LMFDB - Embedded newform 334.2.c.b.107.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [334,2,Mod(3,334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(334, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([94]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("334.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$334 = 2 \cdot 167$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	334.c (of order $83$ , degree $82$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.66700342751$
Analytic rank:	$0$
Dimension:	$574$
Relative dimension:	$7$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			107.5
Character	$\chi$	$=$	334.107
Dual form			334.2.c.b.231.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.862854 - 0.505453i) q^{2} +(1.27594 + 0.398619i) q^{3} +(0.489034 + 0.872265i) q^{4} +(0.223189 - 1.29766i) q^{5} +(-0.899469 - 0.988880i) q^{6} +(-1.07023 - 3.21092i) q^{7} +(0.0189241 - 0.999821i) q^{8} +(-0.997334 - 0.690556i) q^{9} +(-0.848484 + 1.00688i) q^{10} +(0.108040 - 1.90087i) q^{11} +(0.276278 + 1.30790i) q^{12} +(-2.05729 - 0.558210i) q^{13} +(-0.699518 + 3.31151i) q^{14} +(0.802047 - 1.56677i) q^{15} +(-0.521692 + 0.853134i) q^{16} +(-1.26038 - 3.00258i) q^{17} +(0.511510 + 1.09995i) q^{18} +(6.27662 + 3.06458i) q^{19} +(1.24105 - 0.439919i) q^{20} +(-0.0856200 - 4.52357i) q^{21} +(-1.05402 + 1.58557i) q^{22} +(1.18490 - 0.523974i) q^{23} +(0.422694 - 1.26817i) q^{24} +(3.07858 + 1.09128i) q^{25} +(1.49299 + 1.52152i) q^{26} +(-3.46359 - 4.44089i) q^{27} +(2.27740 - 2.50378i) q^{28} +(6.05013 + 2.67542i) q^{29} +(-1.48398 + 0.946496i) q^{30} +(-6.04274 + 2.40308i) q^{31} +(0.881363 - 0.472440i) q^{32} +(0.895577 - 2.38234i) q^{33} +(-0.430134 + 3.22785i) q^{34} +(-4.40554 + 0.672152i) q^{35} +(0.114617 - 1.20764i) q^{36} +(0.217360 - 0.150500i) q^{37} +(-3.86681 - 5.81683i) q^{38} +(-2.40247 - 1.53232i) q^{39} +(-1.29320 - 0.247706i) q^{40} +(3.05750 - 2.88866i) q^{41} +(-2.21258 + 3.94646i) q^{42} +(2.47774 + 2.00903i) q^{43} +(1.71090 - 0.835352i) q^{44} +(-1.11870 + 1.14007i) q^{45} +(-1.28724 - 0.146800i) q^{46} +(-5.06697 - 2.71607i) q^{47} +(-1.00572 + 0.880595i) q^{48} +(-3.56446 + 2.67311i) q^{49} +(-2.10478 - 2.49769i) q^{50} +(-0.411294 - 4.33353i) q^{51} +(-0.519177 - 2.06748i) q^{52} +(0.268525 + 0.920367i) q^{53} +(0.743911 + 5.58252i) q^{54} +(-2.44257 - 0.564452i) q^{55} +(-3.23060 + 1.00928i) q^{56} +(6.78701 + 6.41221i) q^{57} +(-3.86808 - 5.36655i) q^{58} +(3.05645 - 7.28130i) q^{59} +(1.75887 - 0.0666058i) q^{60} +(-0.690509 + 2.74977i) q^{61} +(6.42865 + 0.980816i) q^{62} +(-1.14994 + 3.94142i) q^{63} +(-0.999284 - 0.0378415i) q^{64} +(-1.18353 + 2.54507i) q^{65} +(-1.97691 + 1.60294i) q^{66} +(2.46093 + 14.3083i) q^{67} +(2.00267 - 2.56775i) q^{68} +(1.72073 - 0.196236i) q^{69} +(4.14108 + 1.64683i) q^{70} +(1.15763 - 0.221738i) q^{71} +(-0.709306 + 0.984087i) q^{72} +(6.00329 + 9.81733i) q^{73} +(-0.263620 + 0.0199945i) q^{74} +(3.49309 + 2.61959i) q^{75} +(0.396355 + 6.97356i) q^{76} +(-6.21918 + 1.68747i) q^{77} +(1.29847 + 2.53650i) q^{78} +(-4.92879 - 0.373829i) q^{79} +(0.990640 + 0.867387i) q^{80} +(-1.36855 - 3.64051i) q^{81} +(-4.09826 + 0.947066i) q^{82} +(11.0121 - 6.45079i) q^{83} +(3.90388 - 2.28686i) q^{84} +(-4.17762 + 0.965404i) q^{85} +(-1.12246 - 2.98588i) q^{86} +(6.65315 + 5.82538i) q^{87} +(-1.89849 - 0.143993i) q^{88} +(5.00890 + 9.78470i) q^{89} +(1.54153 - 0.418267i) q^{90} +(0.409408 + 7.20321i) q^{91} +(1.03650 + 0.777308i) q^{92} +(-8.66811 + 0.657441i) q^{93} +(2.99922 + 4.90469i) q^{94} +(5.37765 - 7.46092i) q^{95} +(1.31289 - 0.251478i) q^{96} +(4.43343 + 1.76309i) q^{97} +(4.42674 - 0.504834i) q^{98} +(-1.42041 + 1.82120i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$574 q + 7 q^{2} + 2 q^{3} - 7 q^{4} - 2 q^{6} + 6 q^{7} + 7 q^{8} - 9 q^{9} - 6 q^{11} + 2 q^{12} + 2 q^{13} - 6 q^{14} - 4 q^{15} - 7 q^{16} - 8 q^{17} + 9 q^{18} - 6 q^{21} + 6 q^{22} + 2 q^{23} - 2 q^{24}+ \cdots - 32 q^{99}+O(q^{100})$ 574 * q + 7 * q^2 + 2 * q^3 - 7 * q^4 - 2 * q^6 + 6 * q^7 + 7 * q^8 - 9 * q^9 - 6 * q^11 + 2 * q^12 + 2 * q^13 - 6 * q^14 - 4 * q^15 - 7 * q^16 - 8 * q^17 + 9 * q^18 - 6 * q^21 + 6 * q^22 + 2 * q^23 - 2 * q^24 - 165 * q^25 - 2 * q^26 - 4 * q^27 + 6 * q^28 - 14 * q^29 + 4 * q^30 + 10 * q^31 + 7 * q^32 - 12 * q^33 + 8 * q^34 - 20 * q^35 - 9 * q^36 + 2 * q^37 - 83 * q^38 - 4 * q^39 - 20 * q^41 + 6 * q^42 - 2 * q^43 - 6 * q^44 + 2 * q^45 - 2 * q^46 + 14 * q^47 + 2 * q^48 - 171 * q^49 - q^50 - 417 * q^51 + 2 * q^52 - 4 * q^53 + 4 * q^54 + 18 * q^55 - 6 * q^56 - 6 * q^57 + 14 * q^58 - 2 * q^59 - 4 * q^60 + 16 * q^61 - 10 * q^62 + 40 * q^63 - 7 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 - 8 * q^68 + 16 * q^69 + 20 * q^70 - 4 * q^71 + 9 * q^72 + 22 * q^73 - 2 * q^74 - 533 * q^75 - 239 * q^77 + 4 * q^78 - 10 * q^79 + 17 * q^81 + 20 * q^82 - 14 * q^83 - 6 * q^84 + 6 * q^85 + 2 * q^86 + 10 * q^87 - 160 * q^88 - 16 * q^89 - 417 * q^90 + 10 * q^91 + 2 * q^92 + 10 * q^93 - 14 * q^94 - 38 * q^95 - 2 * q^96 - 8 * q^97 + 5 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/334\mathbb{Z}\right)^\times$ .

$n$	$5$
$\chi(n)$	$e\left(\frac{46}{83}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.862854	−	0.505453i	−0.610130	−	0.357409i
$2$	−0.862854	−	0.505453i	−0.610130	−	0.357409i
$3$	1.27594	+	0.398619i	0.736666	+	0.230143i	0.643434	−	0.765502i	$-0.277509\pi$
$3$	1.27594	+	0.398619i	0.736666	+	0.230143i	0.0932321	+	0.995644i	$0.470280\pi$
$4$	0.489034	+	0.872265i	0.244517	+	0.436132i
$5$	0.223189	−	1.29766i	0.0998131	−	0.580330i	−0.891939	−	0.452156i	$-0.850655\pi$
$5$	0.223189	−	1.29766i	0.0998131	−	0.580330i	0.991752	−	0.128173i	$-0.0409114\pi$
$6$	−0.899469	−	0.988880i	−0.367207	−	0.403709i
$7$	−1.07023	−	3.21092i	−0.404510	−	1.21362i	−0.931499	−	0.363743i	$-0.881499\pi$
$7$	−1.07023	−	3.21092i	−0.404510	−	1.21362i	0.526989	−	0.849872i	$-0.323321\pi$
$8$	0.0189241	−	0.999821i	0.00669069	−	0.353490i
$9$	−0.997334	−	0.690556i	−0.332445	−	0.230185i
$10$	−0.848484	+	1.00688i	−0.268314	+	0.318402i
$11$	0.108040	−	1.90087i	0.0325752	−	0.573135i	−0.940091	−	0.340925i	$-0.889260\pi$
$11$	0.108040	−	1.90087i	0.0325752	−	0.573135i	0.972666	−	0.232210i	$-0.0745956\pi$
$12$	0.276278	+	1.30790i	0.0797546	+	0.377558i
$13$	−2.05729	−	0.558210i	−0.570589	−	0.154820i	−0.0351332	−	0.999383i	$-0.511186\pi$
$13$	−2.05729	−	0.558210i	−0.570589	−	0.154820i	−0.535456	+	0.844563i	$0.679860\pi$
$14$	−0.699518	+	3.31151i	−0.186954	+	0.885039i
$15$	0.802047	−	1.56677i	0.207088	−	0.404538i
$16$	−0.521692	+	0.853134i	−0.130423	+	0.213284i
$17$	−1.26038	−	3.00258i	−0.305688	−	0.728232i	−0.999964	−	0.00852245i	$-0.997287\pi$
$17$	−1.26038	−	3.00258i	−0.305688	−	0.728232i	0.694276	−	0.719709i	$-0.255725\pi$
$18$	0.511510	+	1.09995i	0.120564	+	0.259262i
$19$	6.27662	+	3.06458i	1.43996	+	0.703063i	0.982516	−	0.186177i	$-0.0596099\pi$
$19$	6.27662	+	3.06458i	1.43996	+	0.703063i	0.457440	+	0.889241i	$0.348767\pi$
$20$	1.24105	−	0.439919i	0.277507	−	0.0983688i
$21$	−0.0856200	−	4.52357i	−0.0186838	−	0.987124i
$22$	−1.05402	+	1.58557i	−0.224719	+	0.338044i
$23$	1.18490	−	0.523974i	0.247069	−	0.109256i	−0.277189	−	0.960815i	$-0.589403\pi$
$23$	1.18490	−	0.523974i	0.247069	−	0.109256i	0.524258	+	0.851559i	$0.324343\pi$
$24$	0.422694	−	1.26817i	0.0862820	−	0.258864i
$25$	3.07858	+	1.09128i	0.615716	+	0.218255i
$26$	1.49299	+	1.52152i	0.292800	+	0.298394i
$27$	−3.46359	−	4.44089i	−0.666568	−	0.854649i
$28$	2.27740	−	2.50378i	0.430387	−	0.473169i
$29$	6.05013	+	2.67542i	1.12348	+	0.496813i	0.880892	−	0.473317i	$-0.156943\pi$
$29$	6.05013	+	2.67542i	1.12348	+	0.496813i	0.242588	+	0.970129i	$0.422004\pi$
$30$	−1.48398	+	0.946496i	−0.270936	+	0.172806i
$31$	−6.04274	+	2.40308i	−1.08531	+	0.431606i	−0.842626	−	0.538500i	$-0.818991\pi$
$31$	−6.04274	+	2.40308i	−1.08531	+	0.431606i	−0.242683	+	0.970106i	$0.578027\pi$
$32$	0.881363	−	0.472440i	0.155804	−	0.0835163i
$33$	0.895577	−	2.38234i	0.155900	−	0.414712i
$34$	−0.430134	+	3.22785i	−0.0737675	+	0.553572i
$35$	−4.40554	+	0.672152i	−0.744672	+	0.113614i
$36$	0.114617	−	1.20764i	0.0191029	−	0.201274i
$37$	0.217360	−	0.150500i	0.0357337	−	0.0247421i	−0.551261	−	0.834333i	$-0.685853\pi$
$37$	0.217360	−	0.150500i	0.0357337	−	0.0247421i	0.586995	+	0.809591i	$0.300311\pi$
$38$	−3.86681	−	5.81683i	−0.627279	−	0.943614i
$39$	−2.40247	−	1.53232i	−0.384703	−	0.245367i
$40$	−1.29320	−	0.247706i	−0.204473	−	0.0391658i
$41$	3.05750	−	2.88866i	0.477502	−	0.451133i	−0.409899	−	0.912131i	$-0.634436\pi$
$41$	3.05750	−	2.88866i	0.477502	−	0.451133i	0.887401	+	0.460998i	$0.152508\pi$
$42$	−2.21258	+	3.94646i	−0.341408	+	0.608952i
$43$	2.47774	+	2.00903i	0.377852	+	0.306374i	0.799823	−	0.600236i	$-0.204927\pi$
$43$	2.47774	+	2.00903i	0.377852	+	0.306374i	−0.421971	+	0.906609i	$0.638662\pi$
$44$	1.71090	−	0.835352i	0.257928	−	0.125934i
$45$	−1.11870	+	1.14007i	−0.166766	+	0.169952i
$46$	−1.28724	−	0.146800i	−0.189794	−	0.0216445i
$47$	−5.06697	−	2.71607i	−0.739094	−	0.396179i	0.0593582	−	0.998237i	$-0.481095\pi$
$47$	−5.06697	−	2.71607i	−0.739094	−	0.396179i	−0.798452	+	0.602058i	$0.794348\pi$
$48$	−1.00572	+	0.880595i	−0.145164	+	0.127103i
$49$	−3.56446	+	2.67311i	−0.509208	+	0.381872i
$50$	−2.10478	−	2.49769i	−0.297660	−	0.353227i
$51$	−0.411294	−	4.33353i	−0.0575927	−	0.606816i
$52$	−0.519177	−	2.06748i	−0.0719970	−	0.286708i
$53$	0.268525	+	0.920367i	0.0368847	+	0.126422i	0.976335	−	0.216262i	$-0.0693867\pi$
$53$	0.268525	+	0.920367i	0.0368847	+	0.126422i	−0.939451	+	0.342685i	$0.888664\pi$
$54$	0.743911	+	5.58252i	0.101234	+	0.759685i
$55$	−2.44257	−	0.564452i	−0.329356	−	0.0761107i
$56$	−3.23060	+	1.00928i	−0.431707	+	0.134870i
$57$	6.78701	+	6.41221i	0.898962	+	0.849318i
$58$	−3.86808	−	5.36655i	−0.507904	−	0.704663i
$59$	3.05645	−	7.28130i	0.397916	−	0.947944i	−0.591954	−	0.805972i	$-0.701643\pi$
$59$	3.05645	−	7.28130i	0.397916	−	0.947944i	0.989871	−	0.141973i	$-0.0453445\pi$
$60$	1.75887	−	0.0666058i	0.227069	−	0.00859877i
$61$	−0.690509	+	2.74977i	−0.0884107	+	0.352072i	−0.997984	−	0.0634728i	$-0.979782\pi$
$61$	−0.690509	+	2.74977i	−0.0884107	+	0.352072i	0.909573	+	0.415544i	$0.136409\pi$
$62$	6.42865	+	0.980816i	0.816439	+	0.124564i
$63$	−1.14994	+	3.94142i	−0.144879	+	0.496572i
$64$	−0.999284	−	0.0378415i	−0.124910	−	0.00473018i
$65$	−1.18353	+	2.54507i	−0.146799	+	0.315677i
$66$	−1.97691	+	1.60294i	−0.243341	+	0.197308i
$67$	2.46093	+	14.3083i	0.300651	+	1.74803i	0.605698	+	0.795695i	$0.292894\pi$
$67$	2.46093	+	14.3083i	0.300651	+	1.74803i	−0.305047	+	0.952337i	$0.598672\pi$
$68$	2.00267	−	2.56775i	0.242859	−	0.311385i
$69$	1.72073	−	0.196236i	0.207152	−	0.0236241i
$70$	4.14108	+	1.64683i	0.494954	+	0.196833i
$71$	1.15763	−	0.221738i	0.137385	−	0.0263154i	−0.118972	−	0.992898i	$-0.537960\pi$
$71$	1.15763	−	0.221738i	0.137385	−	0.0263154i	0.256357	+	0.966582i	$0.417478\pi$
$72$	−0.709306	+	0.984087i	−0.0835925	+	0.115976i
$73$	6.00329	+	9.81733i	0.702633	+	1.14903i	0.982006	+	0.188849i	$0.0604756\pi$
$73$	6.00329	+	9.81733i	0.702633	+	1.14903i	−0.279374	+	0.960182i	$0.590127\pi$
$74$	−0.263620	+	0.0199945i	−0.0306452	+	0.00232432i
$75$	3.49309	+	2.61959i	0.403347	+	0.302484i
$76$	0.396355	+	6.97356i	0.0454651	+	0.799922i
$77$	−6.21918	+	1.68747i	−0.708742	+	0.192305i
$78$	1.29847	+	2.53650i	0.147022	+	0.287203i
$79$	−4.92879	−	0.373829i	−0.554532	−	0.0420590i	−0.204620	−	0.978841i	$-0.565596\pi$
$79$	−4.92879	−	0.373829i	−0.554532	−	0.0420590i	−0.349912	+	0.936782i	$0.613789\pi$
$80$	0.990640	+	0.867387i	0.110757	+	0.0969768i
$81$	−1.36855	−	3.64051i	−0.152061	−	0.404501i
$82$	−4.09826	+	0.947066i	−0.452577	+	0.104586i
$83$	11.0121	−	6.45079i	1.20873	−	0.708067i	0.243613	−	0.969873i	$-0.421667\pi$
$83$	11.0121	−	6.45079i	1.20873	−	0.708067i	0.965121	+	0.261806i	$0.0843180\pi$
$84$	3.90388	−	2.28686i	0.425948	−	0.249517i
$85$	−4.17762	+	0.965404i	−0.453126	+	0.104713i
$86$	−1.12246	−	2.98588i	−0.121038	−	0.321976i
$87$	6.65315	+	5.82538i	0.713292	+	0.624546i
$88$	−1.89849	−	0.143993i	−0.202379	−	0.0153497i
$89$	5.00890	+	9.78470i	0.530942	+	1.03718i	0.988953	+	0.148229i	$0.0473573\pi$
$89$	5.00890	+	9.78470i	0.530942	+	1.03718i	−0.458011	+	0.888947i	$0.651438\pi$
$90$	1.54153	−	0.418267i	0.162491	−	0.0440892i
$91$	0.409408	+	7.20321i	0.0429176	+	0.755102i
$92$	1.03650	+	0.777308i	0.108063	+	0.0810399i
$93$	−8.66811	+	0.657441i	−0.898841	+	0.0681735i
$94$	2.99922	+	4.90469i	0.309345	+	0.505880i
$95$	5.37765	−	7.46092i	0.551735	−	0.765474i
$96$	1.31289	−	0.251478i	0.133997	−	0.0256664i
$97$	4.43343	+	1.76309i	0.450146	+	0.179014i	0.583601	−	0.812041i	$-0.301643\pi$
$97$	4.43343	+	1.76309i	0.450146	+	0.179014i	−0.133455	+	0.991055i	$0.542607\pi$
$98$	4.42674	−	0.504834i	0.447168	−	0.0509960i
$99$	−1.42041	+	1.82120i	−0.142757	+	0.183037i
$100$	0.553649	+	3.21901i	0.0553649	+	0.321901i
$101$	0.925823	−	0.750684i	0.0921229	−	0.0746959i	−0.582641	−	0.812730i	$-0.697981\pi$
$101$	0.925823	−	0.750684i	0.0921229	−	0.0746959i	0.674764	+	0.738034i	$0.264246\pi$
$102$	−1.83551	+	3.94709i	−0.181743	+	0.390820i
$103$	−10.2551	−	0.388346i	−1.01046	−	0.0382649i	−0.472583	−	0.881286i	$-0.656678\pi$
$103$	−10.2551	−	0.388346i	−1.01046	−	0.0382649i	−0.537881	+	0.843021i	$0.680775\pi$
$104$	−0.597042	+	2.04636i	−0.0585448	+	0.200662i
$105$	−5.88915	−	0.898506i	−0.574723	−	0.0876852i
$106$	0.233505	−	0.929869i	0.0226800	−	0.0903169i
$107$	−13.6000	+	0.515012i	−1.31476	+	0.0497881i	−0.685880	−	0.727714i	$-0.740583\pi$
$107$	−13.6000	+	0.515012i	−1.31476	+	0.0497881i	−0.628880	+	0.777502i	$0.716486\pi$
$108$	2.17982	−	5.19291i	0.209753	−	0.499688i
$109$	10.4321	+	14.4735i	0.999215	+	1.38631i	0.921085	+	0.389362i	$0.127305\pi$
$109$	10.4321	+	14.4735i	0.999215	+	1.38631i	0.0781302	+	0.996943i	$0.475105\pi$
$110$	1.82227	+	1.72164i	0.173747	+	0.164152i
$111$	0.337331	−	0.105386i	0.0320180	−	0.0100028i
$112$	3.29768	+	0.762060i	0.311601	+	0.0720079i
$113$	−1.67815	−	12.5933i	−0.157867	−	1.18468i	−0.873722	−	0.486426i	$-0.838300\pi$
$113$	−1.67815	−	12.5933i	−0.157867	−	1.18468i	0.715855	−	0.698249i	$-0.246037\pi$
$114$	−2.61513	−	8.96332i	−0.244929	−	0.839492i
$115$	−0.415481	−	1.65454i	−0.0387438	−	0.154287i
$116$	0.625045	+	6.58568i	0.0580340	+	0.611465i
$117$	1.66633	+	1.97739i	0.154052	+	0.182810i
$118$	−6.31763	+	4.73780i	−0.581585	+	0.436150i
$119$	−8.29214	+	7.26045i	−0.760139	+	0.665564i
$120$	−1.55131	−	0.831553i	−0.141615	−	0.0759101i
$121$	7.32752	+	0.835645i	0.666138	+	0.0759678i
$122$	1.98569	−	2.02363i	0.179776	−	0.183211i
$123$	5.05268	−	2.46699i	0.455584	−	0.222441i
$124$	−5.05123	−	4.09568i	−0.453614	−	0.367803i
$125$	5.32279	−	9.49398i	0.476085	−	0.849168i
$126$	2.98444	−	2.81963i	0.265875	−	0.251192i
$127$	−16.7117	−	3.20105i	−1.48293	−	0.284047i	−0.618093	−	0.786105i	$-0.712094\pi$
$127$	−16.7117	−	3.20105i	−1.48293	−	0.284047i	−0.864834	+	0.502058i	$0.832576\pi$
$128$	0.843109	+	0.537743i	0.0745210	+	0.0475302i
$129$	2.36062	+	3.55108i	0.207841	+	0.312655i
$130$	2.30763	−	1.59780i	0.202392	−	0.140137i
$131$	−0.0942777	+	0.993341i	−0.00823709	+	0.0867886i	−0.998699	−	0.0510010i	$-0.983759\pi$
$131$	−0.0942777	+	0.993341i	−0.00823709	+	0.0867886i	0.990462	+	0.137790i	$0.0439998\pi$
$132$	2.51600	−	0.383865i	0.218989	−	0.0334111i
$133$	3.12269	−	23.4336i	0.270772	−	2.03195i
$134$	5.10873	−	13.5898i	0.441327	−	1.17398i
$135$	−6.53578	+	3.50339i	−0.562511	+	0.301524i
$136$	−3.02589	+	1.20334i	−0.259468	+	0.103185i
$137$	3.43774	−	2.19262i	0.293706	−	0.187329i	−0.382670	−	0.923885i	$-0.624995\pi$
$137$	3.43774	−	2.19262i	0.293706	−	0.187329i	0.676376	+	0.736557i	$0.263550\pi$
$138$	−1.58393	−	0.700428i	−0.134833	−	0.0596244i
$139$	−13.1681	+	14.4771i	−1.11691	+	1.22793i	−0.145791	+	0.989315i	$0.546573\pi$
$139$	−13.1681	+	14.4771i	−1.11691	+	1.22793i	−0.971114	+	0.238614i	$0.923307\pi$
$140$	−2.74075	−	3.51409i	−0.231636	−	0.296995i
$141$	−5.38250	−	5.48534i	−0.453288	−	0.461949i
$142$	−1.11094	−	0.393799i	−0.0932281	−	0.0330469i
$143$	−1.28335	+	3.85033i	−0.107319	+	0.321981i
$144$	1.10944	−	0.490603i	0.0924531	−	0.0408836i
$145$	4.82210	−	7.25387i	0.400453	−	0.602401i
$146$	−0.217767	−	11.5053i	−0.0180225	−	0.952186i
$147$	−5.61360	+	1.98987i	−0.463002	+	0.164122i
$148$	0.237572	+	0.115995i	0.0195283	+	0.00953476i
$149$	5.14407	+	11.0618i	0.421419	+	0.906222i	0.996132	+	0.0878672i	$0.0280051\pi$
$149$	5.14407	+	11.0618i	0.421419	+	0.906222i	−0.574713	+	0.818355i	$0.694886\pi$
$150$	−1.68995	−	4.02592i	−0.137984	−	0.328715i
$151$	7.74215	−	12.6609i	0.630047	−	1.03033i	−0.365008	−	0.931005i	$-0.618934\pi$
$151$	7.74215	−	12.6609i	0.630047	−	1.03033i	0.995055	−	0.0993264i	$-0.0316688\pi$
$152$	3.18281	−	6.21750i	0.258160	−	0.504306i
$153$	−0.816422	+	3.86494i	−0.0660038	+	0.312462i
$154$	6.21918	+	1.68747i	0.501156	+	0.135980i
$155$	1.76970	+	8.37775i	0.142146	+	0.672917i
$156$	0.161698	−	2.84495i	0.0129462	−	0.227778i
$157$	13.9505	−	16.5547i	1.11337	−	1.32121i	0.171516	−	0.985181i	$-0.445133\pi$
$157$	13.9505	−	16.5547i	1.11337	−	1.32121i	0.941852	−	0.336027i	$-0.109083\pi$
$158$	4.06387	+	2.81383i	0.323305	+	0.223857i
$159$	−0.0242532	+	1.28138i	−0.00192341	+	0.101620i
$160$	−0.416354	−	1.24915i	−0.0329157	−	0.0987540i
$161$	−2.95056	−	3.24386i	−0.232537	−	0.255652i
$162$	−0.659246	+	3.83296i	−0.0517952	+	0.301146i
$163$	−6.24948	−	11.1469i	−0.489497	−	0.873091i	−0.999913	−	0.0131635i	$-0.995810\pi$
$163$	−6.24948	−	11.1469i	−0.489497	−	0.873091i	0.510416	−	0.859928i	$-0.329491\pi$
$164$	4.01490	+	1.25430i	0.313511	+	0.0979444i
$165$	−2.89158	−	1.69386i	−0.225109	−	0.131867i
$166$	−12.7624			−0.990554
$167$	−3.30396	+	12.4934i	−0.255668	+	0.966765i
$167$	−3.30396	+	12.4934i	−0.255668	+	0.966765i
$168$	−4.52438			−0.349064
$169$	−7.29626	−	4.27410i	−0.561251	−	0.328777i
$170$	4.09264	+	1.27859i	0.313891	+	0.0980632i
$171$	−4.14362	−	7.39077i	−0.316871	−	0.565186i
$172$	−0.540702	+	3.14373i	−0.0412282	+	0.239707i
$173$	−5.86013	−	6.44265i	−0.445537	−	0.489825i	0.475272	−	0.879839i	$-0.342350\pi$
$173$	−5.86013	−	6.44265i	−0.445537	−	0.489825i	−0.920809	+	0.390014i	$0.872470\pi$
$174$	−2.79624	−	8.38931i	−0.211982	−	0.635992i
$175$	0.209206	−	11.0530i	0.0158145	−	0.835529i
$176$	1.56534	+	1.08384i	0.117992	+	0.0816976i
$177$	6.80233	−	8.07216i	0.511294	−	0.606741i
$178$	0.623758	−	10.9745i	0.0467526	−	0.822576i
$179$	−0.126330	−	0.598043i	−0.00944231	−	0.0446998i	0.973433	−	0.228973i	$-0.0735369\pi$
$179$	−0.126330	−	0.598043i	−0.00944231	−	0.0446998i	−0.982875	+	0.184274i	$0.941007\pi$
$180$	−1.54153	−	0.418267i	−0.114899	−	0.0311758i
$181$	1.80737	−	8.55607i	0.134341	−	0.635967i	−0.858125	−	0.513441i	$-0.828370\pi$
$181$	1.80737	−	8.55607i	0.134341	−	0.635967i	0.992465	−	0.122526i	$-0.0390995\pi$
$182$	3.28763	−	6.42226i	0.243695	−	0.476049i
$183$	−1.97716	+	3.23330i	−0.146156	+	0.239012i
$184$	−0.501457	−	1.19461i	−0.0369679	−	0.0880675i
$185$	−0.146785	−	0.315648i	−0.0107919	−	0.0232069i
$186$	7.81162	+	3.81405i	0.572776	+	0.279660i
$187$	−5.84369	+	2.07143i	−0.427333	+	0.151478i
$188$	−0.108795	−	5.74799i	−0.00793471	−	0.419215i
$189$	−10.5525	+	15.8741i	−0.767582	+	1.15467i
$190$	−8.41127	+	3.71954i	−0.610218	+	0.269844i
$191$	2.95677	−	8.87095i	0.213945	−	0.641879i	−0.785782	−	0.618503i	$-0.787739\pi$
$191$	2.95677	−	8.87095i	0.213945	−	0.641879i	0.999727	−	0.0233758i	$-0.00744141\pi$
$192$	−1.25995	−	0.446617i	−0.0909287	−	0.0322318i
$193$	10.8736	+	11.0814i	0.782699	+	0.797654i	0.983295	−	0.182020i	$-0.0582637\pi$
$193$	10.8736	+	11.0814i	0.782699	+	0.797654i	−0.200596	+	0.979674i	$0.564288\pi$
$194$	−2.93424	−	3.76218i	−0.210666	−	0.270109i
$195$	−2.52463	+	2.77559i	−0.180792	+	0.198764i
$196$	−4.07480	−	1.80191i	−0.291057	−	0.128708i
$197$	1.90584	−	1.21556i	0.135785	−	0.0866051i	−0.468104	−	0.883673i	$-0.655063\pi$
$197$	1.90584	−	1.21556i	0.135785	−	0.0866051i	0.603889	+	0.797068i	$0.293617\pi$
$198$	2.14614	−	0.853477i	0.152519	−	0.0606539i
$199$	−6.98038	+	3.74171i	−0.494826	+	0.265243i	−0.700856	−	0.713303i	$-0.747199\pi$
$199$	−6.98038	+	3.74171i	−0.494826	+	0.265243i	0.206030	+	0.978546i	$0.433946\pi$
$200$	1.14934	−	3.05738i	0.0812706	−	0.216189i
$201$	−2.56354	+	19.2375i	−0.180818	+	1.35691i
$202$	−1.17829	+	0.179771i	−0.0829039	+	0.0126486i
$203$	2.11552	−	22.2898i	0.148480	−	1.56444i
$204$	3.57885	−	2.47800i	0.250570	−	0.173495i
$205$	−3.06609	−	4.61231i	−0.214145	−	0.322138i
$206$	8.65235	+	5.51855i	0.602838	+	0.384496i
$207$	−1.54358	−	0.295664i	−0.107286	−	0.0205501i
$208$	1.54950	−	1.46393i	0.107438	−	0.101505i
$209$	6.50350	−	11.6000i	0.449857	−	0.802386i
$210$	4.62733	+	3.75197i	0.319316	+	0.258911i
$211$	9.23287	−	4.50798i	0.635617	−	0.310342i	−0.0925848	−	0.995705i	$-0.529513\pi$
$211$	9.23287	−	4.50798i	0.635617	−	0.310342i	0.728202	+	0.685363i	$0.240356\pi$
$212$	−0.671486	+	0.684316i	−0.0461178	+	0.0469990i
$213$	1.56546	+	0.178528i	0.107263	+	0.0122325i
$214$	11.9951	+	6.42978i	0.819969	+	0.439531i
$215$	3.16003	−	2.76687i	0.215512	−	0.188699i
$216$	−4.50564	+	3.37893i	−0.306570	+	0.229907i
$217$	14.1832	+	16.8309i	0.962821	+	1.14256i
$218$	−1.68573	−	17.7614i	−0.114172	−	1.20296i
$219$	3.74649	+	14.9194i	0.253164	+	1.00816i
$220$	−0.702147	−	2.40660i	−0.0473387	−	0.162253i
$221$	0.916907	+	6.88072i	0.0616778	+	0.462848i
$222$	−0.344335	−	0.0795722i	−0.0231102	−	0.00534054i
$223$	12.0712	−	3.77119i	0.808349	−	0.252537i	0.134029	−	0.990977i	$-0.457208\pi$
$223$	12.0712	−	3.77119i	0.808349	−	0.252537i	0.674319	+	0.738440i	$0.264437\pi$
$224$	−2.46023	−	2.32437i	−0.164381	−	0.155303i
$225$	−2.31679	−	3.21430i	−0.154452	−	0.214287i
$226$	−4.91732	+	11.7144i	−0.327095	+	0.779229i
$227$	12.0936	−	0.457967i	0.802679	−	0.0303963i	0.366684	−	0.930345i	$-0.380493\pi$
$227$	12.0936	−	0.457967i	0.802679	−	0.0303963i	0.435995	+	0.899949i	$0.356397\pi$
$228$	−2.27407	+	9.05586i	−0.150604	+	0.599739i
$229$	−6.78551	−	1.03526i	−0.448399	−	0.0684121i	−0.0773054	−	0.997007i	$-0.524632\pi$
$229$	−6.78551	−	1.03526i	−0.448399	−	0.0684121i	−0.371094	+	0.928595i	$0.621017\pi$
$230$	−0.477794	+	1.63763i	−0.0315048	+	0.107982i
$231$	−8.60798	−	0.325972i	−0.566364	−	0.0214474i
$232$	2.78943	−	5.99841i	0.183135	−	0.393815i
$233$	−4.72420	+	3.83052i	−0.309493	+	0.250946i	−0.771932	−	0.635705i	$-0.780709\pi$
$233$	−4.72420	+	3.83052i	−0.309493	+	0.250946i	0.462439	+	0.886651i	$0.346974\pi$
$234$	−0.438318	−	2.54845i	−0.0286538	−	0.166598i
$235$	−4.65541	+	5.96900i	−0.303686	+	0.389375i
$236$	7.84593	−	0.894766i	0.510726	−	0.0582443i
$237$	−6.13984	−	2.44170i	−0.398826	−	0.158605i
$238$	10.8247	−	2.07342i	0.701663	−	0.134400i
$239$	−5.49469	+	7.62331i	−0.355422	+	0.493111i	−0.950572	−	0.310504i	$-0.899502\pi$
$239$	−5.49469	+	7.62331i	−0.355422	+	0.493111i	0.595150	+	0.803615i	$0.297093\pi$
$240$	0.918243	+	1.50162i	0.0592723	+	0.0969294i
$241$	8.38629	−	0.636066i	0.540209	−	0.0409726i	0.197303	−	0.980343i	$-0.436782\pi$
$241$	8.38629	−	0.636066i	0.540209	−	0.0409726i	0.342906	+	0.939370i	$0.388589\pi$
$242$	−5.90020	−	4.42476i	−0.379279	−	0.284434i
$243$	0.663728	+	11.6778i	0.0425781	+	0.749129i
$244$	−2.73621	+	0.742423i	−0.175168	+	0.0475287i
$245$	2.67323	+	5.22205i	0.170786	+	0.333625i
$246$	−5.60667	−	0.425243i	−0.357468	−	0.0271125i
$247$	−11.2021	−	9.80840i	−0.712775	−	0.624094i
$248$	2.28830	+	6.08714i	0.145307	+	0.386533i
$249$	16.6222	−	3.84122i	1.05339	−	0.243427i
$250$	−9.39155	+	5.50150i	−0.593974	+	0.347945i
$251$	−26.7639	+	15.6781i	−1.68932	+	0.989593i	−0.741419	+	0.671043i	$0.765847\pi$
$251$	−26.7639	+	15.6781i	−1.68932	+	0.989593i	−0.947906	+	0.318551i	$0.896804\pi$
$252$	−4.00032	+	0.924433i	−0.251997	+	0.0582338i
$253$	−0.867991	−	2.30896i	−0.0545702	−	0.145163i
$254$	12.8018	+	11.2090i	0.803257	+	0.703318i
$255$	−5.71523	−	0.433477i	−0.357902	−	0.0271454i
$256$	−0.455676	−	0.890146i	−0.0284797	−	0.0556341i
$257$	2.34950	−	0.637497i	0.146558	−	0.0397660i	−0.187830	−	0.982202i	$-0.560145\pi$
$257$	2.34950	−	0.637497i	0.146558	−	0.0397660i	0.334388	+	0.942436i	$0.391471\pi$
$258$	−0.241969	−	4.25725i	−0.0150643	−	0.265045i
$259$	−0.715870	−	0.536855i	−0.0444820	−	0.0333585i
$260$	−2.79876	+	0.212275i	−0.173572	+	0.0131647i
$261$	−4.18647	−	6.84624i	−0.259136	−	0.423771i
$262$	0.583435	−	0.809455i	0.0360448	−	0.0500083i
$263$	22.0441	−	4.22243i	1.35929	−	0.260366i	0.543841	−	0.839188i	$-0.316969\pi$
$263$	22.0441	−	4.22243i	1.35929	−	0.260366i	0.815454	+	0.578822i	$0.196487\pi$
$264$	−2.36496	−	0.940500i	−0.145553	−	0.0578838i
$265$	1.25425	−	0.143038i	0.0770481	−	0.00878673i
$266$	−14.5390	+	18.6414i	−0.891443	+	1.14298i
$267$	2.49070	+	14.4814i	0.152429	+	0.886245i
$268$	−11.2771	+	9.14381i	−0.688859	+	0.558547i
$269$	−8.01178	+	17.2286i	−0.488487	+	1.05044i	0.494905	+	0.868947i	$0.335203\pi$
$269$	−8.01178	+	17.2286i	−0.488487	+	1.05044i	−0.983391	+	0.181498i	$0.941905\pi$
$270$	7.41023	+	0.280615i	0.450972	+	0.0170777i
$271$	−5.33729	+	18.2935i	−0.324217	+	1.11125i	0.620729	+	0.784025i	$0.286837\pi$
$271$	−5.33729	+	18.2935i	−0.324217	+	1.11125i	−0.944946	+	0.327226i	$0.893886\pi$
$272$	3.21913	+	0.491142i	0.195189	+	0.0297798i
$273$	−2.34896	+	9.35409i	−0.142165	+	0.566135i
$274$	−4.07454	+	0.154297i	−0.246152	+	0.00932143i
$275$	2.40698	−	5.73409i	0.145147	−	0.345779i
$276$	1.01267	+	1.40497i	0.0609554	+	0.0845693i
$277$	8.18324	+	7.73134i	0.491684	+	0.464531i	0.892123	−	0.451792i	$-0.149215\pi$
$277$	8.18324	+	7.73134i	0.491684	+	0.464531i	−0.400440	+	0.916323i	$0.631143\pi$
$278$	18.6797	−	5.83574i	1.12033	−	0.350004i
$279$	7.68609	+	1.77618i	0.460154	+	0.106337i
$280$	0.588660	+	4.41747i	0.0351792	+	0.263994i
$281$	4.91897	+	16.8597i	0.293441	+	1.00577i	0.964438	+	0.264308i	$0.0851434\pi$
$281$	4.91897	+	16.8597i	0.293441	+	1.00577i	−0.670997	+	0.741460i	$0.734134\pi$
$282$	1.87173	+	7.45365i	0.111460	+	0.443858i
$283$	−0.355228	−	3.74280i	−0.0211161	−	0.222486i	−0.999849	−	0.0173498i	$-0.994477\pi$
$283$	−0.355228	−	3.74280i	−0.0211161	−	0.222486i	0.978733	−	0.205137i	$-0.0657638\pi$
$284$	0.759533	+	0.901320i	0.0450700	+	0.0534835i
$285$	9.83564	−	7.37608i	0.582613	−	0.436921i
$286$	3.05351	−	2.67360i	0.180558	−	0.158093i
$287$	−12.5475	−	6.72588i	−0.740656	−	0.397016i
$288$	−1.20526	−	0.137450i	−0.0710206	−	0.00809934i
$289$	4.47964	−	4.56523i	0.263508	−	0.268543i
$290$	−7.82726	+	3.82168i	−0.459632	+	0.224417i
$291$	4.95400	+	4.01685i	0.290409	+	0.235472i
$292$	−5.62749	+	10.0375i	−0.329324	+	0.587398i
$293$	13.3575	−	12.6199i	0.780356	−	0.737262i	−0.189251	−	0.981929i	$-0.560606\pi$
$293$	13.3575	−	12.6199i	0.780356	−	0.737262i	0.969607	+	0.244666i	$0.0786784\pi$
$294$	5.84950	+	1.12044i	0.341150	+	0.0653455i
$295$	−8.76646	−	5.59133i	−0.510403	−	0.325540i
$296$	−0.146360	−	0.220169i	−0.00850699	−	0.0127970i
$297$	−8.81576	+	6.10405i	−0.511543	+	0.354193i
$298$	1.15266	−	12.1448i	0.0667721	−	0.703532i
$299$	−2.73017	+	0.416542i	−0.157890	+	0.0240892i
$300$	−0.576733	+	4.32797i	−0.0332977	+	0.249875i
$301$	3.79907	−	10.1060i	0.218975	−	0.582498i
$302$	−13.0798	+	7.01123i	−0.752661	+	0.403451i
$303$	1.48054	−	0.588780i	0.0850545	−	0.0338245i
$304$	−5.88896	+	3.75603i	−0.337755	+	0.215423i
$305$	3.41414	+	1.50976i	0.195493	+	0.0864487i
$306$	2.65800	−	2.92221i	0.151948	−	0.167052i
$307$	2.50443	+	3.21109i	0.142935	+	0.183266i	0.854654	−	0.519199i	$-0.173769\pi$
$307$	2.50443	+	3.21109i	0.142935	+	0.183266i	−0.711718	+	0.702465i	$0.752083\pi$
$308$	−4.51331	−	4.59955i	−0.257170	−	0.262083i
$309$	−12.9301	−	4.58338i	−0.735568	−	0.260740i
$310$	2.70757	−	8.12327i	0.153779	−	0.461371i
$311$	15.6620	−	6.92585i	0.888108	−	0.392729i	0.0904941	−	0.995897i	$-0.471155\pi$
$311$	15.6620	−	6.92585i	0.888108	−	0.392729i	0.797614	+	0.603168i	$0.206095\pi$
$312$	−1.57751	+	2.37304i	−0.0893089	+	0.134347i
$313$	−0.193922	−	10.2455i	−0.0109611	−	0.579111i	−0.962455	−	0.271442i	$-0.912499\pi$
$313$	−0.193922	−	10.2455i	−0.0109611	−	0.579111i	0.951494	−	0.307669i	$-0.0995489\pi$
$314$	−20.4048	+	7.23298i	−1.15151	+	0.408180i
$315$	4.85796	+	2.37191i	0.273715	+	0.133642i
$316$	−2.08427	−	4.48203i	−0.117249	−	0.252134i
$317$	−7.16400	−	17.0666i	−0.402370	−	0.958555i	−0.988894	−	0.148623i	$-0.952516\pi$
$317$	−7.16400	−	17.0666i	−0.402370	−	0.958555i	0.586524	−	0.809932i	$-0.300496\pi$
$318$	0.668602	−	1.09338i	0.0374934	−	0.0613137i
$319$	5.73928	−	11.2115i	0.321338	−	0.627722i
$320$	−0.272134	+	1.28828i	−0.0152128	+	0.0720171i
$321$	−17.5581	−	4.76409i	−0.979998	−	0.265906i
$322$	0.906285	+	4.29035i	0.0505053	+	0.239092i
$323$	1.29068	−	22.7086i	0.0718156	−	1.26354i
$324$	2.50622	−	2.97407i	0.139234	−	0.165226i
$325$	−5.72437	−	3.96356i	−0.317531	−	0.219859i
$326$	−0.241836	+	12.7770i	−0.0133941	+	0.707650i
$327$	7.54138	+	22.6257i	0.417039	+	1.25121i
$328$	−2.83028	−	3.11162i	−0.156276	−	0.171811i
$329$	−3.29824	+	19.1765i	−0.181838	+	1.05723i
$330$	1.63884	+	2.92311i	0.0902151	+	0.160912i
$331$	−2.67961	−	0.837141i	−0.147285	−	0.0460134i	0.223667	−	0.974666i	$-0.428197\pi$
$331$	−2.67961	−	0.837141i	−0.147285	−	0.0460134i	−0.370951	+	0.928652i	$0.620968\pi$
$332$	11.0121	+	6.45079i	0.604367	+	0.354033i
$333$	−0.320709			−0.0175747
$334$	9.16564	−	9.10994i	0.501522	−	0.498474i
$335$	19.1165			1.04444
$336$	3.90388	+	2.28686i	0.212974	+	0.124759i
$337$	18.6659	+	5.83145i	1.01680	+	0.317660i	0.760778	−	0.649012i	$-0.224817\pi$
$337$	18.6659	+	5.83145i	1.01680	+	0.317660i	0.256021	+	0.966671i	$0.417589\pi$
$338$	4.13525	+	7.37584i	0.224928	+	0.401193i
$339$	2.87870	−	16.7372i	0.156350	−	0.909042i
$340$	−2.88508	−	3.17187i	−0.156466	−	0.172019i
$341$	3.91509	+	11.7461i	0.212014	+	0.636087i
$342$	−0.160346	+	8.47156i	−0.00867050	+	0.458090i
$343$	−7.08067	−	4.90267i	−0.382320	−	0.264719i
$344$	2.05556	−	2.43928i	0.110828	−	0.131517i
$345$	0.129402	−	2.27672i	0.00696675	−	0.122575i
$346$	1.79998	+	8.52108i	0.0967674	+	0.458096i
$347$	7.58621	+	2.05839i	0.407249	+	0.110500i	0.459594	−	0.888129i	$-0.347995\pi$
$347$	7.58621	+	2.05839i	0.407249	+	0.110500i	−0.0523450	+	0.998629i	$0.516670\pi$
$348$	−1.82766	+	8.65211i	−0.0979727	+	0.463802i
$349$	6.89159	−	13.4625i	0.368898	−	0.720629i	−0.629512	−	0.776991i	$-0.716745\pi$
$349$	6.89159	−	13.4625i	0.368898	−	0.720629i	0.998410	+	0.0563617i	$0.0179500\pi$
$350$	−5.76729	+	9.43139i	−0.308275	+	0.504129i
$351$	4.64666	+	11.0696i	0.248020	+	0.590851i
$352$	−0.802825	−	1.72640i	−0.0427907	−	0.0920175i
$353$	−15.2401	−	7.44103i	−0.811148	−	0.396046i	−0.0140545	−	0.999901i	$-0.504474\pi$
$353$	−15.2401	−	7.44103i	−0.811148	−	0.396046i	−0.797094	+	0.603855i	$0.793630\pi$
$354$	−9.94952	+	3.52684i	−0.528811	+	0.187449i
$355$	−0.0293697	−	1.55169i	−0.00155878	−	0.0823553i
$356$	−6.08532	+	9.15414i	−0.322521	+	0.485168i
$357$	−13.4745	+	5.95852i	−0.713144	+	0.315358i
$358$	−0.193279	+	0.579877i	−0.0102151	+	0.0306475i
$359$	−27.7565	−	9.83895i	−1.46493	−	0.519280i	−0.522198	−	0.852824i	$-0.674888\pi$
$359$	−27.7565	−	9.83895i	−1.46493	−	0.519280i	−0.942735	+	0.333544i	$0.891755\pi$
$360$	1.11870	+	1.14007i	0.0589606	+	0.0600871i
$361$	18.3194	+	23.4884i	0.964177	+	1.23623i
$362$	−5.88419	+	6.46910i	−0.309266	+	0.340008i
$363$	9.01639	+	3.98712i	0.473238	+	0.209270i
$364$	−6.08289	+	3.87973i	−0.318830	+	0.203353i
$365$	14.0794	−	5.59910i	0.736949	−	0.293070i
$366$	3.34028	−	1.79050i	0.174599	−	0.0935910i
$367$	4.05668	−	10.7913i	0.211757	−	0.563299i	−0.786788	−	0.617223i	$-0.788257\pi$
$367$	4.05668	−	10.7913i	0.211757	−	0.563299i	0.998545	+	0.0539247i	$0.0171731\pi$
$368$	−0.171133	+	1.28423i	−0.00892095	+	0.0669453i
$369$	−5.04413	+	0.769581i	−0.262587	+	0.0400628i
$370$	−0.0328911	+	0.346551i	−0.00170993	+	0.0180163i
$371$	2.66784	−	1.84722i	0.138508	−	0.0959029i
$372$	−4.81246	−	7.23937i	−0.249515	−	0.375344i
$373$	−18.0903	−	11.5381i	−0.936678	−	0.597422i	−0.0211938	−	0.999775i	$-0.506747\pi$
$373$	−18.0903	−	11.5381i	−0.936678	−	0.597422i	−0.915485	+	0.402353i	$0.868192\pi$
$374$	6.08926	+	1.16637i	0.314868	+	0.0603114i
$375$	10.5761	−	9.99202i	0.546145	−	0.515986i
$376$	−2.81147	+	5.01467i	−0.144990	+	0.258612i
$377$	−10.9534	−	8.88135i	−0.564130	−	0.457413i
$378$	17.1289	−	8.36324i	0.881015	−	0.430158i
$379$	13.1644	−	13.4159i	0.676208	−	0.689128i	−0.286986	−	0.957935i	$-0.592653\pi$
$379$	13.1644	−	13.4159i	0.676208	−	0.689128i	0.963194	+	0.268807i	$0.0866294\pi$
$380$	9.13775	+	1.04209i	0.468757	+	0.0534580i
$381$	−20.0472	−	10.7460i	−1.02705	−	0.550533i
$382$	−7.03511	+	6.15982i	−0.359948	+	0.315164i
$383$	−3.55757	+	2.66794i	−0.181783	+	0.136326i	−0.686973	−	0.726683i	$-0.741061\pi$
$383$	−3.55757	+	2.66794i	−0.181783	+	0.136326i	0.505190	+	0.863008i	$0.331422\pi$
$384$	0.861404	+	1.02221i	0.0439584	+	0.0521644i
$385$	0.801702	+	8.44699i	0.0408585	+	0.430499i
$386$	−3.78122	−	15.0577i	−0.192459	−	0.766416i
$387$	−1.08379	−	3.71469i	−0.0550923	−	0.188828i
$388$	0.630218	+	4.72933i	0.0319945	+	0.240095i
$389$	−31.4149	−	7.25965i	−1.59280	−	0.368079i	−0.666689	−	0.745336i	$-0.732289\pi$
$389$	−31.4149	−	7.25965i	−1.59280	−	0.368079i	−0.926109	+	0.377257i	$0.876867\pi$
$390$	3.58132	−	1.11884i	0.181347	−	0.0566548i
$391$	−3.06670	−	2.89735i	−0.155090	−	0.146525i
$392$	2.60517	+	3.61441i	0.131581	+	0.182555i
$393$	−0.516258	+	1.22987i	−0.0260418	+	0.0620385i
$394$	−2.25887	+	0.0855402i	−0.113800	+	0.00430945i
$395$	−1.58515	+	6.31245i	−0.0797577	+	0.317614i
$396$	−2.28320	−	0.348346i	−0.114735	−	0.0175051i
$397$	2.70743	−	9.27970i	0.135882	−	0.465735i	−0.863363	−	0.504583i	$-0.831646\pi$
$397$	2.70743	−	9.27970i	0.135882	−	0.465735i	0.999245	+	0.0388487i	$0.0123690\pi$
$398$	7.91431	+	0.299704i	0.396709	+	0.0150228i
$399$	13.3255	−	28.6551i	0.667107	−	1.43455i
$400$	−2.53707	+	2.05713i	−0.126854	+	0.102857i
$401$	4.50656	+	26.2019i	0.225047	+	1.30846i	0.849580	+	0.527460i	$0.176856\pi$
$401$	4.50656	+	26.2019i	0.225047	+	1.30846i	−0.624533	+	0.780998i	$0.714711\pi$
$402$	11.9356	−	15.3034i	0.595294	−	0.763265i
$403$	13.7731	−	1.57071i	0.686086	−	0.0782427i
$404$	1.10755	+	0.440453i	0.0551029	+	0.0219133i
$405$	−5.02957	+	0.963389i	−0.249921	+	0.0478712i
$406$	−13.0918	+	18.1636i	−0.649737	+	0.901442i
$407$	−0.262598	−	0.429433i	−0.0130165	−	0.0212862i
$408$	−4.34054	+	0.329212i	−0.214889	+	0.0162984i
$409$	7.09013	+	5.31713i	0.350584	+	0.262915i	0.760679	−	0.649128i	$-0.224866\pi$
$409$	7.09013	+	5.31713i	0.350584	+	0.262915i	−0.410095	+	0.912043i	$0.634504\pi$
$410$	0.314280	+	5.52951i	0.0155212	+	0.273083i
$411$	5.26039	−	1.42732i	0.259476	−	0.0704043i
$412$	−4.67635	−	9.13507i	−0.230387	−	0.450052i
$413$	−26.6508	−	2.02136i	−1.31140	−	0.0994645i
$414$	1.18244	+	1.03532i	0.0581136	+	0.0508833i
$415$	−5.91314	−	15.7297i	−0.290265	−	0.772138i
$416$	−2.07694	+	0.479959i	−0.101830	+	0.0235319i
$417$	−22.5726	+	13.2229i	−1.10539	+	0.647527i
$418$	−11.4748	+	6.72186i	−0.561251	+	0.328777i
$419$	−20.4640	+	4.72903i	−0.999734	+	0.231028i	−0.693133	−	0.720810i	$-0.743770\pi$
$419$	−20.4640	+	4.72903i	−0.999734	+	0.231028i	−0.306601	+	0.951838i	$0.599192\pi$
$420$	−2.09626	−	5.57630i	−0.102287	−	0.272096i
$421$	26.5430	+	23.2406i	1.29363	+	1.13268i	0.983289	+	0.182050i	$0.0582734\pi$
$421$	26.5430	+	23.2406i	1.29363	+	1.13268i	0.310337	+	0.950626i	$0.399558\pi$
$422$	−10.2452	−	0.777057i	−0.498728	−	0.0378265i
$423$	3.17787	+	6.20785i	0.154513	+	0.301836i
$424$	0.925284	−	0.251060i	0.0449357	−	0.0121925i
$425$	−0.603556	−	10.6191i	−0.0292768	−	0.515102i
$426$	−1.26052	−	0.945308i	−0.0610725	−	0.0458003i
$427$	9.56830	−	0.725717i	0.463042	−	0.0351199i
$428$	−7.10008	−	11.6109i	−0.343195	−	0.561235i
$429$	−3.17230	+	4.40124i	−0.153160	+	0.212494i
$430$	−4.12517	+	0.790155i	−0.198933	+	0.0381047i
$431$	20.3955	+	8.11087i	0.982414	+	0.390687i	0.804887	−	0.593429i	$-0.202226\pi$
$431$	20.3955	+	8.11087i	0.982414	+	0.390687i	0.177528	+	0.984116i	$0.443190\pi$
$432$	5.59560	−	0.638134i	0.269218	−	0.0307022i
$433$	−19.0142	+	24.3793i	−0.913764	+	1.17159i	0.0709617	+	0.997479i	$0.477393\pi$
$433$	−19.0142	+	24.3793i	−0.913764	+	1.17159i	−0.984725	+	0.174115i	$0.944294\pi$
$434$	−3.73082	−	21.6916i	−0.179085	−	1.04123i
$435$	9.04425	−	7.33334i	0.433639	−	0.351607i
$436$	−7.52303	+	16.1776i	−0.360288	+	0.774765i
$437$	9.04295	+	0.342444i	0.432583	+	0.0163813i
$438$	4.30838	−	14.7669i	0.205862	−	0.705591i
$439$	31.9029	+	4.86742i	1.52264	+	0.232309i	0.857531	−	0.514433i	$-0.171998\pi$
$439$	31.9029	+	4.86742i	1.52264	+	0.232309i	0.665114	+	0.746742i	$0.268383\pi$
$440$	−0.610574	+	2.43145i	−0.0291080	+	0.115915i
$441$	5.40088	−	0.204524i	0.257185	−	0.00973923i
$442$	2.68673	−	6.40051i	0.127795	−	0.304441i
$443$	1.49943	+	2.08030i	0.0712400	+	0.0988380i	0.845349	−	0.534214i	$-0.179392\pi$
$443$	1.49943	+	2.08030i	0.0712400	+	0.0988380i	−0.774109	+	0.633052i	$0.781802\pi$
$444$	0.256891	+	0.242704i	0.0121915	+	0.0115182i
$445$	13.8151	−	4.31600i	0.654899	−	0.204598i
$446$	−12.3219	−	2.84745i	−0.583457	−	0.134831i
$447$	2.15408	+	16.1648i	0.101884	+	0.764570i
$448$	0.947960	+	3.24912i	0.0447869	+	0.153507i
$449$	−2.24075	−	8.92319i	−0.105748	−	0.421112i	0.893883	−	0.448301i	$-0.147971\pi$
$449$	−2.24075	−	8.92319i	−0.105748	−	0.421112i	−0.999630	+	0.0271895i	$0.991344\pi$
$450$	0.374371	+	3.94450i	0.0176480	+	0.185945i
$451$	−5.16064	−	6.12401i	−0.243005	−	0.288369i
$452$	10.1640	−	7.62232i	0.478074	−	0.358524i
$453$	14.9254	−	13.0684i	0.701258	−	0.614009i
$454$	−10.6665	−	5.71758i	−0.500603	−	0.268339i
$455$	9.43867	+	1.07641i	0.442492	+	0.0504627i
$456$	6.53950	−	6.66445i	0.306240	−	0.312092i
$457$	−22.6175	+	11.0431i	−1.05800	+	0.516573i	−0.883668	−	0.468113i	$-0.844934\pi$
$457$	−22.6175	+	11.0431i	−1.05800	+	0.516573i	−0.174334	+	0.984687i	$0.555777\pi$
$458$	5.33163	+	4.32304i	0.249131	+	0.202002i
$459$	−8.96865	+	15.9969i	−0.418621	+	0.746672i
$460$	1.24001	−	1.17154i	0.0578160	−	0.0546232i
$461$	−39.3543	−	7.53812i	−1.83291	−	0.351085i	−0.848812	−	0.528695i	$-0.822682\pi$
$461$	−39.3543	−	7.53812i	−1.83291	−	0.351085i	−0.984101	+	0.177610i	$0.943163\pi$
$462$	7.26267	+	4.63220i	0.337890	+	0.215509i
$463$	−10.0568	−	15.1284i	−0.467378	−	0.703075i	0.521259	−	0.853399i	$-0.325463\pi$
$463$	−10.0568	−	15.1284i	−0.467378	−	0.703075i	−0.988637	+	0.150323i	$0.951969\pi$
$464$	−5.43879	+	3.76583i	−0.252490	+	0.174824i
$465$	−1.08149	+	11.3950i	−0.0501530	+	0.528429i
$466$	6.01245	−	0.917316i	0.278521	−	0.0424939i
$467$	2.75849	−	20.7005i	0.127648	−	0.957904i	−0.804022	−	0.594599i	$-0.797311\pi$
$467$	2.75849	−	20.7005i	0.127648	−	0.957904i	0.931670	−	0.363305i	$-0.118352\pi$
$468$	−0.909920	+	2.42049i	−0.0420611	+	0.111887i
$469$	43.3090	−	23.2150i	1.99982	−	1.07197i
$470$	7.03399	−	2.79728i	0.324454	−	0.129029i
$471$	24.3990	−	15.5619i	1.12425	−	0.717056i
$472$	−7.22215	−	3.19370i	−0.332427	−	0.147002i
$473$	4.08660	−	4.49282i	0.187902	−	0.206580i
$474$	4.06363	+	5.21023i	0.186649	+	0.239314i
$475$	15.9788	+	16.2841i	0.733157	+	0.747165i
$476$	−10.3882	−	3.68233i	−0.476141	−	0.168779i
$477$	0.367756	−	1.10334i	0.0168384	−	0.0505187i
$478$	8.59434	−	3.80049i	0.393096	−	0.173830i
$479$	−17.1693	+	25.8278i	−0.784487	+	1.18010i	0.195434	+	0.980717i	$0.437388\pi$
$479$	−17.1693	+	25.8278i	−0.784487	+	1.18010i	−0.979921	+	0.199385i	$0.936106\pi$
$480$	−0.0333089	−	1.75981i	−0.00152033	−	0.0803240i
$481$	−0.531182	+	0.188290i	−0.0242198	+	0.00858528i
$482$	−7.55765	−	3.69005i	−0.344241	−	0.168077i
$483$	−2.47169	−	5.31513i	−0.112466	−	0.241847i
$484$	2.85450	+	6.80019i	0.129750	+	0.309100i
$485$	3.27737	−	5.35957i	0.148818	−	0.243365i
$486$	5.32987	−	10.4117i	0.241768	−	0.472284i
$487$	−7.82669	+	37.0515i	−0.354661	+	1.67896i	0.325218	+	0.945639i	$0.394562\pi$
$487$	−7.82669	+	37.0515i	−0.354661	+	1.67896i	−0.679879	+	0.733324i	$0.737968\pi$
$488$	2.73621	+	0.742423i	0.123862	+	0.0336079i
$489$	−3.53063	−	16.7140i	−0.159660	−	0.755831i
$490$	0.332897	−	5.85706i	0.0150387	−	0.264595i
$491$	−12.0269	+	14.2721i	−0.542768	+	0.644090i	−0.964954	−	0.262419i	$-0.915480\pi$
$491$	−12.0269	+	14.2721i	−0.542768	+	0.644090i	0.422186	+	0.906509i	$0.361263\pi$
$492$	4.62280	+	3.20083i	0.208412	+	0.144305i
$493$	0.407661	−	21.5380i	0.0183601	−	0.970024i
$494$	4.70813	+	14.1254i	0.211829	+	0.635531i
$495$	2.04627	+	2.24968i	0.0919730	+	0.101115i
$496$	1.10230	−	6.40894i	0.0494946	−	0.287770i
$497$	−1.95091	−	3.47974i	−0.0875104	−	0.156088i
$498$	−16.2841	−	5.08734i	−0.729708	−	0.227969i
$499$	−9.99005	−	5.85209i	−0.447216	−	0.261976i	0.264578	−	0.964364i	$-0.414767\pi$
$499$	−9.99005	−	5.85209i	−0.447216	−	0.261976i	−0.711794	+	0.702389i	$0.752117\pi$
$500$	10.8843			0.486760
$501$	−9.19576	+	14.6238i	−0.410836	+	0.653343i
$502$	31.0179			1.38440
$503$	19.2050	+	11.2501i	0.856307	+	0.501618i	0.866990	−	0.498325i	$-0.166051\pi$
$503$	19.2050	+	11.2501i	0.856307	+	0.501618i	−0.0106836	+	0.999943i	$0.503401\pi$
$504$	3.91895	+	1.22432i	0.174564	+	0.0545358i
$505$	−0.767497	−	1.36895i	−0.0341532	−	0.0609173i
$506$	−0.418121	+	2.43102i	−0.0185877	+	0.108072i
$507$	−7.60588	−	8.36193i	−0.337789	−	0.371367i
$508$	−5.38045	−	16.1425i	−0.238719	−	0.716207i
$509$	0.0880872	−	4.65392i	0.00390440	−	0.206281i	−0.992535	−	0.121964i	$-0.961081\pi$
$509$	0.0880872	−	4.65392i	0.00390440	−	0.206281i	0.996439	−	0.0843175i	$-0.0268710\pi$
$510$	4.71231	+	3.26281i	0.208664	+	0.144480i
$511$	25.0978	−	29.7829i	1.11026	−	1.31752i
$512$	−0.0567453	+	0.998389i	−0.00250781	+	0.0441230i
$513$	−8.13018	−	38.4882i	−0.358956	−	1.69930i
$514$	−2.34950	−	0.637497i	−0.103632	−	0.0281188i
$515$	−2.79276	+	13.2209i	−0.123064	+	0.582583i
$516$	−1.94306	+	3.79569i	−0.0855383	+	0.167096i
$517$	−5.71033	+	9.33823i	−0.251140	+	0.410695i
$518$	0.346336	+	0.825066i	0.0152171	+	0.0362513i
$519$	−4.90903	−	10.5564i	−0.215482	−	0.463375i
$520$	2.52222	+	1.23148i	0.110606	+	0.0540040i
$521$	−2.57733	+	0.913594i	−0.112915	+	0.0400253i	−0.389962	−	0.920831i	$-0.627512\pi$
$521$	−2.57733	+	0.913594i	−0.112915	+	0.0400253i	0.277047	+	0.960856i	$0.410644\pi$
$522$	0.151862	+	8.02337i	0.00664684	+	0.351173i
$523$	13.9556	−	20.9934i	0.610236	−	0.917976i	−0.389760	−	0.920916i	$-0.627442\pi$
$523$	13.9556	−	20.9934i	0.610236	−	0.917976i	0.999996	+	0.00294070i	$0.000936055\pi$
$524$	−0.912562	+	0.403542i	−0.0398654	+	0.0176288i
$525$	4.67288	−	14.0196i	0.203941	−	0.611866i
$526$	−21.1550	−	7.49890i	−0.922404	−	0.326968i
$527$	14.8316	+	15.1150i	0.646075	+	0.658419i
$528$	1.56524	+	2.00689i	0.0681183	+	0.0873388i
$529$	−14.3466	+	15.7727i	−0.623766	+	0.685771i
$530$	−1.15454	−	0.510545i	−0.0501498	−	0.0221767i
$531$	−8.07645	+	5.15124i	−0.350488	+	0.223545i
$532$	21.9674	−	8.73600i	0.952407	−	0.378754i
$533$	−7.90265	+	4.23608i	−0.342302	+	0.183485i
$534$	5.17054	−	13.7542i	0.223751	−	0.595204i
$535$	−2.36706	+	17.7631i	−0.102337	+	0.767964i
$536$	14.3523	−	2.18972i	0.619924	−	0.0945815i
$537$	0.0772021	−	0.813426i	0.00333151	−	0.0351019i
$538$	15.6212	−	10.8162i	0.673479	−	0.466318i
$539$	4.69613	+	7.06438i	0.202277	+	0.304284i
$540$	−6.25211	−	3.98765i	−0.269048	−	0.171601i
$541$	3.52464	+	0.675127i	0.151536	+	0.0290260i	0.263332	−	0.964705i	$-0.415178\pi$
$541$	3.52464	+	0.675127i	0.151536	+	0.0290260i	−0.111796	+	0.993731i	$0.535660\pi$
$542$	13.8518	−	13.0869i	0.594986	−	0.562129i
$543$	5.71671	−	10.1966i	0.245328	−	0.437578i
$544$	−2.52939	−	2.05090i	−0.108447	−	0.0879318i
$545$	21.1099	−	10.3070i	0.904249	−	0.441503i
$546$	6.75486	−	6.88392i	0.289081	−	0.294605i
$547$	−9.29781	−	1.06034i	−0.397545	−	0.0453369i	−0.0877558	−	0.996142i	$-0.527970\pi$
$547$	−9.29781	−	1.06034i	−0.397545	−	0.0453369i	−0.309790	+	0.950805i	$0.600259\pi$
$548$	3.59372	+	1.92635i	0.153516	+	0.0822897i
$549$	2.58754	−	2.26560i	0.110433	−	0.0966935i
$550$	−4.97519	+	3.73106i	−0.212143	+	0.159093i
$551$	29.7753	+	35.3337i	1.26847	+	1.50527i
$552$	−0.163638	−	1.72414i	−0.00696488	−	0.0733843i
$553$	4.07462	+	16.2261i	0.173270	+	0.690002i
$554$	−3.15311	−	10.8073i	−0.133963	−	0.459157i
$555$	−0.0614663	−	0.461260i	−0.00260910	−	0.0195794i
$556$	−19.0675	−	4.40630i	−0.808642	−	0.186869i
$557$	−1.08822	+	0.339971i	−0.0461092	+	0.0144050i	−0.321165	−	0.947023i	$-0.604075\pi$
$557$	−1.08822	+	0.339971i	−0.0461092	+	0.0144050i	0.275056	+	0.961428i	$0.411303\pi$
$558$	−5.73420	−	5.41754i	−0.242748	−	0.229343i
$559$	−3.97598	−	5.51625i	−0.168166	−	0.233312i
$560$	1.72490	−	4.10917i	0.0728902	−	0.173644i
$561$	−8.28192	+	0.313625i	−0.349663	+	0.0132413i
$562$	4.27745	−	17.0338i	0.180433	−	0.718528i
$563$	−20.5484	−	3.13507i	−0.866013	−	0.132127i	−0.297421	−	0.954747i	$-0.596126\pi$
$563$	−20.5484	−	3.13507i	−0.866013	−	0.132127i	−0.568593	+	0.822619i	$0.692512\pi$
$564$	2.15244	−	7.37748i	0.0906342	−	0.310648i
$565$	−16.7163	−	0.633022i	−0.703260	−	0.0266315i
$566$	−1.58530	+	3.40904i	−0.0666351	+	0.143293i
$567$	−10.2247	+	8.29050i	−0.429398	+	0.348168i
$568$	−0.199791	−	1.16162i	−0.00838304	−	0.0487403i
$569$	−21.4694	+	27.5272i	−0.900043	+	1.15400i	0.0874235	+	0.996171i	$0.472137\pi$
$569$	−21.4694	+	27.5272i	−0.900043	+	1.15400i	−0.987466	+	0.157830i	$0.949550\pi$
$570$	−12.2150	+	1.39302i	−0.511629	+	0.0583473i
$571$	−37.2781	−	14.8248i	−1.56004	−	0.620398i	−0.579196	−	0.815188i	$-0.696633\pi$
$571$	−37.2781	−	14.8248i	−1.56004	−	0.620398i	−0.980845	+	0.194790i	$0.937597\pi$
$572$	−3.98611	+	0.763520i	−0.166668	+	0.0319244i
$573$	7.30880	−	10.1402i	0.305330	−	0.423613i
$574$	7.42705	+	12.1456i	0.309999	+	0.506949i
$575$	4.21962	−	0.320041i	0.175970	−	0.0133466i
$576$	0.970488	+	0.727802i	0.0404370	+	0.0303251i
$577$	0.732810	+	12.8932i	0.0305073	+	0.536752i	0.976895	+	0.213719i	$0.0685577\pi$
$577$	0.732810	+	12.8932i	0.0305073	+	0.536752i	−0.946388	+	0.323032i	$0.895298\pi$
$578$	−6.17278	+	1.67488i	−0.256754	+	0.0696657i
$579$	9.45686	+	18.4736i	0.393014	+	0.767737i
$580$	8.68546	+	0.658757i	0.360644	+	0.0273534i
$581$	−32.4985	−	28.4551i	−1.34827	−	1.18052i
$582$	−2.24425	−	5.96997i	−0.0930272	−	0.247463i
$583$	1.77851	−	0.410996i	0.0736584	−	0.0170217i
$584$	9.92918	−	5.81644i	0.410872	−	0.240686i
$585$	2.93789	−	1.72099i	0.121467	−	0.0711542i
$586$	−17.9044	+	4.13752i	−0.739623	+	0.170919i
$587$	−9.08214	−	24.1596i	−0.374860	−	0.997172i	−0.979637	−	0.200777i	$-0.935653\pi$
$587$	−9.08214	−	24.1596i	−0.374860	−	0.997172i	0.604777	−	0.796395i	$-0.293262\pi$
$588$	−4.48093	−	3.92343i	−0.184791	−	0.161799i
$589$	−45.2924	−	3.43525i	−1.86624	−	0.141547i
$590$	4.73802	+	9.25554i	0.195061	+	0.381045i
$591$	2.91629	−	0.791284i	0.119960	−	0.0325491i
$592$	0.0150022	+	0.263951i	0.000616585	+	0.0108483i
$593$	2.53578	+	1.90167i	0.104132	+	0.0780922i	0.650760	−	0.759283i	$-0.274450\pi$
$593$	2.53578	+	1.90167i	0.104132	+	0.0780922i	−0.546628	+	0.837375i	$0.684089\pi$
$594$	10.6920	−	0.810947i	0.438699	−	0.0332736i
$595$	7.57086	+	12.3808i	0.310375	+	0.507563i
$596$	−7.13323	+	9.89661i	−0.292189	+	0.405381i
$597$	−10.3981	+	1.99170i	−0.425566	+	0.0815149i
$598$	2.56628	+	1.02056i	0.104943	+	0.0417338i
$599$	−8.83118	+	1.00713i	−0.360832	+	0.0411501i	−0.291840	−	0.956467i	$-0.594268\pi$
$599$	−8.83118	+	1.00713i	−0.360832	+	0.0411501i	−0.0689922	+	0.997617i	$0.521978\pi$
$600$	2.68522	−	3.44289i	0.109624	−	0.140555i
$601$	−6.47021	−	37.6188i	−0.263925	−	1.53450i	−0.750503	−	0.660867i	$-0.770189\pi$
$601$	−6.47021	−	37.6188i	−0.263925	−	1.53450i	0.486578	−	0.873637i	$-0.338245\pi$
$602$	−8.38614	+	6.79972i	−0.341793	+	0.277136i
$603$	7.42628	−	15.9695i	0.302421	−	0.650329i
$604$	14.8298	+	0.561586i	0.603418	+	0.0228506i
$605$	2.71980	−	9.32209i	0.110576	−	0.378997i
$606$	−1.57509	−	0.240310i	−0.0639835	−	0.00976194i
$607$	4.06627	−	16.1928i	0.165045	−	0.657247i	−0.829995	−	0.557771i	$-0.811657\pi$
$607$	4.06627	−	16.1928i	0.165045	−	0.657247i	0.995040	−	0.0994760i	$-0.0317167\pi$
$608$	6.97981	−	0.264316i	0.283069	−	0.0107194i
$609$	11.5844	−	27.5973i	0.469425	−	1.11830i
$610$	−2.18279	−	3.02839i	−0.0883786	−	0.122616i
$611$	8.90810	+	8.41616i	0.360383	+	0.340482i
$612$	−3.77051	+	1.17795i	−0.152414	+	0.0476158i
$613$	−19.9942	−	4.62046i	−0.807559	−	0.186619i	−0.198868	−	0.980026i	$-0.563727\pi$
$613$	−19.9942	−	4.62046i	−0.807559	−	0.186619i	−0.608691	+	0.793408i	$0.708305\pi$
$614$	−0.537903	−	4.03657i	−0.0217080	−	0.162903i
$615$	−2.07360	−	7.10724i	−0.0836156	−	0.286592i
$616$	1.56947	+	6.25000i	0.0632359	+	0.251820i
$617$	3.23897	+	34.1268i	0.130396	+	1.37389i	0.785737	+	0.618561i	$0.212284\pi$
$617$	3.23897	+	34.1268i	0.130396	+	1.37389i	−0.655341	+	0.755333i	$0.727475\pi$
$618$	8.84011	+	10.4904i	0.355601	+	0.421984i
$619$	−12.4377	+	9.32744i	−0.499913	+	0.374901i	−0.819887	−	0.572525i	$-0.805964\pi$
$619$	−12.4377	+	9.32744i	−0.499913	+	0.374901i	0.319975	+	0.947426i	$0.396326\pi$
$620$	−6.44217	+	5.64065i	−0.258724	+	0.226534i
$621$	−6.43093	−	3.44719i	−0.258064	−	0.138331i
$622$	−17.0147	−	1.94039i	−0.682226	−	0.0778026i
$623$	26.0572	−	26.5551i	1.04396	−	1.06391i
$624$	2.56062	−	1.25023i	0.102507	−	0.0500493i
$625$	1.55342	+	1.25956i	0.0621370	+	0.0503825i
$626$	−5.01131	+	8.93841i	−0.200292	+	0.357251i
$627$	12.9221	−	12.2085i	0.516058	−	0.487559i
$628$	21.2623	+	4.07269i	0.848459	+	0.162518i
$629$	−0.725844	−	0.462951i	−0.0289413	−	0.0184590i
$630$	−2.99281	−	4.50208i	−0.119237	−	0.179367i
$631$	−18.3494	+	12.7052i	−0.730480	+	0.505786i	−0.875245	−	0.483681i	$-0.839300\pi$
$631$	−18.3494	+	12.7052i	−0.730480	+	0.505786i	0.144765	+	0.989466i	$0.453757\pi$
$632$	−0.467035	+	4.92083i	−0.0185777	+	0.195740i
$633$	13.5776	−	2.07153i	0.539661	−	0.0823358i
$634$	−2.44488	+	18.3470i	−0.0970985	+	0.728654i
$635$	−7.88374	+	20.9717i	−0.312857	+	0.832235i
$636$	−1.12956	+	0.605481i	−0.0447899	+	0.0240089i
$637$	8.82527	−	3.50964i	0.349670	−	0.139057i
$638$	−10.6190	+	6.77292i	−0.420412	+	0.268143i
$639$	−1.30766	−	0.578260i	−0.0517304	−	0.0228756i
$640$	0.885978	−	0.974048i	0.0350214	−	0.0385026i
$641$	29.6025	+	37.9552i	1.16923	+	1.49914i	0.829401	+	0.558653i	$0.188682\pi$
$641$	29.6025	+	37.9552i	1.16923	+	1.49914i	0.339827	+	0.940488i	$0.389631\pi$
$642$	12.7421	+	12.9855i	0.502889	+	0.512497i
$643$	−10.0143	−	3.54982i	−0.394927	−	0.139991i	0.129226	−	0.991615i	$-0.458751\pi$
$643$	−10.0143	−	3.54982i	−0.394927	−	0.139991i	−0.524153	+	0.851624i	$0.675618\pi$
$644$	1.38658	−	4.16003i	0.0546388	−	0.163928i
$645$	5.13495	−	2.27072i	0.202188	−	0.0894094i
$646$	−12.5918	+	18.9418i	−0.495418	+	0.745256i
$647$	−0.0245787	−	1.29857i	−0.000966288	−	0.0510520i	−0.999978	−	0.00660805i	$-0.997897\pi$
$647$	−0.0245787	−	1.29857i	−0.000966288	−	0.0510520i	0.999012	−	0.0444440i	$-0.0141516\pi$
$648$	−3.66575	+	1.29941i	−0.144004	+	0.0510457i
$649$	−13.5106	−	6.59660i	−0.530338	−	0.258939i
$650$	2.93590	+	6.31338i	0.115155	+	0.247631i
$651$	11.3879	+	27.1290i	0.446326	+	1.06327i
$652$	6.66682	−	10.9024i	0.261093	−	0.426971i
$653$	−17.0759	+	33.3572i	−0.668232	+	1.30537i	0.271164	+	0.962533i	$0.412592\pi$
$653$	−17.0759	+	33.3572i	−0.668232	+	1.30537i	−0.939396	+	0.342834i	$0.888613\pi$
$654$	4.92915	−	23.3345i	0.192745	−	0.912452i
$655$	1.26797	+	0.344043i	0.0495439	+	0.0134429i
$656$	0.869340	+	4.11545i	0.0339420	+	0.160681i
$657$	0.792122	−	13.9368i	0.0309036	−	0.543725i
$658$	12.5387	−	14.8794i	0.488810	−	0.580060i
$659$	19.0227	+	13.1713i	0.741019	+	0.513083i	0.878689	−	0.477395i	$-0.158419\pi$
$659$	19.0227	+	13.1713i	0.741019	+	0.513083i	−0.137669	+	0.990478i	$0.543961\pi$
$660$	0.0634181	−	3.35058i	0.00246855	−	0.130421i
$661$	8.16402	+	24.4938i	0.317544	+	0.952698i	0.979201	+	0.202892i	$0.0650341\pi$
$661$	8.16402	+	24.4938i	0.317544	+	0.952698i	−0.661657	+	0.749806i	$0.730147\pi$
$662$	1.88898	+	2.07675i	0.0734172	+	0.0807151i
$663$	−1.57287	+	9.14491i	−0.0610851	+	0.355159i
$664$	−6.24125	−	11.1322i	−0.242207	−	0.432013i
$665$	−29.7118	−	9.28230i	−1.15217	−	0.359952i
$666$	0.276725	+	0.162103i	0.0107229	+	0.00628137i
$667$	8.57066			0.331857
$668$	−12.5133	+	3.22774i	−0.484153	+	0.124885i
$669$	16.9055			0.653603
$670$	−16.4947	−	9.66248i	−0.637247	−	0.373294i
$671$	5.15235	+	1.60965i	0.198904	+	0.0621400i
$672$	−2.21258	−	3.94646i	−0.0853520	−	0.152238i
$673$	−2.64997	+	15.4073i	−0.102149	+	0.593910i	0.888652	+	0.458582i	$0.151642\pi$
$673$	−2.64997	+	15.4073i	−0.102149	+	0.593910i	−0.990801	+	0.135328i	$0.956791\pi$
$674$	−13.1585	−	14.4665i	−0.506845	−	0.557227i
$675$	−5.81671	−	17.4514i	−0.223885	−	0.671703i
$676$	0.160022	−	8.45445i	0.00615468	−	0.325171i
$677$	19.6065	+	13.5756i	0.753539	+	0.521752i	0.882737	−	0.469867i	$-0.155698\pi$
$677$	19.6065	+	13.5756i	0.753539	+	0.521752i	−0.129198	+	0.991619i	$0.541240\pi$
$678$	−10.9438	+	12.9867i	−0.420294	+	0.498753i
$679$	0.916341	−	16.1223i	0.0351660	−	0.618717i
$680$	0.886174	+	4.19514i	0.0339832	+	0.160876i
$681$	15.6133	+	4.23639i	0.598302	+	0.162339i
$682$	2.55896	−	12.1141i	0.0979875	−	0.463872i
$683$	−21.9734	+	42.9242i	−0.840789	+	1.64245i	−0.0769567	+	0.997034i	$0.524520\pi$
$683$	−21.9734	+	42.9242i	−0.840789	+	1.64245i	−0.763832	+	0.645415i	$0.776685\pi$
$684$	4.42033	−	7.22867i	0.169016	−	0.276395i
$685$	−2.07801	−	4.95038i	−0.0793966	−	0.189144i
$686$	3.63151	+	7.80923i	0.138652	+	0.298158i
$687$	−8.24525	−	4.02577i	−0.314576	−	0.153593i
$688$	−3.00659	+	1.06576i	−0.114625	+	0.0406316i
$689$	−0.0386756	−	2.04335i	−0.00147342	−	0.0778456i
$690$	−1.26243	+	1.89907i	−0.0480599	+	0.0722964i
$691$	26.3343	−	11.6453i	1.00181	−	0.443007i	0.162524	−	0.986705i	$-0.448036\pi$
$691$	26.3343	−	11.6453i	1.00181	−	0.443007i	0.839281	+	0.543698i	$0.182976\pi$
$692$	2.75389	−	8.26226i	0.104687	−	0.314084i
$693$	7.36790	+	2.61172i	0.279883	+	0.0992112i
$694$	−5.50538	−	5.61056i	−0.208981	−	0.212974i
$695$	15.8473	+	20.3188i	0.601122	+	0.770737i
$696$	5.95024	−	6.54172i	0.225543	−	0.247963i
$697$	−12.5270	−	5.53957i	−0.474496	−	0.209826i
$698$	−12.7511	+	8.13276i	−0.482636	+	0.307830i
$699$	−7.55473	+	3.00437i	−0.285746	+	0.113636i
$700$	9.74346	−	5.22281i	0.368268	−	0.197404i
$701$	−0.210267	+	0.559334i	−0.00794166	+	0.0211257i	−0.939956	−	0.341296i	$-0.889134\pi$
$701$	−0.210267	+	0.559334i	−0.00794166	+	0.0211257i	0.932014	+	0.362421i	$0.118050\pi$
$702$	1.58578	−	11.9001i	0.0598513	−	0.449141i
$703$	1.82550	−	0.278516i	0.0688502	−	0.0105044i
$704$	−0.179894	+	1.89542i	−0.00678001	+	0.0714364i
$705$	−8.31940	+	5.76037i	−0.313327	+	0.216948i
$706$	9.38889	+	14.1237i	0.353355	+	0.531552i
$707$	−3.40124	−	2.16934i	−0.127917	−	0.0815865i
$708$	10.3676	+	1.98587i	0.389639	+	0.0746334i
$709$	17.9694	−	16.9771i	0.674856	−	0.637589i	−0.270846	−	0.962623i	$-0.587303\pi$
$709$	17.9694	−	16.9771i	0.674856	−	0.637589i	0.945702	+	0.325034i	$0.105376\pi$
$710$	−0.758966	+	1.35373i	−0.0284835	+	0.0508046i
$711$	4.65750	+	3.77644i	0.174670	+	0.141627i
$712$	9.87773	−	4.82284i	0.370184	−	0.180743i
$713$	−5.90091	+	6.01366i	−0.220991	+	0.225213i
$714$	14.6382	+	1.66938i	0.547822	+	0.0624748i
$715$	4.70998	+	2.52471i	0.176143	+	0.0944186i
$716$	0.459872	−	0.402656i	0.0171862	−	0.0150480i
$717$	−10.0497	+	7.53662i	−0.375313	+	0.281460i
$718$	18.9767	+	22.5192i	0.708204	+	0.840409i
$719$	1.12124	+	11.8137i	0.0418151	+	0.440577i	0.991755	+	0.128146i	$0.0409025\pi$
$719$	1.12124	+	11.8137i	0.0418151	+	0.440577i	−0.949940	+	0.312432i	$0.898857\pi$
$720$	−0.389020	−	1.54917i	−0.0144979	−	0.0577340i
$721$	9.72838	+	33.3439i	0.362304	+	1.24179i
$722$	−3.93464	−	29.5266i	−0.146432	−	1.09887i
$723$	10.9540	+	2.53135i	0.407383	+	0.0941420i
$724$	8.34702	−	2.60770i	0.310215	−	0.0969146i
$725$	15.7062	+	14.8388i	0.583313	+	0.551101i
$726$	−5.76452	−	7.99767i	−0.213942	−	0.296821i
$727$	−18.0488	+	42.9972i	−0.669394	+	1.59468i	0.128384	+	0.991725i	$0.459021\pi$
$727$	−18.0488	+	42.9972i	−0.669394	+	1.59468i	−0.797777	+	0.602952i	$0.793991\pi$
$728$	7.20967	−	0.273020i	0.267208	−	0.0101188i
$729$	−6.64982	+	26.4811i	−0.246290	+	0.980783i
$730$	−14.9785	−	2.28527i	−0.554381	−	0.0845816i
$731$	2.90935	−	9.97176i	0.107606	−	0.368819i
$732$	−3.78719	−	0.143416i	−0.139979	−	0.00530079i
$733$	−16.9484	+	36.4461i	−0.626005	+	1.34617i	0.294581	+	0.955626i	$0.404820\pi$
$733$	−16.9484	+	36.4461i	−0.626005	+	1.34617i	−0.920586	+	0.390539i	$0.872289\pi$
$734$	−8.95480	+	7.26081i	−0.330528	+	0.268001i
$735$	1.32928	+	7.72864i	0.0490312	+	0.285075i
$736$	0.796783	−	1.02161i	0.0293698	−	0.0376569i
$737$	27.4641	−	3.13206i	1.01165	−	0.115371i
$738$	4.74134	+	1.88554i	0.174531	+	0.0694076i
$739$	41.6192	−	7.97195i	1.53099	−	0.293253i	0.647631	−	0.761954i	$-0.275760\pi$
$739$	41.6192	−	7.97195i	1.53099	−	0.293253i	0.883357	+	0.468702i	$0.155278\pi$
$740$	0.203546	−	0.282398i	0.00748249	−	0.0103812i
$741$	−10.3835	−	16.9804i	−0.381447	−	0.623789i
$742$	−3.23564	+	0.245410i	−0.118784	+	0.00900930i
$743$	6.26983	+	4.70196i	0.230018	+	0.172498i	0.708743	−	0.705467i	$-0.249262\pi$
$743$	6.26983	+	4.70196i	0.230018	+	0.172498i	−0.478725	+	0.877965i	$0.658901\pi$
$744$	0.493287	+	8.67900i	0.0180848	+	0.318188i
$745$	15.5026	−	4.20636i	0.567971	−	0.154109i
$746$	9.77726	+	19.0995i	0.357971	+	0.699283i
$747$	−15.4374	−	1.17086i	−0.564823	−	0.0428396i
$748$	−4.66460	−	4.08424i	−0.170555	−	0.149335i
$749$	16.2088	+	43.1173i	0.592257	+	1.57547i
$750$	−14.1761	+	3.27595i	−0.517638	+	0.119621i
$751$	−28.6549	+	16.7858i	−1.04563	+	0.612523i	−0.924919	−	0.380164i	$-0.875868\pi$
$751$	−28.6549	+	16.7858i	−1.04563	+	0.612523i	−0.120713	+	0.992687i	$0.538518\pi$
$752$	4.96057	−	2.90586i	0.180893	−	0.105966i
$753$	−40.3989	+	9.33576i	−1.47222	+	0.340214i
$754$	4.96209	+	13.1997i	0.180709	+	0.480706i
$755$	−14.7016	−	12.8724i	−0.535045	−	0.468476i
$756$	−19.0070	−	1.44160i	−0.691276	−	0.0524305i
$757$	−22.6318	−	44.2103i	−0.822566	−	1.60685i	−0.794514	−	0.607246i	$-0.792274\pi$
$757$	−22.6318	−	44.2103i	−0.822566	−	1.60685i	−0.0280521	−	0.999606i	$-0.508930\pi$
$758$	−18.1400	+	4.92198i	−0.658875	+	0.178774i
$759$	−0.187113	−	3.29210i	−0.00679175	−	0.119496i
$760$	−7.35782	−	5.51788i	−0.266896	−	0.200154i
$761$	13.9143	−	1.05534i	0.504392	−	0.0382561i	0.179026	−	0.983844i	$-0.442705\pi$
$761$	13.9143	−	1.05534i	0.504392	−	0.0382561i	0.325366	+	0.945588i	$0.394513\pi$
$762$	11.8662	+	19.4051i	0.429869	+	0.702974i
$763$	35.3084	−	48.9867i	1.27825	−	1.77344i
$764$	9.18378	−	1.75911i	0.332257	−	0.0636422i
$765$	4.83315	+	1.92205i	0.174743	+	0.0694918i
$766$	4.41819	−	0.503859i	0.159636	−	0.0182052i
$767$	−10.3525	+	13.2736i	−0.373807	+	0.479282i
$768$	−0.226587	−	1.31742i	−0.00817627	−	0.0475382i
$769$	−2.49027	+	2.01919i	−0.0898015	+	0.0728137i	−0.673658	−	0.739043i	$-0.735278\pi$
$769$	−2.49027	+	2.01919i	−0.0898015	+	0.0728137i	0.583857	+	0.811857i	$0.301543\pi$
$770$	3.57781	−	7.69374i	0.128935	−	0.277263i
$771$	3.25195	+	0.123147i	0.117116	+	0.00443502i
$772$	−4.34832	+	14.9038i	−0.156499	+	0.536400i
$773$	−38.3044	−	5.84408i	−1.37771	−	0.210197i	−0.580679	−	0.814133i	$-0.697213\pi$
$773$	−38.3044	−	5.84408i	−1.37771	−	0.210197i	−0.797033	+	0.603936i	$0.793598\pi$
$774$	−0.942447	+	3.75304i	−0.0338756	+	0.134900i
$775$	−21.2255	+	0.803780i	−0.762442	+	0.0288726i
$776$	1.84667	−	4.39927i	0.0662916	−	0.157925i
$777$	−0.699408	−	0.970356i	−0.0250911	−	0.0348113i
$778$	23.4370	+	22.1428i	0.840258	+	0.793857i
$779$	28.0433	−	8.76105i	1.00476	−	0.313897i
$780$	−3.65568	−	0.844789i	−0.130894	−	0.0302483i
$781$	−0.296425	−	2.22446i	−0.0106069	−	0.0795974i
$782$	1.18164	+	4.05007i	0.0422554	+	0.144830i
$783$	−9.07393	−	36.1345i	−0.324276	−	1.29134i
$784$	−0.420972	−	4.43550i	−0.0150347	−	0.158411i
$785$	−18.3687	−	21.7977i	−0.655608	−	0.777995i
$786$	1.06710	−	0.800251i	0.0380620	−	0.0285440i
$787$	−20.7575	+	18.1749i	−0.739924	+	0.647865i	−0.943567	−	0.331180i	$-0.892553\pi$
$787$	−20.7575	+	18.1749i	−0.739924	+	0.647865i	0.203643	+	0.979045i	$0.434722\pi$
$788$	1.99231	+	1.06794i	0.0709731	+	0.0380439i
$789$	29.8101	+	3.39961i	1.06127	+	0.121029i
$790$	4.55840	−	4.64550i	0.162181	−	0.165279i
$791$	−38.6400	+	18.8661i	−1.37388	+	0.670802i
$792$	1.79399	+	1.45462i	0.0637467	+	0.0516877i
$793$	2.95552	−	5.27162i	0.104954	−	0.187201i
$794$	−7.02657	+	6.63854i	−0.249364	+	0.235593i
$795$	1.65737	+	0.317461i	0.0587809	+	0.0112592i
$796$	−6.67741	−	4.25892i	−0.236675	−	0.150953i
$797$	−26.1065	−	39.2719i	−0.924740	−	1.39108i	−0.920351	−	0.391093i	$-0.872097\pi$
$797$	−26.1065	−	39.2719i	−0.924740	−	1.39108i	−0.00438852	−	0.999990i	$-0.501397\pi$
$798$	−25.9818	+	17.9898i	−0.919744	+	0.636832i
$799$	−1.76886	+	18.6373i	−0.0625777	+	0.659339i
$800$	3.22891	−	0.492633i	0.114159	−	0.0174172i
$801$	1.76133	−	13.2175i	0.0622336	−	0.467019i
$802$	9.35532	−	24.8862i	0.330348	−	0.878764i
$803$	19.3101	−	10.3508i	0.681438	−	0.365273i
$804$	−18.0339	+	7.17171i	−0.636005	+	0.252927i
$805$	−4.86795	+	3.10482i	−0.171573	+	0.109431i
$806$	−12.6781	−	5.60636i	−0.446566	−	0.197475i
$807$	−17.0902	+	18.7890i	−0.601604	+	0.661406i
$808$	−0.733030	−	0.939864i	−0.0257879	−	0.0330643i
$809$	20.6473	+	21.0418i	0.725921	+	0.739791i	0.973402	−	0.229102i	$-0.0735789\pi$
$809$	20.6473	+	21.0418i	0.725921	+	0.739791i	−0.247482	+	0.968893i	$0.579603\pi$
$810$	4.82673	+	1.71095i	0.169594	+	0.0601167i
$811$	9.81004	−	29.4322i	0.344477	−	1.03350i	−0.623362	−	0.781933i	$-0.714234\pi$
$811$	9.81004	−	29.4322i	0.344477	−	1.03350i	0.967839	−	0.251570i	$-0.0809470\pi$
$812$	20.4772	−	9.05518i	0.718608	−	0.317775i
$813$	−14.1022	+	21.2139i	−0.494586	+	0.744005i
$814$	0.00952563	+	0.503269i	0.000333873	+	0.0176396i
$815$	−15.8596	+	5.62182i	−0.555539	+	0.196924i
$816$	3.91165	+	1.90988i	0.136935	+	0.0668591i
$817$	9.39503	+	20.2031i	0.328691	+	0.706819i
$818$	−3.43019	−	8.17163i	−0.119934	−	0.285714i
$819$	4.56590	−	7.46673i	0.159546	−	0.260909i
$820$	2.52373	−	4.93002i	0.0881326	−	0.172164i
$821$	6.67239	−	31.5870i	0.232868	−	1.10239i	−0.691938	−	0.721957i	$-0.743243\pi$
$821$	6.67239	−	31.5870i	0.232868	−	1.10239i	0.924806	−	0.380438i	$-0.124227\pi$
$822$	−5.26039	−	1.42732i	−0.183477	−	0.0497833i
$823$	9.71746	+	46.0024i	0.338730	+	1.60354i	0.730121	+	0.683318i	$0.239464\pi$
$823$	9.71746	+	46.0024i	0.338730	+	1.60354i	−0.391391	+	0.920224i	$0.628006\pi$
$824$	−0.582345	+	10.2459i	−0.0202869	+	0.356933i
$825$	5.35689	−	6.35690i	0.186503	−	0.221319i
$826$	21.9741	+	15.2149i	0.764575	+	0.529393i
$827$	−0.771652	+	40.7688i	−0.0268330	+	1.41767i	0.691704	+	0.722181i	$0.256860\pi$
$827$	−0.771652	+	40.7688i	−0.0268330	+	1.41767i	−0.718537	+	0.695488i	$0.755188\pi$
$828$	−0.496964	−	1.49100i	−0.0172707	−	0.0518158i
$829$	19.0696	+	20.9652i	0.662315	+	0.728151i	0.975123	−	0.221665i	$-0.0711492\pi$
$829$	19.0696	+	20.9652i	0.662315	+	0.728151i	−0.312808	+	0.949816i	$0.601270\pi$
$830$	−2.84843	+	16.5612i	−0.0988703	+	0.574848i
$831$	7.35950	+	13.1268i	0.255298	+	0.455362i
$832$	2.03469	+	0.635661i	0.0705402	+	0.0220376i
$833$	12.5188	+	7.33341i	0.433750	+	0.254088i
$834$	26.1604			0.905861
$835$	15.4747	+	7.07579i	0.535523	+	0.244868i
$836$	13.2987			0.459944
$837$	31.6014	+	18.5118i	1.09230	+	0.639863i
$838$	20.0478	+	6.26316i	0.692539	+	0.216357i
$839$	−25.0204	−	44.6277i	−0.863802	−	1.54072i	−0.841037	−	0.540977i	$-0.818054\pi$
$839$	−25.0204	−	44.6277i	−0.863802	−	1.54072i	−0.0227645	−	0.999741i	$-0.507247\pi$
$840$	−1.00979	+	5.87110i	−0.0348411	+	0.202572i
$841$	9.93288	+	10.9202i	0.342513	+	0.376560i
$842$	−11.1557	−	33.4695i	−0.384451	−	1.15343i
$843$	−0.444283	+	23.4729i	−0.0153019	+	0.808449i
$844$	8.44734	+	5.84895i	0.290769	+	0.201329i
$845$	−7.17475	+	8.51412i	−0.246819	+	0.292894i
$846$	0.395740	−	6.96274i	0.0136058	−	0.239384i
$847$	−5.15895	−	24.4224i	−0.177264	−	0.839165i
$848$	−0.925284	−	0.251060i	−0.0317744	−	0.00862143i
$849$	1.03870	−	4.91720i	0.0356481	−	0.168758i
$850$	−4.84668	+	9.46780i	−0.166240	+	0.324743i
$851$	0.178692	−	0.292219i	0.00612547	−	0.0100171i
$852$	0.609838	+	1.45280i	0.0208927	+	0.0497720i
$853$	1.96820	+	4.23244i	0.0673900	+	0.144916i	0.937547	−	0.347859i	$-0.113091\pi$
$853$	1.96820	+	4.23244i	0.0673900	+	0.144916i	−0.870157	+	0.492775i	$0.835983\pi$
$854$	−8.62286	−	4.21014i	−0.295068	−	0.144068i
$855$	−10.5155	+	3.72746i	−0.359622	+	0.127477i
$856$	0.257552	+	13.6073i	0.00880296	+	0.465088i
$857$	15.6899	−	23.6023i	0.535958	−	0.806240i	−0.460732	−	0.887539i	$-0.652413\pi$
$857$	15.6899	−	23.6023i	0.535958	−	0.806240i	0.996690	+	0.0812993i	$0.0259069\pi$
$858$	4.96186	−	2.19417i	0.169395	−	0.0749079i
$859$	16.2886	−	48.8692i	0.555759	−	1.66740i	−0.174846	−	0.984596i	$-0.555943\pi$
$859$	16.2886	−	48.8692i	0.555759	−	1.66740i	0.730605	−	0.682800i	$-0.239238\pi$
$860$	3.95880	+	1.40329i	0.134994	+	0.0478519i
$861$	−13.3288	−	13.5835i	−0.454246	−	0.462925i
$862$	−13.4986	−	17.3074i	−0.459765	−	0.589494i
$863$	23.4174	−	25.7451i	0.797137	−	0.876375i	−0.197447	−	0.980314i	$-0.563265\pi$
$863$	23.4174	−	25.7451i	0.797137	−	0.876375i	0.994584	+	0.103939i	$0.0331446\pi$
$864$	−5.15073	−	2.27770i	−0.175231	−	0.0774888i
$865$	−9.66826	+	6.16651i	−0.328731	+	0.209668i
$866$	28.7291	−	11.4250i	0.976253	−	0.388237i
$867$	7.53555	−	4.03930i	0.255921	−	0.137182i
$868$	−7.74494	+	20.6024i	−0.262880	+	0.699292i
$869$	−1.24311	+	9.32862i	−0.0421695	+	0.316452i
$870$	−11.5105	+	1.75616i	−0.390244	+	0.0595393i
$871$	2.92416	−	30.8099i	0.0990815	−	1.04395i
$872$	14.6683	−	10.1563i	0.496731	−	0.343937i
$873$	−3.20410	−	4.81991i	−0.108442	−	0.163129i
$874$	−7.62965	−	4.86627i	−0.258077	−	0.164604i
$875$	−36.1811	−	6.93030i	−1.22314	−	0.234287i
$876$	−11.1815	+	10.5640i	−0.377788	+	0.356925i
$877$	−22.8678	+	40.7882i	−0.772192	+	1.37732i	0.149249	+	0.988800i	$0.452314\pi$
$877$	−22.8678	+	40.7882i	−0.772192	+	1.37732i	−0.921441	+	0.388519i	$0.872987\pi$
$878$	−25.0673	−	20.3253i	−0.845981	−	0.685946i
$879$	22.0740	−	10.7777i	0.744537	−	0.363523i
$880$	1.75582	−	1.78937i	0.0591887	−	0.0603196i
$881$	50.8601	+	5.80020i	1.71352	+	0.195414i	0.914137	−	0.405406i	$-0.132870\pi$
$881$	50.8601	+	5.80020i	1.71352	+	0.195414i	0.799385	+	0.600820i	$0.205159\pi$
$882$	−4.76355	−	2.55342i	−0.160397	−	0.0859781i
$883$	13.7365	−	12.0274i	0.462270	−	0.404756i	−0.395761	−	0.918354i	$-0.629519\pi$
$883$	13.7365	−	12.0274i	0.462270	−	0.404756i	0.858031	+	0.513598i	$0.171688\pi$
$884$	−5.55341	+	4.16469i	−0.186782	+	0.140074i
$885$	−8.95669	−	10.6287i	−0.301076	−	0.357280i
$886$	−0.242294	−	2.55289i	−0.00814001	−	0.0857659i
$887$	−11.0615	−	44.0494i	−0.371408	−	1.47903i	−0.813237	−	0.581933i	$-0.802296\pi$
$887$	−11.0615	−	44.0494i	−0.371408	−	1.47903i	0.441828	−	0.897100i	$-0.354330\pi$
$888$	−0.0989834	−	0.339265i	−0.00332166	−	0.0113850i
$889$	7.60712	+	57.0860i	0.255135	+	1.91460i
$890$	−14.1020	−	3.25882i	−0.472699	−	0.109236i
$891$	−7.06799	+	2.20812i	−0.236787	+	0.0739749i
$892$	9.19271	+	8.68506i	0.307795	+	0.290797i
$893$	−23.4799	−	32.5759i	−0.785724	−	1.09011i
$894$	6.31190	−	15.0367i	0.211102	−	0.502901i
$895$	−0.804250	+	0.0304558i	−0.0268831	+	0.00101803i
$896$	0.824329	−	3.28267i	0.0275389	−	0.109666i
$897$	−3.64959	−	0.556816i	−0.121856	−	0.0185916i
$898$	−2.57681	+	8.83201i	−0.0859894	+	0.294728i
$899$	−42.9886	−	1.62792i	−1.43375	−	0.0542941i
$900$	1.67073	−	3.59275i	0.0556910	−	0.119758i
$901$	2.42503	−	1.96628i	0.0807894	−	0.0655064i
$902$	1.35748	+	7.89259i	0.0451990	+	0.262795i
$903$	8.87583	−	11.3803i	0.295369	−	0.378711i
$904$	−12.6228	+	1.43953i	−0.419827	+	0.0478780i
$905$	−10.6995	−	4.25496i	−0.355662	−	0.141440i
$906$	−19.4840	+	3.73205i	−0.647311	+	0.123989i
$907$	9.58855	−	13.3031i	0.318383	−	0.441722i	−0.621401	−	0.783493i	$-0.713436\pi$
$907$	9.58855	−	13.3031i	0.318383	−	0.441722i	0.939783	+	0.341770i	$0.111027\pi$
$908$	6.31364	+	10.3248i	0.209526	+	0.342642i
$909$	−1.44174	+	0.109351i	−0.0478196	+	0.00362693i
$910$	−7.60012	−	5.69959i	−0.251942	−	0.188940i
$911$	0.231024	+	4.06468i	0.00765416	+	0.134669i	0.999943	+	0.0107184i	$0.00341184\pi$
$911$	0.231024	+	4.06468i	0.00765416	+	0.134669i	−0.992288	+	0.123951i	$0.960444\pi$
$912$	−9.01121	+	2.44504i	−0.298391	+	0.0809632i
$913$	−11.0724	−	21.6295i	−0.366443	−	0.715832i
$914$	25.0974	+	1.90353i	0.830147	+	0.0629633i
$915$	3.75443	+	3.28731i	0.124118	+	0.108675i
$916$	−2.41532	−	6.42504i	−0.0798045	−	0.212289i
$917$	3.29044	−	0.760387i	0.108660	−	0.0251102i
$918$	15.8243	−	9.26977i	0.522281	−	0.305948i
$919$	−20.7154	+	12.1349i	−0.683339	+	0.400295i	−0.805808	−	0.592177i	$-0.798268\pi$
$919$	−20.7154	+	12.1349i	−0.683339	+	0.400295i	0.122468	+	0.992472i	$0.460919\pi$
$920$	−1.66211	+	0.384096i	−0.0547981	+	0.0126633i
$921$	1.91551	+	5.09548i	0.0631182	+	0.167902i
$922$	30.1469	+	26.3961i	0.992834	+	0.869308i
$923$	−2.50535	−	0.190021i	−0.0824646	−	0.00625461i
$924$	−3.92526	−	7.66785i	−0.129132	−	0.252254i
$925$	0.833396	−	0.226128i	0.0274019	−	0.00743503i
$926$	1.03084	+	18.1368i	0.0338755	+	0.596013i
$927$	9.95958	+	7.46902i	0.327115	+	0.245315i
$928$	6.59633	−	0.500305i	0.216535	−	0.0164233i
$929$	−29.7090	−	48.5839i	−0.974722	−	1.59399i	−0.791730	−	0.610871i	$-0.790819\pi$
$929$	−29.7090	−	48.5839i	−0.974722	−	1.59399i	−0.182992	−	0.983114i	$-0.558578\pi$
$930$	6.69279	−	9.28555i	0.219465	−	0.304485i
$931$	−30.5647	+	5.85451i	−1.00172	+	0.191874i
$932$	−5.65152	−	2.24750i	−0.185122	−	0.0736193i
$933$	22.7446	−	2.59384i	0.744623	−	0.0849184i
$934$	−12.8433	+	16.4672i	−0.420246	+	0.538823i
$935$	1.38376	+	8.04542i	0.0452539	+	0.263113i
$936$	2.00857	−	1.62861i	0.0656523	−	0.0532328i
$937$	11.4169	−	24.5509i	0.372973	−	0.802044i	−0.626766	−	0.779208i	$-0.715622\pi$
$937$	11.4169	−	24.5509i	0.372973	−	0.802044i	0.999739	−	0.0228368i	$-0.00726981\pi$
$938$	−49.1034	−	1.85948i	−1.60328	−	0.0607141i
$939$	3.83663	−	13.1500i	0.125204	−	0.429134i
$940$	−7.48320	−	1.14171i	−0.244075	−	0.0372385i
$941$	−0.744802	+	2.96597i	−0.0242798	+	0.0966879i	−0.980822	−	0.194907i	$-0.937559\pi$
$941$	−0.744802	+	2.96597i	−0.0242798	+	0.0966879i	0.956542	+	0.291595i	$0.0941860\pi$
$942$	−28.9186	+	1.09511i	−0.942220	+	0.0356805i
$943$	2.10926	−	5.02483i	0.0686870	−	0.163631i
$944$	4.61740	+	6.40616i	0.150284	+	0.208503i
$945$	18.2439	+	17.2365i	0.593475	+	0.560702i
$946$	−5.79705	+	1.81106i	−0.188478	+	0.0588828i
$947$	24.1175	+	5.57330i	0.783713	+	0.181108i	0.598000	−	0.801496i	$-0.295962\pi$
$947$	24.1175	+	5.57330i	0.783713	+	0.181108i	0.185713	+	0.982604i	$0.440541\pi$
$948$	−0.872787	−	6.54964i	−0.0283468	−	0.212722i
$949$	−6.87038	−	23.5482i	−0.223022	−	0.764406i
$950$	−5.55651	−	22.1273i	−0.180277	−	0.717905i
$951$	−2.33779	−	24.6317i	−0.0758080	−	0.798738i
$952$	7.10223	+	8.42805i	0.230185	+	0.273155i
$953$	−47.3447	+	35.5054i	−1.53364	+	1.15013i	−0.595771	+	0.803154i	$0.703153\pi$
$953$	−47.3447	+	35.5054i	−1.53364	+	1.15013i	−0.937873	+	0.346978i	$0.887208\pi$
$954$	−0.875009	+	0.766142i	−0.0283294	+	0.0248048i
$955$	−10.8515	−	5.81677i	−0.351147	−	0.188226i
$956$	−9.33664	−	1.06477i	−0.301968	−	0.0344371i
$957$	11.7921	−	12.0174i	0.381185	−	0.388468i
$958$	27.8694	−	13.6073i	0.900419	−	0.439632i
$959$	−10.7195	−	8.69171i	−0.346152	−	0.280670i
$960$	−0.860762	+	1.53530i	−0.0277810	+	0.0495515i
$961$	8.20627	−	7.75309i	0.264718	−	0.250100i
$962$	0.553504	+	0.106021i	0.0178457	+	0.00341825i
$963$	13.9194	+	8.87791i	0.448546	+	0.286087i
$964$	4.65600	+	7.00401i	0.149960	+	0.225584i
$965$	16.8067	−	11.6370i	0.541026	−	0.374607i
$966$	−0.553846	+	5.83550i	−0.0178197	+	0.187754i
$967$	2.30834	−	0.352182i	0.0742312	−	0.0113254i	−0.113602	−	0.993526i	$-0.536239\pi$
$967$	2.30834	−	0.352182i	0.0742312	−	0.0113254i	0.187834	+	0.982201i	$0.439853\pi$
$968$	0.974163	−	7.31039i	0.0313108	−	0.234965i
$969$	10.6989	−	28.4604i	0.343699	−	0.914279i
$970$	−5.53690	+	2.96796i	−0.177779	+	0.0952955i
$971$	−2.11931	+	0.842809i	−0.0680120	+	0.0270470i	−0.403290	−	0.915072i	$-0.632134\pi$
$971$	−2.11931	+	0.842809i	−0.0680120	+	0.0270470i	0.335278	+	0.942119i	$0.391170\pi$
$972$	−9.86152	+	6.28977i	−0.316308	+	0.201745i
$973$	60.5778	+	26.7880i	1.94203	+	0.858784i
$974$	25.4811	−	28.0140i	0.816467	−	0.897626i
$975$	−5.72402	−	7.33912i	−0.183315	−	0.235040i
$976$	−1.98569	−	2.02363i	−0.0635603	−	0.0647747i
$977$	−13.7413	−	4.87095i	−0.439625	−	0.155835i	0.105079	−	0.994464i	$-0.466490\pi$
$977$	−13.7413	−	4.87095i	−0.439625	−	0.155835i	−0.544704	+	0.838629i	$0.683358\pi$
$978$	−5.40171	+	16.2063i	−0.172728	+	0.518219i
$979$	19.1406	−	8.46414i	0.611737	−	0.270515i
$980$	−3.24771	+	4.88552i	−0.103744	+	0.156062i
$981$	−0.409569	−	21.6388i	−0.0130765	−	0.690874i
$982$	17.5914	−	6.23567i	0.561363	−	0.198988i
$983$	51.0180	+	24.9097i	1.62722	+	0.794496i	0.999876	+	0.0157558i	$0.00501542\pi$
$983$	51.0180	+	24.9097i	1.62722	+	0.794496i	0.627346	+	0.778741i	$0.284141\pi$
$984$	−2.37093	−	5.09846i	−0.0755824	−	0.162533i
$985$	−1.15202	−	2.74442i	−0.0367064	−	0.0874445i
$986$	−11.2382	+	18.3781i	−0.357898	+	0.585278i
$987$	−11.8525	+	23.1534i	−0.377269	+	0.736980i
$988$	3.07729	−	14.5679i	0.0979017	−	0.463466i
$989$	3.98856	+	1.08223i	0.126829	+	0.0344128i
$990$	−0.628526	−	2.97544i	−0.0199759	−	0.0945656i
$991$	0.555847	−	9.77970i	0.0176571	−	0.310662i	−0.977403	−	0.211386i	$-0.932202\pi$
$991$	0.555847	−	9.77970i	0.0176571	−	0.310662i	0.995060	−	0.0992769i	$-0.0316530\pi$
$992$	−4.19054	+	4.97282i	−0.133050	+	0.157887i
$993$	−3.08533	−	2.13629i	−0.0979100	−	0.0677930i
$994$	−0.0754944	+	3.98861i	−0.00239454	+	0.126511i
$995$	3.29752	+	9.89325i	0.104538	+	0.313637i
$996$	11.4794	+	12.6205i	0.363738	+	0.399895i
$997$	3.50492	−	20.3782i	0.111002	−	0.645383i	−0.875702	−	0.482853i	$-0.839601\pi$
$997$	3.50492	−	20.3782i	0.111002	−	0.645383i	0.986704	−	0.162530i	$-0.0519655\pi$
$998$	5.66199	+	10.0990i	0.179227	+	0.319678i
$999$	−1.42120	−	0.443998i	−0.0449647	−	0.0140475i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	334.2.c.b.107.5	✓	574
167.64	even	83	inner	334.2.c.b.231.5	yes	574

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
334.2.c.b.107.5	✓	574	1.1	even	1	trivial
334.2.c.b.231.5	yes	574	167.64	even	83	inner

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

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Newspace parameters

Newform invariants

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$q$ -expansion

Character values

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	334.2.c.b.107.5

Level	$334$
Weight	$2$
Character	334.107
Analytic conductor	$2.667$
Analytic rank	$0$
Dimension	$574$
Inner twists	$2$