LMFDB - Embedded newform 312.2.bk.b.205.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(205,312)] 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("312.205"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.1
Character	$\chi$	$=$	312.205
Dual form			312.2.bk.b.277.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38505 + 0.285742i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.83670 - 0.791531i) q^{4} +4.32865 q^{5} +(1.05661 - 0.939983i) q^{6} +(1.87318 + 1.08148i) q^{7} +(-2.31774 + 1.62113i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-5.99538 + 1.23688i) q^{10} +(-2.57249 - 4.45568i) q^{11} +(-1.19487 + 1.60384i) q^{12} +(2.72749 - 2.35814i) q^{13} +(-2.90347 - 0.962655i) q^{14} +(-3.74872 + 2.16432i) q^{15} +(2.74696 - 2.90762i) q^{16} +(-2.79961 + 4.84906i) q^{17} +(-0.445063 + 1.34236i) q^{18} +(0.963361 - 1.66859i) q^{19} +(7.95044 - 3.42626i) q^{20} -2.16296 q^{21} +(4.83618 + 5.43625i) q^{22} +(-1.01290 - 1.75439i) q^{23} +(1.19666 - 2.56281i) q^{24} +13.7372 q^{25} +(-3.10387 + 4.04549i) q^{26} +1.00000i q^{27} +(4.29650 + 0.503679i) q^{28} +(0.171090 - 0.0987787i) q^{29} +(4.57371 - 4.06885i) q^{30} +7.11414i q^{31} +(-2.97383 + 4.81210i) q^{32} +(4.45568 + 2.57249i) q^{33} +(2.49200 - 7.51614i) q^{34} +(8.10834 + 4.68135i) q^{35} +(0.232865 - 1.98640i) q^{36} +(-0.231065 - 0.400217i) q^{37} +(-0.857513 + 2.58635i) q^{38} +(-1.18300 + 3.40595i) q^{39} +(-10.0327 + 7.01730i) q^{40} +(-1.21570 + 0.701886i) q^{41} +(2.99580 - 0.618049i) q^{42} +(2.55733 + 1.47647i) q^{43} +(-8.25170 - 6.14755i) q^{44} +(2.16432 - 3.74872i) q^{45} +(1.90422 + 2.14049i) q^{46} -2.20506i q^{47} +(-0.925127 + 3.89155i) q^{48} +(-1.16080 - 2.01056i) q^{49} +(-19.0267 + 3.92529i) q^{50} -5.59922i q^{51} +(3.14304 - 6.49009i) q^{52} +2.10538i q^{53} +(-0.285742 - 1.38505i) q^{54} +(-11.1354 - 19.2871i) q^{55} +(-6.09478 + 0.530072i) q^{56} +1.92672i q^{57} +(-0.208742 + 0.185700i) q^{58} +(-2.18299 + 3.78104i) q^{59} +(-5.17216 + 6.94245i) q^{60} +(-10.6432 - 6.14485i) q^{61} +(-2.03281 - 9.85341i) q^{62} +(1.87318 - 1.08148i) q^{63} +(2.74388 - 7.51473i) q^{64} +(11.8063 - 10.2076i) q^{65} +(-6.90638 - 2.28984i) q^{66} +(5.50969 + 9.54306i) q^{67} +(-1.30386 + 11.1223i) q^{68} +(1.75439 + 1.01290i) q^{69} +(-12.5681 - 4.16700i) q^{70} +(5.01087 + 2.89303i) q^{71} +(0.245068 + 2.81779i) q^{72} +10.1096i q^{73} +(0.434394 + 0.488293i) q^{74} +(-11.8968 + 6.86860i) q^{75} +(0.448667 - 3.82724i) q^{76} -11.1284i q^{77} +(0.665289 - 5.05543i) q^{78} -7.37163 q^{79} +(11.8906 - 12.5860i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.48324 - 1.31952i) q^{82} -2.04171 q^{83} +(-3.97272 + 1.71205i) q^{84} +(-12.1185 + 20.9899i) q^{85} +(-3.96390 - 1.31425i) q^{86} +(-0.0987787 + 0.171090i) q^{87} +(13.1856 + 6.15678i) q^{88} +(-4.34987 + 2.51140i) q^{89} +(-1.92652 + 5.81059i) q^{90} +(7.65936 - 1.46750i) q^{91} +(-3.24905 - 2.42056i) q^{92} +(-3.55707 - 6.16103i) q^{93} +(0.630078 + 3.05411i) q^{94} +(4.17005 - 7.22274i) q^{95} +(0.169365 - 5.65432i) q^{96} +(-7.41183 - 4.27922i) q^{97} +(2.18226 + 2.45303i) q^{98} -5.14497 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} + 6 q^{6} - 12 q^{7} + 24 q^{9} - 4 q^{10} - 8 q^{12} - 36 q^{14} - 2 q^{16} + 12 q^{17} + 54 q^{20} - 14 q^{22} + 20 q^{23} + 18 q^{24} + 48 q^{25} - 42 q^{26} + 6 q^{28} - 6 q^{30} + 12 q^{33}+ \cdots + 24 q^{98}+O(q^{100}) $ 48 * q - 2 * q^4 + 6 * q^6 - 12 * q^7 + 24 * q^9 - 4 * q^10 - 8 * q^12 - 36 * q^14 - 2 * q^16 + 12 * q^17 + 54 * q^20 - 14 * q^22 + 20 * q^23 + 18 * q^24 + 48 * q^25 - 42 * q^26 + 6 * q^28 - 6 * q^30 + 12 * q^33 + 2 * q^36 - 28 * q^38 + 28 * q^39 - 8 * q^40 - 12 * q^41 - 10 * q^42 - 30 * q^46 - 8 * q^48 + 16 * q^49 - 84 * q^50 - 28 * q^52 + 6 * q^54 - 68 * q^55 + 18 * q^56 - 24 * q^58 + 24 * q^62 - 12 * q^63 - 68 * q^64 + 12 * q^65 - 44 * q^66 + 4 * q^68 - 12 * q^71 + 54 * q^74 - 54 * q^76 + 4 * q^78 - 192 * q^79 + 78 * q^80 - 24 * q^81 - 6 * q^82 + 30 * q^84 - 10 * q^88 - 48 * q^89 - 8 * q^90 - 12 * q^92 + 54 * q^94 - 20 * q^95 + 144 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	−1.38505	+	0.285742i	−0.979375	+	0.202050i
$2$	−1.38505	+	0.285742i	−0.979375	+	0.202050i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	1.83670	−	0.791531i	0.918352	−	0.395766i
$5$	4.32865			1.93583			0.967915	−	0.251276i	$-0.0808503\pi$
$5$	4.32865			1.93583			0.967915	+	0.251276i	$0.0808503\pi$
$6$	1.05661	−	0.939983i	0.431361	−	0.383746i
$7$	1.87318	+	1.08148i	0.707996	+	0.408762i	0.810319	−	0.585990i	$-0.199294\pi$
$7$	1.87318	+	1.08148i	0.707996	+	0.408762i	−0.102323	+	0.994751i	$0.532627\pi$
$8$	−2.31774	+	1.62113i	−0.819446	+	0.573156i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−5.99538	+	1.23688i	−1.89590	+	0.391135i
$11$	−2.57249	−	4.45568i	−0.775634	−	1.34344i	−0.934438	−	0.356127i	$-0.884097\pi$
$11$	−2.57249	−	4.45568i	−0.775634	−	1.34344i	0.158804	−	0.987310i	$-0.449236\pi$
$12$	−1.19487	+	1.60384i	−0.344928	+	0.462988i
$13$	2.72749	−	2.35814i	0.756468	−	0.654030i
$13$	2.72749	−	2.35814i	0.756468	−	0.654030i
$14$	−2.90347	−	0.962655i	−0.775984	−	0.257280i
$15$	−3.74872	+	2.16432i	−0.967915	+	0.558826i
$16$	2.74696	−	2.90762i	0.686739	−	0.726904i
$17$	−2.79961	+	4.84906i	−0.679005	+	1.17607i	0.296276	+	0.955102i	$0.404255\pi$
$17$	−2.79961	+	4.84906i	−0.679005	+	1.17607i	−0.975281	+	0.220968i	$0.929078\pi$
$18$	−0.445063	+	1.34236i	−0.104902	+	0.316396i
$19$	0.963361	−	1.66859i	0.221010	−	0.382801i	−0.734105	−	0.679036i	$-0.762398\pi$
$19$	0.963361	−	1.66859i	0.221010	−	0.382801i	0.955115	+	0.296235i	$0.0957312\pi$
$20$	7.95044	−	3.42626i	1.77777	−	0.766135i
$21$	−2.16296			−0.471997
$22$	4.83618	+	5.43625i	1.03108	+	1.15901i
$23$	−1.01290	−	1.75439i	−0.211204	−	0.365816i	0.740887	−	0.671629i	$-0.234405\pi$
$23$	−1.01290	−	1.75439i	−0.211204	−	0.365816i	−0.952092	+	0.305813i	$0.901072\pi$
$24$	1.19666	−	2.56281i	0.244267	−	0.523132i
$25$	13.7372			2.74744
$26$	−3.10387	+	4.04549i	−0.608720	+	0.793385i
$27$			1.00000i			0.192450i
$28$	4.29650	+	0.503679i	0.811963	+	0.0951865i
$29$	0.171090	−	0.0987787i	0.0317706	−	0.0183427i	−0.484031	−	0.875051i	$-0.660828\pi$
$29$	0.171090	−	0.0987787i	0.0317706	−	0.0183427i	0.515801	+	0.856708i	$0.327494\pi$
$30$	4.57371	−	4.06885i	0.835041	−	0.742868i
$31$			7.11414i			1.27774i	0.769316	+	0.638869i	$0.220597\pi$
$31$			7.11414i			1.27774i	−0.769316	+	0.638869i	$0.779403\pi$
$32$	−2.97383	+	4.81210i	−0.525704	+	0.850667i
$33$	4.45568	+	2.57249i	0.775634	+	0.447812i
$34$	2.49200	−	7.51614i	0.427375	−	1.28901i
$35$	8.10834	+	4.68135i	1.37056	+	0.791293i
$36$	0.232865	−	1.98640i	0.0388109	−	0.331066i
$37$	−0.231065	−	0.400217i	−0.0379869	−	0.0657952i	0.846407	−	0.532537i	$-0.178761\pi$
$37$	−0.231065	−	0.400217i	−0.0379869	−	0.0657952i	−0.884394	+	0.466742i	$0.845428\pi$
$38$	−0.857513	+	2.58635i	−0.139107	+	0.419561i
$39$	−1.18300	+	3.40595i	−0.189432	+	0.545389i
$40$	−10.0327	+	7.01730i	−1.58631	+	1.10953i
$41$	−1.21570	+	0.701886i	−0.189861	+	0.109616i	−0.591917	−	0.805999i	$-0.701629\pi$
$41$	−1.21570	+	0.701886i	−0.189861	+	0.109616i	0.402057	+	0.915615i	$0.368295\pi$
$42$	2.99580	−	0.618049i	0.462262	−	0.0953670i
$43$	2.55733	+	1.47647i	0.389989	+	0.225160i	0.682155	−	0.731207i	$-0.261043\pi$
$43$	2.55733	+	1.47647i	0.389989	+	0.225160i	−0.292167	+	0.956367i	$0.594376\pi$
$44$	−8.25170	−	6.14755i	−1.24399	−	0.926778i
$45$	2.16432	−	3.74872i	0.322638	−	0.558826i
$46$	1.90422	+	2.14049i	0.280761	+	0.315598i
$47$		−	2.20506i		−	0.321641i	−0.986984	−	0.160821i	$-0.948586\pi$
$47$		−	2.20506i		−	0.321641i	0.986984	−	0.160821i	$-0.0514141\pi$
$48$	−0.925127	+	3.89155i	−0.133531	+	0.561696i
$49$	−1.16080	−	2.01056i	−0.165828	−	0.287222i
$50$	−19.0267	+	3.92529i	−2.69078	+	0.555120i
$51$		−	5.59922i		−	0.784047i
$52$	3.14304	−	6.49009i	0.435861	−	0.900014i
$53$			2.10538i			0.289196i	0.989490	+	0.144598i	$0.0461890\pi$
$53$			2.10538i			0.289196i	−0.989490	+	0.144598i	$0.953811\pi$
$54$	−0.285742	−	1.38505i	−0.0388845	−	0.188481i
$55$	−11.1354	−	19.2871i	−1.50150	−	2.60067i
$56$	−6.09478	+	0.530072i	−0.814449	+	0.0708339i
$57$			1.92672i			0.255201i
$58$	−0.208742	+	0.185700i	−0.0274091	+	0.0243837i
$59$	−2.18299	+	3.78104i	−0.284200	+	0.492250i	−0.972415	−	0.233258i	$-0.925061\pi$
$59$	−2.18299	+	3.78104i	−0.284200	+	0.492250i	0.688215	+	0.725507i	$0.258395\pi$
$60$	−5.17216	+	6.94245i	−0.667722	+	0.896266i
$61$	−10.6432	−	6.14485i	−1.36272	−	0.786767i	−0.372735	−	0.927938i	$-0.621580\pi$
$61$	−10.6432	−	6.14485i	−1.36272	−	0.786767i	−0.989985	+	0.141171i	$0.954913\pi$
$62$	−2.03281	−	9.85341i	−0.258167	−	1.25138i
$63$	1.87318	−	1.08148i	0.235999	−	0.136254i
$64$	2.74388	−	7.51473i	0.342984	−	0.939341i
$65$	11.8063	−	10.2076i	1.46439	−	1.26609i
$66$	−6.90638	−	2.28984i	−0.850117	−	0.281859i
$67$	5.50969	+	9.54306i	0.673115	+	1.16587i	0.977016	+	0.213166i	$0.0683776\pi$
$67$	5.50969	+	9.54306i	0.673115	+	1.16587i	−0.303901	+	0.952704i	$0.598289\pi$
$68$	−1.30386	+	11.1223i	−0.158117	+	1.34877i
$69$	1.75439	+	1.01290i	0.211204	+	0.121939i
$70$	−12.5681	−	4.16700i	−1.50217	−	0.498051i
$71$	5.01087	+	2.89303i	0.594680	+	0.343339i	0.766946	−	0.641712i	$-0.221775\pi$
$71$	5.01087	+	2.89303i	0.594680	+	0.343339i	−0.172266	+	0.985051i	$0.555109\pi$
$72$	0.245068	+	2.81779i	0.0288815	+	0.332080i
$73$			10.1096i			1.18324i	0.806217	+	0.591619i	$0.201511\pi$
$73$			10.1096i			1.18324i	−0.806217	+	0.591619i	$0.798489\pi$
$74$	0.434394	+	0.488293i	0.0504973	+	0.0567629i
$75$	−11.8968	+	6.86860i	−1.37372	+	0.793118i
$76$	0.448667	−	3.82724i	0.0514657	−	0.439014i
$77$		−	11.1284i		−	1.26820i
$78$	0.665289	−	5.05543i	0.0753292	−	0.572415i
$79$	−7.37163			−0.829373			−0.414687	−	0.909964i	$-0.636109\pi$
$79$	−7.37163			−0.829373			−0.414687	+	0.909964i	$0.636109\pi$
$80$	11.8906	−	12.5860i	1.32941	−	1.40716i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.48324	−	1.31952i	0.163797	−	0.145717i
$83$	−2.04171			−0.224106			−0.112053	−	0.993702i	$-0.535743\pi$
$83$	−2.04171			−0.224106			−0.112053	+	0.993702i	$0.535743\pi$
$84$	−3.97272	+	1.71205i	−0.433459	+	0.186800i
$85$	−12.1185	+	20.9899i	−1.31444	+	2.27667i
$86$	−3.96390	−	1.31425i	−0.427439	−	0.141719i
$87$	−0.0987787	+	0.171090i	−0.0105902	+	0.0183427i
$88$	13.1856	+	6.15678i	1.40559	+	0.656315i
$89$	−4.34987	+	2.51140i	−0.461085	+	0.266208i	−0.712501	−	0.701672i	$-0.752437\pi$
$89$	−4.34987	+	2.51140i	−0.461085	+	0.266208i	0.251415	+	0.967879i	$0.419104\pi$
$90$	−1.92652	+	5.81059i	−0.203073	+	0.612490i
$91$	7.65936	−	1.46750i	0.802919	−	0.153835i
$92$	−3.24905	−	2.42056i	−0.338737	−	0.252361i
$93$	−3.55707	−	6.16103i	−0.368851	−	0.638869i
$94$	0.630078	+	3.05411i	0.0649876	+	0.315008i
$95$	4.17005	−	7.22274i	0.427838	−	0.741038i
$96$	0.169365	−	5.65432i	0.0172857	−	0.577091i
$97$	−7.41183	−	4.27922i	−0.752557	−	0.434489i	0.0740599	−	0.997254i	$-0.476404\pi$
$97$	−7.41183	−	4.27922i	−0.752557	−	0.434489i	−0.826617	+	0.562765i	$0.809738\pi$
$98$	2.18226	+	2.45303i	0.220441	+	0.247793i
$99$	−5.14497			−0.517089
$100$	25.2312	−	10.8734i	2.52312	−	1.08734i
$101$	−3.09840	+	1.78886i	−0.308303	+	0.177999i	−0.646167	−	0.763196i	$-0.723629\pi$
$101$	−3.09840	+	1.78886i	−0.308303	+	0.177999i	0.337864	+	0.941195i	$0.390296\pi$
$102$	1.59993	+	7.75517i	0.158417	+	0.767876i
$103$	−4.69498			−0.462610			−0.231305	−	0.972881i	$-0.574300\pi$
$103$	−4.69498			−0.462610			−0.231305	+	0.972881i	$0.574300\pi$
$104$	−2.49876	+	9.88717i	−0.245024	+	0.969517i
$105$	−9.36271			−0.913707
$106$	−0.601596	−	2.91605i	−0.0584322	−	0.283232i
$107$	−1.85628	+	1.07172i	−0.179453	+	0.103607i	−0.587036	−	0.809561i	$-0.699705\pi$
$107$	−1.85628	+	1.07172i	−0.179453	+	0.103607i	0.407583	+	0.913168i	$0.366372\pi$
$108$	0.791531	+	1.83670i	0.0761651	+	0.176737i
$109$	−9.31589			−0.892300			−0.446150	−	0.894958i	$-0.647205\pi$
$109$	−9.31589			−0.892300			−0.446150	+	0.894958i	$0.647205\pi$
$110$	20.9341	+	23.5316i	1.99599	+	2.24365i
$111$	0.400217	+	0.231065i	0.0379869	+	0.0219317i
$112$	8.29008	−	2.47571i	0.783339	−	0.233932i
$113$	9.68859	−	16.7811i	0.911426	−	1.57864i	0.0993747	−	0.995050i	$-0.468316\pi$
$113$	9.68859	−	16.7811i	0.911426	−	1.57864i	0.812051	−	0.583586i	$-0.198351\pi$
$114$	−0.550545	−	2.66860i	−0.0515633	−	0.249937i
$115$	−4.38449	−	7.59415i	−0.408856	−	0.708159i
$116$	0.236055	−	0.316850i	0.0219171	−	0.0294188i
$117$	−0.678466	−	3.54114i	−0.0627242	−	0.327379i
$118$	1.94313	−	5.86068i	0.178880	−	0.539520i
$119$	−10.4883	+	6.05545i	−0.961465	+	0.555102i
$120$	5.17992	−	11.0935i	0.472860	−	1.01269i
$121$	−7.73537	+	13.3980i	−0.703215	+	1.21800i
$122$	16.4971	+	5.46969i	1.49358	+	0.495202i
$123$	0.701886	−	1.21570i	0.0632869	−	0.109616i
$124$	5.63107	+	13.0666i	0.505685	+	1.17341i
$125$	37.8203			3.38275
$126$	−2.28542	+	2.03315i	−0.203601	+	0.181127i
$127$	3.32924	+	5.76642i	0.295423	+	0.511687i	0.975083	−	0.221840i	$-0.0712062\pi$
$127$	3.32924	+	5.76642i	0.295423	+	0.511687i	−0.679661	+	0.733527i	$0.737873\pi$
$128$	−1.65312	+	11.1923i	−0.146117	+	0.989267i
$129$	−2.95295			−0.259992
$130$	−13.4356	+	17.5115i	−1.17838	+	1.53586i
$131$		−	10.3800i		−	0.906905i	−0.891280	−	0.453453i	$-0.850192\pi$
$131$		−	10.3800i		−	0.906905i	0.891280	−	0.453453i	$-0.149808\pi$
$132$	10.2200	+	1.19809i	0.889533	+	0.104280i
$133$	3.60910	−	2.08371i	0.312949	−	0.180681i
$134$	−10.3580	−	11.6432i	−0.894796	−	1.00582i
$135$			4.32865i			0.372551i
$136$	−1.37219	−	15.7774i	−0.117664	−	1.35290i
$137$	2.55242	+	1.47364i	0.218068	+	0.125902i	0.605056	−	0.796183i	$-0.293151\pi$
$137$	2.55242	+	1.47364i	0.218068	+	0.125902i	−0.386987	+	0.922085i	$0.626484\pi$
$138$	−2.71934	−	0.901608i	−0.231486	−	0.0767500i
$139$	−17.1010	−	9.87324i	−1.45048	−	0.837437i	−0.451976	−	0.892030i	$-0.649281\pi$
$139$	−17.1010	−	9.87324i	−1.45048	−	0.837437i	−0.998509	+	0.0545929i	$0.982614\pi$
$140$	18.5981	+	2.18025i	1.57182	+	0.184265i
$141$	1.10253	+	1.90964i	0.0928498	+	0.160821i
$142$	−7.76694	−	2.57516i	−0.651787	−	0.216102i
$143$	−17.5235	−	6.08651i	−1.46539	−	0.508980i
$144$	−1.14459	−	3.83274i	−0.0953825	−	0.319395i
$145$	0.740587	−	0.427578i	0.0615024	−	0.0355084i
$146$	−2.88874	−	14.0023i	−0.239073	−	1.15883i
$147$	2.01056	+	1.16080i	0.165828	+	0.0957408i
$148$	−0.741182	−	0.552184i	−0.0609248	−	0.0453892i
$149$	−3.78459	+	6.55509i	−0.310045	+	0.537014i	−0.978372	−	0.206854i	$-0.933678\pi$
$149$	−3.78459	+	6.55509i	−0.310045	+	0.537014i	0.668327	+	0.743868i	$0.267011\pi$
$150$	14.5149	−	12.9127i	1.18514	−	1.05432i
$151$			2.09922i			0.170832i	0.996345	+	0.0854161i	$0.0272220\pi$
$151$			2.09922i			0.170832i	−0.996345	+	0.0854161i	$0.972778\pi$
$152$	0.472177	+	5.42910i	0.0382986	+	0.440358i
$153$	2.79961	+	4.84906i	0.226335	+	0.392023i
$154$	3.17985	+	15.4133i	0.256239	+	1.24204i
$155$			30.7946i			2.47348i
$156$	0.523092	+	7.19210i	0.0418809	+	0.575829i
$157$		−	8.35087i		−	0.666472i	−0.942843	−	0.333236i	$-0.891859\pi$
$157$		−	8.35087i		−	0.666472i	0.942843	−	0.333236i	$-0.108141\pi$
$158$	10.2100	−	2.10638i	0.812268	−	0.167575i
$159$	−1.05269	−	1.82331i	−0.0834838	−	0.144598i
$160$	−12.8727	+	20.8299i	−1.01767	+	1.64675i
$161$		−	4.38173i		−	0.345329i
$162$	0.939983	+	1.05661i	0.0738520	+	0.0830154i
$163$	3.81101	−	6.60086i	0.298501	−	0.517019i	−0.677292	−	0.735714i	$-0.736847\pi$
$163$	3.81101	−	6.60086i	0.298501	−	0.517019i	0.975793	+	0.218695i	$0.0701799\pi$
$164$	−1.67732	+	2.25142i	−0.130977	+	0.175807i
$165$	19.2871	+	11.1354i	1.50150	+	0.866889i
$166$	2.82786	−	0.583401i	0.219484	−	0.0452807i
$167$	−10.4948	+	6.05915i	−0.812109	+	0.468871i	−0.847688	−	0.530496i	$-0.822006\pi$
$167$	−10.4948	+	6.05915i	−0.812109	+	0.468871i	0.0355788	+	0.999367i	$0.488673\pi$
$168$	5.01319	−	3.50644i	0.386776	−	0.270528i
$169$	1.87836	−	12.8636i	0.144489	−	0.989506i
$170$	10.7870	−	32.5347i	0.827326	−	2.49530i
$171$	−0.963361	−	1.66859i	−0.0736701	−	0.127600i
$172$	5.86572	+	0.687639i	0.447257	+	0.0524320i
$173$	−4.95047	−	2.85815i	−0.376377	−	0.217301i	0.299864	−	0.953982i	$-0.403059\pi$
$173$	−4.95047	−	2.85815i	−0.376377	−	0.217301i	−0.676241	+	0.736681i	$0.736392\pi$
$174$	0.0879255	−	0.265192i	0.00666561	−	0.0201042i
$175$	25.7323	+	14.8565i	1.94518	+	1.12305i
$176$	−20.0219	−	4.75975i	−1.50921	−	0.358780i
$177$		−	4.36597i		−	0.328166i
$178$	5.30716	−	4.72134i	0.397788	−	0.353880i
$179$	−6.10323	+	3.52370i	−0.456177	+	0.263374i	−0.710435	−	0.703762i	$-0.751502\pi$
$179$	−6.10323	+	3.52370i	−0.456177	+	0.263374i	0.254258	+	0.967136i	$0.418169\pi$
$180$	1.00799	−	8.59842i	0.0751314	−	0.640888i
$181$			7.85231i			0.583658i	0.956471	+	0.291829i	$0.0942638\pi$
$181$			7.85231i			0.583658i	−0.956471	+	0.291829i	$0.905736\pi$
$182$	−10.1892	+	4.22115i	−0.755276	+	0.312892i
$183$	12.2897			0.908480
$184$	5.19174	+	2.42419i	0.382740	+	0.178714i
$185$	−1.00020	−	1.73240i	−0.0735362	−	0.127368i
$186$	6.68717	+	7.51690i	0.490327	+	0.551166i
$187$	28.8078			2.10664
$188$	−1.74537	−	4.05004i	−0.127295	−	0.295380i
$189$	−1.08148	+	1.87318i	−0.0786662	+	0.136254i
$190$	−3.71187	+	11.1954i	−0.269288	+	0.812199i
$191$	10.1668	−	17.6094i	0.735644	−	1.27417i	−0.218796	−	0.975771i	$-0.570213\pi$
$191$	10.1668	−	17.6094i	0.735644	−	1.27417i	0.954440	−	0.298403i	$-0.0964539\pi$
$192$	1.38110	+	7.87988i	0.0996722	+	0.568682i
$193$	−6.49899	+	3.75219i	−0.467808	+	0.270089i	−0.715322	−	0.698795i	$-0.753720\pi$
$193$	−6.49899	+	3.75219i	−0.467808	+	0.270089i	0.247514	+	0.968884i	$0.420386\pi$
$194$	11.4885	+	3.80905i	0.824824	+	0.273474i
$195$	−5.12080	+	14.7432i	−0.366708	+	1.05578i
$196$	−3.72346	−	2.77399i	−0.265961	−	0.198142i
$197$	−2.25982	−	3.91412i	−0.161005	−	0.278869i	0.774224	−	0.632911i	$-0.218140\pi$
$197$	−2.25982	−	3.91412i	−0.161005	−	0.278869i	−0.935229	+	0.354042i	$0.884807\pi$
$198$	7.12602	−	1.47013i	0.506424	−	0.104478i
$199$	12.5909	−	21.8080i	0.892543	−	1.54593i	0.0557276	−	0.998446i	$-0.482252\pi$
$199$	12.5909	−	21.8080i	0.892543	−	1.54593i	0.836816	−	0.547484i	$-0.184414\pi$
$200$	−31.8393	+	22.2698i	−2.25138	+	1.57471i
$201$	−9.54306	−	5.50969i	−0.673115	−	0.388623i
$202$	3.78028	−	3.36300i	0.265979	−	0.236620i
$203$	0.427309			0.0299912
$204$	−4.43195	−	10.2841i	−0.310299	−	0.720031i
$205$	−5.26235	+	3.03822i	−0.367538	+	0.212198i
$206$	6.50277	−	1.34155i	0.453069	−	0.0934705i
$207$	−2.02580			−0.140803
$208$	0.635724	−	14.4082i	0.0440795	−	0.999028i
$209$	−9.91293			−0.685692
$210$	12.9678	−	2.67532i	0.894862	−	0.184614i
$211$	13.5839	−	7.84264i	0.935151	−	0.539910i	0.0467141	−	0.998908i	$-0.485125\pi$
$211$	13.5839	−	7.84264i	0.935151	−	0.539910i	0.888437	+	0.458999i	$0.151792\pi$
$212$	1.66648	+	3.86696i	0.114454	+	0.265584i
$213$	−5.78605			−0.396454
$214$	2.26479	−	2.01480i	0.154818	−	0.137729i
$215$	11.0698	+	6.39113i	0.754952	+	0.435872i
$216$	−1.62113	−	2.31774i	−0.110304	−	0.157703i
$217$	−7.69381	+	13.3261i	−0.522290	+	0.904633i
$218$	12.9029	−	2.66194i	0.873897	−	0.180289i
$219$	−5.05480	−	8.75517i	−0.341572	−	0.591619i
$220$	−35.7187	−	26.6106i	−2.40816	−	1.79409i
$221$	3.79887	+	19.8276i	0.255540	+	1.33375i
$222$	−0.620343	−	0.205677i	−0.0416347	−	0.0138041i
$223$	−19.7231	+	11.3871i	−1.32076	+	0.762540i	−0.983849	−	0.178998i	$-0.942715\pi$
$223$	−19.7231	+	11.3871i	−1.32076	+	0.762540i	−0.336908	+	0.941538i	$0.609381\pi$
$224$	−10.7747	+	5.79779i	−0.719917	+	0.387381i
$225$	6.86860	−	11.8968i	0.457907	−	0.793118i
$226$	−8.62407	+	26.0111i	−0.573665	+	1.73023i
$227$	2.14767	−	3.71988i	0.142546	−	0.246897i	−0.785909	−	0.618343i	$-0.787804\pi$
$227$	2.14767	−	3.71988i	0.142546	−	0.246897i	0.928455	+	0.371446i	$0.121138\pi$
$228$	1.52506	+	3.53882i	0.101000	+	0.234364i
$229$	−20.0355			−1.32398			−0.661991	−	0.749512i	$-0.730288\pi$
$229$	−20.0355			−1.32398			−0.661991	+	0.749512i	$0.730288\pi$
$230$	8.24268	+	9.26542i	0.543506	+	0.610944i
$231$	5.56419	+	9.63746i	0.366097	+	0.634098i
$232$	−0.236409	+	0.506302i	−0.0155210	+	0.0332404i
$233$	−7.21901			−0.472933			−0.236467	−	0.971640i	$-0.575989\pi$
$233$	−7.21901			−0.472933			−0.236467	+	0.971640i	$0.575989\pi$
$234$	1.95156	+	4.71078i	0.127577	+	0.307953i
$235$		−	9.54494i		−	0.622643i
$236$	−1.01668	+	8.67255i	−0.0661805	+	0.564535i
$237$	6.38402	−	3.68582i	0.414687	−	0.239419i
$238$	12.7965	−	11.3840i	0.829476	−	0.737917i
$239$			1.40644i			0.0909750i	0.998965	+	0.0454875i	$0.0144841\pi$
$239$			1.40644i			0.0909750i	−0.998965	+	0.0454875i	$0.985516\pi$
$240$	−4.00455	+	16.8451i	−0.258492	+	1.08735i
$241$	4.79595	+	2.76894i	0.308934	+	0.178363i	0.646449	−	0.762957i	$-0.276253\pi$
$241$	4.79595	+	2.76894i	0.308934	+	0.178363i	−0.337515	+	0.941320i	$0.609586\pi$
$242$	6.88545	−	20.7672i	0.442614	−	1.33497i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−24.4122	−	2.86184i	−1.56283	−	0.183211i
$245$	−5.02468	−	8.70300i	−0.321015	−	0.556014i
$246$	−0.624767	+	1.88436i	−0.0398337	+	0.120142i
$247$	−1.30721	−	6.82280i	−0.0831761	−	0.434124i
$248$	−11.5329	−	16.4888i	−0.732343	−	1.04704i
$249$	1.76817	−	1.02085i	0.112053	−	0.0646939i
$250$	−52.3828	+	10.8068i	−3.31298	+	0.683485i
$251$	19.6157	+	11.3251i	1.23813	+	0.714836i	0.968712	−	0.248187i	$-0.0798346\pi$
$251$	19.6157	+	11.3251i	1.23813	+	0.714836i	0.269420	+	0.963023i	$0.413168\pi$
$252$	2.58445	−	3.46904i	0.162805	−	0.218529i
$253$	−5.21134	+	9.02631i	−0.327634	+	0.567479i
$254$	−6.25886	−	7.03545i	−0.392716	−	0.441443i
$255$		−	24.2370i		−	1.51778i
$256$	−0.908456	−	15.9742i	−0.0567785	−	0.998387i
$257$	9.24512	+	16.0130i	0.576695	+	0.998865i	0.995855	+	0.0909525i	$0.0289912\pi$
$257$	9.24512	+	16.0130i	0.576695	+	0.998865i	−0.419160	+	0.907912i	$0.637676\pi$
$258$	4.08996	−	0.843780i	0.254630	−	0.0525315i
$259$		−	0.999571i		−	0.0621103i
$260$	13.6051	−	28.0933i	0.843754	−	1.74227i
$261$		−	0.197557i		−	0.0122285i
$262$	2.96600	+	14.3768i	0.183240	+	0.888201i
$263$	13.1764	+	22.8222i	0.812493	+	1.40728i	0.911114	+	0.412154i	$0.135224\pi$
$263$	13.1764	+	22.8222i	0.812493	+	1.40728i	−0.0986208	+	0.995125i	$0.531443\pi$
$264$	−14.4975	+	1.26087i	−0.892256	+	0.0776009i
$265$			9.11346i			0.559835i
$266$	−4.40336	+	3.91731i	−0.269988	+	0.240186i
$267$	2.51140	−	4.34987i	0.153695	−	0.266208i
$268$	17.6733	+	13.1667i	1.07957	+	0.804283i
$269$	−27.2381	−	15.7259i	−1.66073	−	0.958825i	−0.972365	−	0.233464i	$-0.924994\pi$
$269$	−27.2381	−	15.7259i	−1.66073	−	0.958825i	−0.688369	−	0.725361i	$-0.741673\pi$
$270$	−1.23688	−	5.99538i	−0.0752739	−	0.364867i
$271$	17.1939	−	9.92693i	1.04446	−	0.603018i	0.123365	−	0.992361i	$-0.460631\pi$
$271$	17.1939	−	9.92693i	1.04446	−	0.603018i	0.921093	+	0.389343i	$0.127298\pi$
$272$	6.40881	+	21.4603i	0.388591	+	1.30122i
$273$	−5.89945	+	5.10057i	−0.357051	+	0.308700i
$274$	−3.95631	−	1.31173i	−0.239009	−	0.0792444i
$275$	−35.3388	−	61.2085i	−2.13101	−	3.69101i
$276$	4.02404	+	0.471739i	0.242219	+	0.0283953i
$277$	−11.0151	−	6.35956i	−0.661832	−	0.382109i	0.131142	−	0.991364i	$-0.458135\pi$
$277$	−11.0151	−	6.35956i	−0.661832	−	0.382109i	−0.792975	+	0.609254i	$0.791469\pi$
$278$	26.5068	+	8.78843i	1.58977	+	0.527095i
$279$	6.16103	+	3.55707i	0.368851	+	0.212956i
$280$	−26.3821	+	2.29450i	−1.57663	+	0.137122i
$281$			20.9908i			1.25221i	0.779740	+	0.626103i	$0.215351\pi$
$281$			20.9908i			1.25221i	−0.779740	+	0.626103i	$0.784649\pi$
$282$	−2.07272	−	2.32990i	−0.123429	−	0.138743i
$283$	−20.0094	+	11.5524i	−1.18944	+	0.686721i	−0.958178	−	0.286172i	$-0.907617\pi$
$283$	−20.0094	+	11.5524i	−1.18944	+	0.686721i	−0.231257	+	0.972893i	$0.574284\pi$
$284$	11.4934	+	1.34737i	0.682007	+	0.0799518i
$285$			8.34011i			0.494025i
$286$	26.0101	+	3.42290i	1.53801	+	0.202400i
$287$	−3.03631			−0.179227
$288$	2.68049	+	4.98147i	0.157949	+	0.293536i
$289$	−7.17561	−	12.4285i	−0.422094	−	0.731089i
$290$	−0.903570	+	0.803832i	−0.0530595	+	0.0472026i
$291$	8.55844			0.501705
$292$	8.00206	+	18.5683i	0.468285	+	1.08663i
$293$	−5.32829	+	9.22886i	−0.311282	+	0.539156i	−0.978640	−	0.205581i	$-0.934092\pi$
$293$	−5.32829	+	9.22886i	−0.311282	+	0.539156i	0.667358	+	0.744737i	$0.267425\pi$
$294$	−3.11640	−	1.03325i	−0.181752	−	0.0602606i
$295$	−9.44938	+	16.3668i	−0.550164	+	0.952912i
$296$	1.18435	+	0.553013i	0.0688391	+	0.0321432i
$297$	4.45568	−	2.57249i	0.258545	−	0.149271i
$298$	3.36876	−	10.1605i	0.195147	−	0.588583i
$299$	−6.89977	−	2.39653i	−0.399024	−	0.138595i
$300$	−16.4141	+	22.0322i	−0.947669	+	1.27203i
$301$	3.19356	+	5.53140i	0.184073	+	0.318825i
$302$	−0.599835	−	2.90752i	−0.0345166	−	0.167309i
$303$	1.78886	−	3.09840i	0.102768	−	0.177999i
$304$	−2.20531	−	7.38463i	−0.126483	−	0.423538i
$305$	−46.0706	−	26.5989i	−2.63800	−	1.52305i
$306$	−5.26316	−	5.91621i	−0.300875	−	0.338207i
$307$	−7.50490			−0.428327			−0.214164	−	0.976798i	$-0.568703\pi$
$307$	−7.50490			−0.428327			−0.214164	+	0.976798i	$0.568703\pi$
$308$	−8.80846	−	20.4395i	−0.501909	−	1.16465i
$309$	4.06598	−	2.34749i	0.231305	−	0.133544i
$310$	−8.79932	−	42.6520i	−0.499768	−	2.42247i
$311$	23.1457			1.31247			0.656237	−	0.754555i	$-0.272147\pi$
$311$	23.1457			1.31247			0.656237	+	0.754555i	$0.272147\pi$
$312$	−2.77959	−	9.81192i	−0.157363	−	0.555491i
$313$	−20.9965			−1.18679			−0.593397	−	0.804910i	$-0.702213\pi$
$313$	−20.9965			−1.18679			−0.593397	+	0.804910i	$0.702213\pi$
$314$	2.38619	+	11.5663i	0.134661	+	0.652726i
$315$	8.10834	−	4.68135i	0.456853	−	0.263764i
$316$	−13.5395	+	5.83488i	−0.761656	+	0.328237i
$317$	1.12069			0.0629444			0.0314722	−	0.999505i	$-0.489980\pi$
$317$	1.12069			0.0629444			0.0314722	+	0.999505i	$0.489980\pi$
$318$	1.97902	+	2.22458i	0.110978	+	0.124748i
$319$	−0.880252	−	0.508213i	−0.0492846	−	0.0284545i
$320$	11.8773	−	32.5286i	0.663960	−	1.81841i
$321$	1.07172	−	1.85628i	0.0598178	−	0.103607i
$322$	1.25204	+	6.06889i	0.0697737	+	0.338206i
$323$	5.39407	+	9.34280i	0.300134	+	0.519847i
$324$	−1.60384	−	1.19487i	−0.0891021	−	0.0663814i
$325$	37.4680	−	32.3942i	2.07835	−	1.79691i
$326$	−3.39228	+	10.2315i	−0.187881	+	0.566668i
$327$	8.06779	−	4.65794i	0.446150	−	0.257585i
$328$	1.67984	−	3.59760i	0.0927535	−	0.198644i
$329$	2.38473	−	4.13048i	0.131475	−	0.227721i
$330$	−29.8953	−	9.91190i	−1.64568	−	0.545632i
$331$	0.633917	−	1.09798i	0.0348432	−	0.0603503i	−0.848078	−	0.529872i	$-0.822240\pi$
$331$	0.633917	−	1.09798i	0.0348432	−	0.0603503i	0.882921	+	0.469521i	$0.155573\pi$
$332$	−3.75001	+	1.61607i	−0.205808	+	0.0886935i
$333$	−0.462130			−0.0253246
$334$	12.8044	−	11.3910i	0.700624	−	0.623288i
$335$	23.8495	+	41.3085i	1.30304	+	2.25693i
$336$	−5.94157	+	6.28906i	−0.324139	+	0.343097i
$337$	10.2889			0.560475			0.280237	−	0.959931i	$-0.409587\pi$
$337$	10.2889			0.560475			0.280237	+	0.959931i	$0.409587\pi$
$338$	1.07405	+	18.3534i	0.0584208	+	0.998292i
$339$			19.3772i			1.05242i
$340$	−5.64397	+	48.1444i	−0.306087	+	2.61100i
$341$	31.6983	−	18.3010i	1.71656	−	0.991056i
$342$	1.81109	+	2.03580i	0.0979323	+	0.110084i
$343$		−	20.1623i		−	1.08866i
$344$	−8.32078	+	0.723671i	−0.448626	+	0.0390177i
$345$	7.59415	+	4.38449i	0.408856	+	0.236053i
$346$	7.67332	+	2.54412i	0.412520	+	0.136773i
$347$	10.8544	+	6.26678i	0.582694	+	0.336418i	0.762203	−	0.647338i	$-0.224118\pi$
$347$	10.8544	+	6.26678i	0.582694	+	0.336418i	−0.179509	+	0.983756i	$0.557451\pi$
$348$	−0.0460043	+	0.392427i	−0.00246609	+	0.0210363i
$349$	12.8044	+	22.1779i	0.685404	+	1.18715i	0.973310	+	0.229496i	$0.0737077\pi$
$349$	12.8044	+	22.1779i	0.685404	+	1.18715i	−0.287906	+	0.957659i	$0.592959\pi$
$350$	−39.8855	−	13.2242i	−2.13197	−	0.706863i
$351$	2.35814	+	2.72749i	0.125868	+	0.145582i
$352$	29.0913	+	0.871376i	1.55057	+	0.0464445i
$353$	14.9054	−	8.60561i	0.793332	−	0.458031i	−0.0478020	−	0.998857i	$-0.515222\pi$
$353$	14.9054	−	8.60561i	0.793332	−	0.458031i	0.841134	+	0.540826i	$0.181888\pi$
$354$	1.24754	+	6.04707i	0.0663060	+	0.321398i
$355$	21.6903	+	12.5229i	1.15120	+	0.664646i
$356$	−6.00157	+	8.05575i	−0.318083	+	0.426954i
$357$	6.05545	−	10.4883i	0.320488	−	0.555102i
$358$	7.44639	−	6.62444i	0.393554	−	0.350112i
$359$		−	15.0466i		−	0.794128i	−0.917791	−	0.397064i	$-0.870029\pi$
$359$		−	15.0466i		−	0.794128i	0.917791	−	0.397064i	$-0.129971\pi$
$360$	1.06081	+	12.1972i	0.0559097	+	0.642850i
$361$	7.64387	+	13.2396i	0.402309	+	0.696820i
$362$	−2.24373	−	10.8758i	−0.117928	−	0.571620i
$363$		−	15.4707i		−	0.812003i
$364$	12.9064	−	8.75797i	0.676479	−	0.459043i
$365$			43.7609i			2.29055i
$366$	−17.0218	+	3.51168i	−0.889743	+	0.183558i
$367$	10.3822	+	17.9826i	0.541949	+	0.938683i	0.998792	+	0.0491356i	$0.0156466\pi$
$367$	10.3822	+	17.9826i	0.541949	+	0.938683i	−0.456843	+	0.889547i	$0.651020\pi$
$368$	−7.88349	−	1.87412i	−0.410956	−	0.0976953i
$369$			1.40377i			0.0730774i
$370$	1.88034	+	2.11365i	0.0977543	+	0.109883i
$371$	−2.27693	+	3.94376i	−0.118212	+	0.204750i
$372$	−11.4099	−	8.50045i	−0.591577	−	0.440728i
$373$	0.716227	+	0.413514i	0.0370848	+	0.0214109i	0.518428	−	0.855121i	$-0.326517\pi$
$373$	0.716227	+	0.413514i	0.0370848	+	0.0214109i	−0.481343	+	0.876532i	$0.659851\pi$
$374$	−39.9001	+	8.23160i	−2.06319	+	0.425646i
$375$	−32.7533	+	18.9101i	−1.69137	+	0.976516i
$376$	3.57469	+	5.11077i	0.184351	+	0.263568i
$377$	0.233711	−	0.672871i	0.0120367	−	0.0346546i
$378$	0.962655	−	2.90347i	0.0495136	−	0.149338i
$379$	4.60242	+	7.97163i	0.236410	+	0.409475i	0.959682	−	0.281089i	$-0.0906957\pi$
$379$	4.60242	+	7.97163i	0.236410	+	0.409475i	−0.723271	+	0.690564i	$0.757362\pi$
$380$	1.94212	−	16.5668i	0.0996288	−	0.849857i
$381$	−5.76642	−	3.32924i	−0.295423	−	0.170562i
$382$	−9.04974	+	27.2949i	−0.463025	+	1.39653i
$383$	−18.2780	−	10.5528i	−0.933964	−	0.539225i	−0.0459012	−	0.998946i	$-0.514616\pi$
$383$	−18.2780	−	10.5528i	−0.933964	−	0.539225i	−0.888063	+	0.459721i	$0.847949\pi$
$384$	−4.16450	−	10.5194i	−0.212519	−	0.536814i
$385$		−	48.1709i		−	2.45501i
$386$	7.92924	−	7.05399i	0.403588	−	0.359039i
$387$	2.55733	−	1.47647i	0.129996	−	0.0750533i
$388$	−17.0005	−	1.99297i	−0.863068	−	0.101178i
$389$		−	23.7270i		−	1.20301i	−0.798871	−	0.601503i	$-0.794569\pi$
$389$		−	23.7270i		−	1.20301i	0.798871	−	0.601503i	$-0.205431\pi$
$390$	2.87980	−	21.8832i	0.145825	−	1.10810i
$391$	11.3429			0.573634
$392$	5.94980	+	2.77816i	0.300510	+	0.140318i
$393$	5.19000	+	8.98935i	0.261801	+	0.453453i
$394$	4.24837	+	4.77550i	0.214030	+	0.240586i
$395$	−31.9092			−1.60553
$396$	−9.44979	+	4.07241i	−0.474870	+	0.204646i
$397$	3.36607	−	5.83020i	0.168938	−	0.292609i	−0.769109	−	0.639118i	$-0.779300\pi$
$397$	3.36607	−	5.83020i	0.168938	−	0.292609i	0.938047	+	0.346509i	$0.112633\pi$
$398$	−11.2075	+	33.8029i	−0.561780	+	1.69438i
$399$	−2.08371	+	3.60910i	−0.104316	+	0.180681i
$400$	37.7355	−	39.9425i	1.88678	−	1.99713i
$401$	3.32956	−	1.92232i	0.166270	−	0.0959962i	−0.414556	−	0.910024i	$-0.636063\pi$
$401$	3.32956	−	1.92232i	0.166270	−	0.0959962i	0.580826	+	0.814028i	$0.302730\pi$
$402$	14.7919	+	4.90432i	0.737754	+	0.244605i
$403$	16.7761	+	19.4037i	0.835679	+	0.966568i
$404$	−4.27490	+	5.73809i	−0.212684	+	0.285481i
$405$	−2.16432	−	3.74872i	−0.107546	−	0.186275i
$406$	−0.591843	+	0.122100i	−0.0293727	+	0.00605973i
$407$	−1.18882	+	2.05910i	−0.0589278	+	0.102066i
$408$	9.07706	+	12.9775i	0.449381	+	0.642484i
$409$	28.4778	+	16.4417i	1.40814	+	0.812988i	0.995208	−	0.0977760i	$-0.0311729\pi$
$409$	28.4778	+	16.4417i	1.40814	+	0.812988i	0.412928	+	0.910764i	$0.364506\pi$
$410$	6.42045	−	5.71174i	0.317083	−	0.282083i
$411$	−2.94729			−0.145379
$412$	−8.62329	+	3.71623i	−0.424839	+	0.183085i
$413$	−8.17825	+	4.72172i	−0.402425	+	0.232340i
$414$	2.80582	−	0.578856i	0.137899	−	0.0284492i
$415$	−8.83783			−0.433832
$416$	3.23652	+	20.1377i	0.158683	+	0.987330i
$417$	19.7465			0.966989
$418$	13.7299	−	2.83254i	0.671550	−	0.138544i
$419$	2.46615	−	1.42383i	0.120480	−	0.0695589i	−0.438549	−	0.898707i	$-0.644507\pi$
$419$	2.46615	−	1.42383i	0.120480	−	0.0695589i	0.559029	+	0.829148i	$0.311174\pi$
$420$	−17.1965	+	7.41087i	−0.839104	+	0.361614i
$421$	1.04860			0.0511058			0.0255529	−	0.999673i	$-0.491865\pi$
$421$	1.04860			0.0511058			0.0255529	+	0.999673i	$0.491865\pi$
$422$	−16.5733	+	14.7439i	−0.806775	+	0.717722i
$423$	−1.90964	−	1.10253i	−0.0928498	−	0.0536069i
$424$	−3.41310	−	4.87974i	−0.165755	−	0.236981i
$425$	−38.4588	+	66.6126i	−1.86552	+	3.23118i
$426$	8.01394	−	1.65332i	0.388277	−	0.0801035i
$427$	−13.2911	−	23.0208i	−0.643200	−	1.11406i
$428$	−2.56113	+	3.43774i	−0.123797	+	0.166169i
$429$	18.2191	−	3.49069i	0.879625	−	0.168532i
$430$	−17.1583	−	5.68891i	−0.827449	−	0.274344i
$431$	19.1618	−	11.0631i	0.922994	−	0.532891i	0.0384048	−	0.999262i	$-0.487772\pi$
$431$	19.1618	−	11.0631i	0.922994	−	0.532891i	0.884589	+	0.466372i	$0.154439\pi$
$432$	2.90762	+	2.74696i	0.139893	+	0.132163i
$433$	8.37706	−	14.5095i	0.402576	−	0.697281i	−0.591460	−	0.806334i	$-0.701448\pi$
$433$	8.37706	−	14.5095i	0.402576	−	0.697281i	0.994036	+	0.109053i	$0.0347817\pi$
$434$	6.84847	−	20.6557i	0.328737	−	0.991504i
$435$	−0.427578	+	0.740587i	−0.0205008	+	0.0355084i
$436$	−17.1105	+	7.37381i	−0.819445	+	0.353142i
$437$	−3.90315			−0.186713
$438$	9.50285	+	10.6819i	0.454064	+	0.510403i
$439$	−3.46657	−	6.00428i	−0.165451	−	0.286569i	0.771365	−	0.636393i	$-0.219574\pi$
$439$	−3.46657	−	6.00428i	−0.165451	−	0.286569i	−0.936815	+	0.349825i	$0.886241\pi$
$440$	57.0758	+	26.6506i	2.72098	+	1.27052i
$441$	−2.32159			−0.110552
$442$	−10.9272	−	26.3767i	−0.519754	−	1.25461i
$443$		−	22.9404i		−	1.08993i	−0.838458	−	0.544966i	$-0.816543\pi$
$443$		−	22.9404i		−	1.08993i	0.838458	−	0.544966i	$-0.183457\pi$
$444$	0.917974	+	0.107614i	0.0435651	+	0.00510714i
$445$	−18.8291	+	10.8710i	−0.892583	+	0.515333i
$446$	24.0636	−	21.4074i	1.13945	−	1.01367i
$447$		−	7.56917i		−	0.358009i
$448$	13.2668	−	11.1090i	0.626798	−	0.524851i
$449$	25.8804	+	14.9420i	1.22137	+	0.705159i	0.965210	−	0.261475i	$-0.0842091\pi$
$449$	25.8804	+	14.9420i	1.22137	+	0.705159i	0.256161	+	0.966634i	$0.417542\pi$
$450$	−6.11392	+	18.4402i	−0.288213	+	0.869280i
$451$	6.25475	+	3.61118i	0.294525	+	0.170044i
$452$	4.51228	−	38.4908i	0.212240	−	1.81045i
$453$	−1.04961	−	1.81798i	−0.0493150	−	0.0854161i
$454$	−1.91170	+	5.76588i	−0.0897205	+	0.270606i
$455$	33.1547	−	6.35227i	1.55432	−	0.297799i
$456$	−3.12347	−	4.46565i	−0.146270	−	0.209123i
$457$	−3.45008	+	1.99190i	−0.161388	+	0.0931773i	−0.578519	−	0.815669i	$-0.696369\pi$
$457$	−3.45008	+	1.99190i	−0.161388	+	0.0931773i	0.417131	+	0.908846i	$0.363036\pi$
$458$	27.7501	−	5.72498i	1.29668	−	0.267511i
$459$	−4.84906	−	2.79961i	−0.226335	−	0.130674i
$460$	−14.0640	−	10.4777i	−0.655738	−	0.488528i
$461$	−0.328552	+	0.569069i	−0.0153022	+	0.0265042i	−0.873575	−	0.486689i	$-0.838204\pi$
$461$	−0.328552	+	0.569069i	−0.0153022	+	0.0265042i	0.858273	+	0.513194i	$0.171538\pi$
$462$	−10.4605	−	11.7584i	−0.486666	−	0.547050i
$463$		−	8.60871i		−	0.400081i	−0.979788	−	0.200040i	$-0.935893\pi$
$463$		−	8.60871i		−	0.400081i	0.979788	−	0.200040i	$-0.0641073\pi$
$464$	0.182766	−	0.768804i	0.00848468	−	0.0356908i
$465$	−15.3973	−	26.6689i	−0.714033	−	1.23674i
$466$	9.99866	−	2.06277i	0.463179	−	0.0955562i
$467$			19.4449i			0.899804i	0.893078	+	0.449902i	$0.148541\pi$
$467$			19.4449i			0.899804i	−0.893078	+	0.449902i	$0.851459\pi$
$468$	−4.04906	−	5.96700i	−0.187168	−	0.275825i
$469$			23.8345i			1.10057i
$470$	2.72739	+	13.2202i	0.125805	+	0.609801i
$471$	4.17544	+	7.23207i	0.192394	+	0.333236i
$472$	−1.06996	−	12.3024i	−0.0492488	−	0.566263i
$473$		−	15.1928i		−	0.698567i
$474$	−7.78897	+	6.92921i	−0.357759	+	0.318269i
$475$	13.2339	−	22.9218i	0.607212	−	1.05172i
$476$	−14.4709	+	19.4239i	−0.663272	+	0.890293i
$477$	1.82331	+	1.05269i	0.0834838	+	0.0481994i
$478$	−0.401879	−	1.94798i	−0.0183815	−	0.0890987i
$479$	−1.92596	+	1.11196i	−0.0879995	+	0.0508066i	−0.543354	−	0.839504i	$-0.682846\pi$
$479$	−1.92596	+	1.11196i	−0.0879995	+	0.0508066i	0.455354	+	0.890310i	$0.349513\pi$
$480$	0.733120	−	24.4756i	0.0334622	−	1.11715i
$481$	−1.57399	−	0.546701i	−0.0717679	−	0.0249274i
$482$	−7.43381	−	2.46471i	−0.338601	−	0.112264i
$483$	2.19086	+	3.79469i	0.0996878	+	0.172664i
$484$	−3.60260	+	30.7310i	−0.163755	+	1.39686i
$485$	−32.0832	−	18.5232i	−1.45682	−	0.841097i
$486$	−1.34236	−	0.445063i	−0.0608905	−	0.0201885i
$487$	−18.3856	−	10.6149i	−0.833129	−	0.481007i	0.0217938	−	0.999762i	$-0.493062\pi$
$487$	−18.3856	−	10.6149i	−0.833129	−	0.481007i	−0.854923	+	0.518755i	$0.826396\pi$
$488$	34.6298	−	3.01181i	1.56762	−	0.136338i
$489$			7.62202i			0.344680i
$490$	9.44622	+	10.6183i	0.426737	+	0.479685i
$491$	10.8716	−	6.27672i	0.490628	−	0.283264i	−0.234207	−	0.972187i	$-0.575249\pi$
$491$	10.8716	−	6.27672i	0.490628	−	0.283264i	0.724835	+	0.688922i	$0.241916\pi$
$492$	0.326890	−	2.78845i	0.0147373	−	0.125713i
$493$			1.10617i			0.0498192i
$494$	3.76011	+	9.07636i	0.169175	+	0.408365i
$495$	−22.2708			−1.00100
$496$	20.6852	+	19.5422i	0.928793	+	0.877473i
$497$	6.25751	+	10.8383i	0.280688	+	0.486165i
$498$	−2.15729	+	1.91917i	−0.0966707	+	0.0859999i
$499$	21.0316			0.941506			0.470753	−	0.882265i	$-0.343982\pi$
$499$	21.0316			0.941506			0.470753	+	0.882265i	$0.343982\pi$
$500$	69.4646	−	29.9359i	3.10655	−	1.33878i
$501$	6.05915	−	10.4948i	0.270703	−	0.468871i
$502$	−30.4047	−	10.0808i	−1.35703	−	0.449928i
$503$	−13.5799	+	23.5210i	−0.605496	+	1.04875i	0.386477	+	0.922299i	$0.373692\pi$
$503$	−13.5799	+	23.5210i	−0.605496	+	1.04875i	−0.991973	+	0.126450i	$0.959642\pi$
$504$	−2.58833	+	5.54327i	−0.115293	+	0.246917i
$505$	−13.4119	+	7.74336i	−0.596822	+	0.344575i
$506$	4.63875	−	13.9909i	0.206218	−	0.621973i
$507$	4.80509	+	12.0794i	0.213401	+	0.536464i
$508$	10.6791	+	7.95600i	0.473810	+	0.352990i
$509$	−9.37387	−	16.2360i	−0.415489	−	0.719649i	0.579990	−	0.814623i	$-0.303056\pi$
$509$	−9.37387	−	16.2360i	−0.415489	−	0.719649i	−0.995480	+	0.0949746i	$0.969723\pi$
$510$	6.92554	+	33.5694i	0.306668	+	1.48648i
$511$	−10.9333	+	18.9371i	−0.483663	+	0.837728i
$512$	5.82275	+	21.8654i	0.257332	+	0.966323i
$513$	1.66859	+	0.963361i	0.0736701	+	0.0425334i
$514$	−17.3805	−	19.5370i	−0.766621	−	0.861742i
$515$	−20.3229			−0.895536
$516$	−5.42368	+	2.33735i	−0.238764	+	0.102896i
$517$	−9.82504	+	5.67249i	−0.432105	+	0.249476i
$518$	0.285619	+	1.38445i	0.0125494	+	0.0608293i
$519$	5.71631			0.250918
$520$	−10.8163	+	42.7981i	−0.474325	+	1.87682i
$521$	22.1856			0.971969			0.485985	−	0.873967i	$-0.338461\pi$
$521$	22.1856			0.971969			0.485985	+	0.873967i	$0.338461\pi$
$522$	0.0564504	+	0.273626i	0.00247077	+	0.0119763i
$523$	−19.8524	+	11.4618i	−0.868084	+	0.501188i	−0.866711	−	0.498811i	$-0.833770\pi$
$523$	−19.8524	+	11.4618i	−0.868084	+	0.501188i	−0.00137276	+	0.999999i	$0.500437\pi$
$524$	−8.21610	−	19.0650i	−0.358922	−	0.832858i
$525$	−29.7131			−1.29678
$526$	−24.7712	−	27.8448i	−1.08008	−	1.21409i
$527$	−34.4969	−	19.9168i	−1.50271	−	0.867590i
$528$	19.7194	−	5.88889i	0.858175	−	0.256281i
$529$	9.44807	−	16.3645i	0.410786	−	0.711502i
$530$	−2.60410	−	12.6226i	−0.113115	−	0.548289i
$531$	2.18299	+	3.78104i	0.0947335	+	0.164083i
$532$	4.97952	−	6.68388i	0.215890	−	0.289783i
$533$	−1.66067	+	4.78118i	−0.0719314	+	0.207096i
$534$	−2.23546	+	6.74238i	−0.0967379	+	0.291771i
$535$	−8.03518	+	4.63911i	−0.347391	+	0.200566i
$536$	−28.2406	−	13.1864i	−1.21981	−	0.569568i
$537$	3.52370	−	6.10323i	0.152059	−	0.263374i
$538$	42.2195	+	13.9980i	1.82021	+	0.603498i
$539$	−5.97226	+	10.3443i	−0.257244	+	0.445559i
$540$	3.42626	+	7.95044i	0.147443	+	0.342133i
$541$	14.3408			0.616560			0.308280	−	0.951296i	$-0.400247\pi$
$541$	14.3408			0.616560			0.308280	+	0.951296i	$0.400247\pi$
$542$	−20.9779	+	18.6623i	−0.901076	+	0.801614i
$543$	−3.92615	−	6.80030i	−0.168487	−	0.291829i
$544$	−15.0086	−	27.8923i	−0.643489	−	1.19587i
$545$	−40.3252			−1.72734
$546$	6.71356	−	8.75024i	0.287314	−	0.374476i
$547$		−	22.9812i		−	0.982605i	−0.870989	−	0.491302i	$-0.836521\pi$
$547$		−	22.9812i		−	0.982605i	0.870989	−	0.491302i	$-0.163479\pi$
$548$	5.85448	+	0.686321i	0.250091	+	0.0293182i
$549$	−10.6432	+	6.14485i	−0.454240	+	0.262256i
$550$	66.4356	+	74.6788i	2.83283	+	3.18432i
$551$		−	0.380638i		−	0.0162157i
$552$	−5.70828	+	0.496458i	−0.242960	+	0.0211306i
$553$	−13.8084	−	7.97228i	−0.587193	−	0.339016i
$554$	17.0736	+	5.66081i	0.725387	+	0.240505i
$555$	1.73240	+	1.00020i	0.0735362	+	0.0424561i
$556$	−39.2244	−	4.59827i	−1.66348	−	0.195010i
$557$	−1.79684	−	3.11221i	−0.0761344	−	0.131869i	0.825445	−	0.564483i	$-0.190924\pi$
$557$	−1.79684	−	3.11221i	−0.0761344	−	0.131869i	−0.901579	+	0.432614i	$0.857591\pi$
$558$	−9.54971	−	3.16624i	−0.404271	−	0.134038i
$559$	10.4568	−	2.00347i	0.442275	−	0.0847378i
$560$	35.8848	−	10.7165i	1.51641	−	0.452853i
$561$	−24.9483	+	14.4039i	−1.05332	+	0.608133i
$562$	−5.99795	−	29.0732i	−0.253008	−	1.22638i
$563$	37.1235	+	21.4332i	1.56457	+	0.903303i	0.996785	+	0.0801243i	$0.0255317\pi$
$563$	37.1235	+	21.4332i	1.56457	+	0.903303i	0.567782	+	0.823179i	$0.307802\pi$
$564$	3.53656	+	2.63475i	0.148916	+	0.110943i
$565$	41.9385	−	72.6396i	1.76437	−	3.05597i
$566$	24.4129	−	21.7182i	1.02615	−	0.912883i
$567$		−	2.16296i		−	0.0908359i
$568$	−16.3039	+	1.41797i	−0.684095	+	0.0594968i
$569$	−1.88614	−	3.26690i	−0.0790712	−	0.136955i	0.823778	−	0.566912i	$-0.191862\pi$
$569$	−1.88614	−	3.26690i	−0.0790712	−	0.136955i	−0.902849	+	0.429957i	$0.858529\pi$
$570$	−2.38312	−	11.5514i	−0.0998178	−	0.483836i
$571$			33.2710i			1.39235i	0.717872	+	0.696175i	$0.245116\pi$
$571$			33.2710i			1.39235i	−0.717872	+	0.696175i	$0.754884\pi$
$572$	−37.0032	+	2.69130i	−1.54718	+	0.112529i
$573$			20.3336i			0.849449i
$574$	4.20542	−	0.867600i	0.175531	−	0.0362129i
$575$	−13.9144	−	24.1005i	−0.580271	−	1.00506i
$576$	−5.13601	−	6.13363i	−0.214000	−	0.255568i
$577$			35.1086i			1.46159i	0.682596	+	0.730796i	$0.260851\pi$
$577$			35.1086i			1.46159i	−0.682596	+	0.730796i	$0.739149\pi$
$578$	13.4899	+	15.1637i	0.561105	+	0.630726i
$579$	3.75219	−	6.49899i	0.155936	−	0.270089i
$580$	1.02180	−	1.37153i	0.0424278	−	0.0569498i
$581$	−3.82448	−	2.20807i	−0.158666	−	0.0916060i
$582$	−11.8538	+	2.44551i	−0.491357	+	0.101369i
$583$	9.38090	−	5.41607i	0.388517	−	0.224311i
$584$	−16.3890	−	23.4315i	−0.678180	−	0.969601i
$585$	−2.93684	−	15.3284i	−0.121423	−	0.633750i
$586$	4.74285	−	14.3049i	0.195925	−	0.590930i
$587$	−0.0738353	−	0.127887i	−0.00304751	−	0.00527844i	0.864498	−	0.502637i	$-0.167637\pi$
$587$	−0.0738353	−	0.127887i	−0.00304751	−	0.00527844i	−0.867545	+	0.497358i	$0.834303\pi$
$588$	4.61160	+	0.540619i	0.190179	+	0.0222947i
$589$	11.8706	+	6.85349i	0.489119	+	0.282393i
$590$	8.41114	−	25.3688i	0.346281	−	1.04442i
$591$	3.91412	+	2.25982i	0.161005	+	0.0929564i
$592$	−1.79840	−	0.427529i	−0.0739139	−	0.0175713i
$593$		−	17.5025i		−	0.718742i	−0.933195	−	0.359371i	$-0.882991\pi$
$593$		−	17.5025i		−	0.718742i	0.933195	−	0.359371i	$-0.117009\pi$
$594$	−5.43625	+	4.83618i	−0.223052	+	0.198431i
$595$	−45.4004	+	26.2119i	−1.86123	+	1.07458i
$596$	−1.76260	+	15.0354i	−0.0721988	+	0.615873i
$597$			25.1817i			1.03062i
$598$	10.2413	+	1.34774i	0.418797	+	0.0551133i
$599$	−41.9746			−1.71504			−0.857518	−	0.514454i	$-0.827995\pi$
$599$	−41.9746			−1.71504			−0.857518	+	0.514454i	$0.827995\pi$
$600$	16.4388	−	35.2059i	0.671110	−	1.43727i
$601$	−20.7461	−	35.9333i	−0.846250	−	1.46575i	−0.884531	−	0.466481i	$-0.845521\pi$
$601$	−20.7461	−	35.9333i	−0.846250	−	1.46575i	0.0382808	−	0.999267i	$-0.487812\pi$
$602$	−6.00377	−	6.74871i	−0.244696	−	0.275057i
$603$	11.0194			0.448744
$604$	1.66160	+	3.85565i	0.0676095	+	0.156884i
$605$	−33.4837	+	57.9955i	−1.36131	+	2.35785i
$606$	−1.59231	+	4.80258i	−0.0646834	+	0.195092i
$607$	4.37951	−	7.58553i	0.177759	−	0.307887i	−0.763354	−	0.645981i	$-0.776449\pi$
$607$	4.37951	−	7.58553i	0.177759	−	0.307887i	0.941113	+	0.338094i	$0.109782\pi$
$608$	5.16455	+	9.59790i	0.209450	+	0.389246i
$609$	−0.370061	+	0.213655i	−0.0149956	+	0.00865772i
$610$	71.4103	+	23.6764i	2.89132	+	0.958628i
$611$	−5.19984	−	6.01427i	−0.210363	−	0.243311i
$612$	8.98023	+	6.69031i	0.363004	+	0.270440i
$613$	3.97286	+	6.88119i	0.160462	+	0.277929i	0.935035	−	0.354557i	$-0.115368\pi$
$613$	3.97286	+	6.88119i	0.160462	+	0.277929i	−0.774572	+	0.632485i	$0.782035\pi$
$614$	10.3946	−	2.14446i	0.419493	−	0.0865435i
$615$	3.03822	−	5.26235i	0.122513	−	0.212198i
$616$	18.0406	+	25.7927i	0.726875	+	1.03922i
$617$	29.8107	+	17.2112i	1.20013	+	0.692898i	0.960585	−	0.277986i	$-0.0896669\pi$
$617$	29.8107	+	17.2112i	1.20013	+	0.692898i	0.239550	+	0.970884i	$0.423000\pi$
$618$	−4.96078	+	4.41320i	−0.199552	+	0.177525i
$619$	31.7543			1.27631			0.638157	−	0.769906i	$-0.279697\pi$
$619$	31.7543			1.27631			0.638157	+	0.769906i	$0.279697\pi$
$620$	24.3749	+	56.5606i	0.978920	+	2.27153i
$621$	1.75439	−	1.01290i	0.0704014	−	0.0406463i
$622$	−32.0579	+	6.61371i	−1.28540	+	0.265185i
$623$	−10.8641			−0.435262
$624$	6.65354	+	12.7957i	0.266355	+	0.512239i
$625$	95.0247			3.80099
$626$	29.0811	−	5.99958i	1.16232	−	0.239792i
$627$	8.58485	−	4.95647i	0.342846	−	0.197942i
$628$	−6.60997	−	15.3381i	−0.263767	−	0.612056i
$629$	2.58757			0.103173
$630$	−9.89277	+	8.80078i	−0.394137	+	0.350632i
$631$	−1.82187	−	1.05185i	−0.0725273	−	0.0418737i	0.463298	−	0.886203i	$-0.346666\pi$
$631$	−1.82187	−	1.05185i	−0.0725273	−	0.0418737i	−0.535825	+	0.844329i	$0.679999\pi$
$632$	17.0856	−	11.9504i	0.679627	−	0.475360i
$633$	−7.84264	+	13.5839i	−0.311717	+	0.539910i
$634$	−1.55221	+	0.320229i	−0.0616462	+	0.0127179i
$635$	14.4111	+	24.9608i	0.571888	+	0.990539i
$636$	−3.37669	−	2.51565i	−0.133895	−	0.0997520i
$637$	−7.90723	−	2.74645i	−0.313296	−	0.108818i
$638$	1.36441	+	0.452374i	0.0540174	+	0.0179097i
$639$	5.01087	−	2.89303i	0.198227	−	0.114446i
$640$	−7.15578	+	48.4475i	−0.282857	+	1.91505i
$641$	4.71373	−	8.16441i	0.186181	−	0.322475i	−0.757793	−	0.652495i	$-0.773722\pi$
$641$	4.71373	−	8.16441i	0.186181	−	0.322475i	0.943974	+	0.330020i	$0.107056\pi$
$642$	−0.953969	+	2.87727i	−0.0376501	+	0.113557i
$643$	−21.6550	+	37.5076i	−0.853991	+	1.47916i	0.0235861	+	0.999722i	$0.492492\pi$
$643$	−21.6550	+	37.5076i	−0.853991	+	1.47916i	−0.877578	+	0.479435i	$0.840842\pi$
$644$	−3.46827	−	8.04793i	−0.136669	−	0.317133i
$645$	−12.7823			−0.503301
$646$	−10.1407	−	11.3989i	−0.398979	−	0.448483i
$647$	−6.58305	−	11.4022i	−0.258807	−	0.448266i	0.707116	−	0.707098i	$-0.249996\pi$
$647$	−6.58305	−	11.4022i	−0.258807	−	0.448266i	−0.965922	+	0.258832i	$0.916663\pi$
$648$	2.56281	+	1.19666i	0.100677	+	0.0470093i
$649$	22.4628			0.881742
$650$	−42.6385	+	55.5737i	−1.67242	+	2.17978i
$651$		−	15.3876i		−	0.603089i
$652$	1.77491	−	15.1404i	0.0695107	−	0.592942i
$653$	31.8783	−	18.4049i	1.24749	−	0.720240i	0.276884	−	0.960903i	$-0.410698\pi$
$653$	31.8783	−	18.4049i	1.24749	−	0.720240i	0.970609	+	0.240663i	$0.0773649\pi$
$654$	−9.84329	+	8.75677i	−0.384903	+	0.342417i
$655$		−	44.9314i		−	1.75562i
$656$	−1.29867	+	5.46284i	−0.0507044	+	0.213288i
$657$	8.75517	+	5.05480i	0.341572	+	0.197206i
$658$	−2.12271	+	6.40232i	−0.0827520	+	0.249588i
$659$	−36.8969	−	21.3024i	−1.43730	−	0.829824i	−0.439636	−	0.898176i	$-0.644893\pi$
$659$	−36.8969	−	21.3024i	−1.43730	−	0.829824i	−0.997661	+	0.0683515i	$0.978226\pi$
$660$	44.2386	+	5.18610i	1.72199	+	0.201868i
$661$	4.76553	+	8.25413i	0.185357	+	0.321049i	0.943697	−	0.330811i	$-0.107322\pi$
$661$	4.76553	+	8.25413i	0.185357	+	0.321049i	−0.758339	+	0.651860i	$0.773989\pi$
$662$	−0.564266	+	1.70188i	−0.0219308	+	0.0661456i
$663$	−13.2037	−	15.2718i	−0.512790	−	0.593107i
$664$	4.73215	−	3.30987i	0.183643	−	0.128448i
$665$	15.6225	−	9.01967i	0.605816	−	0.349768i
$666$	0.640072	−	0.132050i	0.0248023	−	0.00511683i
$667$	−0.346593	−	0.200106i	−0.0134201	−	0.00774813i
$668$	−14.4798	+	19.4358i	−0.560238	+	0.751993i
$669$	11.3871	−	19.7231i	0.440253	−	0.762540i
$670$	−44.8362	−	50.3994i	−1.73217	−	1.94710i
$671$			63.2301i			2.44097i
$672$	6.43229	−	10.4084i	0.248131	−	0.401513i
$673$	−11.8396	−	20.5068i	−0.456383	−	0.790478i	0.542384	−	0.840131i	$-0.317522\pi$
$673$	−11.8396	−	20.5068i	−0.456383	−	0.790478i	−0.998767	+	0.0496527i	$0.984189\pi$
$674$	−14.2507	+	2.93998i	−0.548915	+	0.113244i
$675$			13.7372i			0.528745i
$676$	−6.73194	−	25.1134i	−0.258921	−	0.965899i
$677$			21.0758i			0.810007i	0.914315	+	0.405004i	$0.132730\pi$
$677$			21.0758i			0.810007i	−0.914315	+	0.405004i	$0.867270\pi$
$678$	−5.53687	−	26.8383i	−0.212642	−	1.03072i
$679$	−9.25580	−	16.0315i	−0.355205	−	0.615233i
$680$	−5.93971	−	68.2949i	−0.227778	−	2.61899i
$681$			4.29535i			0.164598i
$682$	−38.6742	+	34.4053i	−1.48091	+	1.31745i
$683$	5.53695	−	9.59027i	0.211865	−	0.366962i	−0.740433	−	0.672130i	$-0.765379\pi$
$683$	5.53695	−	9.59027i	0.211865	−	0.366962i	0.952298	+	0.305169i	$0.0987128\pi$
$684$	−3.09015	−	2.30218i	−0.118155	−	0.0880259i
$685$	11.0486	+	6.37888i	0.422143	+	0.243725i
$686$	5.76120	+	27.9256i	0.219964	+	1.06621i
$687$	17.3512	−	10.0177i	0.661991	−	0.382201i
$688$	11.3179	−	3.37991i	0.431490	−	0.128858i
$689$	4.96478	+	5.74240i	0.189143	+	0.218768i
$690$	−11.7711	−	3.90275i	−0.448117	−	0.148575i
$691$	−17.4252	−	30.1813i	−0.662885	−	1.14815i	−0.979854	−	0.199714i	$-0.935999\pi$
$691$	−17.4252	−	30.1813i	−0.662885	−	1.14815i	0.316970	−	0.948436i	$-0.397335\pi$
$692$	−11.3549	−	1.33113i	−0.431647	−	0.0506020i
$693$	−9.63746	−	5.56419i	−0.366097	−	0.211366i
$694$	−16.8245	−	5.57823i	−0.638649	−	0.211747i
$695$	−74.0240	−	42.7378i	−2.80789	−	1.62114i
$696$	−0.0484149	−	0.556675i	−0.00183516	−	0.0211007i
$697$		−	7.86002i		−	0.297719i
$698$	−24.0718	−	27.0586i	−0.911132	−	1.02418i
$699$	6.25185	−	3.60951i	0.236467	−	0.136524i
$700$	59.0219	+	6.91915i	2.23082	+	0.261519i
$701$		−	35.7266i		−	1.34937i	−0.738104	−	0.674687i	$-0.764279\pi$
$701$		−	35.7266i		−	1.34937i	0.738104	−	0.674687i	$-0.235721\pi$
$702$	−4.04549	−	3.10387i	−0.152687	−	0.117148i
$703$	−0.890397			−0.0335819
$704$	−40.5418	+	7.10571i	−1.52798	+	0.267807i
$705$	4.77247	+	8.26616i	0.179742	+	0.311322i
$706$	−18.1856	+	16.1783i	−0.684425	+	0.608877i
$707$	−7.73849			−0.291036
$708$	−3.45580	−	8.01899i	−0.129877	−	0.301372i
$709$	−11.0711	+	19.1758i	−0.415785	+	0.720160i	−0.995510	−	0.0946513i	$-0.969826\pi$
$709$	−11.0711	+	19.1758i	−0.415785	+	0.720160i	0.579726	+	0.814812i	$0.303160\pi$
$710$	−33.6203	−	11.1470i	−1.26175	−	0.418338i
$711$	−3.68582	+	6.38402i	−0.138229	+	0.239419i
$712$	6.01058	−	12.8725i	0.225256	−	0.482417i
$713$	12.4810	−	7.20591i	0.467417	−	0.269864i
$714$	−5.39011	+	16.2571i	−0.201720	+	0.608408i
$715$	−75.8532	−	26.3464i	−2.83675	−	0.985299i
$716$	−8.42070	+	11.3029i	−0.314697	+	0.422409i
$717$	−0.703220	−	1.21801i	−0.0262622	−	0.0454875i
$718$	4.29944	+	20.8402i	0.160454	+	0.777749i
$719$	−20.9483	+	36.2834i	−0.781238	+	1.35314i	0.149983	+	0.988689i	$0.452078\pi$
$719$	−20.9483	+	36.2834i	−0.781238	+	1.35314i	−0.931221	+	0.364455i	$0.881255\pi$
$720$	−4.95453	−	16.5906i	−0.184644	−	0.618295i
$721$	−8.79455	−	5.07754i	−0.327526	−	0.189097i
$722$	−14.3702	−	16.1532i	−0.534804	−	0.601161i
$723$	−5.53788			−0.205956
$724$	6.21535	+	14.4224i	0.230992	+	0.536003i
$725$	2.35029	−	1.35694i	0.0872877	−	0.0503956i
$726$	4.42064	+	21.4277i	0.164065	+	0.795256i
$727$	−26.1552			−0.970042			−0.485021	−	0.874503i	$-0.661188\pi$
$727$	−26.1552			−0.970042			−0.485021	+	0.874503i	$0.661188\pi$
$728$	−15.3734	+	15.8181i	−0.569777	+	0.586258i
$729$	−1.00000			−0.0370370
$730$	−12.5043	−	60.6108i	−0.462806	−	2.24331i
$731$	−14.3190	+	8.26709i	−0.529608	+	0.305769i
$732$	22.5725	−	9.72767i	0.834304	−	0.359545i
$733$	23.0609			0.851774			0.425887	−	0.904776i	$-0.359962\pi$
$733$	23.0609			0.851774			0.425887	+	0.904776i	$0.359962\pi$
$734$	−19.5183	−	21.9400i	−0.720432	−	0.809822i
$735$	8.70300	+	5.02468i	0.321015	+	0.185338i
$736$	11.4545	+	0.343099i	0.422219	+	0.0126468i
$737$	28.3472	−	49.0988i	1.04418	−	1.80858i
$738$	−0.401116	−	1.94429i	−0.0147653	−	0.0715702i
$739$	−6.46731	−	11.2017i	−0.237904	−	0.412061i	0.722209	−	0.691675i	$-0.243127\pi$
$739$	−6.46731	−	11.2017i	−0.237904	−	0.412061i	−0.960113	+	0.279614i	$0.909794\pi$
$740$	−3.20832	−	2.39021i	−0.117940	−	0.0878659i
$741$	4.54348	+	5.25511i	0.166909	+	0.193051i
$742$	2.02676	−	6.11290i	0.0744046	−	0.224412i
$743$	−19.2118	+	11.0919i	−0.704813	+	0.406924i	−0.809138	−	0.587619i	$-0.800065\pi$
$743$	−19.2118	+	11.0919i	−0.704813	+	0.406924i	0.104324	+	0.994543i	$0.466732\pi$
$744$	18.2322	+	8.51321i	0.668425	+	0.312110i
$745$	−16.3821	+	28.3747i	−0.600195	+	1.03957i
$746$	−1.11017	−	0.368080i	−0.0406460	−	0.0134763i
$747$	−1.02085	+	1.76817i	−0.0373510	+	0.0646939i
$748$	52.9114	−	22.8023i	1.93463	−	0.833734i
$749$	−4.63619			−0.169403
$750$	39.9614	−	35.5504i	1.45919	−	1.29812i
$751$	5.27970	+	9.14471i	0.192659	+	0.333695i	0.946131	−	0.323785i	$-0.104956\pi$
$751$	5.27970	+	9.14471i	0.192659	+	0.333695i	−0.753472	+	0.657480i	$0.771622\pi$
$752$	−6.41147	−	6.05721i	−0.233802	−	0.220884i
$753$	−22.6503			−0.825422
$754$	−0.131433	+	0.998738i	−0.00478650	+	0.0363719i
$755$			9.08679i			0.330702i
$756$	−0.503679	+	4.29650i	−0.0183186	+	0.156262i
$757$	−31.1972	+	18.0117i	−1.13388	+	0.654647i	−0.944908	−	0.327336i	$-0.893849\pi$
$757$	−31.1972	+	18.0117i	−1.13388	+	0.654647i	−0.188973	+	0.981982i	$0.560516\pi$
$758$	−8.65239	−	9.72596i	−0.314269	−	0.353263i
$759$		−	10.4227i		−	0.378319i
$760$	2.04389	+	23.5007i	0.0741397	+	0.852459i
$761$	6.84148	+	3.94993i	0.248004	+	0.143185i	0.618850	−	0.785509i	$-0.287599\pi$
$761$	6.84148	+	3.94993i	0.248004	+	0.143185i	−0.370846	+	0.928694i	$0.620932\pi$
$762$	8.93806	+	2.96345i	0.323792	+	0.107354i
$763$	−17.4503	−	10.0750i	−0.631745	−	0.364738i
$764$	4.73500	−	40.3906i	0.171306	−	1.46128i
$765$	12.1185	+	20.9899i	0.438146	+	0.758891i
$766$	28.3313	+	9.39335i	1.02365	+	0.339396i
$767$	2.96216	+	15.4605i	0.106957	+	0.558247i
$768$	8.77384	+	13.3798i	0.316599	+	0.482803i
$769$	−38.3137	+	22.1204i	−1.38163	+	0.797682i	−0.992352	−	0.123440i	$-0.960607\pi$
$769$	−38.3137	+	22.1204i	−1.38163	+	0.797682i	−0.389274	+	0.921122i	$0.627274\pi$
$770$	13.7644	+	66.7188i	0.496036	+	2.40438i
$771$	−16.0130	−	9.24512i	−0.576695	−	0.332955i
$772$	−8.96674	+	12.0358i	−0.322720	+	0.433179i
$773$	−0.173392	+	0.300323i	−0.00623647	+	0.0108019i	−0.869127	−	0.494589i	$-0.835318\pi$
$773$	−0.173392	+	0.300323i	−0.00623647	+	0.0108019i	0.862890	+	0.505391i	$0.168652\pi$
$774$	−3.12012	+	2.77572i	−0.112150	+	0.0997711i
$775$			97.7284i			3.51051i
$776$	24.1159	−	2.09740i	0.865710	−	0.0752922i
$777$	0.499785	+	0.865654i	0.0179297	+	0.0310551i
$778$	6.77979	+	32.8630i	0.243067	+	1.17819i
$779$			2.70468i			0.0969052i
$780$	2.26428	+	31.1321i	0.0810744	+	1.11471i
$781$		−	29.7691i		−	1.06522i
$782$	−15.7104	+	3.24114i	−0.561803	+	0.115903i
$783$	0.0987787	+	0.171090i	0.00353006	+	0.00611425i
$784$	−9.03458	−	2.14777i	−0.322664	−	0.0767059i
$785$		−	36.1480i		−	1.29018i
$786$	−9.75702	−	10.9677i	−0.348022	−	0.391203i
$787$	−19.9378	+	34.5333i	−0.710706	+	1.23098i	0.253887	+	0.967234i	$0.418291\pi$
$787$	−19.9378	+	34.5333i	−0.710706	+	1.23098i	−0.964593	+	0.263744i	$0.915042\pi$
$788$	−7.24875	−	5.40035i	−0.258226	−	0.192380i
$789$	−22.8222	−	13.1764i	−0.812493	−	0.469093i
$790$	44.1957	−	9.11780i	1.57241	−	0.324397i
$791$	36.2970	−	20.9561i	1.29057	−	0.745112i
$792$	11.9247	−	8.34067i	0.423727	−	0.296373i
$793$	−43.5195	+	8.33813i	−1.54542	+	0.296096i
$794$	−2.99622	+	9.03691i	−0.106332	+	0.320708i
$795$	−4.55673	−	7.89249i	−0.161611	−	0.279918i
$796$	5.86396	−	50.0210i	0.207843	−	1.77295i
$797$	−29.9292	−	17.2796i	−1.06015	−	0.612076i	−0.134674	−	0.990890i	$-0.542999\pi$
$797$	−29.9292	−	17.2796i	−1.06015	−	0.612076i	−0.925473	+	0.378814i	$0.876332\pi$
$798$	1.85477	−	5.59417i	0.0656581	−	0.198032i
$799$	10.6925	+	6.17331i	0.378273	+	0.218396i
$800$	−40.8521	+	66.1048i	−1.44434	+	2.33716i
$801$			5.02280i			0.177472i
$802$	−4.06231	+	3.61390i	−0.143445	+	0.127611i
$803$	45.0451	−	26.0068i	1.58961	−	0.917760i
$804$	−21.8888	−	2.56603i	−0.771960	−	0.0904969i
$805$		−	18.9670i		−	0.668498i
$806$	−28.7802	−	22.0814i	−1.01374	−	0.777784i
$807$	31.4518			1.10716
$808$	4.28132	−	9.16904i	0.150616	−	0.322566i
$809$	−2.06348	−	3.57406i	−0.0725483	−	0.125657i	0.827469	−	0.561511i	$-0.189780\pi$
$809$	−2.06348	−	3.57406i	−0.0725483	−	0.125657i	−0.900017	+	0.435854i	$0.856446\pi$
$810$	4.06885	+	4.57371i	0.142965	+	0.160704i
$811$	29.5522			1.03772			0.518859	−	0.854860i	$-0.326357\pi$
$811$	29.5522			1.03772			0.518859	+	0.854860i	$0.326357\pi$
$812$	0.784840	−	0.338229i	0.0275425	−	0.0118695i
$813$	−9.92693	+	17.1939i	−0.348153	+	0.603018i
$814$	1.05820	−	3.19165i	0.0370900	−	0.111867i
$815$	16.4965	−	28.5728i	0.577848	−	1.00086i
$816$	−16.2804	−	15.3808i	−0.569927	−	0.538436i
$817$	4.92726	−	2.84475i	0.172383	−	0.0995253i
$818$	−44.1411	−	14.6352i	−1.54336	−	0.511706i
$819$	2.55879	−	7.36695i	0.0894114	−	0.257422i
$820$	−7.26053	+	9.74562i	−0.253549	+	0.340332i
$821$	20.9185	+	36.2319i	0.730061	+	1.26450i	0.956857	+	0.290560i	$0.0938416\pi$
$821$	20.9185	+	36.2319i	0.730061	+	1.26450i	−0.226796	+	0.973942i	$0.572825\pi$
$822$	4.08213	−	0.842163i	0.142381	−	0.0293738i
$823$	13.3260	−	23.0813i	0.464515	−	0.804563i	−0.534665	−	0.845064i	$-0.679562\pi$
$823$	13.3260	−	23.0813i	0.464515	−	0.804563i	0.999179	+	0.0405014i	$0.0128955\pi$
$824$	10.8818	−	7.61118i	0.379084	−	0.265148i
$825$	61.2085	+	35.3388i	2.13101	+	1.23034i
$826$	9.97806	−	8.87666i	0.347181	−	0.308859i
$827$	45.2843			1.57469			0.787344	−	0.616514i	$-0.211456\pi$
$827$	45.2843			1.57469			0.787344	+	0.616514i	$0.211456\pi$
$828$	−3.72079	+	1.60348i	−0.129306	+	0.0557249i
$829$	40.4769	−	23.3693i	1.40582	−	0.811651i	0.410839	−	0.911708i	$-0.365236\pi$
$829$	40.4769	−	23.3693i	1.40582	−	0.811651i	0.994982	+	0.100057i	$0.0319026\pi$
$830$	12.2408	−	2.52534i	0.424884	−	0.0876557i
$831$	12.7191			0.441222
$832$	−10.2369	−	26.9668i	−0.354900	−	0.934904i
$833$	12.9991			0.450392
$834$	−27.3498	+	5.64240i	−0.947046	+	0.195380i
$835$	−45.4281	+	26.2279i	−1.57211	+	0.907655i
$836$	−18.2071	+	7.84640i	−0.629706	+	0.271373i
$837$	−7.11414			−0.245901
$838$	−3.00889	+	2.67676i	−0.103940	+	0.0924671i
$839$	−7.87045	−	4.54401i	−0.271718	−	0.156877i	0.357950	−	0.933741i	$-0.383476\pi$
$839$	−7.87045	−	4.54401i	−0.271718	−	0.156877i	−0.629668	+	0.776864i	$0.716809\pi$
$840$	21.7004	−	15.1782i	0.748734	−	0.523696i
$841$	−14.4805	+	25.0809i	−0.499327	+	0.864860i
$842$	−1.45236	+	0.299630i	−0.0500518	+	0.0103259i
$843$	−10.4954	−	18.1786i	−0.361481	−	0.626103i
$844$	18.7418	−	25.1566i	0.645120	−	0.865928i
$845$	8.13075	−	55.6819i	0.279706	−	1.91552i
$846$	2.95998	+	0.981392i	0.101766	+	0.0337409i
$847$	−28.9795	+	16.7313i	−0.995747	+	0.574895i
$848$	6.12164	+	5.78339i	0.210218	+	0.198603i
$849$	11.5524	−	20.0094i	0.396479	−	0.686721i
$850$	34.2332	−	103.251i	1.17419	−	3.54147i
$851$	−0.468092	+	0.810758i	−0.0160460	+	0.0277924i
$852$	−10.6273	+	4.57984i	−0.364084	+	0.156903i
$853$	42.5016			1.45523			0.727613	−	0.685988i	$-0.240630\pi$
$853$	42.5016			1.45523			0.727613	+	0.685988i	$0.240630\pi$
$854$	24.9868	+	28.0871i	0.855029	+	0.961120i
$855$	−4.17005	−	7.22274i	−0.142613	−	0.247013i
$856$	2.56498	−	5.49325i	0.0876691	−	0.187755i
$857$	44.3414			1.51467			0.757337	−	0.653024i	$-0.226500\pi$
$857$	44.3414			1.51467			0.757337	+	0.653024i	$0.226500\pi$
$858$	−24.2368	+	10.0407i	−0.827431	+	0.342784i
$859$			43.6352i			1.48881i	0.667727	+	0.744406i	$0.267267\pi$
$859$			43.6352i			1.48881i	−0.667727	+	0.744406i	$0.732733\pi$
$860$	25.3907	+	2.97655i	0.865814	+	0.101499i
$861$	2.62952	−	1.51815i	0.0896137	−	0.0517385i
$862$	−23.3788	+	20.7982i	−0.796287	+	0.708391i
$863$		−	35.7395i		−	1.21659i	−0.793712	−	0.608293i	$-0.791854\pi$
$863$		−	35.7395i		−	1.21659i	0.793712	−	0.608293i	$-0.208146\pi$
$864$	−4.81210	−	2.97383i	−0.163711	−	0.101172i
$865$	−21.4288	−	12.3719i	−0.728603	−	0.420659i
$866$	−7.45664	+	22.4900i	−0.253387	+	0.764240i
$867$	12.4285	+	7.17561i	0.422094	+	0.243696i
$868$	−3.58325	+	30.5659i	−0.121623	+	1.03748i
$869$	18.9634	+	32.8456i	0.643290	+	1.11421i
$870$	0.380599	−	1.14792i	0.0129035	−	0.0389183i
$871$	37.5314	+	13.0359i	1.27170	+	0.441706i
$872$	21.5918	−	15.1023i	0.731192	−	0.511427i
$873$	−7.41183	+	4.27922i	−0.250852	+	0.144830i
$874$	5.40605	−	1.11529i	0.182862	−	0.0377254i
$875$	70.8442	+	40.9019i	2.39497	+	1.38274i
$876$	−16.2142	−	12.0796i	−0.547826	−	0.408132i
$877$	5.98460	−	10.3656i	0.202085	−	0.350022i	−0.747115	−	0.664695i	$-0.768561\pi$
$877$	5.98460	−	10.3656i	0.202085	−	0.350022i	0.949200	+	0.314673i	$0.101895\pi$
$878$	6.51704	+	7.32566i	0.219939	+	0.247229i
$879$		−	10.6566i		−	0.359437i
$880$	−86.6678	−	20.6033i	−2.92157	−	0.694537i
$881$	4.67299	+	8.09386i	0.157437	+	0.272689i	0.933944	−	0.357420i	$-0.116344\pi$
$881$	4.67299	+	8.09386i	0.157437	+	0.272689i	−0.776507	+	0.630109i	$0.783010\pi$
$882$	3.21551	−	0.663376i	0.108272	−	0.0223370i
$883$			12.2815i			0.413307i	0.978414	+	0.206653i	$0.0662573\pi$
$883$			12.2815i			0.413307i	−0.978414	+	0.206653i	$0.933743\pi$
$884$	22.6716	+	33.4105i	0.762528	+	1.12372i
$885$		−	18.8988i		−	0.635275i
$886$	6.55504	+	31.7735i	0.220221	+	1.06745i
$887$	−5.70155	−	9.87537i	−0.191439	−	0.331582i	0.754288	−	0.656543i	$-0.227982\pi$
$887$	−5.70155	−	9.87537i	−0.191439	−	0.331582i	−0.945727	+	0.324961i	$0.894649\pi$
$888$	−1.30219	+	0.113253i	−0.0436985	+	0.00380053i
$889$			14.4021i			0.483030i
$890$	22.9728	−	20.4370i	0.770051	−	0.685051i
$891$	−2.57249	+	4.45568i	−0.0861815	+	0.149271i
$892$	−27.2122	+	36.5263i	−0.911133	+	1.22299i
$893$	−3.67935	−	2.12427i	−0.123125	−	0.0710860i
$894$	2.16283	+	10.4836i	0.0723358	+	0.350626i
$895$	−26.4187	+	15.2529i	−0.883081	+	0.509847i
$896$	−15.2008	+	19.1773i	−0.507824	+	0.640670i
$897$	7.17364	−	1.37444i	0.239521	−	0.0458910i
$898$	−40.1151	−	13.3003i	−1.33866	−	0.443837i
$899$	0.702726	+	1.21716i	0.0234372	+	0.0405944i
$900$	3.19892	−	27.2875i	0.106631	−	0.909585i
$901$	−10.2091	−	5.89424i	−0.340115	−	0.196366i
$902$	−9.69498	−	3.21441i	−0.322808	−	0.107028i
$903$	−5.53140	−	3.19356i	−0.184073	−	0.106275i
$904$	4.74872	+	54.6008i	0.157940	+	1.81600i
$905$			33.9899i			1.12986i
$906$	1.97323	+	2.21807i	0.0655562	+	0.0736903i
$907$	4.78402	−	2.76206i	0.158851	−	0.0917126i	−0.418467	−	0.908232i	$-0.637433\pi$
$907$	4.78402	−	2.76206i	0.158851	−	0.0917126i	0.577318	+	0.816519i	$0.304099\pi$
$908$	1.00024	−	8.53226i	0.0331940	−	0.283153i
$909$			3.57773i			0.118666i
$910$	−44.1056	+	18.2719i	−1.46209	+	0.605707i
$911$	33.5295			1.11088			0.555441	−	0.831556i	$-0.312549\pi$
$911$	33.5295			1.11088			0.555441	+	0.831556i	$0.312549\pi$
$912$	5.60217	+	5.29262i	0.185506	+	0.175256i
$913$	5.25226	+	9.09718i	0.173824	+	0.301073i
$914$	4.20935	−	3.74471i	0.139233	−	0.123864i
$915$	53.1978			1.75866
$916$	−36.7992	+	15.8587i	−1.21588	+	0.523987i
$917$	11.2258	−	19.4436i	0.370708	−	0.642085i
$918$	7.51614	+	2.49200i	0.248070	+	0.0822484i
$919$	13.6169	−	23.5851i	0.449179	−	0.778001i	−0.549154	−	0.835721i	$-0.685050\pi$
$919$	13.6169	−	23.5851i	0.449179	−	0.778001i	0.998333	+	0.0577205i	$0.0183832\pi$
$920$	22.4732	+	10.4935i	0.740920	+	0.345960i
$921$	6.49943	−	3.75245i	0.214164	−	0.123647i
$922$	0.292453	−	0.882068i	0.00963143	−	0.0290494i
$923$	20.4892	−	3.92564i	0.674411	−	0.129214i
$924$	17.8481	+	13.2969i	0.587160	+	0.437437i
$925$	−3.17419	−	5.49786i	−0.104367	−	0.180768i
$926$	2.45987	+	11.9235i	0.0808363	+	0.391829i
$927$	−2.34749	+	4.06598i	−0.0771017	+	0.133544i
$928$	−0.0334592	+	1.11705i	−0.00109835	+	0.0366690i
$929$	28.3942	+	16.3934i	0.931582	+	0.537849i	0.887312	−	0.461170i	$-0.152570\pi$
$929$	28.3942	+	16.3934i	0.931582	+	0.537849i	0.0442707	+	0.999020i	$0.485904\pi$
$930$	28.9464	+	32.5380i	0.949190	+	1.06696i
$931$	−4.47306			−0.146599
$932$	−13.2592	+	5.71407i	−0.434319	+	0.187171i
$933$	−20.0448	+	11.5729i	−0.656237	+	0.378879i
$934$	−5.55623	−	26.9321i	−0.181805	−	0.881246i
$935$	124.699			4.07809
$936$	7.31316	+	7.10758i	0.239038	+	0.232319i
$937$	39.0993			1.27732			0.638659	−	0.769490i	$-0.279489\pi$
$937$	39.0993			1.27732			0.638659	+	0.769490i	$0.279489\pi$
$938$	−6.81051	−	33.0119i	−0.222371	−	1.07788i
$939$	18.1835	−	10.4983i	0.593397	−	0.342598i
$940$	−7.55512	−	17.5312i	−0.246421	−	0.571805i
$941$	16.6878			0.544007			0.272003	−	0.962296i	$-0.412314\pi$
$941$	16.6878			0.544007			0.272003	+	0.962296i	$0.412314\pi$
$942$	−7.84967	−	8.82365i	−0.255756	−	0.287490i
$943$	2.46277	+	1.42188i	0.0801988	+	0.0463028i
$944$	4.99725	+	16.7336i	0.162647	+	0.544634i
$945$	−4.68135	+	8.10834i	−0.152284	+	0.263764i
$946$	4.34123	+	21.0428i	0.141145	+	0.684159i
$947$	−12.4326	−	21.5339i	−0.404005	−	0.699758i	0.590200	−	0.807257i	$-0.299049\pi$
$947$	−12.4326	−	21.5339i	−0.404005	−	0.699758i	−0.994205	+	0.107499i	$0.965716\pi$
$948$	8.80811	−	11.8229i	0.286074	−	0.383990i
$949$	23.8398	+	27.5738i	0.773874	+	0.895083i
$950$	−11.7798	+	35.5292i	−0.382188	+	1.15272i
$951$	−0.970549	+	0.560346i	−0.0314722	+	0.0181705i
$952$	14.4926	−	31.0379i	0.469709	−	1.00595i
$953$	−28.8903	+	50.0395i	−0.935850	+	1.62094i	−0.162739	+	0.986669i	$0.552033\pi$
$953$	−28.8903	+	50.0395i	−0.935850	+	1.62094i	−0.773111	+	0.634270i	$0.781301\pi$
$954$	−2.82617	−	0.937028i	−0.0915007	−	0.0303374i
$955$	44.0085	−	76.2250i	1.42408	−	2.46658i
$956$	1.11324	+	2.58321i	0.0360048	+	0.0835471i
$957$	1.01643			0.0328564
$958$	2.34982	−	2.09044i	0.0759191	−	0.0675390i
$959$	3.18744	+	5.52080i	0.102928	+	0.178276i
$960$	5.97829	+	34.1093i	0.192948	+	1.10087i
$961$	−19.6110			−0.632614
$962$	2.33627	+	0.307450i	0.0753243	+	0.00991260i
$963$			2.14345i			0.0690716i
$964$	11.0004	+	1.28958i	0.354300	+	0.0415346i
$965$	−28.1319	+	16.2419i	−0.905596	+	0.522846i
$966$	−4.11875	−	4.62979i	−0.132519	−	0.148961i
$967$			38.2787i			1.23096i	0.788153	+	0.615480i	$0.211038\pi$
$967$			38.2787i			1.23096i	−0.788153	+	0.615480i	$0.788962\pi$
$968$	−3.79138	−	43.5933i	−0.121859	−	1.40114i
$969$	−9.34280	−	5.39407i	−0.300134	−	0.173282i
$970$	49.7296	+	16.4880i	1.59672	+	0.529399i
$971$	27.6258	+	15.9498i	0.886554	+	0.511852i	0.872814	−	0.488053i	$-0.162293\pi$
$971$	27.6258	+	15.9498i	0.886554	+	0.511852i	0.0137404	+	0.999906i	$0.495626\pi$
$972$	1.98640	+	0.232865i	0.0637137	+	0.00746916i
$973$	−21.3555	−	36.9887i	−0.684625	−	1.18580i
$974$	28.4980	+	9.44861i	0.913133	+	0.302753i
$975$	−16.2511	+	46.7882i	−0.520453	+	1.49842i
$976$	−47.1032	+	14.0667i	−1.50774	+	0.450263i
$977$	−35.5820	+	20.5433i	−1.13837	+	0.657237i	−0.946026	−	0.324091i	$-0.894942\pi$
$977$	−35.5820	+	20.5433i	−1.13837	+	0.657237i	−0.192342	+	0.981328i	$0.561608\pi$
$978$	−2.17793	−	10.5568i	−0.0696425	−	0.337571i
$979$	22.3800	+	12.9211i	0.715267	+	0.412959i
$980$	−16.1175	−	12.0076i	−0.514856	−	0.383570i
$981$	−4.65794	+	8.06779i	−0.148717	+	0.257585i
$982$	−13.2641	+	11.8000i	−0.423275	+	0.376553i
$983$		−	31.6606i		−	1.00982i	−0.863173	−	0.504909i	$-0.831526\pi$
$983$		−	31.6606i		−	1.00982i	0.863173	−	0.504909i	$-0.168474\pi$
$984$	0.344019	+	3.95553i	0.0109669	+	0.126098i
$985$	−9.78195	−	16.9428i	−0.311679	−	0.539844i
$986$	−0.316078	−	1.53209i	−0.0100660	−	0.0487917i
$987$			4.76947i			0.151814i
$988$	−7.80142	−	11.4968i	−0.248196	−	0.365760i
$989$		−	5.98207i		−	0.190219i
$990$	30.8460	−	6.36369i	0.980352	−	0.202251i
$991$	15.5004	+	26.8476i	0.492388	+	0.852841i	0.999962	−	0.00876746i	$-0.00279080\pi$
$991$	15.5004	+	26.8476i	0.492388	+	0.852841i	−0.507574	+	0.861608i	$0.669457\pi$
$992$	−34.2340	−	21.1563i	−1.08693	−	0.671712i
$993$			1.26783i			0.0402335i
$994$	−11.7639	−	13.2235i	−0.373128	−	0.419425i
$995$	54.5015	−	94.3993i	1.72781	−	2.99266i
$996$	2.43956	−	3.27456i	0.0773005	−	0.103759i
$997$	−23.2481	−	13.4223i	−0.736273	−	0.425088i	0.0844395	−	0.996429i	$-0.473090\pi$
$997$	−23.2481	−	13.4223i	−0.736273	−	0.425088i	−0.820713	+	0.571341i	$0.806423\pi$
$998$	−29.1298	+	6.00962i	−0.922088	+	0.190231i
$999$	0.400217	−	0.231065i	0.0126623	−	0.00731058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bk.b.205.1	✓	48
3.2	odd	2		936.2.dg.e.829.24		48
4.3	odd	2		1248.2.ca.b.49.24		48
8.3	odd	2		1248.2.ca.b.49.1		48
8.5	even	2	inner	312.2.bk.b.205.7	yes	48
13.4	even	6	inner	312.2.bk.b.277.7	yes	48
24.5	odd	2		936.2.dg.e.829.18		48
39.17	odd	6		936.2.dg.e.901.18		48
52.43	odd	6		1248.2.ca.b.433.1		48
104.43	odd	6		1248.2.ca.b.433.24		48
104.69	even	6	inner	312.2.bk.b.277.1	yes	48
312.173	odd	6		936.2.dg.e.901.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.1	✓	48	1.1	even	1	trivial
312.2.bk.b.205.7	yes	48	8.5	even	2	inner
312.2.bk.b.277.1	yes	48	104.69	even	6	inner
312.2.bk.b.277.7	yes	48	13.4	even	6	inner
936.2.dg.e.829.18		48	24.5	odd	2
936.2.dg.e.829.24		48	3.2	odd	2
936.2.dg.e.901.18		48	39.17	odd	6
936.2.dg.e.901.24		48	312.173	odd	6
1248.2.ca.b.49.1		48	8.3	odd	2
1248.2.ca.b.49.24		48	4.3	odd	2
1248.2.ca.b.433.1		48	52.43	odd	6
1248.2.ca.b.433.24		48	104.43	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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38505 + 0.285742i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.83670 - 0.791531i) q^{4} +4.32865 q^{5} +(1.05661 - 0.939983i) q^{6} +(1.87318 + 1.08148i) q^{7} +(-2.31774 + 1.62113i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-5.99538 + 1.23688i) q^{10} +(-2.57249 - 4.45568i) q^{11} +(-1.19487 + 1.60384i) q^{12} +(2.72749 - 2.35814i) q^{13} +(-2.90347 - 0.962655i) q^{14} +(-3.74872 + 2.16432i) q^{15} +(2.74696 - 2.90762i) q^{16} +(-2.79961 + 4.84906i) q^{17} +(-0.445063 + 1.34236i) q^{18} +(0.963361 - 1.66859i) q^{19} +(7.95044 - 3.42626i) q^{20} -2.16296 q^{21} +(4.83618 + 5.43625i) q^{22} +(-1.01290 - 1.75439i) q^{23} +(1.19666 - 2.56281i) q^{24} +13.7372 q^{25} +(-3.10387 + 4.04549i) q^{26} +1.00000i q^{27} +(4.29650 + 0.503679i) q^{28} +(0.171090 - 0.0987787i) q^{29} +(4.57371 - 4.06885i) q^{30} +7.11414i q^{31} +(-2.97383 + 4.81210i) q^{32} +(4.45568 + 2.57249i) q^{33} +(2.49200 - 7.51614i) q^{34} +(8.10834 + 4.68135i) q^{35} +(0.232865 - 1.98640i) q^{36} +(-0.231065 - 0.400217i) q^{37} +(-0.857513 + 2.58635i) q^{38} +(-1.18300 + 3.40595i) q^{39} +(-10.0327 + 7.01730i) q^{40} +(-1.21570 + 0.701886i) q^{41} +(2.99580 - 0.618049i) q^{42} +(2.55733 + 1.47647i) q^{43} +(-8.25170 - 6.14755i) q^{44} +(2.16432 - 3.74872i) q^{45} +(1.90422 + 2.14049i) q^{46} -2.20506i q^{47} +(-0.925127 + 3.89155i) q^{48} +(-1.16080 - 2.01056i) q^{49} +(-19.0267 + 3.92529i) q^{50} -5.59922i q^{51} +(3.14304 - 6.49009i) q^{52} +2.10538i q^{53} +(-0.285742 - 1.38505i) q^{54} +(-11.1354 - 19.2871i) q^{55} +(-6.09478 + 0.530072i) q^{56} +1.92672i q^{57} +(-0.208742 + 0.185700i) q^{58} +(-2.18299 + 3.78104i) q^{59} +(-5.17216 + 6.94245i) q^{60} +(-10.6432 - 6.14485i) q^{61} +(-2.03281 - 9.85341i) q^{62} +(1.87318 - 1.08148i) q^{63} +(2.74388 - 7.51473i) q^{64} +(11.8063 - 10.2076i) q^{65} +(-6.90638 - 2.28984i) q^{66} +(5.50969 + 9.54306i) q^{67} +(-1.30386 + 11.1223i) q^{68} +(1.75439 + 1.01290i) q^{69} +(-12.5681 - 4.16700i) q^{70} +(5.01087 + 2.89303i) q^{71} +(0.245068 + 2.81779i) q^{72} +10.1096i q^{73} +(0.434394 + 0.488293i) q^{74} +(-11.8968 + 6.86860i) q^{75} +(0.448667 - 3.82724i) q^{76} -11.1284i q^{77} +(0.665289 - 5.05543i) q^{78} -7.37163 q^{79} +(11.8906 - 12.5860i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.48324 - 1.31952i) q^{82} -2.04171 q^{83} +(-3.97272 + 1.71205i) q^{84} +(-12.1185 + 20.9899i) q^{85} +(-3.96390 - 1.31425i) q^{86} +(-0.0987787 + 0.171090i) q^{87} +(13.1856 + 6.15678i) q^{88} +(-4.34987 + 2.51140i) q^{89} +(-1.92652 + 5.81059i) q^{90} +(7.65936 - 1.46750i) q^{91} +(-3.24905 - 2.42056i) q^{92} +(-3.55707 - 6.16103i) q^{93} +(0.630078 + 3.05411i) q^{94} +(4.17005 - 7.22274i) q^{95} +(0.169365 - 5.65432i) q^{96} +(-7.41183 - 4.27922i) q^{97} +(2.18226 + 2.45303i) q^{98} -5.14497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 6 q^{6} - 12 q^{7} + 24 q^{9} - 4 q^{10} - 8 q^{12} - 36 q^{14} - 2 q^{16} + 12 q^{17} + 54 q^{20} - 14 q^{22} + 20 q^{23} + 18 q^{24} + 48 q^{25} - 42 q^{26} + 6 q^{28} - 6 q^{30} + 12 q^{33}+ \cdots + 24 q^{98}+O(q^{100}) \) 48 * q - 2 * q^4 + 6 * q^6 - 12 * q^7 + 24 * q^9 - 4 * q^10 - 8 * q^12 - 36 * q^14 - 2 * q^16 + 12 * q^17 + 54 * q^20 - 14 * q^22 + 20 * q^23 + 18 * q^24 + 48 * q^25 - 42 * q^26 + 6 * q^28 - 6 * q^30 + 12 * q^33 + 2 * q^36 - 28 * q^38 + 28 * q^39 - 8 * q^40 - 12 * q^41 - 10 * q^42 - 30 * q^46 - 8 * q^48 + 16 * q^49 - 84 * q^50 - 28 * q^52 + 6 * q^54 - 68 * q^55 + 18 * q^56 - 24 * q^58 + 24 * q^62 - 12 * q^63 - 68 * q^64 + 12 * q^65 - 44 * q^66 + 4 * q^68 - 12 * q^71 + 54 * q^74 - 54 * q^76 + 4 * q^78 - 192 * q^79 + 78 * q^80 - 24 * q^81 - 6 * q^82 + 30 * q^84 - 10 * q^88 - 48 * q^89 - 8 * q^90 - 12 * q^92 + 54 * q^94 - 20 * q^95 + 144 * q^97 + 24 * q^98

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