LMFDB - Embedded newform 105.3.w.a.68.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,3,Mod(17,105)] 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("105.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.w (of order $12$, degree $4$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.28
Character	$\chi$	$=$	105.68
Dual form			105.3.w.a.17.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.72728 - 0.998723i) q^{2} +(0.776828 + 2.89768i) q^{3} +(9.43110 - 5.44505i) q^{4} +(-4.76718 + 1.50798i) q^{5} +(5.78944 + 10.0246i) q^{6} +(-6.13877 - 3.36385i) q^{7} +(18.8000 - 18.8000i) q^{8} +(-7.79308 + 4.50199i) q^{9} +(-16.2626 + 10.3818i) q^{10} +(-2.12166 + 1.22494i) q^{11} +(23.1043 + 23.0984i) q^{12} +(2.54324 - 2.54324i) q^{13} +(-26.2405 - 6.40708i) q^{14} +(-8.07292 - 12.6423i) q^{15} +(29.5169 - 51.1248i) q^{16} +(2.68738 + 0.720080i) q^{17} +(-24.5508 + 24.5633i) q^{18} +(0.652966 - 1.13097i) q^{19} +(-36.7487 + 40.1794i) q^{20} +(4.97858 - 20.4013i) q^{21} +(-6.68464 + 6.68464i) q^{22} +(5.75265 + 21.4692i) q^{23} +(69.0809 + 39.8721i) q^{24} +(20.4520 - 14.3776i) q^{25} +(6.93938 - 12.0194i) q^{26} +(-19.0992 - 19.0846i) q^{27} +(-76.2117 + 1.70114i) q^{28} -14.4234 q^{29} +(-42.7162 - 39.0589i) q^{30} +(5.76876 - 3.33060i) q^{31} +(31.4332 - 117.310i) q^{32} +(-5.19764 - 5.19631i) q^{33} +10.7358 q^{34} +(34.3372 + 6.77892i) q^{35} +(-48.9837 + 84.8924i) q^{36} +(8.72107 + 32.5475i) q^{37} +(1.30426 - 4.86758i) q^{38} +(9.34515 + 5.39383i) q^{39} +(-61.2731 + 117.973i) q^{40} -9.57556 q^{41} +(-1.81870 - 81.0137i) q^{42} +(27.5904 + 27.5904i) q^{43} +(-13.3397 + 23.1050i) q^{44} +(30.3621 - 33.2136i) q^{45} +(42.8835 + 74.2765i) q^{46} +(6.23208 + 23.2584i) q^{47} +(171.073 + 45.8153i) q^{48} +(26.3691 + 41.2998i) q^{49} +(61.8712 - 74.0153i) q^{50} +(0.00106809 + 8.34653i) q^{51} +(10.1375 - 37.8336i) q^{52} +(-53.1174 - 14.2328i) q^{53} +(-90.2484 - 52.0587i) q^{54} +(8.26714 - 9.03892i) q^{55} +(-178.650 + 52.1687i) q^{56} +(3.78443 + 1.01352i) q^{57} +(-53.7600 + 14.4050i) q^{58} +(66.1564 - 38.1954i) q^{59} +(-144.974 - 75.2735i) q^{60} +(-77.6638 - 44.8392i) q^{61} +(18.1755 - 18.1755i) q^{62} +(62.9839 - 1.42200i) q^{63} -232.507i q^{64} +(-8.28893 + 15.9592i) q^{65} +(-24.5628 - 14.1771i) q^{66} +(4.87233 + 1.30554i) q^{67} +(29.2658 - 7.84174i) q^{68} +(-57.7420 + 33.3472i) q^{69} +(134.755 - 9.02642i) q^{70} -120.663i q^{71} +(-61.8725 + 231.148i) q^{72} +(99.1765 + 26.5743i) q^{73} +(65.0118 + 112.604i) q^{74} +(57.5494 + 48.0944i) q^{75} -14.2217i q^{76} +(17.1449 - 0.382694i) q^{77} +(40.2190 + 10.7711i) q^{78} +(-9.38512 - 5.41850i) q^{79} +(-63.6173 + 288.232i) q^{80} +(40.4641 - 70.1688i) q^{81} +(-35.6908 + 9.56333i) q^{82} +(-53.8586 - 53.8586i) q^{83} +(-64.1327 - 219.515i) q^{84} +(-13.8971 + 0.619755i) q^{85} +(130.393 + 75.2822i) q^{86} +(-11.2045 - 41.7943i) q^{87} +(-16.8583 + 62.9162i) q^{88} +(-54.6094 - 31.5288i) q^{89} +(79.9969 - 154.120i) q^{90} +(-24.1674 + 7.05730i) q^{91} +(171.155 + 171.155i) q^{92} +(14.1323 + 14.1287i) q^{93} +(46.4575 + 80.4667i) q^{94} +(-1.40733 + 6.37620i) q^{95} +(364.346 - 0.0466246i) q^{96} +(79.9577 + 79.9577i) q^{97} +(139.532 + 127.601i) q^{98} +(11.0196 - 19.0977i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) $ 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	3.72728	−	0.998723i	1.86364	−	0.499361i	0.863653	−	0.504086i	$-0.168171\pi$
$2$	3.72728	−	0.998723i	1.86364	−	0.499361i	0.999989	+	0.00472484i	$0.00150397\pi$
$3$	0.776828	+	2.89768i	0.258943	+	0.965893i
$3$	0.776828	+	2.89768i	0.258943	+	0.965893i
$4$	9.43110	−	5.44505i	2.35777	−	1.36126i
$5$	−4.76718	+	1.50798i	−0.953436	+	0.301596i
$5$	−4.76718	+	1.50798i	−0.953436	+	0.301596i
$6$	5.78944	+	10.0246i	0.964906	+	1.67077i
$7$	−6.13877	−	3.36385i	−0.876968	−	0.480550i
$7$	−6.13877	−	3.36385i	−0.876968	−	0.480550i
$8$	18.8000	−	18.8000i	2.35001	−	2.35001i
$9$	−7.79308	+	4.50199i	−0.865897	+	0.500222i
$10$	−16.2626	+	10.3818i	−1.62626	+	1.03818i
$11$	−2.12166	+	1.22494i	−0.192878	+	0.111358i	−0.593329	−	0.804960i	$-0.702187\pi$
$11$	−2.12166	+	1.22494i	−0.192878	+	0.111358i	0.400451	+	0.916318i	$0.368853\pi$
$12$	23.1043	+	23.0984i	1.92536	+	1.92487i
$13$	2.54324	−	2.54324i	0.195634	−	0.195634i	−0.602492	−	0.798125i	$-0.705825\pi$
$13$	2.54324	−	2.54324i	0.195634	−	0.195634i	0.798125	+	0.602492i	$0.205825\pi$
$14$	−26.2405	−	6.40708i	−1.87432	−	0.457649i
$15$	−8.07292	−	12.6423i	−0.538194	−	0.842821i
$16$	29.5169	−	51.1248i	1.84481	−	3.19530i
$17$	2.68738	+	0.720080i	0.158081	+	0.0423577i	0.336992	−	0.941508i	$-0.390591\pi$
$17$	2.68738	+	0.720080i	0.158081	+	0.0423577i	−0.178911	+	0.983865i	$0.557257\pi$
$18$	−24.5508	+	24.5633i	−1.36393	+	1.36463i
$19$	0.652966	−	1.13097i	0.0343667	−	0.0595248i	−0.848331	−	0.529467i	$-0.822392\pi$
$19$	0.652966	−	1.13097i	0.0343667	−	0.0595248i	0.882697	+	0.469942i	$0.155725\pi$
$20$	−36.7487	+	40.1794i	−1.83744	+	2.00897i
$21$	4.97858	−	20.4013i	0.237075	−	0.971491i
$22$	−6.68464	+	6.68464i	−0.303847	+	0.303847i
$23$	5.75265	+	21.4692i	0.250115	+	0.933443i	0.970743	+	0.240121i	$0.0771871\pi$
$23$	5.75265	+	21.4692i	0.250115	+	0.933443i	−0.720628	+	0.693322i	$0.756146\pi$
$24$	69.0809	+	39.8721i	2.87837	+	1.66134i
$25$	20.4520	−	14.3776i	0.818080	−	0.575105i
$26$	6.93938	−	12.0194i	0.266899	−	0.462283i
$27$	−19.0992	−	19.0846i	−0.707378	−	0.706835i
$28$	−76.2117	+	1.70114i	−2.72185	+	0.0607548i
$29$	−14.4234			−0.497358			−0.248679	−	0.968586i	$-0.579996\pi$
$29$	−14.4234			−0.497358			−0.248679	+	0.968586i	$0.579996\pi$
$30$	−42.7162	−	39.0589i	−1.42387	−	1.30196i
$31$	5.76876	−	3.33060i	0.186089	−	0.107439i	−0.404061	−	0.914732i	$-0.632402\pi$
$31$	5.76876	−	3.33060i	0.186089	−	0.107439i	0.590150	+	0.807293i	$0.299068\pi$
$32$	31.4332	−	117.310i	0.982288	−	3.66595i
$33$	−5.19764	−	5.19631i	−0.157504	−	0.157464i
$34$	10.7358			0.315758
$35$	34.3372	+	6.77892i	0.981064	+	0.193683i
$36$	−48.9837	+	84.8924i	−1.36066	+	2.35812i
$37$	8.72107	+	32.5475i	0.235704	+	0.879661i	0.977830	+	0.209400i	$0.0671511\pi$
$37$	8.72107	+	32.5475i	0.235704	+	0.879661i	−0.742126	+	0.670261i	$0.766182\pi$
$38$	1.30426	−	4.86758i	0.0343228	−	0.128094i
$39$	9.34515	+	5.39383i	0.239619	+	0.138303i
$40$	−61.2731	+	117.973i	−1.53183	+	2.94933i
$41$	−9.57556			−0.233550			−0.116775	−	0.993158i	$-0.537256\pi$
$41$	−9.57556			−0.233550			−0.116775	+	0.993158i	$0.537256\pi$
$42$	−1.81870	−	81.0137i	−0.0433023	−	1.92890i
$43$	27.5904	+	27.5904i	0.641638	+	0.641638i	0.950958	−	0.309320i	$-0.100101\pi$
$43$	27.5904	+	27.5904i	0.641638	+	0.641638i	−0.309320	+	0.950958i	$0.600101\pi$
$44$	−13.3397	+	23.1050i	−0.303175	+	0.525115i
$45$	30.3621	−	33.2136i	0.674713	−	0.738080i
$46$	42.8835	+	74.2765i	0.932251	+	1.61471i
$47$	6.23208	+	23.2584i	0.132597	+	0.494860i	0.999996	−	0.00275330i	$-0.000876403\pi$
$47$	6.23208	+	23.2584i	0.132597	+	0.494860i	−0.867399	+	0.497614i	$0.834210\pi$
$48$	171.073	+	45.8153i	3.56401	+	0.954486i
$49$	26.3691	+	41.2998i	0.538144	+	0.842853i
$50$	61.8712	−	74.0153i	1.23742	−	1.48031i
$51$	0.00106809	+	8.34653i	2.09429e−5	+	0.163657i
$52$	10.1375	−	37.8336i	0.194952	−	0.727569i
$53$	−53.1174	−	14.2328i	−1.00221	−	0.268543i	−0.279842	−	0.960046i	$-0.590282\pi$
$53$	−53.1174	−	14.2328i	−1.00221	−	0.268543i	−0.722373	+	0.691503i	$0.756949\pi$
$54$	−90.2484	−	52.0587i	−1.67127	−	0.964051i
$55$	8.26714	−	9.03892i	0.150312	−	0.164344i
$56$	−178.650	+	52.1687i	−3.19017	+	0.931585i
$57$	3.78443	+	1.01352i	0.0663935	+	0.0177810i
$58$	−53.7600	+	14.4050i	−0.926897	+	0.248361i
$59$	66.1564	−	38.1954i	1.12129	−	0.647379i	0.179563	−	0.983746i	$-0.442532\pi$
$59$	66.1564	−	38.1954i	1.12129	−	0.647379i	0.941731	+	0.336367i	$0.109198\pi$
$60$	−144.974	−	75.2735i	−2.41624	−	1.25456i
$61$	−77.6638	−	44.8392i	−1.27318	−	0.735069i	−0.297592	−	0.954693i	$-0.596183\pi$
$61$	−77.6638	−	44.8392i	−1.27318	−	0.735069i	−0.975584	+	0.219625i	$0.929517\pi$
$62$	18.1755	−	18.1755i	0.293153	−	0.293153i
$63$	62.9839	−	1.42200i	0.999745	−	0.0225715i
$64$		−	232.507i		−	3.63292i
$65$	−8.28893	+	15.9592i	−0.127522	+	0.245527i
$66$	−24.5628	−	14.1771i	−0.372163	−	0.214805i
$67$	4.87233	+	1.30554i	0.0727213	+	0.0194856i	0.294996	−	0.955498i	$-0.404682\pi$
$67$	4.87233	+	1.30554i	0.0727213	+	0.0194856i	−0.222275	+	0.974984i	$0.571348\pi$
$68$	29.2658	−	7.84174i	0.430379	−	0.115320i
$69$	−57.7420	+	33.3472i	−0.836840	+	0.483293i
$70$	134.755	−	9.02642i	1.92507	−	0.128949i
$71$		−	120.663i		−	1.69948i	−0.527205	−	0.849738i	$-0.676760\pi$
$71$		−	120.663i		−	1.69948i	0.527205	−	0.849738i	$-0.323240\pi$
$72$	−61.8725	+	231.148i	−0.859340	+	3.21039i
$73$	99.1765	+	26.5743i	1.35858	+	0.364031i	0.863296	−	0.504698i	$-0.168396\pi$
$73$	99.1765	+	26.5743i	1.35858	+	0.364031i	0.495287	+	0.868729i	$0.335063\pi$
$74$	65.0118	+	112.604i	0.878538	+	1.52167i
$75$	57.5494	+	48.0944i	0.767325	+	0.641258i
$76$		−	14.2217i		−	0.187128i
$77$	17.1449	−	0.382694i	0.222661	−	0.00497005i
$78$	40.2190	+	10.7711i	0.515628	+	0.138091i
$79$	−9.38512	−	5.41850i	−0.118799	−	0.0685886i	0.439423	−	0.898280i	$-0.355183\pi$
$79$	−9.38512	−	5.41850i	−0.118799	−	0.0685886i	−0.558222	+	0.829692i	$0.688516\pi$
$80$	−63.6173	+	288.232i	−0.795216	+	3.60290i
$81$	40.4641	−	70.1688i	0.499557	−	0.866281i
$82$	−35.6908	+	9.56333i	−0.435254	+	0.116626i
$83$	−53.8586	−	53.8586i	−0.648899	−	0.648899i	0.303828	−	0.952727i	$-0.401735\pi$
$83$	−53.8586	−	53.8586i	−0.648899	−	0.648899i	−0.952727	+	0.303828i	$0.901735\pi$
$84$	−64.1327	−	219.515i	−0.763485	−	2.61328i
$85$	−13.8971	+	0.619755i	−0.163495	+	0.00729123i
$86$	130.393	+	75.2822i	1.51619	+	0.875375i
$87$	−11.2045	−	41.7943i	−0.128787	−	0.480394i
$88$	−16.8583	+	62.9162i	−0.191572	+	0.714956i
$89$	−54.6094	−	31.5288i	−0.613589	−	0.354256i	0.160780	−	0.986990i	$-0.448599\pi$
$89$	−54.6094	−	31.5288i	−0.613589	−	0.354256i	−0.774369	+	0.632735i	$0.781932\pi$
$90$	79.9969	−	154.120i	0.888855	−	1.71244i
$91$	−24.1674	+	7.05730i	−0.265576	+	0.0775527i
$92$	171.155	+	171.155i	1.86038	+	1.86038i
$93$	14.1323	+	14.1287i	0.151961	+	0.151922i
$94$	46.4575	+	80.4667i	0.494228	+	0.856029i
$95$	−1.40733	+	6.37620i	−0.0148140	+	0.0671179i
$96$	364.346	−	0.0466246i	3.79527	−	0.000485672i
$97$	79.9577	+	79.9577i	0.824306	+	0.824306i	0.986722	−	0.162416i	$-0.0519288\pi$
$97$	79.9577	+	79.9577i	0.824306	+	0.824306i	−0.162416	+	0.986722i	$0.551929\pi$
$98$	139.532	+	127.601i	1.42380	+	1.30205i
$99$	11.0196	−	19.0977i	0.111309	−	0.192906i
$100$	114.598	−	246.959i	1.14598	−	2.46959i
$101$	−67.0901	−	116.203i	−0.664259	−	1.15053i	−0.979486	−	0.201513i	$-0.935414\pi$
$101$	−67.0901	−	116.203i	−0.664259	−	1.15053i	0.315227	−	0.949016i	$-0.397919\pi$
$102$	8.33985	+	31.1088i	0.0817632	+	0.304988i
$103$	1.25396	+	4.67983i	0.0121743	+	0.0454353i	0.971746	−	0.236030i	$-0.0758463\pi$
$103$	1.25396	+	4.67983i	0.0121743	+	0.0454353i	−0.959571	+	0.281465i	$0.909180\pi$
$104$		−	95.6260i		−	0.919481i
$105$	7.03100	+	104.764i	0.0669619	+	0.997756i
$106$	−212.198			−2.00187
$107$	138.573	−	37.1306i	1.29508	−	0.347015i	0.455490	−	0.890241i	$-0.349464\pi$
$107$	138.573	−	37.1306i	1.29508	−	0.347015i	0.839586	+	0.543226i	$0.182797\pi$
$108$	−284.043	−	75.9922i	−2.63003	−	0.703631i
$109$	−68.2088	+	39.3803i	−0.625768	+	0.361288i	−0.779111	−	0.626885i	$-0.784329\pi$
$109$	−68.2088	+	39.3803i	−0.625768	+	0.361288i	0.153343	+	0.988173i	$0.450996\pi$
$110$	21.7866	−	41.9472i	0.198060	−	0.381338i
$111$	−87.5373	+	50.5546i	−0.788624	+	0.455447i
$112$	−353.173	+	214.553i	−3.15333	+	1.91565i
$113$	−91.5753	+	91.5753i	−0.810401	+	0.810401i	−0.984694	−	0.174293i	$-0.944236\pi$
$113$	−91.5753	+	91.5753i	−0.810401	+	0.810401i	0.174293	+	0.984694i	$0.444236\pi$
$114$	15.1179	−	0.00193460i	0.132613	−	1.69702e-5i
$115$	−59.7990	−	93.6726i	−0.519991	−	0.814544i
$116$	−136.028	+	78.5360i	−1.17266	+	0.677034i
$117$	−8.37001	+	31.2693i	−0.0715385	+	0.267259i
$118$	208.437	−	208.437i	1.76641	−	1.76641i
$119$	−14.0750	−	13.4603i	−0.118277	−	0.113112i
$120$	−389.447	−	85.9049i	−3.24539	−	0.715874i
$121$	−57.4990	+	99.5913i	−0.475199	+	0.823068i
$122$	−334.257	−	89.5638i	−2.73981	−	0.734130i
$123$	−7.43856	−	27.7469i	−0.0604761	−	0.225584i
$124$	36.2705	−	62.8224i	0.292504	−	0.506632i
$125$	−75.8172	+	99.3818i	−0.606538	+	0.795055i
$126$	233.339	−	68.2037i	1.85190	−	0.541299i
$127$	134.984	−	134.984i	1.06286	−	1.06286i	0.0649759	−	0.997887i	$-0.479303\pi$
$127$	134.984	−	134.984i	1.06286	−	1.06286i	0.997887	−	0.0649759i	$-0.0206971\pi$
$128$	−106.477	−	397.378i	−0.831853	−	3.10452i
$129$	−58.5152	+	101.381i	−0.453606	+	0.785901i
$130$	−14.9563	+	67.7629i	−0.115049	+	0.521253i
$131$	−114.473	+	198.272i	−0.873837	+	1.51353i	−0.0158402	+	0.999875i	$0.505042\pi$
$131$	−114.473	+	198.272i	−0.873837	+	1.51353i	−0.857997	+	0.513655i	$0.828291\pi$
$132$	−77.3136	−	20.7055i	−0.585709	−	0.156860i
$133$	−7.81283	+	4.74629i	−0.0587430	+	0.0356864i
$134$	19.4644			0.145257
$135$	119.828	+	62.1783i	0.887618	+	0.460580i
$136$	64.0603	−	36.9853i	0.471032	−	0.271950i
$137$	11.6803	−	43.5915i	0.0852577	−	0.318186i	−0.910105	−	0.414377i	$-0.863999\pi$
$137$	11.6803	−	43.5915i	0.0852577	−	0.318186i	0.995363	+	0.0961913i	$0.0306660\pi$
$138$	−181.916	+	181.963i	−1.31823	+	1.31857i
$139$	−55.1047			−0.396436			−0.198218	−	0.980158i	$-0.563515\pi$
$139$	−55.1047			−0.396436			−0.198218	+	0.980158i	$0.563515\pi$
$140$	360.750	−	123.035i	2.57678	−	0.878823i
$141$	−62.5542	+	36.1264i	−0.443647	+	0.256215i
$142$	−120.509	−	449.745i	−0.848653	−	3.16722i
$143$	−2.28057	+	8.51119i	−0.0159480	+	0.0595188i
$144$	0.135980	+	531.304i	0.000944303	+	3.68961i
$145$	68.7588	−	21.7502i	0.474199	−	0.150001i
$146$	396.199			2.71369
$147$	−99.1893	+	108.492i	−0.674757	+	0.738040i
$148$	259.472	+	259.472i	1.75319	+	1.75319i
$149$	−50.8418	+	88.0605i	−0.341220	+	0.591010i	−0.984660	−	0.174487i	$-0.944173\pi$
$149$	−50.8418	+	88.0605i	−0.341220	+	0.591010i	0.643440	+	0.765497i	$0.277507\pi$
$150$	262.536	+	121.786i	1.75024	+	0.811904i
$151$	−92.1891	−	159.676i	−0.610524	−	1.05746i	−0.991152	−	0.132730i	$-0.957626\pi$
$151$	−92.1891	−	159.676i	−0.610524	−	1.05746i	0.380629	−	0.924728i	$-0.375708\pi$
$152$	−8.98651	−	33.5381i	−0.0591218	−	0.220645i
$153$	−24.1847	+	6.48691i	−0.158070	+	0.0423981i
$154$	63.5216	−	18.5494i	0.412478	−	0.120451i
$155$	−22.4783	+	24.5767i	−0.145021	+	0.158560i
$156$	117.505	−	0.0150368i	0.753235	−	9.63899e-5i
$157$	−20.9390	+	78.1455i	−0.133370	+	0.497742i	−0.999999	−	0.00120996i	$-0.999615\pi$
$157$	−20.9390	+	78.1455i	−0.133370	+	0.497742i	0.866630	+	0.498952i	$0.166282\pi$
$158$	−40.3926	−	10.8232i	−0.255649	−	0.0685010i
$159$	−0.0211113	−	164.974i	−0.000132775	−	1.03757i
$160$	27.0538	+	606.640i	0.169086	+	3.79150i
$161$	36.9049	−	151.146i	0.229223	−	0.938792i
$162$	80.7420	−	301.951i	0.498407	−	1.86390i
$163$	−229.729	+	61.5557i	−1.40938	+	0.377642i	−0.881704	−	0.471803i	$-0.843603\pi$
$163$	−229.729	+	61.5557i	−1.40938	+	0.377642i	−0.527677	+	0.849445i	$0.676937\pi$
$164$	−90.3080	+	52.1394i	−0.550659	+	0.317923i
$165$	32.6140	+	16.9338i	0.197661	+	0.102629i
$166$	−254.536	−	146.956i	−1.53335	−	0.885280i
$167$	63.1204	−	63.1204i	0.377967	−	0.377967i	−0.492402	−	0.870368i	$-0.663881\pi$
$167$	63.1204	−	63.1204i	0.377967	−	0.377967i	0.870368	+	0.492402i	$0.163881\pi$
$168$	−289.948	−	477.143i	−1.72588	−	2.84014i
$169$			156.064i			0.923455i
$170$	−51.1794	+	16.1893i	−0.301055	+	0.0952313i
$171$	0.00300811	+	11.7534i	1.75913e−5	+	0.0687333i
$172$	410.440	+	109.977i	2.38628	+	0.639401i
$173$	−115.465	+	30.9387i	−0.667428	+	0.178837i	−0.576596	−	0.817030i	$-0.695619\pi$
$173$	−115.465	+	30.9387i	−0.667428	+	0.178837i	−0.0908318	+	0.995866i	$0.528953\pi$
$174$	−83.5032	−	144.589i	−0.479904	−	0.830972i
$175$	−173.914	+	19.4635i	−0.993796	+	0.111220i
$176$			144.626i			0.821736i
$177$	162.070	+	162.029i	0.915650	+	0.915416i
$178$	−235.033	−	62.9770i	−1.32041	−	0.353803i
$179$	−30.3894	−	52.6360i	−0.169773	−	0.294056i	0.768567	−	0.639770i	$-0.220970\pi$
$179$	−30.3894	−	52.6360i	−0.169773	−	0.294056i	−0.938340	+	0.345714i	$0.887637\pi$
$180$	105.498	−	478.564i	0.586101	−	2.65869i
$181$			6.33738i			0.0350131i	0.999847	+	0.0175066i	$0.00557280\pi$
$181$			6.33738i			0.0350131i	−0.999847	+	0.0175066i	$0.994427\pi$
$182$	−83.0306	+	50.4411i	−0.456212	+	0.277149i
$183$	69.5982	−	259.877i	0.380318	−	1.42009i
$184$	511.772	+	295.472i	2.78137	+	1.60582i
$185$	−90.6558	−	142.008i	−0.490031	−	0.767613i
$186$	66.7859	+	38.5475i	0.359064	+	0.207244i
$187$	−6.58374	+	1.76411i	−0.0352072	+	0.00943374i
$188$	185.419	+	185.419i	0.986270	+	0.986270i
$189$	53.0482	+	181.403i	0.280678	+	0.959802i
$190$	1.12255	+	25.1714i	0.00590815	+	0.132481i
$191$	26.6831	+	15.4055i	0.139702	+	0.0806570i	0.568222	−	0.822875i	$-0.307631\pi$
$191$	26.6831	+	15.4055i	0.139702	+	0.0806570i	−0.428520	+	0.903532i	$0.640965\pi$
$192$	673.730	−	180.618i	3.50901	−	0.940718i
$193$	−49.0471	+	183.046i	−0.254130	+	0.948426i	0.714442	+	0.699694i	$0.246680\pi$
$193$	−49.0471	+	183.046i	−0.254130	+	0.948426i	−0.968572	+	0.248732i	$0.919986\pi$
$194$	377.881	+	218.169i	1.94784	+	1.12458i
$195$	−52.6838	−	11.6211i	−0.270173	−	0.0595952i
$196$	473.569	+	245.922i	2.41617	+	1.25470i
$197$	111.387	+	111.387i	0.565418	+	0.565418i	0.930841	−	0.365423i	$-0.119076\pi$
$197$	111.387	+	111.387i	0.565418	+	0.565418i	−0.365423	+	0.930841i	$0.619076\pi$
$198$	21.9997	−	82.1882i	0.111110	−	0.415092i
$199$	−133.135	−	230.596i	−0.669019	−	1.15877i	−0.978179	−	0.207764i	$-0.933381\pi$
$199$	−133.135	−	230.596i	−0.669019	−	1.15877i	0.309160	−	0.951010i	$-0.399952\pi$
$200$	114.199	−	654.798i	0.570994	−	3.27399i
$201$	0.00193649	+	15.1326i	9.63427e−6	+	0.0752867i
$202$	−366.119	−	366.119i	−1.81247	−	1.81247i
$203$	88.5419	+	48.5180i	0.436167	+	0.239005i
$204$	45.4573	+	78.7111i	0.222830	+	0.385839i
$205$	45.6484	−	14.4397i	0.222675	−	0.0704378i
$206$	9.34771	+	16.1907i	0.0453772	+	0.0785957i
$207$	−141.485	−	141.413i	−0.683503	−	0.683153i
$208$	−54.9540	−	205.091i	−0.264202	−	0.986015i
$209$			3.19938i			0.0153080i
$210$	130.837	+	383.464i	0.623034	+	1.82602i
$211$	363.838			1.72435			0.862176	−	0.506608i	$-0.169101\pi$
$211$	363.838			1.72435			0.862176	+	0.506608i	$0.169101\pi$
$212$	−578.453	+	154.996i	−2.72855	+	0.731114i
$213$	349.642	−	93.7342i	1.64151	−	0.440067i
$214$	479.419	−	276.792i	2.24027	−	1.29342i
$215$	−173.134	−	89.9228i	−0.805276	−	0.418246i
$216$	−717.857	+	0.275588i	−3.32341	+	0.00127587i
$217$	−46.6167	+	1.04054i	−0.214824	+	0.00479512i
$218$	−214.903	+	214.903i	−0.985795	+	0.985795i
$219$	0.0394173	+	308.025i	0.000179988	+	1.40651i
$220$	28.7508	−	130.262i	0.130686	−	0.592099i
$221$	8.66598	−	5.00330i	0.0392126	−	0.0226394i
$222$	−275.786	+	275.857i	−1.24228	+	1.24260i
$223$	185.409	−	185.409i	0.831429	−	0.831429i	−0.156284	−	0.987712i	$-0.549951\pi$
$223$	185.409	−	185.409i	0.831429	−	0.831429i	0.987712	+	0.156284i	$0.0499514\pi$
$224$	−587.576	+	614.405i	−2.62311	+	2.74288i
$225$	−94.6561	+	204.121i	−0.420694	+	0.907203i
$226$	−249.869	+	432.786i	−1.10561	+	1.91498i
$227$	271.431	+	72.7298i	1.19573	+	0.320396i	0.801150	−	0.598464i	$-0.204222\pi$
$227$	271.431	+	72.7298i	1.19573	+	0.320396i	0.394584	+	0.918860i	$0.370889\pi$
$228$	41.2100	−	11.0478i	0.180746	−	0.0484554i
$229$	−48.1860	+	83.4605i	−0.210419	+	0.364456i	−0.951846	−	0.306577i	$-0.900816\pi$
$229$	−48.1860	+	83.4605i	−0.210419	+	0.364456i	0.741427	+	0.671034i	$0.234149\pi$
$230$	−316.441	−	289.422i	−1.37583	−	1.25836i
$231$	14.4275	+	49.3830i	0.0624569	+	0.213779i
$232$	−271.160	+	271.160i	−1.16879	+	1.16879i
$233$	−47.4507	−	177.088i	−0.203651	−	0.760035i	−0.989857	−	0.142071i	$-0.954624\pi$
$233$	−47.4507	−	177.088i	−0.203651	−	0.760035i	0.786206	−	0.617965i	$-0.212043\pi$
$234$	0.0319686	+	124.909i	0.000136618	+	0.533799i
$235$	−64.7827	−	101.479i	−0.275671	−	0.431827i
$236$	415.951	−	720.449i	1.76251	−	3.05275i
$237$	8.41045	−	31.4043i	0.0354871	−	0.132508i
$238$	−65.9045	−	36.1135i	−0.276910	−	0.151737i
$239$	215.563			0.901937			0.450968	−	0.892540i	$-0.351079\pi$
$239$	215.563			0.901937			0.450968	+	0.892540i	$0.351079\pi$
$240$	−884.623	+	39.5641i	−3.68593	+	0.164851i
$241$	332.441	−	191.935i	1.37943	−	0.796411i	0.387335	−	0.921939i	$-0.373396\pi$
$241$	332.441	−	191.935i	1.37943	−	0.796411i	0.992090	+	0.125528i	$0.0400624\pi$
$242$	−114.851	+	428.631i	−0.474592	+	1.77120i
$243$	234.760	+	62.7428i	0.966091	+	0.258201i
$244$	−976.606			−4.00248
$245$	−187.985	−	157.119i	−0.767287	−	0.641304i
$246$	−55.4371	−	95.9915i	−0.225354	−	0.390209i
$247$	−1.21568	−	4.53698i	−0.00492178	−	0.0183683i
$248$	45.8376	−	171.068i	0.184829	−	0.689792i
$249$	114.226	−	197.904i	0.458739	−	0.794794i
$250$	−183.337	+	446.145i	−0.733350	+	1.78458i
$251$	−210.985			−0.840578			−0.420289	−	0.907390i	$-0.638071\pi$
$251$	−210.985			−0.840578			−0.420289	+	0.907390i	$0.638071\pi$
$252$	586.265	−	356.362i	2.32645	−	1.41413i
$253$	−38.5036	−	38.5036i	−0.152188	−	0.152188i
$254$	368.311	−	637.933i	1.45004	−	2.51155i
$255$	−12.5915	−	39.7878i	−0.0493784	−	0.156031i
$256$	−328.727	−	569.372i	−1.28409	−	2.22411i
$257$	53.9490	+	201.340i	0.209918	+	0.783425i	0.987894	+	0.155131i	$0.0495800\pi$
$257$	53.9490	+	201.340i	0.209918	+	0.783425i	−0.777976	+	0.628294i	$0.783753\pi$
$258$	−116.851	+	436.317i	−0.452911	+	1.69115i
$259$	55.9480	−	229.138i	0.216016	−	0.884702i
$260$	8.72508	+	195.647i	0.0335580	+	0.752487i
$261$	112.403	−	64.9340i	0.430661	−	0.248789i
$262$	−228.653	+	853.344i	−0.872721	+	3.25704i
$263$	181.683	+	48.6819i	0.690811	+	0.185102i	0.587111	−	0.809507i	$-0.300265\pi$
$263$	181.683	+	48.6819i	0.690811	+	0.185102i	0.103700	+	0.994609i	$0.466932\pi$
$264$	−195.407	+	0.0250058i	−0.740177	+	9.47189e-5i
$265$	274.683	−	12.2498i	1.03654	−	0.0462256i
$266$	−24.3804	+	25.4936i	−0.0916556	+	0.0958407i
$267$	48.9381	−	182.733i	0.183289	−	0.684393i
$268$	53.0601	−	14.2174i	0.197986	−	0.0530501i
$269$	114.316	−	66.0005i	0.424967	−	0.245355i	−0.272233	−	0.962231i	$-0.587762\pi$
$269$	114.316	−	66.0005i	0.424967	−	0.245355i	0.697200	+	0.716876i	$0.254429\pi$
$270$	508.734	+	112.081i	1.88420	+	0.415114i
$271$	29.8453	+	17.2312i	0.110130	+	0.0635838i	0.554053	−	0.832481i	$-0.313080\pi$
$271$	29.8453	+	17.2312i	0.110130	+	0.0635838i	−0.443923	+	0.896065i	$0.646414\pi$
$272$	116.137	−	116.137i	0.426974	−	0.426974i
$273$	−39.2237	−	64.5471i	−0.143677	−	0.236436i
$274$		−	174.143i		−	0.635559i
$275$	−25.7804	+	55.5568i	−0.0937470	+	0.202025i
$276$	−362.993	+	628.909i	−1.31519	+	2.27865i
$277$	−498.589	−	133.597i	−1.79996	−	0.482298i	−0.805990	−	0.591930i	$-0.798366\pi$
$277$	−498.589	−	133.597i	−1.79996	−	0.482298i	−0.993972	+	0.109631i	$0.965033\pi$
$278$	−205.391	+	55.0343i	−0.738816	+	0.197965i
$279$	−29.9621	+	51.9265i	−0.107391	+	0.186117i
$280$	772.986	−	518.098i	2.76066	−	1.85035i
$281$		−	339.109i		−	1.20679i	−0.797441	−	0.603397i	$-0.793813\pi$
$281$		−	339.109i		−	1.20679i	0.797441	−	0.603397i	$-0.206187\pi$
$282$	−197.077	+	197.128i	−0.698855	+	0.699034i
$283$	30.5969	+	8.19840i	0.108116	+	0.0289696i	0.312471	−	0.949927i	$-0.398843\pi$
$283$	30.5969	+	8.19840i	0.108116	+	0.0289696i	−0.204355	+	0.978897i	$0.565510\pi$
$284$	−657.015	−	1137.98i	−2.31343	−	4.00698i
$285$	−19.5694	+	0.875229i	−0.0686647	+	0.00307098i
$286$			34.0013i			0.118886i
$287$	58.7822	+	32.2107i	0.204816	+	0.112232i
$288$	283.169	+	1055.72i	0.983226	+	3.66570i
$289$	−243.578	−	140.630i	−0.842830	−	0.486608i
$290$	234.561	−	149.740i	0.808832	−	0.516345i
$291$	−169.578	+	293.805i	−0.582743	+	1.00964i
$292$	1080.04	−	289.396i	3.69877	−	0.991083i
$293$	137.824	+	137.824i	0.470390	+	0.470390i	0.902041	−	0.431651i	$-0.142069\pi$
$293$	137.824	+	137.824i	0.470390	+	0.470390i	−0.431651	+	0.902041i	$0.642069\pi$
$294$	−261.353	+	503.443i	−0.888957	+	1.71239i
$295$	−257.781	+	281.847i	−0.873835	+	0.955412i
$296$	775.850	+	447.937i	2.62112	+	1.51330i
$297$	63.8994	+	17.0955i	0.215149	+	0.0575606i
$298$	−101.554	+	379.003i	−0.340784	+	1.27182i
$299$	69.2317	+	39.9709i	0.231544	+	0.133682i
$300$	804.630	+	140.224i	2.68210	+	0.467412i
$301$	−76.5614	−	262.182i	−0.254357	−	0.871035i
$302$	−503.087	−	503.087i	−1.66585	−	1.66585i
$303$	284.603	−	284.676i	0.939283	−	0.939524i
$304$	−38.5471	−	66.7655i	−0.126800	−	0.219623i
$305$	437.854	+	96.6411i	1.43559	+	0.316856i
$306$	−83.6647	+	48.3324i	−0.273414	+	0.157949i
$307$	234.301	+	234.301i	0.763197	+	0.763197i	0.976899	−	0.213702i	$-0.0685521\pi$
$307$	234.301	+	234.301i	0.763197	+	0.763197i	−0.213702	+	0.976899i	$0.568552\pi$
$308$	159.611	−	96.9639i	0.518218	−	0.314818i
$309$	−12.5865	+	7.26899i	−0.0407331	+	0.0235242i
$310$	−59.2375	+	114.054i	−0.191089	+	0.367916i
$311$	190.372	+	329.734i	0.612129	+	1.06024i	0.990881	+	0.134740i	$0.0430200\pi$
$311$	190.372	+	329.734i	0.612129	+	1.06024i	−0.378752	+	0.925498i	$0.623647\pi$
$312$	277.094	−	74.2850i	0.888120	−	0.238093i
$313$	−84.9856	−	317.171i	−0.271519	−	1.01332i	−0.958138	−	0.286307i	$-0.907572\pi$
$313$	−84.9856	−	317.171i	−0.271519	−	1.01332i	0.686619	−	0.727018i	$-0.259094\pi$
$314$			312.183i			0.994212i
$315$	−298.111	+	101.757i	−0.946386	+	0.323039i
$316$	−118.016			−0.373468
$317$	−204.906	+	54.9044i	−0.646392	+	0.173200i	−0.567097	−	0.823651i	$-0.691933\pi$
$317$	−204.906	+	54.9044i	−0.646392	+	0.173200i	−0.0792948	+	0.996851i	$0.525267\pi$
$318$	−164.841	−	614.882i	−0.518369	−	1.93359i
$319$	30.6015	−	17.6678i	0.0959293	−	0.0553848i
$320$	350.616	+	1108.40i	1.09567	+	3.46376i
$321$	215.240	+	372.696i	0.670530	+	1.16105i
$322$	−13.3976	−	600.220i	−0.0416075	−	1.86404i
$323$	2.56916	−	2.56916i	0.00795404	−	0.00795404i
$324$	−0.451520	−	882.098i	−0.00139358	−	2.72252i
$325$	15.4486	−	88.5800i	0.0475342	−	0.272554i
$326$	−794.788	+	458.871i	−2.43800	+	1.40758i
$327$	−167.098	−	167.055i	−0.511003	−	0.510872i
$328$	−180.021	+	180.021i	−0.548844	+	0.548844i
$329$	39.9805	−	163.742i	0.121521	−	0.497696i
$330$	138.474	+	30.5448i	0.419618	+	0.0925599i
$331$	129.187	−	223.759i	0.390293	−	0.676008i	−0.602195	−	0.798349i	$-0.705707\pi$
$331$	129.187	−	223.759i	0.390293	−	0.676008i	0.992488	+	0.122341i	$0.0390403\pi$
$332$	−801.208	−	214.683i	−2.41328	−	0.646636i
$333$	−214.492	−	214.383i	−0.644121	−	0.643792i
$334$	172.228	−	298.308i	0.515653	−	0.893136i
$335$	−25.1960	+	1.12364i	−0.0752119	+	0.00335416i
$336$	−896.061	−	856.712i	−2.66685	−	2.54974i
$337$	−62.9036	+	62.9036i	−0.186658	+	0.186658i	−0.794249	−	0.607592i	$-0.792136\pi$
$337$	−62.9036	+	62.9036i	−0.186658	+	0.186658i	0.607592	+	0.794249i	$0.292136\pi$
$338$	155.865	+	581.694i	0.461138	+	1.72099i
$339$	−336.494	−	194.218i	−0.992608	−	0.572913i
$340$	−127.690	+	81.5152i	−0.375559	+	0.239751i
$341$	−8.15956	+	14.1328i	−0.0239283	+	0.0414451i
$342$	11.7496	+	43.8052i	0.0343555	+	0.128085i
$343$	−22.9475	−	342.232i	−0.0669024	−	0.997760i
$344$	1037.40			3.01571
$345$	224.980	−	246.046i	0.652115	−	0.713176i
$346$	−399.472	+	230.635i	−1.15454	+	0.666575i
$347$	74.6257	−	278.507i	0.215060	−	0.802614i	−0.771086	−	0.636731i	$-0.780286\pi$
$347$	74.6257	−	278.507i	0.215060	−	0.802614i	0.986146	−	0.165882i	$-0.0530472\pi$
$348$	−333.243	−	333.157i	−0.957594	−	0.957349i
$349$	412.563			1.18213			0.591065	−	0.806624i	$-0.298708\pi$
$349$	412.563			1.18213			0.591065	+	0.806624i	$0.298708\pi$
$350$	−628.789	+	246.238i	−1.79654	+	0.703538i
$351$	−97.1104	+	0.0372810i	−0.276668	+	0.000106214i
$352$	77.0076	+	287.396i	0.218771	+	0.816466i
$353$	−174.011	+	649.418i	−0.492949	+	1.83971i	0.0482767	+	0.998834i	$0.484627\pi$
$353$	−174.011	+	649.418i	−0.492949	+	1.83971i	−0.541226	+	0.840877i	$0.682040\pi$
$354$	765.903	+	442.063i	2.16357	+	1.24877i
$355$	181.957	+	575.221i	0.512555	+	1.62034i
$356$	−686.703			−1.92894
$357$	28.0699	−	51.2410i	0.0786271	−	0.143532i
$358$	−165.839	−	165.839i	−0.463237	−	0.463237i
$359$	−117.727	+	203.909i	−0.327930	+	0.567992i	−0.982101	−	0.188355i	$-0.939684\pi$
$359$	−117.727	+	203.909i	−0.327930	+	0.567992i	0.654171	+	0.756347i	$0.273018\pi$
$360$	−53.6089	−	1195.23i	−0.148914	−	3.32007i
$361$	179.647	+	311.158i	0.497638	+	0.861934i
$362$	6.32928	+	23.6212i	0.0174842	+	0.0652519i
$363$	−333.250	−	89.2484i	−0.918045	−	0.245863i
$364$	−189.498	+	198.151i	−0.520599	+	0.544371i
$365$	−512.866	+	22.8718i	−1.40511	+	0.0626625i
$366$	−0.132849	−	1038.14i	−0.000362976	−	2.83646i
$367$	−76.2977	+	284.747i	−0.207896	+	0.775878i	0.780652	+	0.624967i	$0.214887\pi$
$367$	−76.2977	+	284.747i	−0.207896	+	0.775878i	−0.988547	+	0.150911i	$0.951779\pi$
$368$	1267.41	+	339.601i	3.44404	+	0.922829i
$369$	74.6231	−	43.1091i	0.202231	−	0.116827i
$370$	−479.727	−	438.766i	−1.29656	−	1.18585i
$371$	278.199	+	266.050i	0.749862	+	0.717117i
$372$	210.215	+	56.2981i	0.565094	+	0.151339i
$373$	−523.121	+	140.170i	−1.40247	+	0.375791i	−0.879231	−	0.476396i	$-0.841943\pi$
$373$	−523.121	+	140.170i	−1.40247	+	0.375791i	−0.523238	+	0.852186i	$0.675276\pi$
$374$	−22.7776	+	13.1507i	−0.0609028	+	0.0351622i
$375$	−346.874	−	142.491i	−0.924996	−	0.379977i
$376$	554.423	+	320.096i	1.47453	+	0.851320i
$377$	−36.6821	+	36.6821i	−0.0973000	+	0.0973000i
$378$	378.897	+	623.158i	1.00237	+	1.64857i
$379$			459.859i			1.21335i	0.794950	+	0.606675i	$0.207497\pi$
$379$			459.859i			1.21335i	−0.794950	+	0.606675i	$0.792503\pi$
$380$	21.4461	+	67.7975i	0.0564370	+	0.178415i
$381$	495.998	+	286.280i	1.30183	+	0.751391i
$382$	114.841	+	30.7716i	0.300632	+	0.0805540i
$383$	426.954	−	114.402i	1.11476	−	0.298700i	0.346000	−	0.938234i	$-0.387540\pi$
$383$	426.954	−	114.402i	1.11476	−	0.298700i	0.768762	+	0.639535i	$0.220873\pi$
$384$	1068.76	−	617.231i	2.78323	−	1.60737i
$385$	−81.1556	+	27.6785i	−0.210794	+	0.0718922i
$386$			731.250i			1.89443i
$387$	−339.226	−	90.8024i	−0.876554	−	0.234632i
$388$	1189.46	+	318.715i	3.06562	+	0.821432i
$389$	147.618	+	255.681i	0.379480	+	0.657278i	0.990987	−	0.133961i	$-0.0427696\pi$
$389$	147.618	+	255.681i	0.379480	+	0.657278i	−0.611507	+	0.791239i	$0.709436\pi$
$390$	−207.974	+	9.30148i	−0.533266	+	0.0238499i
$391$			61.8382i			0.158154i
$392$	1272.18	+	280.698i	3.24535	+	0.716067i
$393$	−663.455	−	177.681i	−1.68818	−	0.452115i
$394$	526.417	+	303.927i	1.33608	+	0.771389i
$395$	52.9115	+	11.6784i	0.133953	+	0.0295656i
$396$	−0.0614539	−	240.115i	−0.000155187	−	0.606350i
$397$	278.785	−	74.7001i	0.702229	−	0.188162i	0.110000	−	0.993932i	$-0.464915\pi$
$397$	278.785	−	74.7001i	0.702229	−	0.188162i	0.592229	+	0.805770i	$0.298248\pi$
$398$	−726.533	−	726.533i	−1.82546	−	1.82546i
$399$	−19.8225	−	18.9520i	−0.0496803	−	0.0474987i
$400$	−131.373	−	1469.99i	−0.328431	−	3.67497i
$401$	−424.590	−	245.137i	−1.05883	−	0.611315i	−0.133720	−	0.991019i	$-0.542692\pi$
$401$	−424.590	−	245.137i	−1.05883	−	0.611315i	−0.925108	+	0.379705i	$0.876026\pi$
$402$	15.1205	+	56.4016i	0.0376132	+	0.140303i
$403$	6.20084	−	23.1419i	0.0153867	−	0.0574239i
$404$	−1265.47	−	730.618i	−3.13234	−	1.80846i
$405$	−87.0865	+	395.526i	−0.215028	+	0.976608i
$406$	378.477	+	92.4118i	0.932209	+	0.227615i
$407$	−58.3718	−	58.3718i	−0.143420	−	0.143420i
$408$	156.935	+	156.895i	0.384645	+	0.384547i
$409$	−291.419	−	504.753i	−0.712516	−	1.23411i	−0.963910	−	0.266229i	$-0.914222\pi$
$409$	−291.419	−	504.753i	−0.712516	−	1.23411i	0.251394	−	0.967885i	$-0.419111\pi$
$410$	155.723	−	99.4111i	0.379813	−	0.242466i
$411$	135.388	−	0.0173253i	0.329410	−	4.21539e-5i
$412$	37.3081	+	37.3081i	0.0905537	+	0.0905537i
$413$	−534.602	+	11.9330i	−1.29444	+	0.0288934i
$414$	−668.587	−	385.781i	−1.61494	−	0.931838i
$415$	337.971	+	175.536i	0.814388	+	0.422978i
$416$	−218.406	−	378.291i	−0.525015	−	0.909352i
$417$	−42.8068	−	159.676i	−0.102654	−	0.382915i
$418$	3.19529	+	11.9250i	0.00764423	+	0.0285287i
$419$		−	35.2066i		−	0.0840252i	−0.999117	−	0.0420126i	$-0.986623\pi$
$419$		−	35.2066i		−	0.0840252i	0.999117	−	0.0420126i	$-0.0133770\pi$
$420$	636.757	+	949.759i	1.51609	+	2.26133i
$421$	−219.332			−0.520979			−0.260490	−	0.965477i	$-0.583884\pi$
$421$	−219.332			−0.520979			−0.260490	+	0.965477i	$0.583884\pi$
$422$	1356.13	−	363.374i	3.21358	−	0.861075i
$423$	−153.276	−	153.198i	−0.362356	−	0.362170i
$424$	−1266.19	+	731.033i	−2.98629	+	1.72413i
$425$	65.3152	−	23.9110i	0.153683	−	0.0562611i
$426$	1209.60	−	698.570i	2.83944	−	1.63983i
$427$	325.928	+	536.507i	0.763297	+	1.25646i
$428$	1104.72	−	1104.72i	2.58112	−	2.58112i
$429$	−26.4343	+	0.00338274i	−0.0616184	+	7.88518e-6i
$430$	−735.129	−	162.255i	−1.70960	−	0.377336i
$431$	98.9389	−	57.1224i	0.229557	−	0.132535i	−0.380811	−	0.924653i	$-0.624355\pi$
$431$	98.9389	−	57.1224i	0.229557	−	0.132535i	0.610368	+	0.792118i	$0.291022\pi$
$432$	−1539.44	+	413.126i	−3.56353	+	0.956310i
$433$	19.7022	−	19.7022i	0.0455017	−	0.0455017i	−0.683990	−	0.729492i	$-0.739757\pi$
$433$	19.7022	−	19.7022i	0.0455017	−	0.0455017i	0.729492	+	0.683990i	$0.239757\pi$
$434$	−172.715	+	50.4356i	−0.397960	+	0.116211i
$435$	116.439	+	182.345i	0.267675	+	0.419184i
$436$	−428.856	+	742.800i	−0.983614	+	1.70367i
$437$	28.0373	+	7.51258i	0.0641586	+	0.0171913i
$438$	307.779	+	1148.06i	0.702691	+	2.62114i
$439$	−67.2260	+	116.439i	−0.153134	+	0.265237i	−0.932378	−	0.361484i	$-0.882270\pi$
$439$	−67.2260	+	116.439i	−0.153134	+	0.265237i	0.779244	+	0.626721i	$0.215603\pi$
$440$	−14.5095	−	325.355i	−0.0329762	−	0.739442i
$441$	−391.428	−	203.139i	−0.887591	−	0.460633i
$442$	27.3036	−	27.3036i	0.0617730	−	0.0617730i
$443$	−88.9837	−	332.092i	−0.200866	−	0.749643i	−0.990670	−	0.136283i	$-0.956484\pi$
$443$	−88.9837	−	332.092i	−0.200866	−	0.749643i	0.789804	−	0.613360i	$-0.210182\pi$
$444$	−550.301	+	953.430i	−1.23942	+	2.14737i
$445$	307.878	+	67.9534i	0.691860	+	0.152704i
$446$	505.899	−	876.242i	1.13430	−	1.96467i
$447$	−294.666	−	78.9152i	−0.659209	−	0.176544i
$448$	−782.118	+	1427.31i	−1.74580	+	3.18595i
$449$	439.282			0.978357			0.489178	−	0.872184i	$-0.337297\pi$
$449$	439.282			0.978357			0.489178	+	0.872184i	$0.337297\pi$
$450$	−148.950	+	855.351i	−0.331000	+	1.90078i
$451$	20.3160	−	11.7295i	0.0450467	−	0.0260077i
$452$	−365.024	+	1362.29i	−0.807575	+	3.01391i
$453$	391.075	−	391.175i	0.863300	−	0.863521i
$454$	1084.34			2.38841
$455$	104.568	−	70.0874i	0.229820	−	0.154038i
$456$	90.2017	−	52.0934i	0.197811	−	0.114240i
$457$	−18.6898	−	69.7512i	−0.0408966	−	0.152628i	0.942458	−	0.334324i	$-0.108508\pi$
$457$	−18.6898	−	69.7512i	−0.0408966	−	0.152628i	−0.983355	+	0.181696i	$0.941841\pi$
$458$	−96.2488	+	359.205i	−0.210150	+	0.784291i
$459$	−37.5844	−	65.0403i	−0.0818831	−	0.141700i
$460$	−1074.02	−	557.827i	−2.33483	−	1.21267i
$461$	83.9387			0.182080			0.0910399	−	0.995847i	$-0.470981\pi$
$461$	83.9387			0.182080			0.0910399	+	0.995847i	$0.470981\pi$
$462$	103.096	+	169.656i	0.223150	+	0.367220i
$463$	227.307	+	227.307i	0.490944	+	0.490944i	0.908604	−	0.417659i	$-0.137149\pi$
$463$	227.307	+	227.307i	0.490944	+	0.490944i	−0.417659	+	0.908604i	$0.637149\pi$
$464$	−425.733	+	737.392i	−0.917529	+	1.58921i
$465$	−88.6772	−	46.0429i	−0.190704	−	0.0990169i
$466$	−353.724	−	612.668i	−0.759065	−	1.31474i
$467$	−112.749	−	420.786i	−0.241433	−	0.901040i	−0.975143	−	0.221577i	$-0.928879\pi$
$467$	−112.749	−	420.786i	−0.241433	−	0.901040i	0.733710	−	0.679463i	$-0.237787\pi$
$468$	91.3245	+	340.479i	0.195138	+	0.727519i
$469$	−25.5185	−	24.4042i	−0.0544104	−	0.0520345i
$470$	−342.813	−	313.542i	−0.729390	−	0.667111i
$471$	−242.706	+	0.0310586i	−0.515300	+	6.59419e-5i
$472$	525.668	−	1961.82i	1.11370	−	4.15639i
$473$	−92.3341	−	24.7408i	−0.195209	−	0.0523062i
$474$	−0.0160539	−	125.452i	−3.38689e−5	−	0.264668i
$475$	−2.90619	−	32.5187i	−0.00611830	−	0.0684604i
$476$	−206.034	−	50.3069i	−0.432845	−	0.105687i
$477$	478.024	−	128.217i	1.00215	−	0.268799i
$478$	803.464	−	215.288i	1.68089	−	0.450392i
$479$	138.709	−	80.0837i	0.289580	−	0.167189i	−0.348172	−	0.937431i	$-0.613198\pi$
$479$	138.709	−	80.0837i	0.289580	−	0.167189i	0.637753	+	0.770241i	$0.279864\pi$
$480$	−1736.83	+	549.648i	−3.61840	+	1.14510i
$481$	104.956	+	60.5962i	0.218203	+	0.125980i
$482$	1047.41	−	1047.41i	2.17306	−	2.17306i
$483$	466.640	−	10.4757i	0.966128	−	0.0216888i
$484$			1252.34i			2.58748i
$485$	−501.747	−	260.598i	−1.03453	−	0.537316i
$486$	937.681	−	0.599965i	1.92938	−	0.00123450i
$487$	−484.246	−	129.753i	−0.994345	−	0.266434i	−0.275270	−	0.961367i	$-0.588767\pi$
$487$	−484.246	−	129.753i	−0.994345	−	0.266434i	−0.719075	+	0.694933i	$0.755434\pi$
$488$	−2303.06	+	617.103i	−4.71939	+	1.26456i
$489$	−356.829	−	617.863i	−0.729711	−	1.26352i
$490$	−857.593	−	397.884i	−1.75019	−	0.812008i
$491$			47.0322i			0.0957886i	0.998852	+	0.0478943i	$0.0152511\pi$
$491$			47.0322i			0.0957886i	−0.998852	+	0.0478943i	$0.984749\pi$
$492$	−221.237	−	221.180i	−0.449669	−	0.449553i
$493$	−38.7610	−	10.3860i	−0.0786228	−	0.0210669i
$494$	−9.06237	−	15.6965i	−0.0183449	−	0.0317743i
$495$	−23.7333	+	107.660i	−0.0479460	+	0.217494i
$496$		−	393.236i		−	0.792814i
$497$	−405.891	+	740.722i	−0.816682	+	1.49039i
$498$	228.102	−	851.724i	0.458036	−	1.71029i
$499$	208.153	+	120.177i	0.417141	+	0.240837i	0.693853	−	0.720116i	$-0.255912\pi$
$499$	208.153	+	120.177i	0.417141	+	0.240837i	−0.276712	+	0.960953i	$0.589245\pi$
$500$	−173.901	+	1350.11i	−0.347801	+	2.70022i
$501$	231.936	+	133.869i	0.462947	+	0.267204i
$502$	−786.401	+	210.716i	−1.56654	+	0.419752i
$503$	428.825	+	428.825i	0.852535	+	0.852535i	0.990445	−	0.137910i	$-0.0440385\pi$
$503$	428.825	+	428.825i	0.852535	+	0.852535i	−0.137910	+	0.990445i	$0.544038\pi$
$504$	1157.37	−	1210.84i	2.29636	−	2.40245i
$505$	495.063	+	452.792i	0.980323	+	0.896619i
$506$	−181.968	−	105.059i	−0.359621	−	0.207627i
$507$	−452.223	+	121.235i	−0.891958	+	0.239122i
$508$	538.051	−	2008.04i	1.05916	−	3.95283i
$509$	505.629	+	291.925i	0.993377	+	0.573527i	0.906282	−	0.422673i	$-0.138908\pi$
$509$	505.629	+	291.925i	0.993377	+	0.573527i	0.0870951	+	0.996200i	$0.472242\pi$
$510$	−86.6690	−	135.725i	−0.169939	−	0.266127i
$511$	−519.430	−	496.748i	−1.01650	−	0.972110i
$512$	−630.301	−	630.301i	−1.23106	−	1.23106i
$513$	−34.0552	+	9.13908i	−0.0663844	+	0.0178150i
$514$	402.166	+	696.573i	0.782425	+	1.35520i
$515$	−13.0349	−	20.4187i	−0.0253105	−	0.0396479i
$516$	0.163128	+	1274.75i	0.000316139	+	2.47045i
$517$	−41.7125	−	41.7125i	−0.0806818	−	0.0806818i
$518$	−20.3109	−	909.938i	−0.0392102	−	1.75664i
$519$	−179.347	−	310.546i	−0.345563	−	0.598355i
$520$	144.202	+	455.867i	0.277312	+	0.876666i
$521$	−251.052	−	434.835i	−0.481866	−	0.834616i	0.517917	−	0.855431i	$-0.326707\pi$
$521$	−251.052	−	434.835i	−0.481866	−	0.834616i	−0.999783	+	0.0208143i	$0.993374\pi$
$522$	354.105	−	354.286i	0.678362	−	0.678709i
$523$	194.977	+	727.663i	0.372805	+	1.39133i	0.856526	+	0.516104i	$0.172618\pi$
$523$	194.977	+	727.663i	0.372805	+	1.39133i	−0.483721	+	0.875222i	$0.660715\pi$
$524$			2493.24i			4.75808i
$525$	−191.500	−	488.828i	−0.364763	−	0.931101i
$526$	725.804			1.37986
$527$	17.9011	−	4.79659i	0.0339680	−	0.00910170i
$528$	−419.078	+	112.349i	−0.793709	+	0.212783i
$529$	30.2942	−	17.4904i	0.0572670	−	0.0330631i
$530$	1011.59	−	319.990i	1.90865	−	0.603756i
$531$	−343.606	+	595.495i	−0.647092	+	1.12146i
$532$	−47.8397	+	87.3040i	−0.0899243	+	0.164105i
$533$	−24.3529	+	24.3529i	−0.0456903	+	0.0456903i
$534$	−0.0934131	−	729.973i	−0.000174931	−	1.36699i
$535$	−604.611	+	385.974i	−1.13011	+	0.721446i
$536$	116.144	−	67.0559i	0.216687	−	0.125104i
$537$	128.915	−	128.948i	0.240065	−	0.240126i
$538$	360.173	−	360.173i	0.669466	−	0.669466i
$539$	−106.536	−	55.3235i	−0.197655	−	0.102641i
$540$	1468.68	−	66.0623i	2.71977	−	0.122338i
$541$	−235.346	+	407.630i	−0.435019	+	0.753476i	−0.997297	−	0.0734727i	$-0.976592\pi$
$541$	−235.346	+	407.630i	−0.435019	+	0.753476i	0.562278	+	0.826948i	$0.309925\pi$
$542$	128.451	+	34.4184i	0.236995	+	0.0635026i
$543$	−18.3637	+	4.92305i	−0.0338189	+	0.00906639i
$544$	168.946	−	292.623i	0.310562	−	0.537909i
$545$	265.779	−	290.591i	0.487667	−	0.533194i
$546$	−210.663	−	201.412i	−0.385829	−	0.368886i
$547$	372.080	−	372.080i	0.680219	−	0.680219i	−0.279831	−	0.960049i	$-0.590278\pi$
$547$	372.080	−	372.080i	0.680219	−	0.680219i	0.960049	+	0.279831i	$0.0902783\pi$
$548$	−127.200	−	474.716i	−0.232116	−	0.866269i
$549$	807.105	−	0.206567i	1.47014	−	0.000376261i
$550$	−40.6051	+	232.824i	−0.0738275	+	0.423315i
$551$	−9.41798	+	16.3124i	−0.0170925	+	0.0296051i
$552$	−458.623	+	1712.48i	−0.830839	+	3.10232i
$553$	39.3861	+	64.8331i	0.0712226	+	0.117239i
$554$	−1991.81			−3.59533
$555$	341.071	−	373.007i	0.614542	−	0.672085i
$556$	−519.697	+	300.047i	−0.934708	+	0.539654i
$557$	93.0408	−	347.233i	0.167039	−	0.623399i	−0.830732	−	0.556672i	$-0.812078\pi$
$557$	93.0408	−	347.233i	0.167039	−	0.623399i	0.997771	−	0.0667262i	$-0.0212554\pi$
$558$	−59.8170	+	223.469i	−0.107199	+	0.400482i
$559$	140.338			0.251052
$560$	1360.10	−	1555.39i	2.42875	−	2.77748i
$561$	−10.2263	−	17.7072i	−0.0182286	−	0.0315636i
$562$	−338.676	−	1263.96i	−0.602626	−	2.24903i
$563$	−53.8708	+	201.049i	−0.0956853	+	0.357102i	−0.997122	−	0.0758076i	$-0.975847\pi$
$563$	−53.8708	+	201.049i	−0.0956853	+	0.357102i	0.901437	+	0.432910i	$0.142513\pi$
$564$	−393.245	+	681.322i	−0.697243	+	1.20802i
$565$	298.462	−	574.650i	0.528252	−	1.01708i
$566$	122.231			0.215956
$567$	−484.437	+	294.635i	−0.854386	+	0.519639i
$568$	−2268.47	−	2268.47i	−3.99378	−	3.99378i
$569$	217.518	−	376.753i	0.382282	−	0.662132i	−0.609106	−	0.793089i	$-0.708472\pi$
$569$	217.518	−	376.753i	0.382282	−	0.662132i	0.991388	+	0.130957i	$0.0418049\pi$
$570$	−72.0667	+	22.8067i	−0.126433	+	0.0400117i
$571$	318.278	+	551.273i	0.557404	+	0.965452i	0.997712	+	0.0676055i	$0.0215359\pi$
$571$	318.278	+	551.273i	0.557404	+	0.965452i	−0.440308	+	0.897847i	$0.645131\pi$
$572$	24.8356	+	92.6877i	0.0434189	+	0.162041i
$573$	−23.9120	+	89.2865i	−0.0417312	+	0.155823i
$574$	251.267	+	61.3514i	0.437748	+	0.106884i
$575$	426.329	+	356.378i	0.741442	+	0.619789i
$576$	1046.75	+	1811.94i	1.81727	+	3.14574i
$577$	−121.851	+	454.755i	−0.211181	+	0.788136i	0.776296	+	0.630369i	$0.217096\pi$
$577$	−121.851	+	454.755i	−0.211181	+	0.788136i	−0.987476	+	0.157768i	$0.949570\pi$
$578$	−1048.33	−	280.900i	−1.81373	−	0.485987i
$579$	−568.510	+	0.0727510i	−0.981883	+	0.000125649i
$580$	530.041	−	579.523i	0.913863	−	0.999178i
$581$	149.454	+	511.798i	0.257235	+	0.880891i
$582$	−338.637	+	1264.46i	−0.581850	+	2.17261i
$583$	130.131	−	34.8685i	0.223209	−	0.0598088i
$584$	2364.12	−	1364.93i	4.04815	−	2.33720i
$585$	−7.25213	−	161.688i	−0.0123968	−	0.276390i
$586$	651.359	+	376.062i	1.11153	+	0.641744i
$587$	134.856	−	134.856i	0.229738	−	0.229738i	−0.582845	−	0.812583i	$-0.698061\pi$
$587$	134.856	−	134.856i	0.229738	−	0.229738i	0.812583	+	0.582845i	$0.198061\pi$
$588$	−344.720	+	1563.29i	−0.586259	+	2.65865i
$589$		−	8.69907i		−	0.0147692i
$590$	−679.338	+	1307.97i	−1.15142	+	2.21691i
$591$	−236.236	+	409.293i	−0.399722	+	0.692544i
$592$	1921.40	+	514.838i	3.24561	+	0.869658i
$593$	203.880	−	54.6296i	0.343812	−	0.0921241i	−0.0827813	−	0.996568i	$-0.526380\pi$
$593$	203.880	−	54.6296i	0.343812	−	0.0921241i	0.426593	+	0.904444i	$0.359714\pi$
$594$	255.245	−	0.0979894i	0.429705	−	0.000164965i
$595$	87.3957	+	42.9431i	0.146884	+	0.0721732i
$596$			1107.34i			1.85796i
$597$	564.771	−	564.915i	0.946014	−	0.946256i
$598$	297.966	+	79.8397i	0.498271	+	0.133511i
$599$	−33.2136	−	57.5277i	−0.0554484	−	0.0960395i	0.836969	−	0.547251i	$-0.184326\pi$
$599$	−33.2136	−	57.5277i	−0.0554484	−	0.0960395i	−0.892417	+	0.451211i	$0.850992\pi$
$600$	1986.11	−	177.754i	3.31018	−	0.296257i
$601$		−	1104.49i		−	1.83776i	−0.394539	−	0.918879i	$-0.629096\pi$
$601$		−	1104.49i		−	1.83776i	0.394539	−	0.918879i	$-0.370904\pi$
$602$	−547.213	−	900.761i	−0.908992	−	1.49628i
$603$	−43.8480	+	11.7611i	−0.0727163	+	0.0195042i
$604$	−1738.89	−	1003.95i	−2.87895	−	1.66217i
$605$	123.927	−	561.477i	0.204838	−	0.928061i
$606$	776.484	−	1345.31i	1.28133	−	2.21998i
$607$	144.311	−	38.6680i	0.237745	−	0.0637035i	−0.137979	−	0.990435i	$-0.544061\pi$
$607$	144.311	−	38.6680i	0.237745	−	0.0637035i	0.375724	+	0.926732i	$0.377394\pi$
$608$	−112.150	−	112.150i	−0.184457	−	0.184457i
$609$	−71.8079	+	294.256i	−0.117911	+	0.483179i
$610$	1728.52	−	77.0853i	2.83364	−	0.126369i
$611$	75.0014	+	43.3021i	0.122752	+	0.0708709i
$612$	−192.767	+	192.866i	−0.314979	+	0.315140i
$613$	−170.287	+	635.521i	−0.277793	+	1.03674i	0.676153	+	0.736761i	$0.263646\pi$
$613$	−170.287	+	635.521i	−0.277793	+	1.03674i	−0.953946	+	0.299978i	$0.903021\pi$
$614$	1107.31	+	639.306i	1.80344	+	1.04121i
$615$	77.3027	+	121.057i	0.125695	+	0.196841i
$616$	315.130	−	329.519i	0.511574	−	0.534934i
$617$	382.686	+	382.686i	0.620237	+	0.620237i	0.945592	−	0.325355i	$-0.105484\pi$
$617$	382.686	+	382.686i	0.620237	+	0.620237i	−0.325355	+	0.945592i	$0.605484\pi$
$618$	−39.6539	+	39.6641i	−0.0641649	+	0.0641813i
$619$	24.7022	+	42.7855i	0.0399067	+	0.0691204i	0.885289	−	0.465042i	$-0.153961\pi$
$619$	24.7022	+	42.7855i	0.0399067	+	0.0691204i	−0.845382	+	0.534162i	$0.820627\pi$
$620$	−78.1732	+	354.181i	−0.126086	+	0.571259i
$621$	299.859	−	519.831i	0.482864	−	0.837088i
$622$	1038.88	+	1038.88i	1.67023	+	1.67023i
$623$	229.177	+	377.246i	0.367860	+	0.605531i
$624$	551.598	−	318.559i	0.883971	−	0.510512i
$625$	211.569	−	588.102i	0.338510	−	0.940963i
$626$	−633.531	−	1097.31i	−1.01203	−	1.75289i
$627$	−9.27076	+	2.48536i	−0.0147859	+	0.00396390i
$628$	228.028	+	851.012i	0.363102	+	1.35511i
$629$			93.7471i			0.149042i
$630$	−1009.52	+	677.010i	−1.60241	+	1.07462i
$631$	−961.487			−1.52375			−0.761875	−	0.647724i	$-0.775721\pi$
$631$	−961.487			−1.52375			−0.761875	+	0.647724i	$0.775721\pi$
$632$	−278.309	+	74.5726i	−0.440362	+	0.117995i
$633$	282.640	+	1054.29i	0.446509	+	1.66554i
$634$	−708.909	+	409.289i	−1.11815	+	0.645566i
$635$	−439.939	+	847.043i	−0.692817	+	1.33393i
$636$	−898.488	−	1555.77i	−1.41272	−	2.44617i
$637$	172.098	+	37.9724i	0.270170	+	0.0596113i
$638$	96.4151	−	96.4151i	0.151121	−	0.151121i
$639$	543.223	+	940.334i	0.850115	+	1.47157i
$640$	1106.83	+	1733.81i	1.72943	+	2.70907i
$641$	383.389	−	221.349i	0.598110	−	0.345319i	−0.170188	−	0.985412i	$-0.554437\pi$
$641$	383.389	−	221.349i	0.598110	−	0.345319i	0.768298	+	0.640093i	$0.221104\pi$
$642$	1174.48	+	1174.18i	1.82941	+	1.82894i
$643$	−810.278	+	810.278i	−1.26015	+	1.26015i	−0.309134	+	0.951019i	$0.600039\pi$
$643$	−810.278	+	810.278i	−1.26015	+	1.26015i	−0.951019	+	0.309134i	$0.899961\pi$
$644$	−474.941	−	1626.42i	−0.737487	−	2.52549i
$645$	126.072	−	571.542i	0.195460	−	0.886112i
$646$	7.01010	−	12.1418i	0.0108515	−	0.0187954i
$647$	−735.012	−	196.946i	−1.13603	−	0.304399i	−0.358677	−	0.933462i	$-0.616772\pi$
$647$	−735.012	−	196.946i	−1.13603	−	0.304399i	−0.777354	+	0.629063i	$0.783439\pi$
$648$	−558.450	−	2079.90i	−0.861805	−	3.20973i
$649$	−93.5740	+	162.075i	−0.144182	+	0.249730i
$650$	−30.8855	−	345.592i	−0.0475162	−	0.531680i
$651$	−39.2283	−	134.272i	−0.0602586	−	0.206255i
$652$	−1831.42	+	1831.42i	−2.80893	+	2.80893i
$653$	−144.698	−	540.019i	−0.221589	−	0.826982i	−0.983742	−	0.179585i	$-0.942524\pi$
$653$	−144.698	−	540.019i	−0.221589	−	0.826982i	0.762153	−	0.647396i	$-0.224142\pi$
$654$	−789.664	−	455.778i	−1.20744	−	0.696908i
$655$	246.721	−	1117.82i	0.376673	−	1.70660i
$656$	−282.641	+	489.548i	−0.430855	+	0.746263i
$657$	−892.528	+	239.397i	−1.35849	+	0.364379i
$658$	−14.5142	−	650.243i	−0.0220580	−	0.988211i
$659$	−680.452			−1.03255			−0.516276	−	0.856422i	$-0.672682\pi$
$659$	−680.452			−1.03255			−0.516276	+	0.856422i	$0.672682\pi$
$660$	399.791	−	17.8804i	0.605745	−	0.0270915i
$661$	226.750	−	130.914i	0.343040	−	0.198054i	−0.318575	−	0.947898i	$-0.603204\pi$
$661$	226.750	−	130.914i	0.343040	−	0.198054i	0.661616	+	0.749843i	$0.269871\pi$
$662$	258.044	−	963.034i	0.389795	−	1.45473i
$663$	21.2299	+	21.2245i	0.0320210	+	0.0320128i
$664$	−2025.09			−3.04983
$665$	30.0878	−	34.4080i	0.0452449	−	0.0517414i
$666$	−1013.58	−	584.847i	−1.52190	−	0.878148i
$667$	−82.9727	−	309.658i	−0.124397	−	0.464255i
$668$	251.601	−	938.989i	0.376649	−	1.40567i
$669$	681.285	+	393.224i	1.01836	+	0.587778i
$670$	−92.7904	+	29.3519i	−0.138493	+	0.0438089i
$671$	219.701			0.327423
$672$	−2236.79	−	1225.32i	−3.32856	−	1.82339i
$673$	−96.6114	−	96.6114i	−0.143553	−	0.143553i	0.631678	−	0.775231i	$-0.282367\pi$
$673$	−96.6114	−	96.6114i	−0.143553	−	0.143553i	−0.775231	+	0.631678i	$0.782367\pi$
$674$	−171.636	+	297.283i	−0.254653	+	0.441072i
$675$	−665.007	−	115.716i	−0.985196	−	0.171431i
$676$	849.775	+	1471.85i	1.25706	+	2.17730i
$677$	−106.294	−	396.695i	−0.157008	−	0.585961i	−0.998925	−	0.0463543i	$-0.985240\pi$
$677$	−106.294	−	396.695i	−0.157008	−	0.585961i	0.841917	−	0.539607i	$-0.181427\pi$
$678$	−1448.18	−	387.840i	−2.13596	−	0.572035i
$679$	−221.877	−	759.807i	−0.326770	−	1.11901i
$680$	−249.614	+	272.917i	−0.367080	+	0.401349i
$681$	0.107879	+	843.020i	0.000158413	+	1.23791i
$682$	−16.2983	+	60.8260i	−0.0238978	+	0.0891877i
$683$	−302.986	−	81.1849i	−0.443611	−	0.118865i	0.0300976	−	0.999547i	$-0.490418\pi$
$683$	−302.986	−	81.1849i	−0.443611	−	0.118865i	−0.473708	+	0.880682i	$0.657085\pi$
$684$	64.0262	+	110.831i	0.0936055	+	0.162034i
$685$	10.0529	+	225.422i	0.0146758	+	0.329083i
$686$	−427.326	−	1252.68i	−0.622925	−	1.82606i
$687$	−279.274	−	74.7929i	−0.406512	−	0.108869i
$688$	2224.94	−	596.171i	3.23392	−	0.866527i
$689$	−171.288	+	98.8929i	−0.248603	+	0.143531i
$690$	592.831	−	1141.77i	0.859175	−	1.65475i
$691$	−289.130	−	166.930i	−0.418423	−	0.241577i	0.275979	−	0.961164i	$-0.410998\pi$
$691$	−289.130	−	166.930i	−0.418423	−	0.241577i	−0.694402	+	0.719587i	$0.744331\pi$
$692$	−920.499	+	920.499i	−1.33020	+	1.33020i
$693$	−131.888	+	80.1685i	−0.190315	+	0.115683i
$694$		−	1112.60i		−	1.60318i
$695$	262.694	−	83.0967i	0.377977	−	0.119564i
$696$	−996.380	−	575.090i	−1.43158	−	0.826279i
$697$	−25.7331	−	6.89517i	−0.0369198	−	0.00989264i
$698$	1537.74	−	412.036i	2.20307	−	0.590310i
$699$	476.284	−	275.064i	0.681379	−	0.393511i
$700$	−1534.22	+	1130.53i	−2.19175	+	1.61505i
$701$		−	396.476i		−	0.565586i	−0.959181	−	0.282793i	$-0.908739\pi$
$701$		−	396.476i		−	0.565586i	0.959181	−	0.282793i	$-0.0912609\pi$
$702$	−361.921	+	97.1254i	−0.515557	+	0.138355i
$703$	42.5048	+	11.3891i	0.0604620	+	0.0162007i
$704$	284.807	+	493.300i	0.404555	+	0.700710i
$705$	243.729	−	266.551i	0.345715	−	0.378087i
$706$			2594.35i			3.67472i
$707$	20.9602	+	939.028i	0.0296467	+	1.32819i
$708$	2410.75	+	645.628i	3.40502	+	0.911905i
$709$	−669.988	−	386.818i	−0.944977	−	0.545582i	−0.0534597	−	0.998570i	$-0.517025\pi$
$709$	−669.988	−	386.818i	−0.944977	−	0.545582i	−0.891517	+	0.452988i	$0.850358\pi$
$710$	1252.69	+	1962.29i	1.76435	+	2.76379i
$711$	97.5330	−	0.0249622i	0.137177	−	3.51085e-5i
$712$	−1619.40	+	433.918i	−2.27444	+	0.609435i
$713$	104.691	+	104.691i	0.146832	+	0.146832i
$714$	53.4489	−	219.024i	0.0748584	−	0.306756i
$715$	−1.96283	−	44.0134i	−0.00274521	−	0.0615573i
$716$	−573.211	−	330.944i	−0.800574	−	0.462212i
$717$	167.455	+	624.632i	0.233550	+	0.871174i
$718$	−235.153	+	877.604i	−0.327511	+	1.22229i
$719$	−1103.74	−	637.243i	−1.53510	−	0.886290i	−0.999115	−	0.0420625i	$-0.986607\pi$
$719$	−1103.74	−	637.243i	−1.53510	−	0.886290i	−0.535985	−	0.844228i	$-0.680060\pi$
$720$	−801.844	−	2532.62i	−1.11367	−	3.51752i
$721$	8.04448	−	32.9466i	0.0111574	−	0.0456956i
$722$	980.357	+	980.357i	1.35784	+	1.35784i
$723$	814.416	+	814.208i	1.12644	+	1.12615i
$724$	34.5073	+	59.7684i	0.0476620	+	0.0825531i
$725$	−294.987	+	207.374i	−0.406879	+	0.286033i
$726$	−1331.25	+	0.170358i	−1.83368	+	0.000234652i
$727$	−846.968	−	846.968i	−1.16502	−	1.16502i	−0.983362	−	0.181656i	$-0.941854\pi$
$727$	−846.968	−	846.968i	−1.16502	−	1.16502i	−0.181656	−	0.983362i	$-0.558146\pi$
$728$	−321.671	+	587.027i	−0.441856	+	0.806355i
$729$	0.559731	+	729.000i	0.000767807	+	1.00000i
$730$	−1888.75	+	597.460i	−2.58733	+	0.818439i
$731$	54.2786	+	94.0132i	0.0742525	+	0.128609i
$732$	−758.655	−	2829.89i	−1.03641	−	3.86597i
$733$	−243.099	−	907.256i	−0.331649	−	1.23773i	−0.907457	−	0.420145i	$-0.861979\pi$
$733$	−243.099	−	907.256i	−0.331649	−	1.23773i	0.575808	−	0.817585i	$-0.304688\pi$
$734$			1137.53i			1.54977i
$735$	309.250	−	666.776i	0.420748	−	0.907178i
$736$	2699.38			3.66764
$737$	−11.9366	+	3.19841i	−0.0161962	+	0.00433976i
$738$	235.087	−	235.208i	0.318546	−	0.318710i
$739$	−115.539	+	66.7062i	−0.156344	+	0.0902655i	−0.576131	−	0.817357i	$-0.695438\pi$
$739$	−115.539	+	66.7062i	−0.156344	+	0.0902655i	0.419787	+	0.907623i	$0.362105\pi$
$740$	−1628.23	−	845.670i	−2.20031	−	1.14280i
$741$	12.2023	−	7.04710i	0.0164674	−	0.00951026i
$742$	1302.64	+	713.802i	1.75557	+	0.961998i
$743$	−36.7081	+	36.7081i	−0.0494053	+	0.0494053i	−0.731378	−	0.681973i	$-0.761122\pi$
$743$	−36.7081	+	36.7081i	−0.0494053	+	0.0494053i	0.681973	+	0.731378i	$0.261122\pi$
$744$	531.309	−	0.0679905i	0.714125	−	9.13851e-5i
$745$	109.578	−	496.469i	0.147085	−	0.666401i
$746$	−1809.83	+	1044.91i	−2.42605	+	1.40068i
$747$	662.195	+	177.253i	0.886473	+	0.237287i
$748$	−52.4863	+	52.4863i	−0.0701688	+	0.0701688i
$749$	−975.571	−	238.203i	−1.30250	−	0.318028i
$750$	−1435.21	−	184.675i	−1.91361	−	0.246233i
$751$	359.128	−	622.028i	0.478200	−	0.828266i	−0.521488	−	0.853259i	$-0.674623\pi$
$751$	359.128	−	622.028i	0.478200	−	0.828266i	0.999688	+	0.0249923i	$0.00795613\pi$
$752$	1373.03	+	367.903i	1.82584	+	0.489233i
$753$	−163.899	−	611.367i	−0.217662	−	0.811908i
$754$	−100.089	+	173.360i	−0.132745	+	0.229920i
$755$	680.270	+	622.186i	0.901020	+	0.824087i
$756$	1488.05	+	1421.98i	1.96832	+	1.88092i
$757$	539.096	−	539.096i	0.712148	−	0.712148i	−0.254837	−	0.966984i	$-0.582022\pi$
$757$	539.096	−	539.096i	0.712148	−	0.712148i	0.966984	+	0.254837i	$0.0820217\pi$
$758$	459.272	+	1714.03i	0.605900	+	2.26125i
$759$	81.6604	−	141.482i	0.107589	−	0.186405i
$760$	93.4151	+	146.331i	0.122915	+	0.192540i
$761$	−273.235	+	473.257i	−0.359047	+	0.621888i	−0.987802	−	0.155716i	$-0.950232\pi$
$761$	−273.235	+	473.257i	−0.359047	+	0.621888i	0.628755	+	0.777604i	$0.283565\pi$
$762$	2134.64	+	571.682i	2.80136	+	0.750239i
$763$	551.188	−	12.3032i	0.722395	−	0.0161247i
$764$	335.535			0.439181
$765$	105.511	−	67.3943i	0.137923	−	0.0880972i
$766$	1477.12	−	852.817i	1.92836	−	1.11334i
$767$	71.1114	−	265.391i	0.0927137	−	0.346012i
$768$	1394.49	−	1394.85i	1.81575	−	1.81621i
$769$	457.090			0.594396			0.297198	−	0.954816i	$-0.403948\pi$
$769$	457.090			0.594396			0.297198	+	0.954816i	$0.403948\pi$
$770$	−274.847	+	184.218i	−0.356944	+	0.239244i
$771$	−541.510	+	312.734i	−0.702348	+	0.405621i
$772$	534.127	+	1993.39i	0.691875	+	2.58211i
$773$	−192.739	+	719.311i	−0.249339	+	0.930544i	0.721814	+	0.692087i	$0.243308\pi$
$773$	−192.739	+	719.311i	−0.249339	+	0.930544i	−0.971153	+	0.238457i	$0.923358\pi$
$774$	−1355.08	+	0.346813i	−1.75075	+	0.000448079i
$775$	70.0967	−	151.058i	0.0904474	−	0.194914i
$776$	3006.42			3.87425
$777$	707.430	−	15.8812i	0.910463	−	0.0204392i
$778$	805.568	+	805.568i	1.03543	+	1.03543i
$779$	−6.25252	+	10.8297i	−0.00802634	+	0.0139020i
$780$	−560.143	+	177.266i	−0.718132	+	0.227264i
$781$	147.805	+	256.005i	0.189250	+	0.327791i
$782$	61.7592	+	230.488i	0.0789759	+	0.294742i
$783$	275.475	+	275.264i	0.351820	+	0.351550i
$784$	2889.78	−	129.071i	3.68594	−	0.164631i
$785$	−18.0217	−	404.109i	−0.0229576	−	0.514789i
$786$	−2650.34	+	0.339158i	−3.37193	+	0.000431499i
$787$	152.483	−	569.075i	0.193752	−	0.723094i	−0.798834	−	0.601552i	$-0.794549\pi$
$787$	152.483	−	569.075i	0.193752	−	0.723094i	0.992586	−	0.121542i	$-0.0387840\pi$
$788$	1657.01	+	443.996i	2.10281	+	0.563446i
$789$	0.0722093	+	564.277i	9.15200e−5	+	0.715180i
$790$	208.880	−	9.31522i	0.264405	−	0.0117914i
$791$	870.205	−	254.115i	1.10013	−	0.321258i
$792$	−151.870	−	566.207i	−0.191755	−	0.714907i
$793$	−311.554	+	83.4807i	−0.392881	+	0.105272i
$794$	964.505	−	556.857i	1.21474	−	0.701332i
$795$	248.877	+	786.426i	0.313053	+	0.989216i
$796$	−2511.21	−	1449.85i	−3.15479	−	1.82142i
$797$	−517.339	+	517.339i	−0.649108	+	0.649108i	−0.952778	−	0.303669i	$-0.901788\pi$
$797$	−517.339	+	517.339i	−0.649108	+	0.649108i	0.303669	+	0.952778i	$0.401788\pi$
$798$	−92.8117	−	50.8424i	−0.116305	−	0.0637122i
$799$			66.9918i			0.0838445i
$800$	−1043.77	−	2851.17i	−1.30471	−	3.56396i
$801$	567.518	−	0.145248i	0.708512	−	0.000181333i
$802$	−1827.39	−	489.648i	−2.27854	−	0.610534i
$803$	−242.970	+	65.1037i	−0.302578	+	0.0810756i
$804$	82.4161	+	142.707i	0.102508	+	0.177496i
$805$	51.9923	+	776.190i	0.0645866	+	0.964211i
$806$		−	92.4492i		−	0.114701i
$807$	280.052	+	279.981i	0.347029	+	0.346940i
$808$	−3445.93	−	923.334i	−4.26476	−	1.14274i
$809$	201.098	+	348.312i	0.248576	+	0.430547i	0.963131	−	0.269033i	$-0.0867040\pi$
$809$	201.098	+	348.312i	0.248576	+	0.430547i	−0.714555	+	0.699580i	$0.753371\pi$
$810$	70.4248	+	1561.21i	0.0869442	+	1.92742i
$811$		−	671.468i		−	0.827950i	−0.910288	−	0.413975i	$-0.864140\pi$
$811$		−	671.468i		−	0.827950i	0.910288	−	0.413975i	$-0.135860\pi$
$812$	1099.23	−	24.5361i	1.35373	−	0.0302169i
$813$	−26.7458	+	99.8678i	−0.0328977	+	0.122839i
$814$	−275.865	−	159.271i	−0.338901	−	0.195665i
$815$	1002.33	−	639.874i	1.22986	−	0.785121i
$816$	426.746	+	246.309i	0.522973	+	0.301849i
$817$	49.2196	−	13.1884i	0.0602443	−	0.0161424i
$818$	−1590.31	−	1590.31i	−1.94414	−	1.94414i
$819$	156.567	−	163.800i	0.191168	−	0.200000i
$820$	351.890	−	384.740i	0.429134	−	0.469196i
$821$	804.438	+	464.443i	0.979828	+	0.565704i	0.902218	−	0.431280i	$-0.141938\pi$
$821$	804.438	+	464.443i	0.979828	+	0.565704i	0.0776095	+	0.996984i	$0.475271\pi$
$822$	504.611	−	135.279i	0.613882	−	0.164573i
$823$	−199.399	+	744.166i	−0.242283	+	0.904211i	0.732447	+	0.680824i	$0.238378\pi$
$823$	−199.399	+	744.166i	−0.242283	+	0.904211i	−0.974730	+	0.223387i	$0.928289\pi$
$824$	111.556	+	64.4066i	0.135383	+	0.0781634i
$825$	−181.013	−	31.5453i	−0.219409	−	0.0382367i
$826$	−1980.70	+	578.397i	−2.39794	+	0.700239i
$827$	−587.764	−	587.764i	−0.710718	−	0.710718i	0.255967	−	0.966685i	$-0.417606\pi$
$827$	−587.764	−	587.764i	−0.710718	−	0.710718i	−0.966685	+	0.255967i	$0.917606\pi$
$828$	−2104.36	−	563.284i	−2.54150	−	0.680295i
$829$	286.905	+	496.935i	0.346086	+	0.599439i	0.985550	−	0.169382i	$-0.0541771\pi$
$829$	286.905	+	496.935i	0.346086	+	0.599439i	−0.639464	+	0.768821i	$0.720844\pi$
$830$	1435.03	+	316.733i	1.72895	+	0.381606i
$831$	−0.198162	−	1548.53i	−0.000238463	−	1.86346i
$832$	−591.321	−	591.321i	−0.710722	−	0.710722i
$833$	41.1244	+	129.976i	0.0493691	+	0.156033i
$834$	−319.025	−	552.404i	−0.382524	−	0.662355i
$835$	−205.722	+	396.091i	−0.246374	+	0.474360i
$836$	17.4208	+	30.1736i	0.0208382	+	0.0360929i
$837$	−173.742	−	46.4825i	−0.207577	−	0.0555346i
$838$	−35.1616	−	131.225i	−0.0419589	−	0.156593i
$839$		−	996.548i		−	1.18778i	−0.804546	−	0.593891i	$-0.797591\pi$
$839$		−	996.548i		−	1.18778i	0.804546	−	0.593891i	$-0.202409\pi$
$840$	2101.76	+	1837.39i	2.50209	+	2.18737i
$841$	−632.966			−0.752635
$842$	−817.513	+	219.052i	−0.970918	+	0.260157i
$843$	982.629	−	263.429i	1.16563	−	0.312491i
$844$	3431.40	−	1981.12i	4.06564	−	2.34730i
$845$	−235.341	−	743.984i	−0.278510	−	0.880455i
$846$	−724.307	−	417.932i	−0.856155	−	0.494009i
$847$	687.983	−	417.950i	0.812259	−	0.493448i
$848$	−2295.51	+	2295.51i	−2.70697	+	2.70697i
$849$	0.0121606	+	95.0286i	1.43234e−5	+	0.111930i
$850$	219.568	−	154.355i	0.258315	−	0.181594i
$851$	−648.598	+	374.468i	−0.762160	+	0.440033i
$852$	2787.12	−	2787.83i	3.27127	−	3.27211i
$853$	459.861	−	459.861i	0.539111	−	0.539111i	−0.384157	−	0.923268i	$-0.625508\pi$
$853$	459.861	−	459.861i	0.539111	−	0.539111i	0.923268	+	0.384157i	$0.125508\pi$
$854$	1750.65	+	1674.20i	2.04994	+	1.96042i
$855$	−17.7382	−	56.0260i	−0.0207464	−	0.0655275i
$856$	1907.13	−	3303.24i	2.22795	−	3.85893i
$857$	−900.042	−	241.166i	−1.05022	−	0.281407i	−0.307880	−	0.951425i	$-0.599619\pi$
$857$	−900.042	−	241.166i	−1.05022	−	0.281407i	−0.742344	+	0.670019i	$0.766286\pi$
$858$	−98.5248	+	26.4132i	−0.114831	+	0.0307846i
$859$	−843.166	+	1460.41i	−0.981567	+	1.70012i	−0.325271	+	0.945621i	$0.605456\pi$
$859$	−843.166	+	1460.41i	−0.981567	+	1.70012i	−0.656296	+	0.754503i	$0.727878\pi$
$860$	−2122.48	+	94.6544i	−2.46800	+	0.110063i
$861$	−47.6726	+	195.354i	−0.0553689	+	0.226892i
$862$	311.724	−	311.724i	0.361629	−	0.361629i
$863$	−311.431	−	1162.27i	−0.360870	−	1.34678i	−0.872934	−	0.487838i	$-0.837786\pi$
$863$	−311.431	−	1162.27i	−0.360870	−	1.34678i	0.512065	−	0.858947i	$-0.328881\pi$
$864$	−2839.17	+	1640.65i	−3.28607	+	1.89890i
$865$	503.787	−	321.609i	0.582413	−	0.371803i
$866$	53.7587	−	93.1129i	0.0620771	−	0.107521i
$867$	218.282	−	815.055i	0.251767	−	0.940087i
$868$	−433.981	+	263.644i	−0.499979	+	0.303737i
$869$	26.5493			0.0305516
$870$	616.112	+	563.361i	0.708175	+	0.647541i
$871$	15.7118	−	9.07121i	0.0180388	−	0.0104147i
$872$	−541.976	+	2022.68i	−0.621532	+	2.31959i
$873$	−983.085	−	263.147i	−1.12610	−	0.301429i
$874$	112.006			0.128153
$875$	799.730	−	355.045i	0.913977	−	0.405766i
$876$	1677.58	+	2904.80i	1.91505	+	3.31598i
$877$	58.6896	+	219.033i	0.0669209	+	0.249752i	0.991280	−	0.131771i	$-0.0420663\pi$
$877$	58.6896	+	219.033i	0.0669209	+	0.249752i	−0.924359	+	0.381523i	$0.875400\pi$
$878$	−134.280	+	501.141i	−0.152939	+	0.570776i
$879$	−292.305	+	506.436i	−0.332542	+	0.576150i
$880$	−218.092	−	689.456i	−0.247832	−	0.783473i
$881$	−754.788			−0.856740			−0.428370	−	0.903604i	$-0.640912\pi$
$881$	−754.788			−0.856740			−0.428370	+	0.903604i	$0.640912\pi$
$882$	−1661.84	−	366.229i	−1.88417	−	0.415226i
$883$	−446.257	−	446.257i	−0.505387	−	0.505387i	0.407720	−	0.913107i	$-0.366324\pi$
$883$	−446.257	−	446.257i	−0.505387	−	0.505387i	−0.913107	+	0.407720i	$0.866324\pi$
$884$	54.4865	−	94.3733i	0.0616363	−	0.106757i
$885$	−1016.95	−	528.021i	−1.14910	−	0.596634i
$886$	−663.335	−	1148.93i	−0.748685	−	1.29676i
$887$	117.642	+	439.047i	0.132630	+	0.494980i	0.999996	−	0.00268920i	$-0.000856001\pi$
$887$	117.642	+	439.047i	0.132630	+	0.494980i	−0.867367	+	0.497669i	$0.834189\pi$
$888$	−695.276	+	2596.13i	−0.782969	+	2.92358i
$889$	−1282.70	+	374.569i	−1.44285	+	0.421338i
$890$	1215.41	−	54.2027i	1.36563	−	0.0609019i
$891$	0.101576	+	198.440i	0.000114002	+	0.222716i
$892$	739.048	−	2758.17i	0.828529	−	3.09211i
$893$	30.3740	+	8.13868i	0.0340134	+	0.00911386i
$894$	−1177.12	+	0.150633i	−1.31669	+	0.000168494i
$895$	224.246	+	205.099i	0.250554	+	0.229161i
$896$	−683.080	+	2797.59i	−0.762366	+	3.12231i
$897$	−62.0418	+	231.662i	−0.0691658	+	0.258263i
$898$	1637.33	−	438.721i	1.82331	−	0.488554i
$899$	−83.2051	+	48.0385i	−0.0925529	+	0.0534354i
$900$	218.736	+	2440.49i	0.243040	+	2.71165i
$901$	−132.498	−	76.4976i	−0.147056	−	0.0849030i
$902$	64.0092	−	64.0092i	0.0709636	−	0.0709636i
$903$	700.243	−	425.520i	0.775462	−	0.471230i
$904$			3443.24i			3.80889i
$905$	−9.55663	−	30.2114i	−0.0105598	−	0.0333828i
$906$	1066.97	−	1848.60i	1.17767	−	2.04039i
$907$	868.142	+	232.618i	0.957158	+	0.256470i	0.703397	−	0.710797i	$-0.251666\pi$
$907$	868.142	+	232.618i	0.957158	+	0.256470i	0.253761	+	0.967267i	$0.418332\pi$
$908$	2955.91	−	792.035i	3.25541	−	0.872285i
$909$	1045.99	+	603.543i	1.15070	+	0.663964i
$910$	319.758	−	365.670i	0.351382	−	0.401836i
$911$		−	865.000i		−	0.949506i	−0.880119	−	0.474753i	$-0.842537\pi$
$911$		−	865.000i		−	0.949506i	0.880119	−	0.474753i	$-0.157463\pi$
$912$	163.521	−	163.562i	0.179299	−	0.179345i
$913$	180.243	+	48.2959i	0.197418	+	0.0528981i
$914$	−139.324	−	241.317i	−0.152433	−	0.264022i
$915$	60.1020	+	1343.83i	0.0656852	+	1.46867i
$916$			1049.50i			1.14574i
$917$	1369.68	−	832.081i	1.49365	−	0.907395i
$918$	−205.045	−	204.887i	−0.223360	−	0.223189i
$919$	846.227	+	488.569i	0.920813	+	0.531632i	0.883894	−	0.467687i	$-0.154912\pi$
$919$	846.227	+	488.569i	0.920813	+	0.531632i	0.0369185	+	0.999318i	$0.488246\pi$
$920$	−2885.27	−	636.825i	−3.13617	−	0.692201i
$921$	−496.918	+	860.942i	−0.539542	+	0.934791i
$922$	312.864	−	83.8315i	0.339331	−	0.0909236i
$923$	−306.874	−	306.874i	−0.332475	−	0.332475i
$924$	404.961	+	387.178i	0.438269	+	0.419024i
$925$	646.318	+	540.273i	0.698722	+	0.584078i
$926$	1074.26	+	620.222i	1.16010	+	0.669786i
$927$	−30.8408	−	30.8250i	−0.0332694	−	0.0332524i
$928$	−453.373	+	1692.01i	−0.488549	+	1.82329i
$929$	1273.67	+	735.355i	1.37101	+	0.791555i	0.991056	−	0.133449i	$-0.0426052\pi$
$929$	1273.67	+	735.355i	1.37101	+	0.791555i	0.379958	+	0.925004i	$0.375938\pi$
$930$	−376.509	−	83.0509i	−0.404849	−	0.0893021i
$931$	63.9270	−	2.85527i	0.0686648	−	0.00306689i
$932$	−1411.77	−	1411.77i	−1.51477	−	1.51477i
$933$	−807.577	+	807.784i	−0.865570	+	0.865792i
$934$	−840.497	−	1455.78i	−0.899889	−	1.55865i
$935$	28.7256	−	18.3380i	0.0307226	−	0.0196128i
$936$	430.508	+	745.221i	0.459944	+	0.796176i
$937$	−250.386	−	250.386i	−0.267221	−	0.267221i	0.560758	−	0.827979i	$-0.310510\pi$
$937$	−250.386	−	250.386i	−0.267221	−	0.267221i	−0.827979	+	0.560758i	$0.810510\pi$
$938$	−119.488	−	65.4754i	−0.127386	−	0.0698032i
$939$	853.039	−	492.648i	0.908455	−	0.524652i
$940$	−1163.53	−	604.317i	−1.23780	−	0.642890i
$941$	108.981	+	188.761i	0.115814	+	0.200596i	0.918105	−	0.396337i	$-0.129719\pi$
$941$	108.981	+	188.761i	0.115814	+	0.200596i	−0.802291	+	0.596934i	$0.796386\pi$
$942$	−904.605	+	242.512i	−0.960302	+	0.257444i
$943$	−55.0849	−	205.580i	−0.0584145	−	0.218006i
$944$		−	4509.64i		−	4.77716i
$945$	−526.442	−	784.783i	−0.557081	−	0.830458i
$946$	−368.865			−0.389920
$947$	−511.668	+	137.101i	−0.540304	+	0.144774i	−0.518642	−	0.854991i	$-0.673562\pi$
$947$	−511.668	+	137.101i	−0.540304	+	0.144774i	−0.0216619	+	0.999765i	$0.506896\pi$
$948$	−91.6781	−	341.972i	−0.0967069	−	0.360730i
$949$	319.814	−	184.645i	0.337001	−	0.194568i
$950$	−43.3094	−	118.304i	−0.0455888	−	0.124531i
$951$	−318.272	−	551.101i	−0.334671	−	0.579496i
$952$	−517.665	+	11.5549i	−0.543765	+	0.0121375i
$953$	710.730	−	710.730i	0.745782	−	0.745782i	−0.227902	−	0.973684i	$-0.573187\pi$
$953$	710.730	−	710.730i	0.745782	−	0.745782i	0.973684	+	0.227902i	$0.0731866\pi$
$954$	1653.68	−	955.315i	1.73341	−	1.00138i
$955$	−150.434	−	33.2032i	−0.157523	−	0.0347678i
$956$	2032.99	−	1173.75i	2.12656	−	1.22777i
$957$	74.9676	+	74.9484i	0.0783360	+	0.0783160i
$958$	437.026	−	437.026i	0.456186	−	0.456186i
$959$	−218.338	+	228.308i	−0.227672	+	0.238068i
$960$	−2939.43	+	1877.01i	−3.06190	+	1.95522i
$961$	−458.314	+	793.824i	−0.476914	+	0.826039i
$962$	451.719	+	121.038i	0.469562	+	0.125819i
$963$	−912.750	+	913.217i	−0.947819	+	0.948305i
$964$	2090.19	−	3620.32i	2.16825	−	3.75552i
$965$	−42.2136	−	946.576i	−0.0437447	−	0.980908i
$966$	1728.84	−	505.090i	1.78969	−	0.522867i
$967$	236.165	−	236.165i	0.244224	−	0.244224i	−0.574371	−	0.818595i	$-0.694753\pi$
$967$	236.165	−	236.165i	0.244224	−	0.244224i	0.818595	+	0.574371i	$0.194753\pi$
$968$	791.336	+	2953.31i	0.817496	+	3.05094i
$969$	9.44038	+	5.44879i	0.00974239	+	0.00562311i
$970$	−2130.42	−	470.217i	−2.19631	−	0.484760i
$971$	−731.438	+	1266.89i	−0.753283	+	1.30472i	0.192941	+	0.981210i	$0.438197\pi$
$971$	−731.438	+	1266.89i	−0.753283	+	1.30472i	−0.946224	+	0.323514i	$0.895136\pi$
$972$	2555.68	−	686.546i	2.62930	−	0.706324i
$973$	338.275	+	185.364i	0.347662	+	0.190507i
$974$	−1934.51			−1.98615
$975$	268.677	−	24.0463i	0.275567	−	0.0246629i
$976$	−4584.79	+	2647.03i	−4.69753	+	2.71212i
$977$	−38.0332	+	141.942i	−0.0389286	+	0.145283i	−0.982655	−	0.185444i	$-0.940628\pi$
$977$	−38.0332	+	141.942i	−0.0389286	+	0.145283i	0.943726	+	0.330728i	$0.107294\pi$
$978$	−1947.08	−	1946.58i	−1.99087	−	1.99037i
$979$	154.483			0.157797
$980$	−2628.43	−	458.221i	−2.68207	−	0.467572i
$981$	354.266	−	613.969i	0.361127	−	0.625861i
$982$	46.9721	+	175.302i	0.0478331	+	0.178516i
$983$	409.391	−	1527.87i	0.416471	−	1.55429i	−0.365401	−	0.930850i	$-0.619068\pi$
$983$	409.391	−	1527.87i	0.416471	−	1.55429i	0.781872	−	0.623439i	$-0.214265\pi$
$984$	−661.488	−	381.798i	−0.672244	−	0.388006i
$985$	−698.973	−	363.034i	−0.709618	−	0.368562i
$986$	−154.846			−0.157045
$987$	505.530	−	11.3487i	0.512188	−	0.0114982i
$988$	−36.1693	−	36.1693i	−0.0366086	−	0.0366086i
$989$	−433.626	+	751.063i	−0.438449	+	0.759416i
$990$	19.0615	+	424.981i	0.0192540	+	0.429274i
$991$	198.059	+	343.048i	0.199858	+	0.346164i	0.948482	−	0.316831i	$-0.102619\pi$
$991$	198.059	+	343.048i	0.199858	+	0.346164i	−0.748624	+	0.662994i	$0.769285\pi$
$992$	−209.383	−	781.427i	−0.211071	−	0.787729i
$993$	748.736	+	200.521i	0.754015	+	0.201934i
$994$	−773.096	+	3166.25i	−0.777763	+	3.18536i
$995$	982.411	+	898.529i	0.987348	+	0.903044i
$996$	−0.318437	−	2488.42i	−0.000319716	−	2.49841i
$997$	−433.012	+	1616.02i	−0.434315	+	1.62089i	0.308385	+	0.951262i	$0.400211\pi$
$997$	−433.012	+	1616.02i	−0.434315	+	1.62089i	−0.742700	+	0.669624i	$0.766455\pi$
$998$	895.871	+	240.048i	0.897666	+	0.240529i
$999$	454.588	−	788.068i	0.455043	−	0.788857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.68.28	yes	112
3.2	odd	2	inner	105.3.w.a.68.1	yes	112
5.2	odd	4	inner	105.3.w.a.47.28	yes	112
7.3	odd	6	inner	105.3.w.a.38.1	yes	112
15.2	even	4	inner	105.3.w.a.47.1	yes	112
21.17	even	6	inner	105.3.w.a.38.28	yes	112
35.17	even	12	inner	105.3.w.a.17.1	✓	112
105.17	odd	12	inner	105.3.w.a.17.28	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.1	✓	112	35.17	even	12	inner
105.3.w.a.17.28	yes	112	105.17	odd	12	inner
105.3.w.a.38.1	yes	112	7.3	odd	6	inner
105.3.w.a.38.28	yes	112	21.17	even	6	inner
105.3.w.a.47.1	yes	112	15.2	even	4	inner
105.3.w.a.47.28	yes	112	5.2	odd	4	inner
105.3.w.a.68.1	yes	112	3.2	odd	2	inner
105.3.w.a.68.28	yes	112	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.72728 - 0.998723i) q^{2} +(0.776828 + 2.89768i) q^{3} +(9.43110 - 5.44505i) q^{4} +(-4.76718 + 1.50798i) q^{5} +(5.78944 + 10.0246i) q^{6} +(-6.13877 - 3.36385i) q^{7} +(18.8000 - 18.8000i) q^{8} +(-7.79308 + 4.50199i) q^{9} +(-16.2626 + 10.3818i) q^{10} +(-2.12166 + 1.22494i) q^{11} +(23.1043 + 23.0984i) q^{12} +(2.54324 - 2.54324i) q^{13} +(-26.2405 - 6.40708i) q^{14} +(-8.07292 - 12.6423i) q^{15} +(29.5169 - 51.1248i) q^{16} +(2.68738 + 0.720080i) q^{17} +(-24.5508 + 24.5633i) q^{18} +(0.652966 - 1.13097i) q^{19} +(-36.7487 + 40.1794i) q^{20} +(4.97858 - 20.4013i) q^{21} +(-6.68464 + 6.68464i) q^{22} +(5.75265 + 21.4692i) q^{23} +(69.0809 + 39.8721i) q^{24} +(20.4520 - 14.3776i) q^{25} +(6.93938 - 12.0194i) q^{26} +(-19.0992 - 19.0846i) q^{27} +(-76.2117 + 1.70114i) q^{28} -14.4234 q^{29} +(-42.7162 - 39.0589i) q^{30} +(5.76876 - 3.33060i) q^{31} +(31.4332 - 117.310i) q^{32} +(-5.19764 - 5.19631i) q^{33} +10.7358 q^{34} +(34.3372 + 6.77892i) q^{35} +(-48.9837 + 84.8924i) q^{36} +(8.72107 + 32.5475i) q^{37} +(1.30426 - 4.86758i) q^{38} +(9.34515 + 5.39383i) q^{39} +(-61.2731 + 117.973i) q^{40} -9.57556 q^{41} +(-1.81870 - 81.0137i) q^{42} +(27.5904 + 27.5904i) q^{43} +(-13.3397 + 23.1050i) q^{44} +(30.3621 - 33.2136i) q^{45} +(42.8835 + 74.2765i) q^{46} +(6.23208 + 23.2584i) q^{47} +(171.073 + 45.8153i) q^{48} +(26.3691 + 41.2998i) q^{49} +(61.8712 - 74.0153i) q^{50} +(0.00106809 + 8.34653i) q^{51} +(10.1375 - 37.8336i) q^{52} +(-53.1174 - 14.2328i) q^{53} +(-90.2484 - 52.0587i) q^{54} +(8.26714 - 9.03892i) q^{55} +(-178.650 + 52.1687i) q^{56} +(3.78443 + 1.01352i) q^{57} +(-53.7600 + 14.4050i) q^{58} +(66.1564 - 38.1954i) q^{59} +(-144.974 - 75.2735i) q^{60} +(-77.6638 - 44.8392i) q^{61} +(18.1755 - 18.1755i) q^{62} +(62.9839 - 1.42200i) q^{63} -232.507i q^{64} +(-8.28893 + 15.9592i) q^{65} +(-24.5628 - 14.1771i) q^{66} +(4.87233 + 1.30554i) q^{67} +(29.2658 - 7.84174i) q^{68} +(-57.7420 + 33.3472i) q^{69} +(134.755 - 9.02642i) q^{70} -120.663i q^{71} +(-61.8725 + 231.148i) q^{72} +(99.1765 + 26.5743i) q^{73} +(65.0118 + 112.604i) q^{74} +(57.5494 + 48.0944i) q^{75} -14.2217i q^{76} +(17.1449 - 0.382694i) q^{77} +(40.2190 + 10.7711i) q^{78} +(-9.38512 - 5.41850i) q^{79} +(-63.6173 + 288.232i) q^{80} +(40.4641 - 70.1688i) q^{81} +(-35.6908 + 9.56333i) q^{82} +(-53.8586 - 53.8586i) q^{83} +(-64.1327 - 219.515i) q^{84} +(-13.8971 + 0.619755i) q^{85} +(130.393 + 75.2822i) q^{86} +(-11.2045 - 41.7943i) q^{87} +(-16.8583 + 62.9162i) q^{88} +(-54.6094 - 31.5288i) q^{89} +(79.9969 - 154.120i) q^{90} +(-24.1674 + 7.05730i) q^{91} +(171.155 + 171.155i) q^{92} +(14.1323 + 14.1287i) q^{93} +(46.4575 + 80.4667i) q^{94} +(-1.40733 + 6.37620i) q^{95} +(364.346 - 0.0466246i) q^{96} +(79.9577 + 79.9577i) q^{97} +(139.532 + 127.601i) q^{98} +(11.0196 - 19.0977i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) \) 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Introduction

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