626i
$617$	−871.820	+	503.346i	−1.41300	+	0.815795i	−0.995670	−	0.0929603i	$-0.970367\pi$
$617$	−871.820	+	503.346i	−1.41300	+	0.815795i	−0.417329	+	0.908755i	$0.637034\pi$
$618$	148.665	+	145.184i	0.240559	+	0.234926i
$619$	151.087			0.244083			0.122041	−	0.992525i	$-0.461056\pi$
$619$	151.087			0.244083			0.122041	+	0.992525i	$0.461056\pi$
$620$	−54.1124	+	31.2418i	−0.0872780	+	0.0503900i
$621$	2.62628	−	2.81989i	0.00422911	−	0.00454088i
$622$	9.81499			0.0157797
$623$	480.276	+	595.883i	0.770908	+	0.956474i
$624$	−66.7406	−	17.0384i	−0.106956	−	0.0273052i
$625$	227.807			0.364491
$626$	485.136	+	280.094i	0.774978	+	0.447434i
$627$	9.26314	−	36.2843i	0.0147737	−	0.0578697i
$628$	192.632	+	333.649i	0.306739	+	0.531288i
$629$			794.614i			1.26330i
$630$	137.783	+	162.896i	0.218703	+	0.258565i
$631$	318.002			0.503965			0.251982	−	0.967732i	$-0.418917\pi$
$631$	318.002			0.503965			0.251982	+	0.967732i	$0.418917\pi$
$632$	−152.584	+	88.0944i	−0.241430	+	0.139390i
$633$	546.012	−	559.102i	0.862577	−	0.883258i
$634$	39.9494	−	69.1944i	0.0630117	−	0.109139i
$635$		−	77.7030i		−	0.122367i
$636$	−150.631	+	42.2799i	−0.236841	+	0.0664778i
$637$	59.7410	−	274.847i	0.0937849	−	0.431471i
$638$		−	299.952i		−	0.470144i
$639$	472.046	+	774.633i	0.738727	+	1.21226i
$640$	13.5462	+	23.4627i	0.0211659	+	0.0366604i
$641$			435.010i			0.678643i	0.940671	+	0.339321i	$0.110197\pi$
$641$			435.010i			0.678643i	−0.940671	+	0.339321i	$0.889803\pi$
$642$	154.175	+	549.280i	0.240148	+	0.855577i
$643$	−267.589	−	463.477i	−0.416157	−	0.720805i	0.579392	−	0.815049i	$-0.303290\pi$
$643$	−267.589	−	463.477i	−0.416157	−	0.720805i	−0.995549	+	0.0942441i	$0.969957\pi$
$644$	1.25387	+	1.55569i	0.00194700	+	0.00241567i
$645$	−142.586	+	558.518i	−0.221064	+	0.865919i
$646$	37.3935	+	64.7674i	0.0578846	+	0.100259i
$647$	217.880	−	125.793i	0.336755	−	0.194425i	−0.322081	−	0.946712i	$-0.604382\pi$
$647$	217.880	−	125.793i	0.336755	−	0.194425i	0.658836	+	0.752287i	$0.271049\pi$
$648$	203.611	+	105.026i	0.314215	+	0.162077i
$649$	66.4425	−	115.082i	0.102377	−	0.177322i
$650$	135.441	+	78.1966i	0.208370	+	0.120302i
$651$	−223.179	−	158.916i	−0.342825	−	0.244110i
$652$	−226.076	−	391.575i	−0.346742	−	0.600575i
$653$		−	670.666i		−	1.02705i	−0.858074	−	0.513526i	$-0.828339\pi$
$653$		−	670.666i		−	1.02705i	0.858074	−	0.513526i	$-0.171661\pi$
$654$	−174.360	+	682.979i	−0.266606	+	1.04431i
$655$	438.221			0.669039
$656$	−109.577	−	63.2645i	−0.167039	−	0.0964398i
$657$	69.0266	+	37.7013i	0.105063	+	0.0573840i
$658$	−471.521	+	380.041i	−0.716597	+	0.577570i
$659$	−240.616	−	138.920i	−0.365123	−	0.210804i	0.306203	−	0.951966i	$-0.400942\pi$
$659$	−240.616	−	138.920i	−0.365123	−	0.210804i	−0.671326	+	0.741162i	$0.734275\pi$
$660$	−81.2926	−	20.7535i	−0.123171	−	0.0314446i
$661$	391.617	−	678.301i	0.592462	−	1.02617i	−0.401438	−	0.915886i	$-0.631490\pi$
$661$	391.617	−	678.301i	0.592462	−	1.02617i	0.993900	−	0.110287i	$-0.0351771\pi$
$662$	−270.499	−	156.173i	−0.408609	−	0.235911i
$663$	−105.376	+	412.764i	−0.158938	+	0.622569i
$664$	84.1614	−	145.772i	0.126749	−	0.219536i
$665$	−22.4862	−	27.8989i	−0.0338139	−	0.0419533i
$666$	−212.744	−	349.116i	−0.319436	−	0.524198i
$667$	−2.59194	+	4.48937i	−0.00388597	+	0.00673069i
$668$			261.772i			0.391875i
$669$	690.623	+	176.311i	1.03232	+	0.263545i
$670$	237.864			0.355021
$671$	−519.179	+	299.748i	−0.773739	+	0.446718i
$672$	−68.9045	+	96.7687i	−0.102536	+	0.144001i
$673$	292.102	−	505.936i	0.434030	−	0.751762i	−0.563186	−	0.826330i	$-0.690425\pi$
$673$	292.102	−	505.936i	0.434030	−	0.751762i	0.997216	+	0.0745684i	$0.0237579\pi$
$674$	419.919	+	242.441i	0.623026	+	0.359704i
$675$	−380.653	−	354.518i	−0.563930	−	0.525212i
$676$	−136.051	−	235.648i	−0.201259	−	0.348591i
$677$	166.562	−	96.1649i	0.246030	−	0.142046i	−0.371915	−	0.928267i	$-0.621299\pi$
$677$	166.562	−	96.1649i	0.246030	−	0.142046i	0.617945	+	0.786221i	$0.287965\pi$
$678$	−829.040	−	211.649i	−1.22277	−	0.312166i
$679$	−870.497	+	701.611i	−1.28203	+	1.03330i
$680$	145.107	−	83.7777i	0.213393	−	0.123202i
$681$	681.733	−	191.353i	1.00108	−	0.280988i
$682$	107.740			0.157977
$683$	−715.412	+	413.043i	−1.04746	+	0.604749i	−0.921936	−	0.387343i	$-0.873393\pi$
$683$	−715.412	+	413.043i	−1.04746	+	0.604749i	−0.125519	+	0.992091i	$0.540060\pi$
$684$	−33.7693	−	18.4442i	−0.0493703	−	0.0269653i
$685$	−73.8140			−0.107758
$686$	−404.989	−	266.987i	−0.590363	−	0.389194i
$687$	−322.878	−	1150.32i	−0.469982	−	1.67441i
$688$	−320.955			−0.466505
$689$	129.622	+	74.8375i	0.188131	+	0.108618i
$690$	1.03737	+	1.01308i	0.00150343	+	0.00146823i
$691$	475.146	+	822.976i	0.687620	+	1.19099i	0.972606	+	0.232461i	$0.0746780\pi$
$691$	475.146	+	822.976i	0.687620	+	1.19099i	−0.284985	+	0.958532i	$0.591989\pi$
$692$			160.350i			0.231720i
$693$	−65.3091	−	362.039i	−0.0942411	−	0.522422i
$694$	516.814			0.744689
$695$	−115.244	+	66.5362i	−0.165819	+	0.0957356i
$696$	−298.624	−	76.2367i	−0.429057	−	0.109536i
$697$	−391.265	+	677.692i	−0.561356	+	0.972298i
$698$		−	7.42760i		−	0.0106413i
$699$	112.995	−	442.607i	0.161652	−	0.633201i
$700$	210.000	−	169.258i	0.300001	−	0.241797i
$701$			275.965i			0.393673i	0.980436	+	0.196836i	$0.0630668\pi$
$701$			275.965i			0.393673i	−0.980436	+	0.196836i	$0.936933\pi$
$702$	−64.2132	−	209.561i	−0.0914718	−	0.298520i
$703$	34.3316	+	59.4641i	0.0488359	+	0.0845863i
$704$		−	46.7152i		−	0.0663568i
$705$	−307.059	+	314.421i	−0.435545	+	0.445987i
$706$	106.134	+	183.830i	0.150332	+	0.260382i
$707$	321.302	−	831.310i	0.454458	−	1.17583i
$708$	−97.6850	−	95.3978i	−0.137973	−	0.134743i
$709$	234.272	+	405.770i	0.330425	+	0.572314i	0.982595	−	0.185759i	$-0.0594745\pi$
$709$	234.272	+	405.770i	0.330425	+	0.572314i	−0.652170	+	0.758073i	$0.726141\pi$
$710$	−295.607	+	170.669i	−0.416347	+	0.240378i
$711$	−492.023	−	268.735i	−0.692016	−	0.377968i
$712$	−154.622	+	267.812i	−0.217165	+	0.376141i
$713$	−1.61254	−	0.931002i	−0.00226163	−	0.00130575i
$714$	598.475	+	426.146i	0.838200	+	0.596843i
$715$	40.1328	+	69.5120i	0.0561297	+	0.0972196i
$716$		−	209.396i		−	0.292452i
$717$	−148.841	−	145.357i	−0.207589	−	0.202729i
$718$	34.4649			0.0480012
$719$	946.861	+	546.670i	1.31691	+	0.760321i	0.983231	−	0.182365i	$-0.0583752\pi$
$719$	946.861	+	546.670i	1.31691	+	0.760321i	0.333683	+	0.942685i	$0.391709\pi$
$720$	−41.3231	+	75.6578i	−0.0573932	+	0.105080i
$721$	−319.794	−	123.601i	−0.443542	−	0.171429i
$722$	−436.536	−	252.034i	−0.604621	−	0.349078i
$723$	−24.9318	−	88.8247i	−0.0344838	−	0.122856i
$724$	−177.386	+	307.241i	−0.245008	+	0.424367i
$725$	606.015	+	349.883i	0.835882	+	0.482597i
$726$	−263.774	−	257.598i	−0.363325	−	0.354818i
$727$	437.186	−	757.228i	0.601356	−	1.04158i	−0.391260	−	0.920280i	$-0.627961\pi$
$727$	437.186	−	757.228i	0.601356	−	1.04158i	0.992616	−	0.121299i	$-0.0387061\pi$
$728$	112.289	−	17.5207i	0.154244	−	0.0240669i
$729$	51.7658	+	727.160i	0.0710093	+	0.997476i
$730$	−14.7976	+	25.6302i	−0.0202707	+	0.0351099i
$731$			1984.98i			2.71543i
$732$	166.465	+	593.065i	0.227411	+	0.810198i
$733$	331.228			0.451880			0.225940	−	0.974141i	$-0.427455\pi$
$733$	331.228			0.451880			0.225940	+	0.974141i	$0.427455\pi$
$734$	665.992	−	384.511i	0.907346	−	0.523856i
$735$	−314.797	−	157.532i	−0.428295	−	0.214329i
$736$	−0.403675	+	0.699185i	−0.000548471	+	0.000949979i
$737$	−355.198	−	205.074i	−0.481952	−	0.278255i
$738$	−9.53688	−	402.500i	−0.0129226	−	0.545393i
$739$	−626.471	−	1085.08i	−0.847729	−	1.46831i	−0.883230	−	0.468939i	$-0.844636\pi$
$739$	−626.471	−	1085.08i	−0.847729	−	1.46831i	0.0355017	−	0.999370i	$-0.488697\pi$
$740$	133.226	−	76.9178i	0.180035	−	0.103943i
$741$	9.94793	+	35.4415i	0.0134250	+	0.0478293i
$742$	200.979	−	161.987i	0.270861	−	0.218311i
$743$	−567.386	+	327.580i	−0.763642	+	0.440889i	−0.830602	−	0.556867i	$-0.812003\pi$
$743$	−567.386	+	327.580i	−0.763642	+	0.440889i	0.0669598	+	0.997756i	$0.478670\pi$
$744$	27.3835	−	107.263i	0.0368058	−	0.144171i
$745$	17.6759			0.0237260
$746$	−357.492	+	206.398i	−0.479212	+	0.276673i
$747$	535.450	−	12.6870i	0.716800	−	0.0169840i
$748$	−288.915			−0.386249
$749$	−590.691	−	732.877i	−0.788640	−	0.978474i
$750$	314.213	−	321.746i	0.418951	−	0.428995i
$751$	−1497.02			−1.99337			−0.996683	−	0.0813774i	$-0.974068\pi$
$751$	−1497.02			−1.99337			−0.996683	+	0.0813774i	$0.974068\pi$
$752$	−211.919	−	122.352i	−0.281808	−	0.162702i
$753$	−860.274	+	241.467i	−1.14246	+	0.320673i
$754$	147.426	+	255.349i	0.195525	+	0.338659i
$755$			82.7035i			0.109541i
$756$	−377.035	−	26.9969i	−0.498723	−	0.0357102i
$757$	1042.92			1.37771			0.688853	−	0.724901i	$-0.258115\pi$
$757$	1042.92			1.37771			0.688853	+	0.724901i	$0.258115\pi$
$758$	474.692	−	274.064i	0.626243	−	0.361562i
$759$	−0.675660	−	2.40718i	−0.000890198	−	0.00317151i
$760$	7.23930	−	12.5388i	0.00952539	−	0.0164985i
$761$			1095.82i			1.43998i	0.693985	+	0.719989i	$0.255853\pi$
$761$			1095.82i			1.43998i	−0.693985	+	0.719989i	$0.744147\pi$
$762$	98.4920	+	96.1860i	0.129255	+	0.126228i
$763$	−179.295	−	1149.10i	−0.234987	−	1.50602i
$764$			351.429i			0.459986i
$765$	467.913	+	255.567i	0.611651	+	0.334074i
$766$	247.782	+	429.171i	0.323475	+	0.560276i
$767$			130.625i			0.170307i
$768$	−46.5083	−	11.8733i	−0.0605577	−	0.0154600i
$769$	176.993	+	306.561i	0.230160	+	0.398649i	0.957855	−	0.287252i	$-0.0927418\pi$
$769$	176.993	+	306.561i	0.230160	+	0.398649i	−0.727695	+	0.685901i	$0.759408\pi$
$770$	136.773	−	21.3409i	0.177627	−	0.0277154i
$771$	304.928	−	85.5888i	0.395496	−	0.111010i
$772$	81.6816	+	141.477i	0.105805	+	0.183260i
$773$	40.8414	−	23.5798i	0.0528349	−	0.0305043i	−0.473350	−	0.880875i	$-0.656955\pi$
$773$	40.8414	−	23.5798i	0.0528349	−	0.0305043i	0.526185	+	0.850370i	$0.323622\pi$
$774$	−531.444	−	872.105i	−0.686620	−	1.12675i
$775$	−125.675	+	217.675i	−0.162161	+	0.280871i
$776$	−391.234	−	225.879i	−0.504167	−	0.291081i
$777$	549.471	+	391.253i	0.707170	+	0.503543i
$778$	363.412	+	629.448i	0.467111	+	0.809059i
$779$			67.6191i			0.0868025i
$780$	79.4045	−	22.2877i	0.101801	−	0.0285740i
$781$	588.566			0.753605
$782$	4.32418	+	2.49656i	0.00552964	+	0.00319254i
$783$	−287.315	−	937.660i	−0.366942	−	1.19752i
$784$	41.6306	−	191.528i	0.0531003	−	0.244296i
$785$	−399.486	−	230.643i	−0.508899	−	0.293813i
$786$	−542.459	+	555.464i	−0.690151	+	0.706697i
$787$	341.919	−	592.220i	0.434458	−	0.752504i	−0.562793	−	0.826598i	$-0.690273\pi$
$787$	341.919	−	592.220i	0.434458	−	0.752504i	0.997251	+	0.0740942i	$0.0236066\pi$
$788$	552.283	+	318.861i	0.700867	+	0.404646i
$789$	306.485	−	86.0260i	0.388448	−	0.109032i
$790$	105.478	−	182.693i	0.133516	−	0.231256i
$791$	1394.84	−	217.639i	1.76339	−	0.275144i
$792$	126.935	−	77.3519i	0.160272	−	0.0976665i
$793$	294.651	−	510.350i	0.371564	−	0.643569i
$794$		−	632.959i		−	0.797177i
$795$	130.880	−	134.018i	0.164629	−	0.168576i
$796$	751.511			0.944109
$797$	173.916	−	100.410i	0.218213	−	0.125985i	−0.386910	−	0.922118i	$-0.626457\pi$
$797$	173.916	−	100.410i	0.218213	−	0.125985i	0.605123	+	0.796132i	$0.293124\pi$
$798$	63.1981	+	6.03285i	0.0791956	+	0.00755996i
$799$	−756.695	+	1310.64i	−0.947053	+	1.64034i
$800$	94.3821	+	54.4915i	0.117978	+	0.0681144i
$801$	−983.729	+	23.3086i	−1.22813	+	0.0290994i
$802$	−220.434	−	381.804i	−0.274856	−	0.476064i
$803$	44.1940	−	25.5154i	0.0550361	−	0.0317751i
$804$	−294.444	+	301.503i	−0.366224	+	0.375004i
$805$	−2.23148	−	0.862471i	−0.00277203	−	0.00107139i
$806$	−91.7189	+	52.9539i	−0.113795	+	0.0656997i
$807$	−483.730	−	472.405i	−0.599418	−	0.585384i
$808$	360.116			0.445688
$809$	−264.760	+	152.859i	−0.327268	+	0.188948i	−0.654628	−	0.755951i	$-0.727175\pi$
$809$	−264.760	+	152.859i	−0.327268	+	0.188948i	0.327359	+	0.944900i	$0.393841\pi$
$810$	−274.002	+	12.9918i	−0.338274	+	0.0160392i
$811$	−902.926			−1.11335			−0.556674	−	0.830731i	$-0.687923\pi$
$811$	−902.926			−1.11335			−0.556674	+	0.830731i	$0.687923\pi$
$812$	502.427	−	78.3946i	0.618753	−	0.0965450i
$813$	488.397	+	124.684i	0.600734	+	0.153363i
$814$	−265.258			−0.325869
$815$	468.842	+	270.686i	0.575266	+	0.332130i
$816$	−73.4314	+	287.635i	−0.0899895	+	0.352494i
$817$	85.7618	+	148.544i	0.104972	+	0.181816i
$818$			418.450i			0.511552i
$819$	233.539	+	276.104i	0.285151	+	0.337123i
$820$	151.496			0.184752
$821$	−41.3545	+	23.8760i	−0.0503708	+	0.0290816i	−0.524974	−	0.851118i	$-0.675925\pi$
$821$	−41.3545	+	23.8760i	−0.0503708	+	0.0290816i	0.474603	+	0.880200i	$0.342592\pi$
$822$	91.3718	−	93.5625i	0.111158	−	0.113823i
$823$	−740.074	+	1281.85i	−0.899239	+	1.55753i	−0.0707708	+	0.997493i	$0.522546\pi$
$823$	−740.074	+	1281.85i	−0.899239	+	1.55753i	−0.828469	+	0.560036i	$0.810787\pi$
$824$		−	138.532i		−	0.168121i
$825$	−324.942	+	91.2065i	−0.393869	+	0.110553i
$826$	210.130	+	81.2155i	0.254395	+	0.0983239i
$827$		−	1050.14i		−	1.26982i	−0.772587	−	0.634909i	$-0.781038\pi$
$827$		−	1050.14i		−	1.26982i	0.772587	−	0.634909i	$-0.218962\pi$
$828$	−2.56825	+	0.0608524i	−0.00310175	+	7.34932e-5i
$829$	182.182	+	315.549i	0.219762	+	0.380638i	0.954735	−	0.297458i	$-0.0961387\pi$
$829$	182.182	+	315.549i	0.219762	+	0.380638i	−0.734973	+	0.678096i	$0.762805\pi$
$830$			201.537i			0.242816i
$831$	−272.029	−	969.159i	−0.327351	−	1.16626i
$832$	22.9604	+	39.7686i	0.0275966	+	0.0477987i
$833$	−1184.52	−	257.469i	−1.42200	−	0.309086i
$834$	58.3192	−	228.440i	0.0699271	−	0.273909i
$835$	−156.713	−	271.435i	−0.187680	−	0.325072i
$836$	−21.6206	+	12.4827i	−0.0258620	+	0.0149314i
$837$	336.799	−	103.201i	0.402388	−	0.123299i
$838$	267.173	−	462.757i	0.318822	−	0.552216i
$839$	1021.16	+	589.566i	1.21711	+	0.702701i	0.964299	−	0.264814i	$-0.0853106\pi$
$839$	1021.16	+	589.566i	1.21711	+	0.702701i	0.252814	+	0.967515i	$0.418644\pi$
$840$	13.5162	−	141.591i	0.0160907	−	0.168561i
$841$	239.140	+	414.203i	0.284352	+	0.492513i
$842$		−	797.716i		−	0.947407i
$843$	−401.765	+	1573.74i	−0.476590	+	1.86683i
$844$	−520.992			−0.617289
$845$	282.147	+	162.898i	0.333902	+	0.192778i
$846$	−18.4440	−	778.423i	−0.0218015	−	0.920121i
$847$	567.404	+	219.302i	0.669899	+	0.258916i
$848$	90.3276	+	52.1507i	0.106518	+	0.0614984i
$849$	920.021	+	234.875i	1.08365	+	0.276649i
$850$	337.008	−	583.715i	0.396480	−	0.686723i
$851$	3.97011	+	2.29214i	0.00466522	+	0.00269347i
$852$	149.592	−	585.959i	0.175577	−	0.687746i
$853$	152.043	−	263.345i	0.178244	−	0.308729i	−0.763035	−	0.646357i	$-0.776292\pi$
$853$	152.043	−	263.345i	0.178244	−	0.308729i	0.941279	+	0.337629i	$0.109625\pi$
$854$	−637.777	−	791.297i	−0.746811	−	0.926577i
$855$	46.0577	−	1.09130i	0.0538686	−	0.00127637i
$856$	190.169	−	329.383i	0.222160	−	0.384793i
$857$		−	1528.94i		−	1.78406i	−0.451980	−	0.892028i	$-0.649282\pi$
$857$		−	1528.94i		−	1.78406i	0.451980	−	0.892028i	$-0.350718\pi$
$858$	−137.789	−	35.1765i	−0.160593	−	0.0409983i
$859$	−454.355			−0.528935			−0.264467	−	0.964395i	$-0.585196\pi$
$859$	−454.355			−0.528935			−0.264467	+	0.964395i	$0.585196\pi$
$860$	332.803	−	192.144i	0.386980	−	0.223423i
$861$	275.968	+	604.240i	0.320521	+	0.701789i
$862$	−531.933	+	921.335i	−0.617092	+	1.06883i
$863$	190.804	+	110.161i	0.221094	+	0.127649i	0.606457	−	0.795116i	$-0.292590\pi$
$863$	190.804	+	110.161i	0.221094	+	0.127649i	−0.385363	+	0.922765i	$0.625924\pi$
$864$	−44.7471	−	146.033i	−0.0517907	−	0.169020i
$865$	−95.9957	−	166.269i	−0.110978	−	0.192219i
$866$	552.680	−	319.090i	0.638199	−	0.368464i
$867$	938.851	+	239.683i	1.08287	+	0.276450i
$868$	28.1586	+	180.467i	0.0324408	+	0.207912i
$869$	−315.016	+	181.874i	−0.362504	+	0.209292i
$870$	355.287	−	99.7239i	0.408376	−	0.114625i
$871$	403.173			0.462885
$872$	406.965	−	234.961i	0.466703	−	0.269451i
$873$	−34.0504	−	1437.08i	−0.0390039	−	1.64614i
$874$	0.431460			0.000493662
$875$	−267.501	+	692.109i	−0.305715	+	0.790982i
$876$	−14.1700	−	50.4834i	−0.0161757	−	0.0576294i
$877$	−1648.07			−1.87921			−0.939606	−	0.342259i	$-0.888808\pi$
$877$	−1648.07			−1.87921			−0.939606	+	0.342259i	$0.888808\pi$
$878$	−162.803	−	93.9944i	−0.185425	−	0.107055i
$879$	−556.644	−	543.611i	−0.633269	−	0.618442i
$880$	27.9666	+	48.4396i	0.0317802	+	0.0550450i
$881$		−	1387.66i		−	1.57510i	−0.616252	−	0.787549i	$-0.711350\pi$
$881$		−	1387.66i		−	1.57510i	0.616252	−	0.787549i	$-0.288650\pi$
$882$	589.355	−	204.016i	0.668203	−	0.231310i
$883$	−117.311			−0.132855			−0.0664274	−	0.997791i	$-0.521160\pi$
$883$	−117.311			−0.132855			−0.0664274	+	0.997791i	$0.521160\pi$
$884$	245.952	−	142.001i	0.278227	−	0.160634i
$885$	158.402	+	40.4390i	0.178985	+	0.0456938i
$886$	293.628	−	508.578i	0.331408	−	0.574016i
$887$		−	369.393i		−	0.416453i	−0.978081	−	0.208226i	$-0.933231\pi$
$887$		−	369.393i		−	0.416453i	0.978081	−	0.208226i	$-0.0667690\pi$
$888$	−67.4187	+	264.083i	−0.0759220	+	0.297391i
$889$	−211.866	−	81.8865i	−0.238320	−	0.0921107i
$890$		−	370.264i		−	0.416027i
$891$	420.364	+	216.830i	0.471789	+	0.243356i
$892$	−237.591	−	411.520i	−0.266358	−	0.461345i
$893$			130.773i			0.146443i
$894$	−21.8804	+	22.4050i	−0.0244747	+	0.0250615i
$895$	125.357	+	217.125i	0.140064	+	0.242598i
$896$	78.2492	−	12.2093i	0.0873317	−	0.0136265i
$897$	1.75831	+	1.71714i	0.00196021	+	0.00191432i
$898$	185.850	+	321.902i	0.206960	+	0.358466i
$899$	−410.387	+	236.937i	−0.456493	+	0.263556i
$900$	8.21439	+	346.685i	0.00912710	+	0.385205i
$901$	322.531	−	558.640i	0.357970	−	0.620022i
$902$	−226.227	−	130.612i	−0.250806	−	0.144803i
$903$	1372.60	+	977.365i	1.52004	+	1.08235i
$904$	285.210	+	493.998i	0.315498	+	0.546458i
$905$		−	424.777i		−	0.469367i
$906$	−104.830	−	102.376i	−0.115707	−	0.112998i
$907$	−595.216			−0.656247			−0.328124	−	0.944635i	$-0.606416\pi$
$907$	−595.216			−0.656247			−0.328124	+	0.944635i	$0.606416\pi$
$908$	−408.810	−	236.026i	−0.450231	−	0.259941i
$909$	596.287	+	978.513i	0.655981	+	1.07647i
$910$	−105.945	+	85.3909i	−0.116424	+	0.0938362i
$911$	−451.079	−	260.431i	−0.495148	−	0.285874i	0.231560	−	0.972821i	$-0.425617\pi$
$911$	−451.079	−	260.431i	−0.495148	−	0.285874i	−0.726707	+	0.686947i	$0.758950\pi$
$912$	6.93224	+	24.6975i	0.00760114	+	0.0270806i
$913$	173.754	−	300.952i	0.190312	−	0.329629i
$914$	−619.753	−	357.815i	−0.678067	−	0.391482i
$915$	−527.655	−	515.301i	−0.576672	−	0.563170i
$916$	−398.258	+	689.803i	−0.434779	+	0.753060i
$917$	461.814	−	1194.86i	0.503614	−	1.30301i
$918$	−903.156	+	276.743i	−0.983830	+	0.301463i
$919$	−430.710	+	746.012i	−0.468673	+	0.811765i	−0.999359	−	0.0358037i	$-0.988601\pi$
$919$	−430.710	+	746.012i	−0.468673	+	0.811765i	0.530686	+	0.847568i	$0.321934\pi$
$920$		−	0.966659i		−	0.00105072i
$921$	150.713	+	536.947i	0.163641	+	0.583004i
$922$	−1078.16			−1.16937
$923$	−501.045	+	289.278i	−0.542844	+	0.313411i
$924$	−142.256	+	199.783i	−0.153957	+	0.216215i
$925$	309.413	−	535.919i	0.334501	−	0.579372i
$926$	34.8096	+	20.0973i	0.0375913	+	0.0217034i
$927$	376.421	−	229.384i	0.406063	−	0.247447i
$928$	102.734	+	177.940i	0.110705	+	0.191746i
$929$	−739.874	+	427.167i	−0.796420	+	0.459813i	−0.842218	−	0.539137i	$-0.818750\pi$
$929$	−739.874	+	427.167i	−0.796420	+	0.459813i	0.0457978	+	0.998951i	$0.485417\pi$
$930$	35.8199	+	127.616i	0.0385161	+	0.137221i
$931$	−99.7665	+	31.9104i	−0.107161	+	0.0342754i
$932$	−263.735	+	152.268i	−0.282978	+	0.163377i
$933$	5.15021	−	20.1737i	0.00552006	−	0.0216224i
$934$	−206.835			−0.221450
$935$	299.579	−	172.962i	0.320406	−	0.184986i
$936$	−70.0415	+	128.238i	−0.0748307	+	0.137006i
$937$	−336.030			−0.358623			−0.179311	−	0.983792i	$-0.557387\pi$
$937$	−336.030			−0.358623			−0.179311	+	0.983792i	$0.557387\pi$
$938$	250.670	−	648.564i	0.267239	−	0.691433i
$939$	830.269	−	850.175i	0.884206	−	0.905404i
$940$	292.989			0.311691
$941$	1212.36	+	699.955i	1.28837	+	0.743842i	0.978364	−	0.206892i	$-0.0663350\pi$
$941$	1212.36	+	699.955i	1.28837	+	0.743842i	0.310008	+	0.950734i	$0.399668\pi$
$942$	786.861	−	220.860i	0.835309	−	0.234459i
$943$	2.25729	+	3.90973i	0.00239373	+	0.00414606i
$944$			91.0265i			0.0964264i
$945$	407.114	−	197.723i	0.430809	−	0.209231i
$946$	−662.624			−0.700449
$947$	696.571	−	402.166i	0.735556	−	0.424673i	−0.0848954	−	0.996390i	$-0.527056\pi$
$947$	696.571	−	402.166i	0.735556	−	0.424673i	0.820451	+	0.571717i	$0.193722\pi$
$948$	101.004	+	359.847i	0.106544	+	0.379585i
$949$	−25.0815	+	43.4425i	−0.0264294	+	0.0457771i
$950$		−	58.2423i		−	0.0613077i
$951$	−121.259	−	118.420i	−0.127507	−	0.124522i
$952$	−75.5099	−	483.939i	−0.0793171	−	0.508340i
$953$			998.754i			1.04801i	0.851715	+	0.524005i	$0.175563\pi$
$953$			998.754i			1.04801i	−0.851715	+	0.524005i	$0.824437\pi$
$954$	7.86152	+	331.792i	0.00824058	+	0.347790i
$955$	−210.387	−	364.402i	−0.220301	−	0.381572i
$956$			138.696i			0.145079i
$957$	−616.521	−	157.394i	−0.644222	−	0.164466i
$958$	38.9630	+	67.4858i	0.0406712	+	0.0704445i
$959$	−77.7880	+	201.262i	−0.0811137	+	0.209867i
$960$	55.3332	−	15.5312i	0.0576388	−	0.0161784i
$961$	395.394	+	684.843i	0.411441	+	0.712636i
$962$	225.813	−	130.373i	0.234733	−	0.135523i
$963$	1209.89	−	28.6673i	1.25638	−	0.0297687i
$964$	−30.7525	+	53.2648i	−0.0319009	+	0.0552540i
$965$	−169.393	−	97.7994i	−0.175537	−	0.101347i
$966$	3.85550	−	1.76088i	0.00399120	−	0.00182286i
$967$	568.912	+	985.384i	0.588327	+	1.01901i	0.994452	+	0.105194i	$0.0335464\pi$
$967$	568.912	+	985.384i	0.588327	+	1.01901i	−0.406125	+	0.913818i	$0.633120\pi$
$968$			245.794i			0.253920i
$969$	152.744	−	42.8731i	0.157631	−	0.0442447i
$970$	540.901			0.557630
$971$	−1389.34	−	802.138i	−1.43084	−	0.826095i	−0.433653	−	0.901080i	$-0.642776\pi$
$971$	−1389.34	−	802.138i	−1.43084	−	0.826095i	−0.997185	+	0.0749853i	$0.976109\pi$
$972$	322.711	−	363.392i	0.332007	−	0.373860i
$973$	59.9699	+	384.345i	0.0616341	+	0.395010i
$974$	−585.257	−	337.898i	−0.600880	−	0.346918i
$975$	231.795	−	237.352i	0.237738	−	0.243438i
$976$	205.328	−	355.639i	0.210377	−	0.364384i
$977$	978.287	+	564.814i	1.00132	+	0.578111i	0.908638	−	0.417585i	$-0.137123\pi$
$977$	978.287	+	564.814i	1.00132	+	0.578111i	0.0926796	+	0.995696i	$0.470457\pi$
$978$	−923.471	+	259.205i	−0.944244	+	0.265036i
$979$	−319.222	+	552.909i	−0.326070	+	0.564769i
$980$	71.4931	+	223.520i	0.0729521	+	0.228082i
$981$	1312.30	+	716.759i	1.33772	+	0.730641i
$982$	−336.681	+	583.149i	−0.342852	+	0.593838i
$983$			559.556i			0.569233i	0.958641	+	0.284617i	$0.0918663\pi$
$983$			559.556i			0.569233i	−0.958641	+	0.284617i	$0.908134\pi$
$984$	−187.532	+	192.028i	−0.190581	+	0.195151i
$985$	−763.560			−0.775188
$986$	1100.49	−	635.367i	1.11611	−	0.644389i
$987$	533.714	+	1168.58i	0.540744	+	1.18397i
$988$	12.2704	−	21.2530i	0.0124194	−	0.0215111i
$989$	9.91748	+	5.72586i	0.0100278	+	0.00578955i
$990$	−85.3132	+	156.199i	−0.0861750	+	0.157776i
$991$	−820.211	−	1420.65i	−0.827660	−	1.43355i	−0.899870	−	0.436159i	$-0.856338\pi$
$991$	−820.211	−	1420.65i	−0.827660	−	1.43355i	0.0722098	−	0.997389i	$-0.476995\pi$
$992$	−63.9146	+	36.9011i	−0.0644300	+	0.0371987i
$993$	−462.937	+	474.035i	−0.466200	+	0.477377i
$994$	153.826	+	985.863i	0.154754	+	0.991814i
$995$	−779.252	+	449.901i	−0.783167	+	0.452162i
$996$	−255.457	−	249.476i	−0.256483	−	0.250478i
$997$	78.3056			0.0785412			0.0392706	−	0.999229i	$-0.487497\pi$
$997$	78.3056			0.0785412			0.0392706	+	0.999229i	$0.487497\pi$
$998$	−61.1832	+	35.3241i	−0.0613058	+	0.0353949i
$999$	−829.204	+	254.083i	−0.830034	+	0.254337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.i.a.65.5	✓	32
3.2	odd	2		378.3.i.a.359.11		32
7.4	even	3		126.3.r.a.11.6	yes	32
9.4	even	3		378.3.r.a.233.6		32
9.5	odd	6		126.3.r.a.23.14	yes	32
21.11	odd	6		378.3.r.a.305.14		32
63.4	even	3		378.3.i.a.179.14		32
63.32	odd	6	inner	126.3.i.a.95.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.5	✓	32	1.1	even	1	trivial
126.3.i.a.95.5	yes	32	63.32	odd	6	inner
126.3.r.a.11.6	yes	32	7.4	even	3
126.3.r.a.23.14	yes	32	9.5	odd	6
378.3.i.a.179.14		32	63.4	even	3
378.3.i.a.359.11		32	3.2	odd	2
378.3.r.a.233.6		32	9.4	even	3
378.3.r.a.305.14		32	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.810726 + 2.88838i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.39465i q^{5} +(-3.03532 - 2.96426i) q^{6} +(6.52929 + 2.52357i) q^{7} +2.82843i q^{8} +(-7.68545 + 4.68336i) q^{9} +(-1.69327 - 2.93283i) q^{10} +5.83940i q^{11} +(5.81354 + 1.48416i) q^{12} +(-2.87005 - 4.97107i) q^{13} +(-9.78115 + 1.52617i) q^{14} +(-6.91665 + 1.94140i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-21.4241 + 12.3692i) q^{17} +(6.10108 - 11.1704i) q^{18} +(-1.06883 + 1.85127i) q^{19} +(4.14765 + 2.39465i) q^{20} +(-1.99557 + 20.9050i) q^{21} +(-4.12908 - 7.15177i) q^{22} +0.142721i q^{23} +(-8.16956 + 2.29308i) q^{24} +19.2657 q^{25} +(7.03015 + 4.05886i) q^{26} +(-19.7581 - 18.4016i) q^{27} +(10.9002 - 8.78548i) q^{28} +(31.4557 + 18.1610i) q^{29} +(7.09835 - 7.26853i) q^{30} +(-6.52325 + 11.2986i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-16.8664 + 4.73415i) q^{33} +(17.4927 - 30.2982i) q^{34} +(-6.04307 + 15.6353i) q^{35} +(0.426375 + 17.9949i) q^{36} +(16.0604 - 27.8173i) q^{37} -3.02311i q^{38} +(12.0315 - 12.3200i) q^{39} -6.77309 q^{40} +(27.3943 - 15.8161i) q^{41} +(-12.3380 - 27.0143i) q^{42} +(40.1194 - 69.4888i) q^{43} +(10.1141 + 5.83940i) q^{44} +(-11.2150 - 18.4040i) q^{45} +(-0.100919 - 0.174796i) q^{46} +(52.9798 - 30.5879i) q^{47} +(8.38418 - 8.58519i) q^{48} +(36.2631 + 32.9543i) q^{49} +(-23.5955 + 13.6229i) q^{50} +(-53.0959 - 51.8528i) q^{51} -11.4802 q^{52} +(-22.5819 + 13.0377i) q^{53} +(37.2105 + 8.56611i) q^{54} -13.9833 q^{55} +(-7.13774 + 18.4676i) q^{56} +(-6.21370 - 1.58632i) q^{57} -51.3669 q^{58} +(-19.7078 - 11.3783i) q^{59} +(-3.55404 + 13.9214i) q^{60} +(51.3320 + 88.9096i) q^{61} -18.4505i q^{62} +(-61.9993 + 11.1842i) q^{63} -8.00000 q^{64} +(11.9040 - 6.87276i) q^{65} +(17.3095 - 17.7245i) q^{66} +(-35.1190 + 60.8279i) q^{67} +49.4768i q^{68} +(-0.412231 + 0.115707i) q^{69} +(-3.65464 - 23.4224i) q^{70} -100.792i q^{71} +(-13.2466 - 21.7377i) q^{72} +(-4.36953 - 7.56824i) q^{73} +45.4255i q^{74} +(15.6192 + 55.6465i) q^{75} +(2.13766 + 3.70254i) q^{76} +(-14.7362 + 38.1271i) q^{77} +(-6.02400 + 23.5964i) q^{78} +(31.1461 + 53.9466i) q^{79} +(8.29531 - 4.78930i) q^{80} +(37.1322 - 71.9875i) q^{81} +(-22.3674 + 38.7414i) q^{82} +(-51.5381 - 29.7555i) q^{83} +(34.2129 + 24.3614i) q^{84} +(-29.6199 - 51.3031i) q^{85} +113.475i q^{86} +(-26.9537 + 105.579i) q^{87} -16.5163 q^{88} +(94.6860 + 54.6670i) q^{89} +(26.7491 + 14.6099i) q^{90} +(-6.19450 - 39.7003i) q^{91} +(0.247199 + 0.142721i) q^{92} +(-37.9232 - 9.68155i) q^{93} +(-43.2578 + 74.9248i) q^{94} +(-4.43315 - 2.55948i) q^{95} +(-4.19784 + 16.4432i) q^{96} +(-79.8603 + 138.322i) q^{97} +(-67.7153 - 14.7187i) q^{98} +(-27.3480 - 44.8784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 8 q^{6} + 2 q^{7} + 4 q^{9} + 10 q^{13} + 36 q^{14} + 10 q^{15} - 64 q^{16} + 54 q^{17} + 24 q^{18} + 28 q^{19} + 16 q^{21} + 8 q^{24} - 160 q^{25} + 72 q^{26} - 126 q^{27} - 4 q^{28}+ \cdots + 394 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 + 8 * q^6 + 2 * q^7 + 4 * q^9 + 10 * q^13 + 36 * q^14 + 10 * q^15 - 64 * q^16 + 54 * q^17 + 24 * q^18 + 28 * q^19 + 16 * q^21 + 8 * q^24 - 160 * q^25 + 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 - 80 * q^30 - 8 * q^31 - 106 * q^33 + 90 * q^35 + 40 * q^36 + 22 * q^37 - 170 * q^39 + 72 * q^41 + 72 * q^42 + 16 * q^43 - 72 * q^44 - 250 * q^45 - 12 * q^46 - 108 * q^47 + 74 * q^49 - 288 * q^50 + 122 * q^51 + 40 * q^52 + 72 * q^53 + 8 * q^54 - 24 * q^55 - 282 * q^57 + 48 * q^58 - 90 * q^59 + 52 * q^60 - 62 * q^61 - 438 * q^63 - 256 * q^64 + 378 * q^65 + 224 * q^66 + 70 * q^67 + 218 * q^69 - 108 * q^70 + 48 * q^72 + 196 * q^73 + 166 * q^75 - 56 * q^76 + 630 * q^77 + 32 * q^78 - 38 * q^79 + 400 * q^81 + 184 * q^84 + 60 * q^85 - 98 * q^87 + 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 - 182 * q^93 + 168 * q^94 - 72 * q^95 - 16 * q^96 - 38 * q^97 - 288 * q^98 + 394 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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